nhanes proj.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "81859937",
   "metadata": {},
   "outputs": [],
   "source": [
    "nhanes_data <- read.csv(file_path)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85b1876d",
   "metadata": {},
   "source": [
    "# Structure & Summary of the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b7749f02",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t2278 obs. of  10 variables:\n",
      " $ SEQN     : num  73564 73568 73576 73577 73580 ...\n",
      " $ age_group: Factor w/ 2 levels \"Adult\",\"Senior\": 1 1 1 1 1 1 1 1 2 1 ...\n",
      " $ RIDAGEYR : num  61 26 16 32 38 50 14 57 75 43 ...\n",
      " $ RIAGENDR : num  2 2 1 1 2 1 1 2 1 1 ...\n",
      " $ PAQ605   : num  2 2 2 2 1 2 2 2 2 1 ...\n",
      " $ BMXBMI   : num  35.7 20.3 23.2 28.9 35.9 23.6 38.7 38.3 38.9 28.9 ...\n",
      " $ LBXGLU   : num  110 89 89 104 103 110 94 107 89 90 ...\n",
      " $ DIQ010   : num  2 2 2 2 2 2 2 2 2 2 ...\n",
      " $ LBXGLT   : num  150 80 68 84 81 100 202 164 113 95 ...\n",
      " $ LBXIN    : num  14.91 3.85 6.14 16.15 10.92 ...\n"
     ]
    }
   ],
   "source": [
    "str(nhanes_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "81ccd020",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      SEQN        age_group       RIDAGEYR       RIAGENDR         PAQ605     \n",
       " Min.   :73564   Adult :1914   Min.   :12.0   Min.   :1.000   Min.   :1.000  \n",
       " 1st Qu.:76172   Senior: 364   1st Qu.:24.0   1st Qu.:1.000   1st Qu.:2.000  \n",
       " Median :78749                 Median :41.0   Median :2.000   Median :2.000  \n",
       " Mean   :78692                 Mean   :41.8   Mean   :1.511   Mean   :1.823  \n",
       " 3rd Qu.:81214                 3rd Qu.:58.0   3rd Qu.:2.000   3rd Qu.:2.000  \n",
       " Max.   :83727                 Max.   :80.0   Max.   :2.000   Max.   :7.000  \n",
       "     BMXBMI          LBXGLU           DIQ010          LBXGLT   \n",
       " Min.   :14.50   Min.   : 63.00   Min.   :1.000   Min.   : 40  \n",
       " 1st Qu.:22.80   1st Qu.: 91.00   1st Qu.:2.000   1st Qu.: 87  \n",
       " Median :26.80   Median : 97.00   Median :2.000   Median :105  \n",
       " Mean   :27.96   Mean   : 99.55   Mean   :2.016   Mean   :115  \n",
       " 3rd Qu.:31.20   3rd Qu.:104.00   3rd Qu.:2.000   3rd Qu.:130  \n",
       " Max.   :70.10   Max.   :405.00   Max.   :3.000   Max.   :604  \n",
       "     LBXIN       \n",
       " Min.   :  0.14  \n",
       " 1st Qu.:  5.86  \n",
       " Median :  9.04  \n",
       " Mean   : 11.83  \n",
       " 3rd Qu.: 14.44  \n",
       " Max.   :102.29  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(nhanes_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2137c8e0",
   "metadata": {},
   "source": [
    "# Checking for missing values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "adfcc832",
   "metadata": {},
   "outputs": [],
   "source": [
    "missing_values <- colSums(is.na(nhanes_data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "82b2b47a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     SEQN age_group  RIDAGEYR  RIAGENDR    PAQ605    BMXBMI    LBXGLU    DIQ010 \n",
      "        0         0         0         0         0         0         0         0 \n",
      "   LBXGLT     LBXIN \n",
      "        0         0 \n"
     ]
    }
   ],
   "source": [
    "print(missing_values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a337222e",
   "metadata": {},
   "source": [
    "# Visualizations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a398dd7a",
   "metadata": {},
   "source": [
    "Histograms:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0bcbf50",
   "metadata": {},
   "source": [
    "Firstly, let's have a quick look at the brief descriptions of the variables:\n",
    "1)RIDAGEYR:\n",
    "Variable representing the participant's age in years.\n",
    "2)RIAGENDER:\n",
    "Variable representing the participant's gender (male=1 or female=2).\n",
    "3)PAQ60:\n",
    "Variable representing physical activity frequency in the past 7 days.\n",
    "4)BMXBMI:\n",
    "Variable representing body mass index (BMI), a measure of body fat based on height and weight.\n",
    "5)LBXGLU:\n",
    "Variable representing fasting glucose levels in the blood.\n",
    "6)DIQ010:\n",
    "Variable representing whether the participant has been told by a doctor that they have diabetes.\n",
    "7)LBXGLT:\n",
    "Variable representing non-fasting glucose levels in the blood.\n",
    "8)LBXIN:\n",
    "Variable representing insulin levels in the blood."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b6117ec8",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "file_path <- \"/users/banog/desktop/xx.csv\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6b876b3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "nhanes_data <- read.csv(file_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4b375ef7",
   "metadata": {},
   "outputs": [],
   "source": [
    "attach(nhanes_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ea5f1388",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ahr7U59f23x2h3aaoxMU88/SLfTGOXO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\nMIAgARhAkAAM+AdlgK4arHLc7QAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Distribution of Age\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Histogram_for_ages\n",
    "hist(nhanes_data$RIDAGEYR, main = \"Distribution of Age\", xlab = \"Age\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "877fc16b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WXDaP5VIzQx/4vPrDb/9dVR3bxGOW40fxGadW7FWv+RPn273a5suDx2ZPd32v5/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\nQJEAAxQJMECRAAMUCTDwDzLHbYRvQT+BAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Distribution of Gender\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#histogram_for_gender\n",
    "hist(nhanes_data$RIAGENDR, main = \"Distribution of Gender\", xlab = \"1=Male, 2=Female\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c82e7ae3",
   "metadata": {},
   "source": [
    "For PAQ60 data, the data is categorized as follows:\n",
    "The coding for PAQ60 is as follows:\n",
    "\n",
    "1: None (no reported moderate or vigorous activity)\n",
    "2: 1-2 days\n",
    "3: 3-4 days\n",
    "4: 5-6 days\n",
    "5: 7 days\n",
    "6: Refused\n",
    "7: Don't know"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "bcea1715",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Plot with title \"Distribution of Activtites\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#histogram_for_activities\n",
    "hist(nhanes_data$PAQ605, main = \"Distribution of Activtites\", xlab = \"1-7\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e4c6e2fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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s+Z/oSUOoHyLT+QNT5e9/8SaoQEjYen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",
      "text/plain": [
       "Plot with title \"Distribution of BMI\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#histogram_for_BMI\n",
    "hist(nhanes_data$BMXBMI, main = \"Distribution of BMI\", xlab = \"BMXBMI\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18a75047",
   "metadata": {},
   "source": [
    "The distribution of body mass index is pretty much skewed to the right, as visible in the histogram, we'll ahead analyze this distribution separetly for both age groups, senior and non-senior, note that: respondents 65 years old and older were labeled as “senior” and all individuals under\n",
    "65 years old as “non-senior\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "add80ab6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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W8RaCEkI+3JyNNb/kUS8z2AkIx0/xlF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\nQgICEBIQgJCAAIQEBCAkIAAhAQH+ARZCsUVMaWIjAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Distribution of Diabetes Test\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#histogram_for_diabetes_test\n",
    "hist(nhanes_data$DIQ010, main = \"Distribution of Diabetes Test\", xlab = \"Responds (1-3)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea31ede5",
   "metadata": {},
   "source": [
    "The coding for DIQ010 is as follows:\n",
    "\n",
    "1: Yes\n",
    "2: No\n",
    "3: Borderline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "02e5c5ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Al6aBbh6LBHWpXRUF0MsrIg8XQd50iL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\nAgQJAgQJAgQJAgQJAgQJAv4D1EYvt/Ly5FgAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Distribution of Glucose levels\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#histogram_for_glucose_levels\n",
    "hist(nhanes_data$LBXGLU, main = \"Distribution of Glucose levels\", xlab = \"Fasting Glucose level\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "386a83a7",
   "metadata": {},
   "source": [
    "Hence, starting from 50 and ending at 400, the distribution is highly right skewed, and majority of the individuals glucose level fall in between 75 and hundred."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a4a57c3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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STkb/ltFOV/fh2seorUQ1EkpLH8aMfO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\nLeECvXIcAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Distribution of Glucose level\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#histogram_for_nonfasting_glucoselevels\n",
    "hist(nhanes_data$LBXGLT, main = \"Distribution of Glucose level\", xlab = \"Non-Fasting Glucose level\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b48812e",
   "metadata": {},
   "source": [
    "The similarity between the two distributions is visible"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ab37fc71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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08R6nT6T5CYjGZffVSfIrTtMM4WCWpM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\nAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Distribution of Insulin level\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#histogram_for_insulinlevels\n",
    "hist(nhanes_data$LBXIN, main = \"Distribution of Insulin level\", xlab = \"Level of Insulin in blood\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1d5d5bb",
   "metadata": {},
   "source": [
    "The right skewed distributions rightly fits the type of data, as the data is taken for all ages, min=12, max=80"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1625dfcd",
   "metadata": {},
   "source": [
    "# Separating the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "3fea577e",
   "metadata": {},
   "outputs": [],
   "source": [
    "senior_data<-subset(nhanes_data, age_group == 'Senior')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "e7d33370",
   "metadata": {},
   "outputs": [],
   "source": [
    "adult_data<-subset(nhanes_data, age_group == 'Adult')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18334f3e",
   "metadata": {},
   "source": [
    "# Summaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "c12b7bfa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      SEQN        age_group       RIDAGEYR        RIAGENDR         PAQ605     \n",
       " Min.   :73564   Adult :1914   Min.   :12.00   Min.   :1.000   Min.   :1.000  \n",
       " 1st Qu.:76136   Senior:   0   1st Qu.:21.00   1st Qu.:1.000   1st Qu.:2.000  \n",
       " Median :78719                 Median :35.50   Median :2.000   Median :2.000  \n",
       " Mean   :78669                 Mean   :35.78   Mean   :1.512   Mean   :1.806  \n",
       " 3rd Qu.:81176                 3rd Qu.:50.00   3rd Qu.:2.000   3rd Qu.:2.000  \n",
       " Max.   :83727                 Max.   :64.00   Max.   :2.000   Max.   :7.000  \n",
       "     BMXBMI          LBXGLU           DIQ010          LBXGLT   \n",
       " Min.   :14.50   Min.   : 63.00   Min.   :1.000   Min.   : 40  \n",
       " 1st Qu.:22.60   1st Qu.: 91.00   1st Qu.:2.000   1st Qu.: 84  \n",
       " Median :26.75   Median : 96.00   Median :2.000   Median :101  \n",
       " Mean   :27.97   Mean   : 98.64   Mean   :2.014   Mean   :110  \n",
       " 3rd Qu.:31.40   3rd Qu.:103.00   3rd Qu.:2.000   3rd Qu.:124  \n",
       " Max.   :70.10   Max.   :405.00   Max.   :3.000   Max.   :604  \n",
       "     LBXIN        \n",
       " Min.   :  0.140  \n",
       " 1st Qu.:  5.982  \n",
       " Median :  9.200  \n",
       " Mean   : 12.107  \n",
       " 3rd Qu.: 14.790  \n",
       " Max.   :102.290  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(adult_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "d4bb6fef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      SEQN        age_group      RIDAGEYR        RIAGENDR         PAQ605     \n",
       " Min.   :73607   Adult :  0   Min.   :65.00   Min.   :1.000   Min.   :1.000  \n",
       " 1st Qu.:76401   Senior:364   1st Qu.:68.75   1st Qu.:1.000   1st Qu.:2.000  \n",
       " Median :78860                Median :73.00   Median :2.000   Median :2.000  \n",
       " Mean   :78814                Mean   :73.43   Mean   :1.508   Mean   :1.909  \n",
       " 3rd Qu.:81370                3rd Qu.:80.00   3rd Qu.:2.000   3rd Qu.:2.000  \n",
       " Max.   :83702                Max.   :80.00   Max.   :2.000   Max.   :2.000  \n",
       "     BMXBMI          LBXGLU          DIQ010          LBXGLT     \n",
       " Min.   :16.80   Min.   : 80.0   Min.   :1.000   Min.   : 48.0  \n",
       " 1st Qu.:24.20   1st Qu.: 95.0   1st Qu.:2.000   1st Qu.:104.0  \n",
       " Median :27.20   Median :101.0   Median :2.000   Median :131.0  \n",
       " Mean   :27.89   Mean   :104.3   Mean   :2.027   Mean   :141.2  \n",
       " 3rd Qu.:30.60   3rd Qu.:111.0   3rd Qu.:2.000   3rd Qu.:166.2  \n",
       " Max.   :52.20   Max.   :208.0   Max.   :3.000   Max.   :346.0  \n",
       "     LBXIN       \n",
       " Min.   : 1.020  \n",
       " 1st Qu.: 5.247  \n",
       " Median : 8.465  \n",
       " Mean   :10.405  \n",
       " 3rd Qu.:13.213  \n",
       " Max.   :52.890  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(senior_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11c0fc47",
   "metadata": {},
   "source": [
    "# Visualizations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bfee233",
   "metadata": {},
   "source": [
    "We now compare variables for senior and adult data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "f855b0f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nqBckoeL0QiXH+T8cW2/so8GbwjIqT1vBhLE8/x5ctgksH/3yNcf6PxXb8V0/o7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",
      "text/plain": [
       "Plot with title \"Histogram of Senior data\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kNIQgjJDiEJISQ7hCSEkOwQkhBCskNI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\nhAQEQEhAAIQEBPB/L2MBHXj6Dg4AAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Histogram of adult_data$DIQ010\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#histogram_for_diabetes_test\n",
    "hist(senior_data$DIQ010, col = \"skyblue\", main = \"Histogram of Senior data\", xlab = \"responses\")\n",
    "hist(adult_data$DIQ010, col = \"salmon\", add = FALSE)  \n",
    "legend(\"topright\", legend = c(\"Senior\", \"Adult\"), fill = c(\"skyblue\", \"salmon\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a40b78ef",
   "metadata": {},
   "source": [
    "No significant difference here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "03e698b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vq+EPukvybjoaj6Y17gFTNn//dhnvl9L9wjAev3xnOk07W9lHyOBKzf7Lu37egu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",
      "text/plain": [
       "Plot with title \"Histogram of senior data\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZCgY/U6UnkLPYU2QoKO1etI4afQRkjQ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\nhAQIICRAACEBAggJEEBIgID/A87/3GEe5jtIAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Histogram of adult data\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#histogram for BMIs\n",
    "hist(senior_data$BMXBMI, col = \"skyblue\", main = \"Histogram of senior data\", xlab = \"BMXBMI\")\n",
    "hist(adult_data$BMXBMI, col = \"salmon\", main = \"Histogram of adult data\", xlab = \"BMXBMI\", add = FALSE) \n",
    "legend(\"topright\", legend = c(\"Senior\", \"Adult\"), fill = c(\"skyblue\", \"salmon\"))h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "44812acf",
   "metadata": {},
   "outputs": [],
   "source": [
    "file_path <- \"/users/banog/Desktop/xxx.csv\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "335d3ce8",
   "metadata": {},
   "outputs": [],
   "source": [
    "nhanes_data<-(read.csv(file_path))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "884e2179",
   "metadata": {},
   "outputs": [],
   "source": [
    "senior_data<-(subset(nhanes_data, age_group == 'Senior'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "40c53d23",
   "metadata": {},
   "outputs": [],
   "source": [
    "adult_data<-(subset(nhanes_data, age_group == 'Adult'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "b98798fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hpifEfwnCZISMyL10g78VXgBAnzN5od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\nAQL/A42p1z/9OS05AAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Histogram of senior data\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQ\n4P+MAKwjHjhLmAAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Histogram of adult data\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#histogram for insulin level\n",
    "hist(senior_data$LBXIN, col = \"skyblue\", main = \"Histogram of senior data\", xlab = \"LBXIN\")\n",
    "hist(adult_data$LBXIN, col = \"salmon\", main = \"Histogram of adult data\", xlab = \"LBXIN\", add = FALSE) \n",
    "legend(\"topright\", legend = c(\"Senior\", \"Adult\"), fill = c(\"skyblue\", \"salmon\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d145f002",
   "metadata": {},
   "source": [
    "As we can see, more of the senior individuals (65+) have higher level of insulin in their blood."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "a4eab643",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JAggJAggJAggJAggJAggJAggJAggJAggJAggJAggJAggJAggJAggJAggJAggJAg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\nZj+dMBIYAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Histogram of senior data\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ojlFQQJXiwWX1P3j+dirZsoggT/5ovv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\nUECQAAUECVDwfyrznmN7dbUFAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Histogram of adult data\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#histogram for fasting glucose level\n",
    "hist(senior_data$LBXGLU, col = \"skyblue\", main = \"Histogram of senior data\", xlab = \"LBXGLU\")\n",
    "hist(adult_data$LBXGLU, col = \"salmon\", main = \"Histogram of adult data\", xlab = \"LBXGLU\", add = FALSE) \n",
    "legend(\"topright\", legend = c(\"Senior\", \"Adult\"), fill = c(\"skyblue\", \"salmon\"))b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17de86da",
   "metadata": {},
   "source": [
    "Similar thing we may depict from barchart of fasting glucose levels, the seniors' dataset contain higher levels of fasting glucose level."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c35b7100",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vs42v+spxZSZ+5+hLCQdr2QIs59efjEJSikbnbAaX+Xcrvi3qP9z3paIZXyvf+L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\n+K4HZp8AAAAFSURBVB9OJsjf/HjexQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Histogram of senior data\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JISEs/v6nmk/ZXRYnv+RtXFFG03JST6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",
      "text/plain": [
       "Plot with title \"Histogram of adult data\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#histogram for non-fasting glucose level\n",
    "hist(senior_data$LBXGLT, col = \"skyblue\", main = \"Histogram of senior data\", xlab = \"LBXGLT\")\n",
    "hist(adult_data$LBXGLT, col = \"salmon\", main = \"Histogram of adult data\", xlab = \"LBXGLT\", add = FALSE) \n",
    "legend(\"topright\", legend = c(\"Senior\", \"Adult\"), fill = c(\"skyblue\", \"salmon\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d729bb1f",
   "metadata": {},
   "source": [
    "As for the non fasting glucose levels, results do not differ significantly."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a13bf0a4",
   "metadata": {},
   "source": [
    "# Box Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26b61136",
   "metadata": {},
   "source": [
    "Let's now compare the values of glucose levels and insulins by boxplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "4a7bbf73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAANlBMVEUAAABNTU1oaGh8fHyH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\nAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Boxplot of Insulin levels\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Boxplot for insulin levels\n",
    "boxplot(senior_data$LBXIN, adult_data$LBXIN, col = c(\"skyblue\", \"salmon\"), names = c(\"Seniors\", \"Adults\"), main = \"Boxplot of Insulin levels\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "9714a393",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AgQJEAgZpCanXPFbXIQ75DFqsT8FKGs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\nCBIgQJAAAYIECBAkQIAgAQL/B0mm8sJaNUYXAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Boxplot of Fasting Glucose\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Boxplot for fasting glucose levels\n",
    "boxplot(senior_data$LBXGLU, adult_data$LBXGLU, col = c(\"skyblue\", \"salmon\"), names = c(\"Seniors\", \"Adults\"), main = \"Boxplot of Fasting Glucose\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c911d50",
   "metadata": {},
   "source": [
    "We realize a significant variation throughout the age level by boxplot as well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "3e252cc7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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I+0JkiYGqYIAQIECRAgSIAAQQIECBIg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\nECRAgCABAgQJECBIgMD/AdlZ0U+J8FGYAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Boxplot of Non-Fasting Glucose levels\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Boxplot for non fasting glucose levels\n",
    "boxplot(senior_data$LBXGLT, adult_data$LBXGLT, col = c(\"skyblue\", \"salmon\"), names = c(\"Seniors\", \"Adults\"), main = \"Boxplot of Non-Fasting Glucose levels\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bff5d81",
   "metadata": {},
   "source": [
    "The Adult data is scattered much"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4713e746",
   "metadata": {},
   "source": [
    "# Data Encoding"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56d9a871",
   "metadata": {},
   "source": [
    "Variable Types:\n",
    "3) Identify categorical and ordinal variables in the dataset.\n",
    "2) Encode categorical variables using techniques such as one-hot encoding or label encoding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "8e213747",
   "metadata": {},
   "outputs": [],
   "source": [
    "nhanes_data_encoded <- model.matrix(~ . - 1, data = nhanes_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "db82fda6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>SEQN</th><th scope=col>age_groupAdult</th><th scope=col>age_groupSenior</th><th scope=col>RIDAGEYR</th><th scope=col>RIAGENDR</th><th scope=col>PAQ605</th><th scope=col>BMXBMI</th><th scope=col>LBXGLU</th><th scope=col>DIQ010</th><th scope=col>LBXGLT</th><th scope=col>LBXIN</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>73564</td><td>1    </td><td>0    </td><td>61   </td><td>2    </td><td>2    </td><td>35.7 </td><td>110  </td><td>2    </td><td>150  </td><td>14.91</td></tr>\n",
       "\t<tr><td>73568</td><td>1    </td><td>0    </td><td>26   </td><td>2    </td><td>2    </td><td>20.3 </td><td> 89  </td><td>2    </td><td> 80  </td><td> 3.85</td></tr>\n",
       "\t<tr><td>73576</td><td>1    </td><td>0    </td><td>16   </td><td>1    </td><td>2    </td><td>23.2 </td><td> 89  </td><td>2    </td><td> 68  </td><td> 6.14</td></tr>\n",
       "\t<tr><td>73577</td><td>1    </td><td>0    </td><td>32   </td><td>1    </td><td>2    </td><td>28.9 </td><td>104  </td><td>2    </td><td> 84  </td><td>16.15</td></tr>\n",
       "\t<tr><td>73580</td><td>1    </td><td>0    </td><td>38   </td><td>2    </td><td>1    </td><td>35.9 </td><td>103  </td><td>2    </td><td> 81  </td><td>10.92</td></tr>\n",
       "\t<tr><td>73581</td><td>1    </td><td>0    </td><td>50   </td><td>1    </td><td>2    </td><td>23.6 </td><td>110  </td><td>2    </td><td>100  </td><td> 6.08</td></tr>\n",
       "\t<tr><td>73587</td><td>1    </td><td>0    </td><td>14   </td><td>1    </td><td>2    </td><td>38.7 </td><td> 94  </td><td>2    </td><td>202  </td><td>21.11</td></tr>\n",
       "\t<tr><td>73596</td><td>1    </td><td>0    </td><td>57   </td><td>2    </td><td>2    </td><td>38.3 </td><td>107  </td><td>2    </td><td>164  </td><td>20.93</td></tr>\n",
       "\t<tr><td>73607</td><td>0    </td><td>1    </td><td>75   </td><td>1    </td><td>2    </td><td>38.9 </td><td> 89  </td><td>2    </td><td>113  </td><td>17.47</td></tr>\n",
       "\t<tr><td>73610</td><td>1    </td><td>0    </td><td>43   </td><td>1    </td><td>1    </td><td>28.9 </td><td> 90  </td><td>2    </td><td> 95  </td><td> 3.24</td></tr>\n",
       "\t<tr><td>73618</td><td>1    </td><td>0    </td><td>54   </td><td>2    </td><td>2    </td><td>32.7 </td><td> 98  </td><td>2    </td><td> 80  </td><td> 7.16</td></tr>\n",
       "\t<tr><td>73619</td><td>1    </td><td>0    </td><td>36   </td><td>2    </td><td>1    </td><td>27.3 </td><td> 85  </td><td>2    </td><td> 91  </td><td> 9.86</td></tr>\n",
       "\t<tr><td>73621</td><td>0    </td><td>1    </td><td>80   </td><td>1    </td><td>2    </td><td>24.6 </td><td>100  </td><td>2    </td><td> 97  </td><td> 4.33</td></tr>\n",
       "\t<tr><td>73633</td><td>1    </td><td>0    </td><td>43   </td><td>2    </td><td>2    </td><td>30.5 </td><td>102  </td><td>2    </td><td>124  </td><td>12.06</td></tr>\n",
       "\t<tr><td>73639</td><td>0    </td><td>1    </td><td>71   </td><td>1    </td><td>2    </td><td>30.3 </td><td>133  </td><td>2    </td><td>295  </td><td>22.92</td></tr>\n",
       "\t<tr><td>73640</td><td>0    </td><td>1    </td><td>67   </td><td>2    </td><td>1    </td><td>22.1 </td><td>114  </td><td>2    </td><td>150  </td><td>10.09</td></tr>\n",
       "\t<tr><td>73642</td><td>1    </td><td>0    </td><td>57   </td><td>2    </td><td>2    </td><td>37.8 </td><td> 96  </td><td>2    </td><td>120  </td><td> 9.61</td></tr>\n",
       "\t<tr><td>73656</td><td>1    </td><td>0    </td><td>54   </td><td>1    </td><td>2    </td><td>28.0 </td><td> 89  </td><td>2    </td><td> 82  </td><td> 8.39</td></tr>\n",
       "\t<tr><td>73659</td><td>0    </td><td>1    </td><td>70   </td><td>2    </td><td>2    </td><td>46.1 </td><td>139  </td><td>2    </td><td>154  </td><td>42.67</td></tr>\n",
       "\t<tr><td>73661</td><td>1    </td><td>0    </td><td>25   </td><td>1    </td><td>2    </td><td>21.0 </td><td> 86  </td><td>2    </td><td> 84  </td><td> 4.47</td></tr>\n",
       "\t<tr><td>73663</td><td>1    </td><td>0    </td><td>25   </td><td>1    </td><td>2    </td><td>33.0 </td><td>108  </td><td>2    </td><td> 77  </td><td> 8.02</td></tr>\n",
       "\t<tr><td>73667</td><td>1    </td><td>0    </td><td>24   </td><td>1    </td><td>2    </td><td>29.1 </td><td> 99  </td><td>2    </td><td> 95  </td><td> 6.12</td></tr>\n",
       "\t<tr><td>73668</td><td>1    </td><td>0    </td><td>30   </td><td>2    </td><td>2    </td><td>32.3 </td><td>108  </td><td>2    </td><td>160  </td><td> 6.76</td></tr>\n",
       "\t<tr><td>73676</td><td>1    </td><td>0    </td><td>44   </td><td>1    </td><td>1    </td><td>37.6 </td><td>105  </td><td>2    </td><td> 72  </td><td>15.98</td></tr>\n",
       "\t<tr><td>73677</td><td>1    </td><td>0    </td><td>61   </td><td>2    </td><td>2    </td><td>36.4 </td><td> 86  </td><td>2    </td><td> 76  </td><td>15.42</td></tr>\n",
       "\t<tr><td>73680</td><td>1    </td><td>0    </td><td>12   </td><td>1    </td><td>2    </td><td>18.0 </td><td> 96  </td><td>2    </td><td> 83  </td><td>10.80</td></tr>\n",
       "\t<tr><td>73688</td><td>1    </td><td>0    </td><td>58   </td><td>1    </td><td>2    </td><td>33.6 </td><td>105  </td><td>2    </td><td>158  </td><td>16.01</td></tr>\n",
       "\t<tr><td>73690</td><td>0    </td><td>1    </td><td>77   </td><td>2    </td><td>2    </td><td>21.4 </td><td> 90  </td><td>2    </td><td> 76  </td><td> 3.47</td></tr>\n",
       "\t<tr><td>73691</td><td>1    </td><td>0    </td><td>14   </td><td>1    </td><td>2    </td><td>18.9 </td><td> 86  </td><td>2    </td><td> 78  </td><td> 4.06</td></tr>\n",
       "\t<tr><td>73714</td><td>1    </td><td>0    </td><td>29   </td><td>2    </td><td>2    </td><td>26.4 </td><td> 87  </td><td>2    </td><td> 67  </td><td> 6.43</td></tr>\n",
       "\t<tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr>\n",
       "\t<tr><td>83589</td><td>1    </td><td>0    </td><td>59   </td><td>1    </td><td>2    </td><td>26.6 </td><td> 96  </td><td>2    </td><td>117  </td><td> 6.45</td></tr>\n",
       "\t<tr><td>83612</td><td>0    </td><td>1    </td><td>72   </td><td>1    </td><td>2    </td><td>30.5 </td><td>114  </td><td>2    </td><td>134  </td><td>15.86</td></tr>\n",
       "\t<tr><td>83615</td><td>0    </td><td>1    </td><td>80   </td><td>1    </td><td>2    </td><td>24.9 </td><td>105  </td><td>2    </td><td>100  </td><td> 9.50</td></tr>\n",
       "\t<tr><td>83618</td><td>1    </td><td>0    </td><td>40   </td><td>1    </td><td>2    </td><td>29.4 </td><td> 96  </td><td>2    </td><td> 92  </td><td>10.10</td></tr>\n",
       "\t<tr><td>83619</td><td>1    </td><td>0    </td><td>31   </td><td>1    </td><td>2    </td><td>26.7 </td><td> 94  </td><td>2    </td><td>117  </td><td> 5.04</td></tr>\n",
       "\t<tr><td>83624</td><td>1    </td><td>0    </td><td>50   </td><td>2    </td><td>2    </td><td>34.3 </td><td>333  </td><td>2    </td><td>510  </td><td>21.87</td></tr>\n",
       "\t<tr><td>83625</td><td>1    </td><td>0    </td><td>58   </td><td>2    </td><td>2    </td><td>24.6 </td><td> 96  </td><td>2    </td><td>107  </td><td>10.08</td></tr>\n",
       "\t<tr><td>83628</td><td>1    </td><td>0    </td><td>13   </td><td>1    </td><td>2    </td><td>36.4 </td><td> 96  </td><td>2    </td><td>107  </td><td>29.18</td></tr>\n",
       "\t<tr><td>83630</td><td>0    </td><td>1    </td><td>80   </td><td>2    </td><td>2    </td><td>26.0 </td><td>106  </td><td>2    </td><td>166  </td><td>13.32</td></tr>\n",
       "\t<tr><td>83633</td><td>1    </td><td>0    </td><td>45   </td><td>1    </td><td>1    </td><td>29.7 </td><td> 96  </td><td>2    </td><td>110  </td><td> 7.04</td></tr>\n",
       "\t<tr><td>83637</td><td>1    </td><td>0    </td><td>40   </td><td>1    </td><td>2    </td><td>48.0 </td><td> 98  </td><td>2    </td><td> 83  </td><td>52.64</td></tr>\n",
       "\t<tr><td>83638</td><td>0    </td><td>1    </td><td>80   </td><td>1    </td><td>2    </td><td>24.2 </td><td>116  </td><td>2    </td><td>157  </td><td>13.81</td></tr>\n",
       "\t<tr><td>83642</td><td>1    </td><td>0    </td><td>33   </td><td>1    </td><td>2    </td><td>27.4 </td><td>100  </td><td>2    </td><td>115  </td><td>12.86</td></tr>\n",
       "\t<tr><td>83648</td><td>1    </td><td>0    </td><td>18   </td><td>2    </td><td>2    </td><td>20.5 </td><td> 88  </td><td>2    </td><td>144  </td><td> 3.74</td></tr>\n",
       "\t<tr><td>83658</td><td>1    </td><td>0    </td><td>50   </td><td>2    </td><td>2    </td><td>32.7 </td><td>106  </td><td>2    </td><td>126  </td><td> 7.71</td></tr>\n",
       "\t<tr><td>83673</td><td>1    </td><td>0    </td><td>17   </td><td>2    </td><td>2    </td><td>29.1 </td><td> 90  </td><td>2    </td><td>111  </td><td> 9.74</td></tr>\n",
       "\t<tr><td>83677</td><td>1    </td><td>0    </td><td>18   </td><td>2    </td><td>2    </td><td>26.8 </td><td> 98  </td><td>2    </td><td>114  </td><td> 9.85</td></tr>\n",
       "\t<tr><td>83678</td><td>1    </td><td>0    </td><td>42   </td><td>2    </td><td>2    </td><td>18.3 </td><td> 97  </td><td>2    </td><td>154  </td><td> 3.39</td></tr>\n",
       "\t<tr><td>83679</td><td>1    </td><td>0    </td><td>14   </td><td>2    </td><td>2    </td><td>19.3 </td><td> 94  </td><td>2    </td><td>100  </td><td>16.10</td></tr>\n",
       "\t<tr><td>83683</td><td>1    </td><td>0    </td><td>33   </td><td>2    </td><td>2    </td><td>30.0 </td><td>101  </td><td>2    </td><td>149  </td><td>15.82</td></tr>\n",
       "\t<tr><td>83692</td><td>0    </td><td>1    </td><td>68   </td><td>1    </td><td>2    </td><td>19.1 </td><td> 89  </td><td>2    </td><td>136  </td><td> 1.56</td></tr>\n",
       "\t<tr><td>83694</td><td>1    </td><td>0    </td><td>36   </td><td>2    </td><td>2    </td><td>25.3 </td><td> 99  </td><td>2    </td><td>128  </td><td>20.72</td></tr>\n",
       "\t<tr><td>83699</td><td>1    </td><td>0    </td><td>37   </td><td>2    </td><td>2    </td><td>20.8 </td><td> 83  </td><td>2    </td><td>113  </td><td> 1.93</td></tr>\n",
       "\t<tr><td>83702</td><td>0    </td><td>1    </td><td>80   </td><td>2    </td><td>2    </td><td>27.9 </td><td>111  </td><td>2    </td><td> 72  </td><td>13.91</td></tr>\n",
       "\t<tr><td>83707</td><td>1    </td><td>0    </td><td>18   </td><td>1    </td><td>2    </td><td>22.5 </td><td> 98  </td><td>2    </td><td> 79  </td><td> 3.51</td></tr>\n",
       "\t<tr><td>83711</td><td>1    </td><td>0    </td><td>38   </td><td>2    </td><td>2    </td><td>33.5 </td><td>100  </td><td>2    </td><td> 73  </td><td> 6.53</td></tr>\n",
       "\t<tr><td>83712</td><td>1    </td><td>0    </td><td>61   </td><td>1    </td><td>2    </td><td>30.0 </td><td> 93  </td><td>2    </td><td>208  </td><td>13.02</td></tr>\n",
       "\t<tr><td>83713</td><td>1    </td><td>0    </td><td>34   </td><td>1    </td><td>2    </td><td>23.7 </td><td>103  </td><td>2    </td><td>124  </td><td>21.41</td></tr>\n",
       "\t<tr><td>83718</td><td>1    </td><td>0    </td><td>60   </td><td>2    </td><td>2    </td><td>27.4 </td><td> 90  </td><td>2    </td><td>108  </td><td> 4.99</td></tr>\n",
       "\t<tr><td>83727</td><td>1    </td><td>0    </td><td>26   </td><td>1    </td><td>2    </td><td>24.5 </td><td>108  </td><td>2    </td><td>108  </td><td> 3.76</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllll}\n",
       " SEQN & age\\_groupAdult & age\\_groupSenior & RIDAGEYR & RIAGENDR & PAQ605 & BMXBMI & LBXGLU & DIQ010 & LBXGLT & LBXIN\\\\\n",
       "\\hline\n",
       "\t 73564 & 1     & 0     & 61    & 2     & 2     & 35.7  & 110   & 2     & 150   & 14.91\\\\\n",
       "\t 73568 & 1     & 0     & 26    & 2     & 2     & 20.3  &  89   & 2     &  80   &  3.85\\\\\n",
       "\t 73576 & 1     & 0     & 16    & 1     & 2     & 23.2  &  89   & 2     &  68   &  6.14\\\\\n",
       "\t 73577 & 1     & 0     & 32    & 1     & 2     & 28.9  & 104   & 2     &  84   & 16.15\\\\\n",
       "\t 73580 & 1     & 0     & 38    & 2     & 1     & 35.9  & 103   & 2     &  81   & 10.92\\\\\n",
       "\t 73581 & 1     & 0     & 50    & 1     & 2     & 23.6  & 110   & 2     & 100   &  6.08\\\\\n",
       "\t 73587 & 1     & 0     & 14    & 1     & 2     & 38.7  &  94   & 2     & 202   & 21.11\\\\\n",
       "\t 73596 & 1     & 0     & 57    & 2     & 2     & 38.3  & 107   & 2     & 164   & 20.93\\\\\n",
       "\t 73607 & 0     & 1     & 75    & 1     & 2     & 38.9  &  89   & 2     & 113   & 17.47\\\\\n",
       "\t 73610 & 1     & 0     & 43    & 1     & 1     & 28.9  &  90   & 2     &  95   &  3.24\\\\\n",
       "\t 73618 & 1     & 0     & 54    & 2     & 2     & 32.7  &  98   & 2     &  80   &  7.16\\\\\n",
       "\t 73619 & 1     & 0     & 36    & 2     & 1     & 27.3  &  85   & 2     &  91   &  9.86\\\\\n",
       "\t 73621 & 0     & 1     & 80    & 1     & 2     & 24.6  & 100   & 2     &  97   &  4.33\\\\\n",
       "\t 73633 & 1     & 0     & 43    & 2     & 2     & 30.5  & 102   & 2     & 124   & 12.06\\\\\n",
       "\t 73639 & 0     & 1     & 71    & 1     & 2     & 30.3  & 133   & 2     & 295   & 22.92\\\\\n",
       "\t 73640 & 0     & 1     & 67    & 2     & 1     & 22.1  & 114   & 2     & 150   & 10.09\\\\\n",
       "\t 73642 & 1     & 0     & 57    & 2     & 2     & 37.8  &  96   & 2     & 120   &  9.61\\\\\n",
       "\t 73656 & 1     & 0     & 54    & 1     & 2     & 28.0  &  89   & 2     &  82   &  8.39\\\\\n",
       "\t 73659 & 0     & 1     & 70    & 2     & 2     & 46.1  & 139   & 2     & 154   & 42.67\\\\\n",
       "\t 73661 & 1     & 0     & 25    & 1     & 2     & 21.0  &  86   & 2     &  84   &  4.47\\\\\n",
       "\t 73663 & 1     & 0     & 25    & 1     & 2     & 33.0  & 108   & 2     &  77   &  8.02\\\\\n",
       "\t 73667 & 1     & 0     & 24    & 1     & 2     & 29.1  &  99   & 2     &  95   &  6.12\\\\\n",
       "\t 73668 & 1     & 0     & 30    & 2     & 2     & 32.3  & 108   & 2     & 160   &  6.76\\\\\n",
       "\t 73676 & 1     & 0     & 44    & 1     & 1     & 37.6  & 105   & 2     &  72   & 15.98\\\\\n",
       "\t 73677 & 1     & 0     & 61    & 2     & 2     & 36.4  &  86   & 2     &  76   & 15.42\\\\\n",
       "\t 73680 & 1     & 0     & 12    & 1     & 2     & 18.0  &  96   & 2     &  83   & 10.80\\\\\n",
       "\t 73688 & 1     & 0     & 58    & 1     & 2     & 33.6  & 105   & 2     & 158   & 16.01\\\\\n",
       "\t 73690 & 0     & 1     & 77    & 2     & 2     & 21.4  &  90   & 2     &  76   &  3.47\\\\\n",
       "\t 73691 & 1     & 0     & 14    & 1     & 2     & 18.9  &  86   & 2     &  78   &  4.06\\\\\n",
       "\t 73714 & 1     & 0     & 29    & 2     & 2     & 26.4  &  87   & 2     &  67   &  6.43\\\\\n",
       "\t ... & ... & ... & ... & ... & ... & ... & ... & ... & ... & ...\\\\\n",
       "\t 83589 & 1     & 0     & 59    & 1     & 2     & 26.6  &  96   & 2     & 117   &  6.45\\\\\n",
       "\t 83612 & 0     & 1     & 72    & 1     & 2     & 30.5  & 114   & 2     & 134   & 15.86\\\\\n",
       "\t 83615 & 0     & 1     & 80    & 1     & 2     & 24.9  & 105   & 2     & 100   &  9.50\\\\\n",
       "\t 83618 & 1     & 0     & 40    & 1     & 2     & 29.4  &  96   & 2     &  92   & 10.10\\\\\n",
       "\t 83619 & 1     & 0     & 31    & 1     & 2     & 26.7  &  94   & 2     & 117   &  5.04\\\\\n",
       "\t 83624 & 1     & 0     & 50    & 2     & 2     & 34.3  & 333   & 2     & 510   & 21.87\\\\\n",
       "\t 83625 & 1     & 0     & 58    & 2     & 2     & 24.6  &  96   & 2     & 107   & 10.08\\\\\n",
       "\t 83628 & 1     & 0     & 13    & 1     & 2     & 36.4  &  96   & 2     & 107   & 29.18\\\\\n",
       "\t 83630 & 0     & 1     & 80    & 2     & 2     & 26.0  & 106   & 2     & 166   & 13.32\\\\\n",
       "\t 83633 & 1     & 0     & 45    & 1     & 1     & 29.7  &  96   & 2     & 110   &  7.04\\\\\n",
       "\t 83637 & 1     & 0     & 40    & 1     & 2     & 48.0  &  98   & 2     &  83   & 52.64\\\\\n",
       "\t 83638 & 0     & 1     & 80    & 1     & 2     & 24.2  & 116   & 2     & 157   & 13.81\\\\\n",
       "\t 83642 & 1     & 0     & 33    & 1     & 2     & 27.4  & 100   & 2     & 115   & 12.86\\\\\n",
       "\t 83648 & 1     & 0     & 18    & 2     & 2     & 20.5  &  88   & 2     & 144   &  3.74\\\\\n",
       "\t 83658 & 1     & 0     & 50    & 2     & 2     & 32.7  & 106   & 2     & 126   &  7.71\\\\\n",
       "\t 83673 & 1     & 0     & 17    & 2     & 2     & 29.1  &  90   & 2     & 111   &  9.74\\\\\n",
       "\t 83677 & 1     & 0     & 18    & 2     & 2     & 26.8  &  98   & 2     & 114   &  9.85\\\\\n",
       "\t 83678 & 1     & 0     & 42    & 2     & 2     & 18.3  &  97   & 2     & 154   &  3.39\\\\\n",
       "\t 83679 & 1     & 0     & 14    & 2     & 2     & 19.3  &  94   & 2     & 100   & 16.10\\\\\n",
       "\t 83683 & 1     & 0     & 33    & 2     & 2     & 30.0  & 101   & 2     & 149   & 15.82\\\\\n",
       "\t 83692 & 0     & 1     & 68    & 1     & 2     & 19.1  &  89   & 2     & 136   &  1.56\\\\\n",
       "\t 83694 & 1     & 0     & 36    & 2     & 2     & 25.3  &  99   & 2     & 128   & 20.72\\\\\n",
       "\t 83699 & 1     & 0     & 37    & 2     & 2     & 20.8  &  83   & 2     & 113   &  1.93\\\\\n",
       "\t 83702 & 0     & 1     & 80    & 2     & 2     & 27.9  & 111   & 2     &  72   & 13.91\\\\\n",
       "\t 83707 & 1     & 0     & 18    & 1     & 2     & 22.5  &  98   & 2     &  79   &  3.51\\\\\n",
       "\t 83711 & 1     & 0     & 38    & 2     & 2     & 33.5  & 100   & 2     &  73   &  6.53\\\\\n",
       "\t 83712 & 1     & 0     & 61    & 1     & 2     & 30.0  &  93   & 2     & 208   & 13.02\\\\\n",
       "\t 83713 & 1     & 0     & 34    & 1     & 2     & 23.7  & 103   & 2     & 124   & 21.41\\\\\n",
       "\t 83718 & 1     & 0     & 60    & 2     & 2     & 27.4  &  90   & 2     & 108   &  4.99\\\\\n",
       "\t 83727 & 1     & 0     & 26    & 1     & 2     & 24.5  & 108   & 2     & 108   &  3.76\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| SEQN | age_groupAdult | age_groupSenior | RIDAGEYR | RIAGENDR | PAQ605 | BMXBMI | LBXGLU | DIQ010 | LBXGLT | LBXIN |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 73564 | 1     | 0     | 61    | 2     | 2     | 35.7  | 110   | 2     | 150   | 14.91 |\n",
       "| 73568 | 1     | 0     | 26    | 2     | 2     | 20.3  |  89   | 2     |  80   |  3.85 |\n",
       "| 73576 | 1     | 0     | 16    | 1     | 2     | 23.2  |  89   | 2     |  68   |  6.14 |\n",
       "| 73577 | 1     | 0     | 32    | 1     | 2     | 28.9  | 104   | 2     |  84   | 16.15 |\n",
       "| 73580 | 1     | 0     | 38    | 2     | 1     | 35.9  | 103   | 2     |  81   | 10.92 |\n",
       "| 73581 | 1     | 0     | 50    | 1     | 2     | 23.6  | 110   | 2     | 100   |  6.08 |\n",
       "| 73587 | 1     | 0     | 14    | 1     | 2     | 38.7  |  94   | 2     | 202   | 21.11 |\n",
       "| 73596 | 1     | 0     | 57    | 2     | 2     | 38.3  | 107   | 2     | 164   | 20.93 |\n",
       "| 73607 | 0     | 1     | 75    | 1     | 2     | 38.9  |  89   | 2     | 113   | 17.47 |\n",
       "| 73610 | 1     | 0     | 43    | 1     | 1     | 28.9  |  90   | 2     |  95   |  3.24 |\n",
       "| 73618 | 1     | 0     | 54    | 2     | 2     | 32.7  |  98   | 2     |  80   |  7.16 |\n",
       "| 73619 | 1     | 0     | 36    | 2     | 1     | 27.3  |  85   | 2     |  91   |  9.86 |\n",
       "| 73621 | 0     | 1     | 80    | 1     | 2     | 24.6  | 100   | 2     |  97   |  4.33 |\n",
       "| 73633 | 1     | 0     | 43    | 2     | 2     | 30.5  | 102   | 2     | 124   | 12.06 |\n",
       "| 73639 | 0     | 1     | 71    | 1     | 2     | 30.3  | 133   | 2     | 295   | 22.92 |\n",
       "| 73640 | 0     | 1     | 67    | 2     | 1     | 22.1  | 114   | 2     | 150   | 10.09 |\n",
       "| 73642 | 1     | 0     | 57    | 2     | 2     | 37.8  |  96   | 2     | 120   |  9.61 |\n",
       "| 73656 | 1     | 0     | 54    | 1     | 2     | 28.0  |  89   | 2     |  82   |  8.39 |\n",
       "| 73659 | 0     | 1     | 70    | 2     | 2     | 46.1  | 139   | 2     | 154   | 42.67 |\n",
       "| 73661 | 1     | 0     | 25    | 1     | 2     | 21.0  |  86   | 2     |  84   |  4.47 |\n",
       "| 73663 | 1     | 0     | 25    | 1     | 2     | 33.0  | 108   | 2     |  77   |  8.02 |\n",
       "| 73667 | 1     | 0     | 24    | 1     | 2     | 29.1  |  99   | 2     |  95   |  6.12 |\n",
       "| 73668 | 1     | 0     | 30    | 2     | 2     | 32.3  | 108   | 2     | 160   |  6.76 |\n",
       "| 73676 | 1     | 0     | 44    | 1     | 1     | 37.6  | 105   | 2     |  72   | 15.98 |\n",
       "| 73677 | 1     | 0     | 61    | 2     | 2     | 36.4  |  86   | 2     |  76   | 15.42 |\n",
       "| 73680 | 1     | 0     | 12    | 1     | 2     | 18.0  |  96   | 2     |  83   | 10.80 |\n",
       "| 73688 | 1     | 0     | 58    | 1     | 2     | 33.6  | 105   | 2     | 158   | 16.01 |\n",
       "| 73690 | 0     | 1     | 77    | 2     | 2     | 21.4  |  90   | 2     |  76   |  3.47 |\n",
       "| 73691 | 1     | 0     | 14    | 1     | 2     | 18.9  |  86   | 2     |  78   |  4.06 |\n",
       "| 73714 | 1     | 0     | 29    | 2     | 2     | 26.4  |  87   | 2     |  67   |  6.43 |\n",
       "| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |\n",
       "| 83589 | 1     | 0     | 59    | 1     | 2     | 26.6  |  96   | 2     | 117   |  6.45 |\n",
       "| 83612 | 0     | 1     | 72    | 1     | 2     | 30.5  | 114   | 2     | 134   | 15.86 |\n",
       "| 83615 | 0     | 1     | 80    | 1     | 2     | 24.9  | 105   | 2     | 100   |  9.50 |\n",
       "| 83618 | 1     | 0     | 40    | 1     | 2     | 29.4  |  96   | 2     |  92   | 10.10 |\n",
       "| 83619 | 1     | 0     | 31    | 1     | 2     | 26.7  |  94   | 2     | 117   |  5.04 |\n",
       "| 83624 | 1     | 0     | 50    | 2     | 2     | 34.3  | 333   | 2     | 510   | 21.87 |\n",
       "| 83625 | 1     | 0     | 58    | 2     | 2     | 24.6  |  96   | 2     | 107   | 10.08 |\n",
       "| 83628 | 1     | 0     | 13    | 1     | 2     | 36.4  |  96   | 2     | 107   | 29.18 |\n",
       "| 83630 | 0     | 1     | 80    | 2     | 2     | 26.0  | 106   | 2     | 166   | 13.32 |\n",
       "| 83633 | 1     | 0     | 45    | 1     | 1     | 29.7  |  96   | 2     | 110   |  7.04 |\n",
       "| 83637 | 1     | 0     | 40    | 1     | 2     | 48.0  |  98   | 2     |  83   | 52.64 |\n",
       "| 83638 | 0     | 1     | 80    | 1     | 2     | 24.2  | 116   | 2     | 157   | 13.81 |\n",
       "| 83642 | 1     | 0     | 33    | 1     | 2     | 27.4  | 100   | 2     | 115   | 12.86 |\n",
       "| 83648 | 1     | 0     | 18    | 2     | 2     | 20.5  |  88   | 2     | 144   |  3.74 |\n",
       "| 83658 | 1     | 0     | 50    | 2     | 2     | 32.7  | 106   | 2     | 126   |  7.71 |\n",
       "| 83673 | 1     | 0     | 17    | 2     | 2     | 29.1  |  90   | 2     | 111   |  9.74 |\n",
       "| 83677 | 1     | 0     | 18    | 2     | 2     | 26.8  |  98   | 2     | 114   |  9.85 |\n",
       "| 83678 | 1     | 0     | 42    | 2     | 2     | 18.3  |  97   | 2     | 154   |  3.39 |\n",
       "| 83679 | 1     | 0     | 14    | 2     | 2     | 19.3  |  94   | 2     | 100   | 16.10 |\n",
       "| 83683 | 1     | 0     | 33    | 2     | 2     | 30.0  | 101   | 2     | 149   | 15.82 |\n",
       "| 83692 | 0     | 1     | 68    | 1     | 2     | 19.1  |  89   | 2     | 136   |  1.56 |\n",
       "| 83694 | 1     | 0     | 36    | 2     | 2     | 25.3  |  99   | 2     | 128   | 20.72 |\n",
       "| 83699 | 1     | 0     | 37    | 2     | 2     | 20.8  |  83   | 2     | 113   |  1.93 |\n",
       "| 83702 | 0     | 1     | 80    | 2     | 2     | 27.9  | 111   | 2     |  72   | 13.91 |\n",
       "| 83707 | 1     | 0     | 18    | 1     | 2     | 22.5  |  98   | 2     |  79   |  3.51 |\n",
       "| 83711 | 1     | 0     | 38    | 2     | 2     | 33.5  | 100   | 2     |  73   |  6.53 |\n",
       "| 83712 | 1     | 0     | 61    | 1     | 2     | 30.0  |  93   | 2     | 208   | 13.02 |\n",
       "| 83713 | 1     | 0     | 34    | 1     | 2     | 23.7  | 103   | 2     | 124   | 21.41 |\n",
       "| 83718 | 1     | 0     | 60    | 2     | 2     | 27.4  |  90   | 2     | 108   |  4.99 |\n",
       "| 83727 | 1     | 0     | 26    | 1     | 2     | 24.5  | 108   | 2     | 108   |  3.76 |\n",
       "\n"
      ],
      "text/plain": [
       "     SEQN  age_groupAdult age_groupSenior RIDAGEYR RIAGENDR PAQ605 BMXBMI\n",
       "1    73564 1              0               61       2        2      35.7  \n",
       "2    73568 1              0               26       2        2      20.3  \n",
       "3    73576 1              0               16       1        2      23.2  \n",
       "4    73577 1              0               32       1        2      28.9  \n",
       "5    73580 1              0               38       2        1      35.9  \n",
       "6    73581 1              0               50       1        2      23.6  \n",
       "7    73587 1              0               14       1        2      38.7  \n",
       "8    73596 1              0               57       2        2      38.3  \n",
       "9    73607 0              1               75       1        2      38.9  \n",
       "10   73610 1              0               43       1        1      28.9  \n",
       "11   73618 1              0               54       2        2      32.7  \n",
       "12   73619 1              0               36       2        1      27.3  \n",
       "13   73621 0              1               80       1        2      24.6  \n",
       "14   73633 1              0               43       2        2      30.5  \n",
       "15   73639 0              1               71       1        2      30.3  \n",
       "16   73640 0              1               67       2        1      22.1  \n",
       "17   73642 1              0               57       2        2      37.8  \n",
       "18   73656 1              0               54       1        2      28.0  \n",
       "19   73659 0              1               70       2        2      46.1  \n",
       "20   73661 1              0               25       1        2      21.0  \n",
       "21   73663 1              0               25       1        2      33.0  \n",
       "22   73667 1              0               24       1        2      29.1  \n",
       "23   73668 1              0               30       2        2      32.3  \n",
       "24   73676 1              0               44       1        1      37.6  \n",
       "25   73677 1              0               61       2        2      36.4  \n",
       "26   73680 1              0               12       1        2      18.0  \n",
       "27   73688 1              0               58       1        2      33.6  \n",
       "28   73690 0              1               77       2        2      21.4  \n",
       "29   73691 1              0               14       1        2      18.9  \n",
       "30   73714 1              0               29       2        2      26.4  \n",
       "...  ...   ...            ...             ...      ...      ...    ...   \n",
       "2249 83589 1              0               59       1        2      26.6  \n",
       "2250 83612 0              1               72       1        2      30.5  \n",
       "2251 83615 0              1               80       1        2      24.9  \n",
       "2252 83618 1              0               40       1        2      29.4  \n",
       "2253 83619 1              0               31       1        2      26.7  \n",
       "2254 83624 1              0               50       2        2      34.3  \n",
       "2255 83625 1              0               58       2        2      24.6  \n",
       "2256 83628 1              0               13       1        2      36.4  \n",
       "2257 83630 0              1               80       2        2      26.0  \n",
       "2258 83633 1              0               45       1        1      29.7  \n",
       "2259 83637 1              0               40       1        2      48.0  \n",
       "2260 83638 0              1               80       1        2      24.2  \n",
       "2261 83642 1              0               33       1        2      27.4  \n",
       "2262 83648 1              0               18       2        2      20.5  \n",
       "2263 83658 1              0               50       2        2      32.7  \n",
       "2264 83673 1              0               17       2        2      29.1  \n",
       "2265 83677 1              0               18       2        2      26.8  \n",
       "2266 83678 1              0               42       2        2      18.3  \n",
       "2267 83679 1              0               14       2        2      19.3  \n",
       "2268 83683 1              0               33       2        2      30.0  \n",
       "2269 83692 0              1               68       1        2      19.1  \n",
       "2270 83694 1              0               36       2        2      25.3  \n",
       "2271 83699 1              0               37       2        2      20.8  \n",
       "2272 83702 0              1               80       2        2      27.9  \n",
       "2273 83707 1              0               18       1        2      22.5  \n",
       "2274 83711 1              0               38       2        2      33.5  \n",
       "2275 83712 1              0               61       1        2      30.0  \n",
       "2276 83713 1              0               34       1        2      23.7  \n",
       "2277 83718 1              0               60       2        2      27.4  \n",
       "2278 83727 1              0               26       1        2      24.5  \n",
       "     LBXGLU DIQ010 LBXGLT LBXIN\n",
       "1    110    2      150    14.91\n",
       "2     89    2       80     3.85\n",
       "3     89    2       68     6.14\n",
       "4    104    2       84    16.15\n",
       "5    103    2       81    10.92\n",
       "6    110    2      100     6.08\n",
       "7     94    2      202    21.11\n",
       "8    107    2      164    20.93\n",
       "9     89    2      113    17.47\n",
       "10    90    2       95     3.24\n",
       "11    98    2       80     7.16\n",
       "12    85    2       91     9.86\n",
       "13   100    2       97     4.33\n",
       "14   102    2      124    12.06\n",
       "15   133    2      295    22.92\n",
       "16   114    2      150    10.09\n",
       "17    96    2      120     9.61\n",
       "18    89    2       82     8.39\n",
       "19   139    2      154    42.67\n",
       "20    86    2       84     4.47\n",
       "21   108    2       77     8.02\n",
       "22    99    2       95     6.12\n",
       "23   108    2      160     6.76\n",
       "24   105    2       72    15.98\n",
       "25    86    2       76    15.42\n",
       "26    96    2       83    10.80\n",
       "27   105    2      158    16.01\n",
       "28    90    2       76     3.47\n",
       "29    86    2       78     4.06\n",
       "30    87    2       67     6.43\n",
       "...  ...    ...    ...    ...  \n",
       "2249  96    2      117     6.45\n",
       "2250 114    2      134    15.86\n",
       "2251 105    2      100     9.50\n",
       "2252  96    2       92    10.10\n",
       "2253  94    2      117     5.04\n",
       "2254 333    2      510    21.87\n",
       "2255  96    2      107    10.08\n",
       "2256  96    2      107    29.18\n",
       "2257 106    2      166    13.32\n",
       "2258  96    2      110     7.04\n",
       "2259  98    2       83    52.64\n",
       "2260 116    2      157    13.81\n",
       "2261 100    2      115    12.86\n",
       "2262  88    2      144     3.74\n",
       "2263 106    2      126     7.71\n",
       "2264  90    2      111     9.74\n",
       "2265  98    2      114     9.85\n",
       "2266  97    2      154     3.39\n",
       "2267  94    2      100    16.10\n",
       "2268 101    2      149    15.82\n",
       "2269  89    2      136     1.56\n",
       "2270  99    2      128    20.72\n",
       "2271  83    2      113     1.93\n",
       "2272 111    2       72    13.91\n",
       "2273  98    2       79     3.51\n",
       "2274 100    2       73     6.53\n",
       "2275  93    2      208    13.02\n",
       "2276 103    2      124    21.41\n",
       "2277  90    2      108     4.99\n",
       "2278 108    2      108     3.76"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nhanes_data_encoded"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b66e4122",
   "metadata": {},
   "source": [
    "# Scaling"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94e6e349",
   "metadata": {},
   "source": [
    "Normalization:\n",
    "1) Scale numerical features to a similar range, often between 0 and 1, to prevent certain features from dominating others.\n",
    "2) This is crucial for algorithms sensitive to the scale of input features, such as distance-based algorithms.\n",
    "Standardization:\n",
    "1) Standardize features (subtract mean and divide by standard deviation) to transform them into a standard normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "ecb452bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "numeric_features <- sapply(nhanes_data, is.numeric)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "62406e8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "numeric_data <- nhanes_data[, numeric_features]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "cb38ed34",
   "metadata": {},
   "outputs": [],
   "source": [
    "scaled_data <- scale(numeric_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "14a1538d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>SEQN</th><th scope=col>RIDAGEYR</th><th scope=col>RIAGENDR</th><th scope=col>PAQ605</th><th scope=col>BMXBMI</th><th scope=col>LBXGLU</th><th scope=col>DIQ010</th><th scope=col>LBXGLT</th><th scope=col>LBXIN</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>-1.755294   </td><td> 0.95276943 </td><td> 0.9772131  </td><td> 0.4445743  </td><td> 1.068404047</td><td> 0.58395642 </td><td>-0.08753347 </td><td> 0.74415957 </td><td> 0.31641794 </td></tr>\n",
       "\t<tr><td>-1.753924   </td><td>-0.78367665 </td><td> 0.9772131  </td><td> 0.4445743  </td><td>-1.056038134</td><td>-0.58989463 </td><td>-0.08753347 </td><td>-0.74326409 </td><td>-0.82158128 </td></tr>\n",
       "\t<tr><td>-1.751186   </td><td>-1.27980410 </td><td>-1.0228690  </td><td> 0.4445743  </td><td>-0.655980840</td><td>-0.58989463 </td><td>-0.08753347 </td><td>-0.99825100 </td><td>-0.58595576 </td></tr>\n",
       "\t<tr><td>-1.750844   </td><td>-0.48600018 </td><td>-1.0228690  </td><td> 0.4445743  </td><td> 0.130338669</td><td> 0.24857041 </td><td>-0.08753347 </td><td>-0.65826845 </td><td> 0.44400555 </td></tr>\n",
       "\t<tr><td>-1.749817   </td><td>-0.18832371 </td><td> 0.9772131  </td><td>-2.0622083  </td><td> 1.095994206</td><td> 0.19267274 </td><td>-0.08753347 </td><td>-0.72201518 </td><td>-0.09412608 </td></tr>\n",
       "\t<tr><td>-1.749474   </td><td> 0.40702923 </td><td>-1.0228690  </td><td> 0.4445743  </td><td>-0.600800523</td><td> 0.58395642 </td><td>-0.08753347 </td><td>-0.31828590 </td><td>-0.59212936 </td></tr>\n",
       "\t<tr><td>-1.747421   </td><td>-1.37902959 </td><td>-1.0228690  </td><td> 0.4445743  </td><td> 1.482256420</td><td>-0.31040628 </td><td>-0.08753347 </td><td> 1.84910285 </td><td> 0.95435602 </td></tr>\n",
       "\t<tr><td>-1.744340   </td><td> 0.75431845 </td><td> 0.9772131  </td><td> 0.4445743  </td><td> 1.427076104</td><td> 0.41626342 </td><td>-0.08753347 </td><td> 1.04164430 </td><td> 0.93583523 </td></tr>\n",
       "\t<tr><td>-1.740575   </td><td> 1.64734787 </td><td>-1.0228690  </td><td> 0.4445743  </td><td> 1.509846578</td><td>-0.58989463 </td><td>-0.08753347 </td><td>-0.04205008 </td><td> 0.57982463 </td></tr>\n",
       "\t<tr><td>-1.739548   </td><td> 0.05974002 </td><td>-1.0228690  </td><td>-2.0622083  </td><td> 0.130338669</td><td>-0.53399696 </td><td>-0.08753347 </td><td>-0.42453045 </td><td>-0.88434616 </td></tr>\n",
       "\t<tr><td>-1.736809   </td><td> 0.60548022 </td><td> 0.9772131  </td><td> 0.4445743  </td><td> 0.654551674</td><td>-0.08681561 </td><td>-0.08753347 </td><td>-0.74326409 </td><td>-0.48100466 </td></tr>\n",
       "\t<tr><td>-1.736467   </td><td>-0.28754920 </td><td> 0.9772131  </td><td>-2.0622083  </td><td>-0.090382597</td><td>-0.81348531 </td><td>-0.08753347 </td><td>-0.50952609 </td><td>-0.20319292 </td></tr>\n",
       "\t<tr><td>-1.735782   </td><td> 1.89541159 </td><td>-1.0228690  </td><td> 0.4445743  </td><td>-0.462849732</td><td> 0.02497973 </td><td>-0.08753347 </td><td>-0.38203263 </td><td>-0.77219253 </td></tr>\n",
       "\t<tr><td>-1.731675   </td><td> 0.05974002 </td><td> 0.9772131  </td><td> 0.4445743  </td><td> 0.351059934</td><td> 0.13677507 </td><td>-0.08753347 </td><td> 0.19168792 </td><td> 0.02317221 </td></tr>\n",
       "\t<tr><td>-1.729621   </td><td> 1.44889688 </td><td>-1.0228690  </td><td> 0.4445743  </td><td> 0.323469776</td><td> 1.86960282 </td><td>-0.08753347 </td><td> 3.82525142 </td><td> 1.14059278 </td></tr>\n",
       "\t<tr><td>-1.729278   </td><td> 1.25044590 </td><td> 0.9772131  </td><td>-2.0622083  </td><td>-0.807726710</td><td> 0.80754710 </td><td>-0.08753347 </td><td> 0.74415957 </td><td>-0.17952747 </td></tr>\n",
       "\t<tr><td>-1.728594   </td><td> 0.75431845 </td><td> 0.9772131  </td><td> 0.4445743  </td><td> 1.358100708</td><td>-0.19861095 </td><td>-0.08753347 </td><td> 0.10669229 </td><td>-0.22891623 </td></tr>\n",
       "\t<tr><td>-1.723802   </td><td> 0.60548022 </td><td>-1.0228690  </td><td> 0.4445743  </td><td> 0.006182957</td><td>-0.58989463 </td><td>-0.08753347 </td><td>-0.70076627 </td><td>-0.35444598 </td></tr>\n",
       "\t<tr><td>-1.722775   </td><td> 1.39928414 </td><td> 0.9772131  </td><td> 0.4445743  </td><td> 2.503092273</td><td> 2.20498883 </td><td>-0.08753347 </td><td> 0.82915520 </td><td> 3.17273424 </td></tr>\n",
       "\t<tr><td>-1.722090   </td><td>-0.83328940 </td><td>-1.0228690  </td><td> 0.4445743  </td><td>-0.959472580</td><td>-0.75758764 </td><td>-0.08753347 </td><td>-0.65826845 </td><td>-0.75778747 </td></tr>\n",
       "\t<tr><td>-1.721405   </td><td>-0.83328940 </td><td>-1.0228690  </td><td> 0.4445743  </td><td> 0.695936912</td><td> 0.47216109 </td><td>-0.08753347 </td><td>-0.80701082 </td><td>-0.39251648 </td></tr>\n",
       "\t<tr><td>-1.720036   </td><td>-0.88290214 </td><td>-1.0228690  </td><td> 0.4445743  </td><td> 0.157928827</td><td>-0.03091794 </td><td>-0.08753347 </td><td>-0.42453045 </td><td>-0.58801363 </td></tr>\n",
       "\t<tr><td>-1.719694   </td><td>-0.58522567 </td><td> 0.9772131  </td><td> 0.4445743  </td><td> 0.599371358</td><td> 0.47216109 </td><td>-0.08753347 </td><td> 0.95664866 </td><td>-0.52216196 </td></tr>\n",
       "\t<tr><td>-1.716955   </td><td> 0.10935276 </td><td>-1.0228690  </td><td>-2.0622083  </td><td> 1.330510550</td><td> 0.30446808 </td><td>-0.08753347 </td><td>-0.91325536 </td><td> 0.42651370 </td></tr>\n",
       "\t<tr><td>-1.716613   </td><td> 0.95276943 </td><td> 0.9772131  </td><td> 0.4445743  </td><td> 1.164969601</td><td>-0.75758764 </td><td>-0.08753347 </td><td>-0.82825973 </td><td> 0.36889349 </td></tr>\n",
       "\t<tr><td>-1.715586   </td><td>-1.47825509 </td><td>-1.0228690  </td><td> 0.4445743  </td><td>-1.373324953</td><td>-0.19861095 </td><td>-0.08753347 </td><td>-0.67951736 </td><td>-0.10647327 </td></tr>\n",
       "\t<tr><td>-1.712848   </td><td> 0.80393120 </td><td>-1.0228690  </td><td> 0.4445743  </td><td> 0.778707386</td><td> 0.30446808 </td><td>-0.08753347 </td><td> 0.91415084 </td><td> 0.42960050 </td></tr>\n",
       "\t<tr><td>-1.712163   </td><td> 1.74657336 </td><td> 0.9772131  </td><td> 0.4445743  </td><td>-0.904292263</td><td>-0.53399696 </td><td>-0.08753347 </td><td>-0.82825973 </td><td>-0.86068071 </td></tr>\n",
       "\t<tr><td>-1.711821   </td><td>-1.37902959 </td><td>-1.0228690  </td><td> 0.4445743  </td><td>-1.249169241</td><td>-0.75758764 </td><td>-0.08753347 </td><td>-0.78576191 </td><td>-0.79997370 </td></tr>\n",
       "\t<tr><td>-1.703948   </td><td>-0.63483842 </td><td> 0.9772131  </td><td> 0.4445743  </td><td>-0.214538309</td><td>-0.70168997 </td><td>-0.08753347 </td><td>-1.01949991 </td><td>-0.55611672 </td></tr>\n",
       "\t<tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr>\n",
       "\t<tr><td>1.676321     </td><td> 0.85354394  </td><td>-1.0228690   </td><td> 0.4445743   </td><td>-0.186948150 </td><td>-0.19861095  </td><td>-0.08753347  </td><td> 0.0429455570</td><td>-0.5540589   </td></tr>\n",
       "\t<tr><td>1.684194     </td><td> 1.49850963  </td><td>-1.0228690   </td><td> 0.4445743   </td><td> 0.351059934 </td><td> 0.80754710  </td><td>-0.08753347  </td><td> 0.4041770162</td><td> 0.4141665   </td></tr>\n",
       "\t<tr><td>1.685221     </td><td> 1.89541159  </td><td>-1.0228690   </td><td> 0.4445743   </td><td>-0.421464495 </td><td> 0.30446808  </td><td>-0.08753347  </td><td>-0.3182859023</td><td>-0.2402345   </td></tr>\n",
       "\t<tr><td>1.686248     </td><td>-0.08909822  </td><td>-1.0228690   </td><td> 0.4445743   </td><td> 0.199314064 </td><td>-0.19861095  </td><td>-0.08753347  </td><td>-0.4882771773</td><td>-0.1784985   </td></tr>\n",
       "\t<tr><td>1.686590     </td><td>-0.53561293  </td><td>-1.0228690   </td><td> 0.4445743   </td><td>-0.173153071 </td><td>-0.31040628  </td><td>-0.08753347  </td><td> 0.0429455570</td><td>-0.6991383   </td></tr>\n",
       "\t<tr><td>1.688302     </td><td> 0.40702923  </td><td> 0.9772131   </td><td> 0.4445743   </td><td> 0.875272940 </td><td>13.04913667  </td><td>-0.08753347  </td><td> 8.3937669394</td><td> 1.0325549   </td></tr>\n",
       "\t<tr><td>1.688644     </td><td> 0.80393120  </td><td> 0.9772131   </td><td> 0.4445743   </td><td>-0.462849732 </td><td>-0.19861095  </td><td>-0.08753347  </td><td>-0.1695435367</td><td>-0.1805564   </td></tr>\n",
       "\t<tr><td>1.689671     </td><td>-1.42864234  </td><td>-1.0228690   </td><td> 0.4445743   </td><td> 1.164969601 </td><td>-0.19861095  </td><td>-0.08753347  </td><td>-0.1695435367</td><td> 1.7847045   </td></tr>\n",
       "\t<tr><td>1.690356     </td><td> 1.89541159  </td><td> 0.9772131   </td><td> 0.4445743   </td><td>-0.269718625 </td><td> 0.36036575  </td><td>-0.08753347  </td><td> 1.0841421161</td><td> 0.1528177   </td></tr>\n",
       "\t<tr><td>1.691383     </td><td> 0.15896551  </td><td>-1.0228690   </td><td>-2.0622083   </td><td> 0.240699302 </td><td>-0.19861095  </td><td>-0.08753347  </td><td>-0.1057968086</td><td>-0.4933518   </td></tr>\n",
       "\t<tr><td>1.692752     </td><td>-0.08909822  </td><td>-1.0228690   </td><td> 0.4445743   </td><td> 2.765198776 </td><td>-0.08681561  </td><td>-0.08753347  </td><td>-0.6795173616</td><td> 4.1985798   </td></tr>\n",
       "\t<tr><td>1.693094     </td><td> 1.89541159  </td><td>-1.0228690   </td><td> 0.4445743   </td><td>-0.518030049 </td><td> 0.91934244  </td><td>-0.08753347  </td><td> 0.8929019318</td><td> 0.2032354   </td></tr>\n",
       "\t<tr><td>1.694463     </td><td>-0.43638743  </td><td>-1.0228690   </td><td> 0.4445743   </td><td>-0.076587518 </td><td> 0.02497973  </td><td>-0.08753347  </td><td> 0.0004477382</td><td> 0.1054868   </td></tr>\n",
       "\t<tr><td>1.696517     </td><td>-1.18057861  </td><td> 0.9772131   </td><td> 0.4445743   </td><td>-1.028447975 </td><td>-0.64579230  </td><td>-0.08753347  </td><td> 0.6166661099</td><td>-0.8328995   </td></tr>\n",
       "\t<tr><td>1.699940     </td><td> 0.40702923  </td><td> 0.9772131   </td><td> 0.4445743   </td><td> 0.654551674 </td><td> 0.36036575  </td><td>-0.08753347  </td><td> 0.2341857413</td><td>-0.4244134   </td></tr>\n",
       "\t<tr><td>1.705075     </td><td>-1.23019136  </td><td> 0.9772131   </td><td> 0.4445743   </td><td> 0.157928827 </td><td>-0.53399696  </td><td>-0.08753347  </td><td>-0.0845478993</td><td>-0.2155401   </td></tr>\n",
       "\t<tr><td>1.706444     </td><td>-1.18057861  </td><td> 0.9772131   </td><td> 0.4445743   </td><td>-0.159357992 </td><td>-0.08681561  </td><td>-0.08753347  </td><td>-0.0208011712</td><td>-0.2042218   </td></tr>\n",
       "\t<tr><td>1.706786     </td><td> 0.01012727  </td><td> 0.9772131   </td><td> 0.4445743   </td><td>-1.331939715 </td><td>-0.14271328  </td><td>-0.08753347  </td><td> 0.8291552036</td><td>-0.8689122   </td></tr>\n",
       "\t<tr><td>1.707129     </td><td>-1.37902959  </td><td> 0.9772131   </td><td> 0.4445743   </td><td>-1.193988925 </td><td>-0.31040628  </td><td>-0.08753347  </td><td>-0.3182859023</td><td> 0.4388609   </td></tr>\n",
       "\t<tr><td>1.708498     </td><td>-0.43638743  </td><td> 0.9772131   </td><td> 0.4445743   </td><td> 0.282084539 </td><td> 0.08087740  </td><td>-0.08753347  </td><td> 0.7229106568</td><td> 0.4100508   </td></tr>\n",
       "\t<tr><td>1.711579     </td><td> 1.30005865  </td><td>-1.0228690   </td><td> 0.4445743   </td><td>-1.221579083 </td><td>-0.58989463  </td><td>-0.08753347  </td><td> 0.4466748350</td><td>-1.0572068   </td></tr>\n",
       "\t<tr><td>1.712263     </td><td>-0.28754920  </td><td> 0.9772131   </td><td> 0.4445743   </td><td>-0.366284179 </td><td>-0.03091794  </td><td>-0.08753347  </td><td> 0.2766835600</td><td> 0.9142277   </td></tr>\n",
       "\t<tr><td>1.713975     </td><td>-0.23793645  </td><td> 0.9772131   </td><td> 0.4445743   </td><td>-0.987062738 </td><td>-0.92528065  </td><td>-0.08753347  </td><td>-0.0420500805</td><td>-1.0191363   </td></tr>\n",
       "\t<tr><td>1.715002     </td><td> 1.89541159  </td><td> 0.9772131   </td><td> 0.4445743   </td><td>-0.007612122 </td><td> 0.63985409  </td><td>-0.08753347  </td><td>-0.9132553647</td><td> 0.2135247   </td></tr>\n",
       "\t<tr><td>1.716713     </td><td>-1.18057861  </td><td>-1.0228690   </td><td> 0.4445743   </td><td>-0.752546393 </td><td>-0.08681561  </td><td>-0.08753347  </td><td>-0.7645129991</td><td>-0.8565650   </td></tr>\n",
       "\t<tr><td>1.718082     </td><td>-0.18832371  </td><td> 0.9772131   </td><td> 0.4445743   </td><td> 0.764912307 </td><td> 0.02497973  </td><td>-0.08753347  </td><td>-0.8920064553</td><td>-0.5458274   </td></tr>\n",
       "\t<tr><td>1.718425     </td><td> 0.95276943  </td><td>-1.0228690   </td><td> 0.4445743   </td><td> 0.282084539 </td><td>-0.36630395  </td><td>-0.08753347  </td><td> 1.9765963096</td><td> 0.1219497   </td></tr>\n",
       "\t<tr><td>1.718767     </td><td>-0.38677469  </td><td>-1.0228690   </td><td> 0.4445743   </td><td>-0.587005444 </td><td> 0.19267274  </td><td>-0.08753347  </td><td> 0.1916879225</td><td> 0.9852240   </td></tr>\n",
       "\t<tr><td>1.720479     </td><td> 0.90315669  </td><td> 0.9772131   </td><td> 0.4445743   </td><td>-0.076587518 </td><td>-0.53399696  </td><td>-0.08753347  </td><td>-0.1482946274</td><td>-0.7042830   </td></tr>\n",
       "\t<tr><td>1.723559     </td><td>-0.78367665  </td><td>-1.0228690   </td><td> 0.4445743   </td><td>-0.476644812 </td><td> 0.47216109  </td><td>-0.08753347  </td><td>-0.1482946274</td><td>-0.8308417   </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lllllllll}\n",
       " SEQN & RIDAGEYR & RIAGENDR & PAQ605 & BMXBMI & LBXGLU & DIQ010 & LBXGLT & LBXIN\\\\\n",
       "\\hline\n",
       "\t -1.755294    &  0.95276943  &  0.9772131   &  0.4445743   &  1.068404047 &  0.58395642  & -0.08753347  &  0.74415957  &  0.31641794 \\\\\n",
       "\t -1.753924    & -0.78367665  &  0.9772131   &  0.4445743   & -1.056038134 & -0.58989463  & -0.08753347  & -0.74326409  & -0.82158128 \\\\\n",
       "\t -1.751186    & -1.27980410  & -1.0228690   &  0.4445743   & -0.655980840 & -0.58989463  & -0.08753347  & -0.99825100  & -0.58595576 \\\\\n",
       "\t -1.750844    & -0.48600018  & -1.0228690   &  0.4445743   &  0.130338669 &  0.24857041  & -0.08753347  & -0.65826845  &  0.44400555 \\\\\n",
       "\t -1.749817    & -0.18832371  &  0.9772131   & -2.0622083   &  1.095994206 &  0.19267274  & -0.08753347  & -0.72201518  & -0.09412608 \\\\\n",
       "\t -1.749474    &  0.40702923  & -1.0228690   &  0.4445743   & -0.600800523 &  0.58395642  & -0.08753347  & -0.31828590  & -0.59212936 \\\\\n",
       "\t -1.747421    & -1.37902959  & -1.0228690   &  0.4445743   &  1.482256420 & -0.31040628  & -0.08753347  &  1.84910285  &  0.95435602 \\\\\n",
       "\t -1.744340    &  0.75431845  &  0.9772131   &  0.4445743   &  1.427076104 &  0.41626342  & -0.08753347  &  1.04164430  &  0.93583523 \\\\\n",
       "\t -1.740575    &  1.64734787  & -1.0228690   &  0.4445743   &  1.509846578 & -0.58989463  & -0.08753347  & -0.04205008  &  0.57982463 \\\\\n",
       "\t -1.739548    &  0.05974002  & -1.0228690   & -2.0622083   &  0.130338669 & -0.53399696  & -0.08753347  & -0.42453045  & -0.88434616 \\\\\n",
       "\t -1.736809    &  0.60548022  &  0.9772131   &  0.4445743   &  0.654551674 & -0.08681561  & -0.08753347  & -0.74326409  & -0.48100466 \\\\\n",
       "\t -1.736467    & -0.28754920  &  0.9772131   & -2.0622083   & -0.090382597 & -0.81348531  & -0.08753347  & -0.50952609  & -0.20319292 \\\\\n",
       "\t -1.735782    &  1.89541159  & -1.0228690   &  0.4445743   & -0.462849732 &  0.02497973  & -0.08753347  & -0.38203263  & -0.77219253 \\\\\n",
       "\t -1.731675    &  0.05974002  &  0.9772131   &  0.4445743   &  0.351059934 &  0.13677507  & -0.08753347  &  0.19168792  &  0.02317221 \\\\\n",
       "\t -1.729621    &  1.44889688  & -1.0228690   &  0.4445743   &  0.323469776 &  1.86960282  & -0.08753347  &  3.82525142  &  1.14059278 \\\\\n",
       "\t -1.729278    &  1.25044590  &  0.9772131   & -2.0622083   & -0.807726710 &  0.80754710  & -0.08753347  &  0.74415957  & -0.17952747 \\\\\n",
       "\t -1.728594    &  0.75431845  &  0.9772131   &  0.4445743   &  1.358100708 & -0.19861095  & -0.08753347  &  0.10669229  & -0.22891623 \\\\\n",
       "\t -1.723802    &  0.60548022  & -1.0228690   &  0.4445743   &  0.006182957 & -0.58989463  & -0.08753347  & -0.70076627  & -0.35444598 \\\\\n",
       "\t -1.722775    &  1.39928414  &  0.9772131   &  0.4445743   &  2.503092273 &  2.20498883  & -0.08753347  &  0.82915520  &  3.17273424 \\\\\n",
       "\t -1.722090    & -0.83328940  & -1.0228690   &  0.4445743   & -0.959472580 & -0.75758764  & -0.08753347  & -0.65826845  & -0.75778747 \\\\\n",
       "\t -1.721405    & -0.83328940  & -1.0228690   &  0.4445743   &  0.695936912 &  0.47216109  & -0.08753347  & -0.80701082  & -0.39251648 \\\\\n",
       "\t -1.720036    & -0.88290214  & -1.0228690   &  0.4445743   &  0.157928827 & -0.03091794  & -0.08753347  & -0.42453045  & -0.58801363 \\\\\n",
       "\t -1.719694    & -0.58522567  &  0.9772131   &  0.4445743   &  0.599371358 &  0.47216109  & -0.08753347  &  0.95664866  & -0.52216196 \\\\\n",
       "\t -1.716955    &  0.10935276  & -1.0228690   & -2.0622083   &  1.330510550 &  0.30446808  & -0.08753347  & -0.91325536  &  0.42651370 \\\\\n",
       "\t -1.716613    &  0.95276943  &  0.9772131   &  0.4445743   &  1.164969601 & -0.75758764  & -0.08753347  & -0.82825973  &  0.36889349 \\\\\n",
       "\t -1.715586    & -1.47825509  & -1.0228690   &  0.4445743   & -1.373324953 & -0.19861095  & -0.08753347  & -0.67951736  & -0.10647327 \\\\\n",
       "\t -1.712848    &  0.80393120  & -1.0228690   &  0.4445743   &  0.778707386 &  0.30446808  & -0.08753347  &  0.91415084  &  0.42960050 \\\\\n",
       "\t -1.712163    &  1.74657336  &  0.9772131   &  0.4445743   & -0.904292263 & -0.53399696  & -0.08753347  & -0.82825973  & -0.86068071 \\\\\n",
       "\t -1.711821    & -1.37902959  & -1.0228690   &  0.4445743   & -1.249169241 & -0.75758764  & -0.08753347  & -0.78576191  & -0.79997370 \\\\\n",
       "\t -1.703948    & -0.63483842  &  0.9772131   &  0.4445743   & -0.214538309 & -0.70168997  & -0.08753347  & -1.01949991  & -0.55611672 \\\\\n",
       "\t ... & ... & ... & ... & ... & ... & ... & ... & ...\\\\\n",
       "\t 1.676321      &  0.85354394   & -1.0228690    &  0.4445743    & -0.186948150  & -0.19861095   & -0.08753347   &  0.0429455570 & -0.5540589   \\\\\n",
       "\t 1.684194      &  1.49850963   & -1.0228690    &  0.4445743    &  0.351059934  &  0.80754710   & -0.08753347   &  0.4041770162 &  0.4141665   \\\\\n",
       "\t 1.685221      &  1.89541159   & -1.0228690    &  0.4445743    & -0.421464495  &  0.30446808   & -0.08753347   & -0.3182859023 & -0.2402345   \\\\\n",
       "\t 1.686248      & -0.08909822   & -1.0228690    &  0.4445743    &  0.199314064  & -0.19861095   & -0.08753347   & -0.4882771773 & -0.1784985   \\\\\n",
       "\t 1.686590      & -0.53561293   & -1.0228690    &  0.4445743    & -0.173153071  & -0.31040628   & -0.08753347   &  0.0429455570 & -0.6991383   \\\\\n",
       "\t 1.688302      &  0.40702923   &  0.9772131    &  0.4445743    &  0.875272940  & 13.04913667   & -0.08753347   &  8.3937669394 &  1.0325549   \\\\\n",
       "\t 1.688644      &  0.80393120   &  0.9772131    &  0.4445743    & -0.462849732  & -0.19861095   & -0.08753347   & -0.1695435367 & -0.1805564   \\\\\n",
       "\t 1.689671      & -1.42864234   & -1.0228690    &  0.4445743    &  1.164969601  & -0.19861095   & -0.08753347   & -0.1695435367 &  1.7847045   \\\\\n",
       "\t 1.690356      &  1.89541159   &  0.9772131    &  0.4445743    & -0.269718625  &  0.36036575   & -0.08753347   &  1.0841421161 &  0.1528177   \\\\\n",
       "\t 1.691383      &  0.15896551   & -1.0228690    & -2.0622083    &  0.240699302  & -0.19861095   & -0.08753347   & -0.1057968086 & -0.4933518   \\\\\n",
       "\t 1.692752      & -0.08909822   & -1.0228690    &  0.4445743    &  2.765198776  & -0.08681561   & -0.08753347   & -0.6795173616 &  4.1985798   \\\\\n",
       "\t 1.693094      &  1.89541159   & -1.0228690    &  0.4445743    & -0.518030049  &  0.91934244   & -0.08753347   &  0.8929019318 &  0.2032354   \\\\\n",
       "\t 1.694463      & -0.43638743   & -1.0228690    &  0.4445743    & -0.076587518  &  0.02497973   & -0.08753347   &  0.0004477382 &  0.1054868   \\\\\n",
       "\t 1.696517      & -1.18057861   &  0.9772131    &  0.4445743    & -1.028447975  & -0.64579230   & -0.08753347   &  0.6166661099 & -0.8328995   \\\\\n",
       "\t 1.699940      &  0.40702923   &  0.9772131    &  0.4445743    &  0.654551674  &  0.36036575   & -0.08753347   &  0.2341857413 & -0.4244134   \\\\\n",
       "\t 1.705075      & -1.23019136   &  0.9772131    &  0.4445743    &  0.157928827  & -0.53399696   & -0.08753347   & -0.0845478993 & -0.2155401   \\\\\n",
       "\t 1.706444      & -1.18057861   &  0.9772131    &  0.4445743    & -0.159357992  & -0.08681561   & -0.08753347   & -0.0208011712 & -0.2042218   \\\\\n",
       "\t 1.706786      &  0.01012727   &  0.9772131    &  0.4445743    & -1.331939715  & -0.14271328   & -0.08753347   &  0.8291552036 & -0.8689122   \\\\\n",
       "\t 1.707129      & -1.37902959   &  0.9772131    &  0.4445743    & -1.193988925  & -0.31040628   & -0.08753347   & -0.3182859023 &  0.4388609   \\\\\n",
       "\t 1.708498      & -0.43638743   &  0.9772131    &  0.4445743    &  0.282084539  &  0.08087740   & -0.08753347   &  0.7229106568 &  0.4100508   \\\\\n",
       "\t 1.711579      &  1.30005865   & -1.0228690    &  0.4445743    & -1.221579083  & -0.58989463   & -0.08753347   &  0.4466748350 & -1.0572068   \\\\\n",
       "\t 1.712263      & -0.28754920   &  0.9772131    &  0.4445743    & -0.366284179  & -0.03091794   & -0.08753347   &  0.2766835600 &  0.9142277   \\\\\n",
       "\t 1.713975      & -0.23793645   &  0.9772131    &  0.4445743    & -0.987062738  & -0.92528065   & -0.08753347   & -0.0420500805 & -1.0191363   \\\\\n",
       "\t 1.715002      &  1.89541159   &  0.9772131    &  0.4445743    & -0.007612122  &  0.63985409   & -0.08753347   & -0.9132553647 &  0.2135247   \\\\\n",
       "\t 1.716713      & -1.18057861   & -1.0228690    &  0.4445743    & -0.752546393  & -0.08681561   & -0.08753347   & -0.7645129991 & -0.8565650   \\\\\n",
       "\t 1.718082      & -0.18832371   &  0.9772131    &  0.4445743    &  0.764912307  &  0.02497973   & -0.08753347   & -0.8920064553 & -0.5458274   \\\\\n",
       "\t 1.718425      &  0.95276943   & -1.0228690    &  0.4445743    &  0.282084539  & -0.36630395   & -0.08753347   &  1.9765963096 &  0.1219497   \\\\\n",
       "\t 1.718767      & -0.38677469   & -1.0228690    &  0.4445743    & -0.587005444  &  0.19267274   & -0.08753347   &  0.1916879225 &  0.9852240   \\\\\n",
       "\t 1.720479      &  0.90315669   &  0.9772131    &  0.4445743    & -0.076587518  & -0.53399696   & -0.08753347   & -0.1482946274 & -0.7042830   \\\\\n",
       "\t 1.723559      & -0.78367665   & -1.0228690    &  0.4445743    & -0.476644812  &  0.47216109   & -0.08753347   & -0.1482946274 & -0.8308417   \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| SEQN | RIDAGEYR | RIAGENDR | PAQ605 | BMXBMI | LBXGLU | DIQ010 | LBXGLT | LBXIN |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| -1.755294    |  0.95276943  |  0.9772131   |  0.4445743   |  1.068404047 |  0.58395642  | -0.08753347  |  0.74415957  |  0.31641794  |\n",
       "| -1.753924    | -0.78367665  |  0.9772131   |  0.4445743   | -1.056038134 | -0.58989463  | -0.08753347  | -0.74326409  | -0.82158128  |\n",
       "| -1.751186    | -1.27980410  | -1.0228690   |  0.4445743   | -0.655980840 | -0.58989463  | -0.08753347  | -0.99825100  | -0.58595576  |\n",
       "| -1.750844    | -0.48600018  | -1.0228690   |  0.4445743   |  0.130338669 |  0.24857041  | -0.08753347  | -0.65826845  |  0.44400555  |\n",
       "| -1.749817    | -0.18832371  |  0.9772131   | -2.0622083   |  1.095994206 |  0.19267274  | -0.08753347  | -0.72201518  | -0.09412608  |\n",
       "| -1.749474    |  0.40702923  | -1.0228690   |  0.4445743   | -0.600800523 |  0.58395642  | -0.08753347  | -0.31828590  | -0.59212936  |\n",
       "| -1.747421    | -1.37902959  | -1.0228690   |  0.4445743   |  1.482256420 | -0.31040628  | -0.08753347  |  1.84910285  |  0.95435602  |\n",
       "| -1.744340    |  0.75431845  |  0.9772131   |  0.4445743   |  1.427076104 |  0.41626342  | -0.08753347  |  1.04164430  |  0.93583523  |\n",
       "| -1.740575    |  1.64734787  | -1.0228690   |  0.4445743   |  1.509846578 | -0.58989463  | -0.08753347  | -0.04205008  |  0.57982463  |\n",
       "| -1.739548    |  0.05974002  | -1.0228690   | -2.0622083   |  0.130338669 | -0.53399696  | -0.08753347  | -0.42453045  | -0.88434616  |\n",
       "| -1.736809    |  0.60548022  |  0.9772131   |  0.4445743   |  0.654551674 | -0.08681561  | -0.08753347  | -0.74326409  | -0.48100466  |\n",
       "| -1.736467    | -0.28754920  |  0.9772131   | -2.0622083   | -0.090382597 | -0.81348531  | -0.08753347  | -0.50952609  | -0.20319292  |\n",
       "| -1.735782    |  1.89541159  | -1.0228690   |  0.4445743   | -0.462849732 |  0.02497973  | -0.08753347  | -0.38203263  | -0.77219253  |\n",
       "| -1.731675    |  0.05974002  |  0.9772131   |  0.4445743   |  0.351059934 |  0.13677507  | -0.08753347  |  0.19168792  |  0.02317221  |\n",
       "| -1.729621    |  1.44889688  | -1.0228690   |  0.4445743   |  0.323469776 |  1.86960282  | -0.08753347  |  3.82525142  |  1.14059278  |\n",
       "| -1.729278    |  1.25044590  |  0.9772131   | -2.0622083   | -0.807726710 |  0.80754710  | -0.08753347  |  0.74415957  | -0.17952747  |\n",
       "| -1.728594    |  0.75431845  |  0.9772131   |  0.4445743   |  1.358100708 | -0.19861095  | -0.08753347  |  0.10669229  | -0.22891623  |\n",
       "| -1.723802    |  0.60548022  | -1.0228690   |  0.4445743   |  0.006182957 | -0.58989463  | -0.08753347  | -0.70076627  | -0.35444598  |\n",
       "| -1.722775    |  1.39928414  |  0.9772131   |  0.4445743   |  2.503092273 |  2.20498883  | -0.08753347  |  0.82915520  |  3.17273424  |\n",
       "| -1.722090    | -0.83328940  | -1.0228690   |  0.4445743   | -0.959472580 | -0.75758764  | -0.08753347  | -0.65826845  | -0.75778747  |\n",
       "| -1.721405    | -0.83328940  | -1.0228690   |  0.4445743   |  0.695936912 |  0.47216109  | -0.08753347  | -0.80701082  | -0.39251648  |\n",
       "| -1.720036    | -0.88290214  | -1.0228690   |  0.4445743   |  0.157928827 | -0.03091794  | -0.08753347  | -0.42453045  | -0.58801363  |\n",
       "| -1.719694    | -0.58522567  |  0.9772131   |  0.4445743   |  0.599371358 |  0.47216109  | -0.08753347  |  0.95664866  | -0.52216196  |\n",
       "| -1.716955    |  0.10935276  | -1.0228690   | -2.0622083   |  1.330510550 |  0.30446808  | -0.08753347  | -0.91325536  |  0.42651370  |\n",
       "| -1.716613    |  0.95276943  |  0.9772131   |  0.4445743   |  1.164969601 | -0.75758764  | -0.08753347  | -0.82825973  |  0.36889349  |\n",
       "| -1.715586    | -1.47825509  | -1.0228690   |  0.4445743   | -1.373324953 | -0.19861095  | -0.08753347  | -0.67951736  | -0.10647327  |\n",
       "| -1.712848    |  0.80393120  | -1.0228690   |  0.4445743   |  0.778707386 |  0.30446808  | -0.08753347  |  0.91415084  |  0.42960050  |\n",
       "| -1.712163    |  1.74657336  |  0.9772131   |  0.4445743   | -0.904292263 | -0.53399696  | -0.08753347  | -0.82825973  | -0.86068071  |\n",
       "| -1.711821    | -1.37902959  | -1.0228690   |  0.4445743   | -1.249169241 | -0.75758764  | -0.08753347  | -0.78576191  | -0.79997370  |\n",
       "| -1.703948    | -0.63483842  |  0.9772131   |  0.4445743   | -0.214538309 | -0.70168997  | -0.08753347  | -1.01949991  | -0.55611672  |\n",
       "| ... | ... | ... | ... | ... | ... | ... | ... | ... |\n",
       "| 1.676321      |  0.85354394   | -1.0228690    |  0.4445743    | -0.186948150  | -0.19861095   | -0.08753347   |  0.0429455570 | -0.5540589    |\n",
       "| 1.684194      |  1.49850963   | -1.0228690    |  0.4445743    |  0.351059934  |  0.80754710   | -0.08753347   |  0.4041770162 |  0.4141665    |\n",
       "| 1.685221      |  1.89541159   | -1.0228690    |  0.4445743    | -0.421464495  |  0.30446808   | -0.08753347   | -0.3182859023 | -0.2402345    |\n",
       "| 1.686248      | -0.08909822   | -1.0228690    |  0.4445743    |  0.199314064  | -0.19861095   | -0.08753347   | -0.4882771773 | -0.1784985    |\n",
       "| 1.686590      | -0.53561293   | -1.0228690    |  0.4445743    | -0.173153071  | -0.31040628   | -0.08753347   |  0.0429455570 | -0.6991383    |\n",
       "| 1.688302      |  0.40702923   |  0.9772131    |  0.4445743    |  0.875272940  | 13.04913667   | -0.08753347   |  8.3937669394 |  1.0325549    |\n",
       "| 1.688644      |  0.80393120   |  0.9772131    |  0.4445743    | -0.462849732  | -0.19861095   | -0.08753347   | -0.1695435367 | -0.1805564    |\n",
       "| 1.689671      | -1.42864234   | -1.0228690    |  0.4445743    |  1.164969601  | -0.19861095   | -0.08753347   | -0.1695435367 |  1.7847045    |\n",
       "| 1.690356      |  1.89541159   |  0.9772131    |  0.4445743    | -0.269718625  |  0.36036575   | -0.08753347   |  1.0841421161 |  0.1528177    |\n",
       "| 1.691383      |  0.15896551   | -1.0228690    | -2.0622083    |  0.240699302  | -0.19861095   | -0.08753347   | -0.1057968086 | -0.4933518    |\n",
       "| 1.692752      | -0.08909822   | -1.0228690    |  0.4445743    |  2.765198776  | -0.08681561   | -0.08753347   | -0.6795173616 |  4.1985798    |\n",
       "| 1.693094      |  1.89541159   | -1.0228690    |  0.4445743    | -0.518030049  |  0.91934244   | -0.08753347   |  0.8929019318 |  0.2032354    |\n",
       "| 1.694463      | -0.43638743   | -1.0228690    |  0.4445743    | -0.076587518  |  0.02497973   | -0.08753347   |  0.0004477382 |  0.1054868    |\n",
       "| 1.696517      | -1.18057861   |  0.9772131    |  0.4445743    | -1.028447975  | -0.64579230   | -0.08753347   |  0.6166661099 | -0.8328995    |\n",
       "| 1.699940      |  0.40702923   |  0.9772131    |  0.4445743    |  0.654551674  |  0.36036575   | -0.08753347   |  0.2341857413 | -0.4244134    |\n",
       "| 1.705075      | -1.23019136   |  0.9772131    |  0.4445743    |  0.157928827  | -0.53399696   | -0.08753347   | -0.0845478993 | -0.2155401    |\n",
       "| 1.706444      | -1.18057861   |  0.9772131    |  0.4445743    | -0.159357992  | -0.08681561   | -0.08753347   | -0.0208011712 | -0.2042218    |\n",
       "| 1.706786      |  0.01012727   |  0.9772131    |  0.4445743    | -1.331939715  | -0.14271328   | -0.08753347   |  0.8291552036 | -0.8689122    |\n",
       "| 1.707129      | -1.37902959   |  0.9772131    |  0.4445743    | -1.193988925  | -0.31040628   | -0.08753347   | -0.3182859023 |  0.4388609    |\n",
       "| 1.708498      | -0.43638743   |  0.9772131    |  0.4445743    |  0.282084539  |  0.08087740   | -0.08753347   |  0.7229106568 |  0.4100508    |\n",
       "| 1.711579      |  1.30005865   | -1.0228690    |  0.4445743    | -1.221579083  | -0.58989463   | -0.08753347   |  0.4466748350 | -1.0572068    |\n",
       "| 1.712263      | -0.28754920   |  0.9772131    |  0.4445743    | -0.366284179  | -0.03091794   | -0.08753347   |  0.2766835600 |  0.9142277    |\n",
       "| 1.713975      | -0.23793645   |  0.9772131    |  0.4445743    | -0.987062738  | -0.92528065   | -0.08753347   | -0.0420500805 | -1.0191363    |\n",
       "| 1.715002      |  1.89541159   |  0.9772131    |  0.4445743    | -0.007612122  |  0.63985409   | -0.08753347   | -0.9132553647 |  0.2135247    |\n",
       "| 1.716713      | -1.18057861   | -1.0228690    |  0.4445743    | -0.752546393  | -0.08681561   | -0.08753347   | -0.7645129991 | -0.8565650    |\n",
       "| 1.718082      | -0.18832371   |  0.9772131    |  0.4445743    |  0.764912307  |  0.02497973   | -0.08753347   | -0.8920064553 | -0.5458274    |\n",
       "| 1.718425      |  0.95276943   | -1.0228690    |  0.4445743    |  0.282084539  | -0.36630395   | -0.08753347   |  1.9765963096 |  0.1219497    |\n",
       "| 1.718767      | -0.38677469   | -1.0228690    |  0.4445743    | -0.587005444  |  0.19267274   | -0.08753347   |  0.1916879225 |  0.9852240    |\n",
       "| 1.720479      |  0.90315669   |  0.9772131    |  0.4445743    | -0.076587518  | -0.53399696   | -0.08753347   | -0.1482946274 | -0.7042830    |\n",
       "| 1.723559      | -0.78367665   | -1.0228690    |  0.4445743    | -0.476644812  |  0.47216109   | -0.08753347   | -0.1482946274 | -0.8308417    |\n",
       "\n"
      ],
      "text/plain": [
       "      SEQN      RIDAGEYR    RIAGENDR   PAQ605     BMXBMI       LBXGLU     \n",
       " [1,] -1.755294  0.95276943  0.9772131  0.4445743  1.068404047  0.58395642\n",
       " [2,] -1.753924 -0.78367665  0.9772131  0.4445743 -1.056038134 -0.58989463\n",
       " [3,] -1.751186 -1.27980410 -1.0228690  0.4445743 -0.655980840 -0.58989463\n",
       " [4,] -1.750844 -0.48600018 -1.0228690  0.4445743  0.130338669  0.24857041\n",
       " [5,] -1.749817 -0.18832371  0.9772131 -2.0622083  1.095994206  0.19267274\n",
       " [6,] -1.749474  0.40702923 -1.0228690  0.4445743 -0.600800523  0.58395642\n",
       " [7,] -1.747421 -1.37902959 -1.0228690  0.4445743  1.482256420 -0.31040628\n",
       " [8,] -1.744340  0.75431845  0.9772131  0.4445743  1.427076104  0.41626342\n",
       " [9,] -1.740575  1.64734787 -1.0228690  0.4445743  1.509846578 -0.58989463\n",
       "[10,] -1.739548  0.05974002 -1.0228690 -2.0622083  0.130338669 -0.53399696\n",
       "[11,] -1.736809  0.60548022  0.9772131  0.4445743  0.654551674 -0.08681561\n",
       "[12,] -1.736467 -0.28754920  0.9772131 -2.0622083 -0.090382597 -0.81348531\n",
       "[13,] -1.735782  1.89541159 -1.0228690  0.4445743 -0.462849732  0.02497973\n",
       "[14,] -1.731675  0.05974002  0.9772131  0.4445743  0.351059934  0.13677507\n",
       "[15,] -1.729621  1.44889688 -1.0228690  0.4445743  0.323469776  1.86960282\n",
       "[16,] -1.729278  1.25044590  0.9772131 -2.0622083 -0.807726710  0.80754710\n",
       "[17,] -1.728594  0.75431845  0.9772131  0.4445743  1.358100708 -0.19861095\n",
       "[18,] -1.723802  0.60548022 -1.0228690  0.4445743  0.006182957 -0.58989463\n",
       "[19,] -1.722775  1.39928414  0.9772131  0.4445743  2.503092273  2.20498883\n",
       "[20,] -1.722090 -0.83328940 -1.0228690  0.4445743 -0.959472580 -0.75758764\n",
       "[21,] -1.721405 -0.83328940 -1.0228690  0.4445743  0.695936912  0.47216109\n",
       "[22,] -1.720036 -0.88290214 -1.0228690  0.4445743  0.157928827 -0.03091794\n",
       "[23,] -1.719694 -0.58522567  0.9772131  0.4445743  0.599371358  0.47216109\n",
       "[24,] -1.716955  0.10935276 -1.0228690 -2.0622083  1.330510550  0.30446808\n",
       "[25,] -1.716613  0.95276943  0.9772131  0.4445743  1.164969601 -0.75758764\n",
       "[26,] -1.715586 -1.47825509 -1.0228690  0.4445743 -1.373324953 -0.19861095\n",
       "[27,] -1.712848  0.80393120 -1.0228690  0.4445743  0.778707386  0.30446808\n",
       "[28,] -1.712163  1.74657336  0.9772131  0.4445743 -0.904292263 -0.53399696\n",
       "[29,] -1.711821 -1.37902959 -1.0228690  0.4445743 -1.249169241 -0.75758764\n",
       "[30,] -1.703948 -0.63483842  0.9772131  0.4445743 -0.214538309 -0.70168997\n",
       "[31,] ...       ...         ...        ...        ...          ...        \n",
       "[32,] 1.676321   0.85354394 -1.0228690  0.4445743 -0.186948150 -0.19861095\n",
       "[33,] 1.684194   1.49850963 -1.0228690  0.4445743  0.351059934  0.80754710\n",
       "[34,] 1.685221   1.89541159 -1.0228690  0.4445743 -0.421464495  0.30446808\n",
       "[35,] 1.686248  -0.08909822 -1.0228690  0.4445743  0.199314064 -0.19861095\n",
       "[36,] 1.686590  -0.53561293 -1.0228690  0.4445743 -0.173153071 -0.31040628\n",
       "[37,] 1.688302   0.40702923  0.9772131  0.4445743  0.875272940 13.04913667\n",
       "[38,] 1.688644   0.80393120  0.9772131  0.4445743 -0.462849732 -0.19861095\n",
       "[39,] 1.689671  -1.42864234 -1.0228690  0.4445743  1.164969601 -0.19861095\n",
       "[40,] 1.690356   1.89541159  0.9772131  0.4445743 -0.269718625  0.36036575\n",
       "[41,] 1.691383   0.15896551 -1.0228690 -2.0622083  0.240699302 -0.19861095\n",
       "[42,] 1.692752  -0.08909822 -1.0228690  0.4445743  2.765198776 -0.08681561\n",
       "[43,] 1.693094   1.89541159 -1.0228690  0.4445743 -0.518030049  0.91934244\n",
       "[44,] 1.694463  -0.43638743 -1.0228690  0.4445743 -0.076587518  0.02497973\n",
       "[45,] 1.696517  -1.18057861  0.9772131  0.4445743 -1.028447975 -0.64579230\n",
       "[46,] 1.699940   0.40702923  0.9772131  0.4445743  0.654551674  0.36036575\n",
       "[47,] 1.705075  -1.23019136  0.9772131  0.4445743  0.157928827 -0.53399696\n",
       "[48,] 1.706444  -1.18057861  0.9772131  0.4445743 -0.159357992 -0.08681561\n",
       "[49,] 1.706786   0.01012727  0.9772131  0.4445743 -1.331939715 -0.14271328\n",
       "[50,] 1.707129  -1.37902959  0.9772131  0.4445743 -1.193988925 -0.31040628\n",
       "[51,] 1.708498  -0.43638743  0.9772131  0.4445743  0.282084539  0.08087740\n",
       "[52,] 1.711579   1.30005865 -1.0228690  0.4445743 -1.221579083 -0.58989463\n",
       "[53,] 1.712263  -0.28754920  0.9772131  0.4445743 -0.366284179 -0.03091794\n",
       "[54,] 1.713975  -0.23793645  0.9772131  0.4445743 -0.987062738 -0.92528065\n",
       "[55,] 1.715002   1.89541159  0.9772131  0.4445743 -0.007612122  0.63985409\n",
       "[56,] 1.716713  -1.18057861 -1.0228690  0.4445743 -0.752546393 -0.08681561\n",
       "[57,] 1.718082  -0.18832371  0.9772131  0.4445743  0.764912307  0.02497973\n",
       "[58,] 1.718425   0.95276943 -1.0228690  0.4445743  0.282084539 -0.36630395\n",
       "[59,] 1.718767  -0.38677469 -1.0228690  0.4445743 -0.587005444  0.19267274\n",
       "[60,] 1.720479   0.90315669  0.9772131  0.4445743 -0.076587518 -0.53399696\n",
       "[61,] 1.723559  -0.78367665 -1.0228690  0.4445743 -0.476644812  0.47216109\n",
       "      DIQ010      LBXGLT        LBXIN      \n",
       " [1,] -0.08753347  0.74415957    0.31641794\n",
       " [2,] -0.08753347 -0.74326409   -0.82158128\n",
       " [3,] -0.08753347 -0.99825100   -0.58595576\n",
       " [4,] -0.08753347 -0.65826845    0.44400555\n",
       " [5,] -0.08753347 -0.72201518   -0.09412608\n",
       " [6,] -0.08753347 -0.31828590   -0.59212936\n",
       " [7,] -0.08753347  1.84910285    0.95435602\n",
       " [8,] -0.08753347  1.04164430    0.93583523\n",
       " [9,] -0.08753347 -0.04205008    0.57982463\n",
       "[10,] -0.08753347 -0.42453045   -0.88434616\n",
       "[11,] -0.08753347 -0.74326409   -0.48100466\n",
       "[12,] -0.08753347 -0.50952609   -0.20319292\n",
       "[13,] -0.08753347 -0.38203263   -0.77219253\n",
       "[14,] -0.08753347  0.19168792    0.02317221\n",
       "[15,] -0.08753347  3.82525142    1.14059278\n",
       "[16,] -0.08753347  0.74415957   -0.17952747\n",
       "[17,] -0.08753347  0.10669229   -0.22891623\n",
       "[18,] -0.08753347 -0.70076627   -0.35444598\n",
       "[19,] -0.08753347  0.82915520    3.17273424\n",
       "[20,] -0.08753347 -0.65826845   -0.75778747\n",
       "[21,] -0.08753347 -0.80701082   -0.39251648\n",
       "[22,] -0.08753347 -0.42453045   -0.58801363\n",
       "[23,] -0.08753347  0.95664866   -0.52216196\n",
       "[24,] -0.08753347 -0.91325536    0.42651370\n",
       "[25,] -0.08753347 -0.82825973    0.36889349\n",
       "[26,] -0.08753347 -0.67951736   -0.10647327\n",
       "[27,] -0.08753347  0.91415084    0.42960050\n",
       "[28,] -0.08753347 -0.82825973   -0.86068071\n",
       "[29,] -0.08753347 -0.78576191   -0.79997370\n",
       "[30,] -0.08753347 -1.01949991   -0.55611672\n",
       "[31,] ...         ...           ...        \n",
       "[32,] -0.08753347  0.0429455570 -0.5540589 \n",
       "[33,] -0.08753347  0.4041770162  0.4141665 \n",
       "[34,] -0.08753347 -0.3182859023 -0.2402345 \n",
       "[35,] -0.08753347 -0.4882771773 -0.1784985 \n",
       "[36,] -0.08753347  0.0429455570 -0.6991383 \n",
       "[37,] -0.08753347  8.3937669394  1.0325549 \n",
       "[38,] -0.08753347 -0.1695435367 -0.1805564 \n",
       "[39,] -0.08753347 -0.1695435367  1.7847045 \n",
       "[40,] -0.08753347  1.0841421161  0.1528177 \n",
       "[41,] -0.08753347 -0.1057968086 -0.4933518 \n",
       "[42,] -0.08753347 -0.6795173616  4.1985798 \n",
       "[43,] -0.08753347  0.8929019318  0.2032354 \n",
       "[44,] -0.08753347  0.0004477382  0.1054868 \n",
       "[45,] -0.08753347  0.6166661099 -0.8328995 \n",
       "[46,] -0.08753347  0.2341857413 -0.4244134 \n",
       "[47,] -0.08753347 -0.0845478993 -0.2155401 \n",
       "[48,] -0.08753347 -0.0208011712 -0.2042218 \n",
       "[49,] -0.08753347  0.8291552036 -0.8689122 \n",
       "[50,] -0.08753347 -0.3182859023  0.4388609 \n",
       "[51,] -0.08753347  0.7229106568  0.4100508 \n",
       "[52,] -0.08753347  0.4466748350 -1.0572068 \n",
       "[53,] -0.08753347  0.2766835600  0.9142277 \n",
       "[54,] -0.08753347 -0.0420500805 -1.0191363 \n",
       "[55,] -0.08753347 -0.9132553647  0.2135247 \n",
       "[56,] -0.08753347 -0.7645129991 -0.8565650 \n",
       "[57,] -0.08753347 -0.8920064553 -0.5458274 \n",
       "[58,] -0.08753347  1.9765963096  0.1219497 \n",
       "[59,] -0.08753347  0.1916879225  0.9852240 \n",
       "[60,] -0.08753347 -0.1482946274 -0.7042830 \n",
       "[61,] -0.08753347 -0.1482946274 -0.8308417 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scaled_data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdd49667",
   "metadata": {},
   "source": [
    "# Feature Engineering"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "474d2710",
   "metadata": {},
   "source": [
    "Create New Features:\n",
    "Derive new features based on domain knowledge or insights gained during exploratory data analysis.\n",
    "For example, calculate BMI from height and weight.\n",
    "Handling Missing Values:\n",
    "Impute or handle missing values appropriately based on the nature of the data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2013aaef",
   "metadata": {},
   "source": [
    "a) Blood Glucose Ratio:\n",
    "Creating a new variable representing the ratio of fasting to non-fasting blood glucose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "1780c040",
   "metadata": {},
   "outputs": [],
   "source": [
    "nhanes_data$Glucose_Ratio <- nhanes_data$LBXGLU / nhanes_data$LBXGLT"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "318327e8",
   "metadata": {},
   "source": [
    "b) Insulin Level Grouping:\n",
    "Creating ordinal categories for insulin levels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "f41989b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "nhanes_data$Insulin_Category <- cut(nhanes_data$LBXIN, breaks = c(0, 10, 20, 30, Inf), labels = c(\"Low\", \"Moderate\", \"High\", \"Very High\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "28e49077",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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H4XPr9m3Ts//1TtqkafYEjjroR3yqZ9ifP+O189iXTVqmo3LN3q1VrzBlWOZzWG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\nD5v462uMasn7AAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Insulin Level Grouping\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "barplot(table(nhanes_data$Insulin_Category), col = \"skyblue\", main = \"Insulin Level Grouping\", xlab = \"Insulin Category\", ylab = \"Count\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e2abbf1",
   "metadata": {},
   "source": [
    "This featuring helps us analyze data better and more precisely, similarly for blood glucose ratio:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "680508c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JH9jDT+yYbHOdL5Vt7iHOkXUTRR6DlS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\nIvgHoXOQ1N/qlroAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Blood Glucose Ratio\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "barplot(table(nhanes_data$Glucose_Ratio), col = \"salmon\", main = \"Blood Glucose Ratio\", xlab = \"Glucose Ratio\", ylab = \"Count\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfd768ed",
   "metadata": {},
   "source": [
    "We can see clearly which count has the most individuals."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8003014",
   "metadata": {},
   "source": [
    "We now do this separately for age groups, senior & adult(non-senior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "2586b481",
   "metadata": {},
   "outputs": [],
   "source": [
    "senior_data$Glucose_Ratio <- senior_data$LBXGLU / senior_data$LBXGLT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "5c21e8de",
   "metadata": {},
   "outputs": [],
   "source": [
    "adult_data$Glucose_Ratio <- adult_data$LBXGLU / adult_data$LBXGLT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "3a48949a",
   "metadata": {},
   "outputs": [],
   "source": [
    "senior_data$Insulin_Category <- cut(senior_data$LBXIN, breaks = c(0, 10, 20, 30, Inf), labels = c(\"Low\", \"Moderate\", \"High\", \"Very High\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "704eef97",
   "metadata": {},
   "outputs": [],
   "source": [
    "adult_data$Insulin_Category <- cut(adult_data$LBXIN, breaks = c(0, 10, 20, 30, Inf), labels = c(\"Low\", \"Moderate\", \"High\", \"Very High\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e1e3889",
   "metadata": {},
   "source": [
    "We separated the data to perform comparative analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "c5e461ee",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+Hr3tv7V7PSHL5qdXnxterxZeul7GZlUWbxHoc/yRLSKA4hNe3Cv+9iFXs9q+sh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",
      "text/plain": [
       "Plot with title \"Insulin Level Grouping\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#boxplots\n",
    "barplot(table(senior_data$Insulin_Category), col = \"skyblue\", main = \"Insulin Level Grouping\", xlab = \"Insulin Category\", ylab = \"Count\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "3cc5725d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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giJlK9CWtT9Z0lCqkdI98oB2SAkUoQU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\nRK5CYII=",
      "text/plain": [
       "Plot with title \"Insulin Level Grouping\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#boxplots\n",
    "barplot(table(adult_data$Insulin_Category), col = \"skyblue\", main = \"Insulin Level Grouping\", xlab = \"Insulin Category\", ylab = \"Count\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a69e1a6b",
   "metadata": {},
   "source": [
    "Hence, the strength does not vary significantly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "02bab91e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CItDdDl8SuS9i8aQ6TFR0WkpQG6cI6U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\niAytju7c3VcAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Blood Glucose Ratio\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "barplot(table(senior_data$Glucose_Ratio), col = \"salmon\", main = \"Blood Glucose Ratio\", xlab = \"Glucose Ratio\", ylab = \"Count\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "15c397b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iOEtE+EJOPPZOBOo9dL8mWzU1B8zI6Q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\nVHcAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Blood Glucose Ratio\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "barplot(table(adult_data$Glucose_Ratio), col = \"salmon\", main = \"Blood Glucose Ratio\", xlab = \"Glucose Ratio\", ylab = \"Count\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10ba9850",
   "metadata": {},
   "source": [
    "We now perform a regression analysis for Insulin level and Glucose ratio:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "76f07e54",
   "metadata": {},
   "outputs": [],
   "source": [
    "modelINSXGLR <- lm(LBXIN ~ Glucose_Ratio, data = senior_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "af514bf6",
   "metadata": {},
   "outputs": [],
   "source": [
    "modelINSXGLR2 <- lm(LBXIN ~ Glucose_Ratio, data = adult_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "60b45554",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AJQAJEAFEAkAAUQCUABRAJQAJEAFEAk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\n2TYGDuodUv3h4IEaIq2FA4kURkDimXrTRyQR3ufmYGdfa8FltPk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      "text/plain": [
       "Plot with title \"Regression Analysis\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(senior_data$Glucose_Ratio, senior_data$LBXIN, col = \"blue\", main = \"Regression Analysis\", xlab = \"Glucose Ratio\", ylab = \"Insulin Level\")\n",
    "abline(modelINSXGLR, col = \"red\", lwd = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "2745cc00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xJ7bJutGQGTMybDnPzhNzykt1AwhmHjQtGG4qQ3caChsA2xU5GK65+woy8qPTE0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\nAJEAUAAiAaAARAJAAYgEgAL/A+UFENcweTzgAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Regression Analysis (adults)\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(adult_data$Glucose_Ratio, adult_data$LBXIN, col = \"blue\", main = \"Regression Analysis (adults)\", xlab = \"Glucose Ratio\", ylab = \"Insulin Level\")\n",
    "abline(modelINSXGLR2, col = \"red\", lwd = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d13693f",
   "metadata": {},
   "source": [
    "The results clearly depict a negative relation between glucose ratio & insulin levels, the higher the glucose ratio, the lower the insulin level, keep in mind that glucose ratio is fasting glucose levels/non-fasting glucose levels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "1c64bb5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = LBXIN ~ Glucose_Ratio, data = senior_data)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-10.187  -5.047  -1.662   2.650  42.136 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)     13.361      1.291  10.346   <2e-16 ***\n",
       "Glucose_Ratio   -3.632      1.512  -2.402   0.0168 *  \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 7.482 on 362 degrees of freedom\n",
       "Multiple R-squared:  0.01569,\tAdjusted R-squared:  0.01297 \n",
       "F-statistic:  5.77 on 1 and 362 DF,  p-value: 0.0168\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = LBXIN ~ Glucose_Ratio, data = adult_data)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-14.453  -5.982  -2.726   2.559  89.181 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)    17.9907     0.8190  21.966  < 2e-16 ***\n",
       "Glucose_Ratio  -6.0189     0.8051  -7.476 1.16e-13 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 9.919 on 1912 degrees of freedom\n",
       "Multiple R-squared:  0.0284,\tAdjusted R-squared:  0.0279 \n",
       "F-statistic:  55.9 on 1 and 1912 DF,  p-value: 1.157e-13\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#summaries\n",
    "summary(modelINSXGLR)\n",
    "summary(modelINSXGLR2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "452d47c6",
   "metadata": {},
   "source": [
    "The adult is more negatively related than the senior data, the slopes: -3.63 & -6.01"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4e30aee",
   "metadata": {},
   "source": [
    "# Linear Discriminant Analysis (LDA)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d73ff72",
   "metadata": {},
   "source": [
    "1) Objective: LDA is a supervised dimensionality reduction technique. It seeks to find the linear combinations of features that best separate different classes in the dataset.\n",
    "2) Difference from PCA: LDA considers class information when projecting the data onto a lower-dimensional space. It maximizes the distance between class means while minimizing the spread within each class.\n",
    "3) Visualization: LDA is particularly useful for visualizing class separation in the reduced space."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8577cb95",
   "metadata": {},
   "source": [
    "# Principal Component Analysis (PCA)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7052332",
   "metadata": {},
   "source": [
    "1) Objective: PCA is an unsupervised dimensionality reduction technique. It focuses on finding the directions (principal components) along which the data varies the most.\n",
    "2) Difference from LDA: PCA does not consider class labels during dimensionality reduction. It aims to capture the overall variance in the dataset.\n",
    "3) Visualization: PCA is often used for general feature reduction and visualization of data variability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "dcdda745",
   "metadata": {},
   "outputs": [],
   "source": [
    "file_path <- \"/users/banog/desktop/xx.csv\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1c6c2b90",
   "metadata": {},
   "outputs": [],
   "source": [
    "nhanes_data<-read.csv(file_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "78325d9b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "package 'R6' successfully unpacked and MD5 sums checked\n",
      "\n",
      "The downloaded binary packages are in\n",
      "\tC:\\Users\\banog\\AppData\\Local\\Temp\\RtmpQtKUga\\downloaded_packages\n"
     ]
    }
   ],
   "source": [
    "install.packages('R6')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "160f6b98",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "  There is a binary version available but the source version is later:\n",
      "         binary source needs_compilation\n",
      "generics  0.1.2  0.1.3             FALSE\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "installing the source package 'generics'\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "install.packages('generics')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a86c4c55",
   "metadata": {},
   "outputs": [],
   "source": [
    "file_path <- \"/users/banog/desktop/xx.csv\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1b3b2078",
   "metadata": {},
   "outputs": [],
   "source": [
    "nhanes_data<-read.csv(file_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "844eef94",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "  There is a binary version available but the source version is later:\n",
      "     binary source needs_compilation\n",
      "MASS 7.3-56 7.3-60              TRUE\n",
      "\n",
      "  Binaries will be installed\n",
      "package 'MASS' successfully unpacked and MD5 sums checked\n",
      "\n",
      "The downloaded binary packages are in\n",
      "\tC:\\Users\\banog\\AppData\\Local\\Temp\\Rtmp6LhMqb\\downloaded_packages\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "also installing the dependencies 'cli', 'pillar', 'tibble', 'tzdb', 'gtable', 'rlang', 'vctrs', 'dplyr', 'clock', 'hardhat', 'lifecycle', 'purrr', 'ggplot2', 'recipes'\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "  There are binary versions available but the source versions are later:\n",
      "          binary source needs_compilation\n",
      "cli        3.2.0  3.6.2              TRUE\n",
      "pillar     1.7.0  1.9.0             FALSE\n",
      "tibble     3.1.6  3.2.1              TRUE\n",
      "tzdb       0.3.0  0.4.0              TRUE\n",
      "gtable     0.3.0  0.3.4             FALSE\n",
      "rlang      1.0.2  1.1.2              TRUE\n",
      "vctrs      0.4.1  0.6.5              TRUE\n",
      "dplyr      1.0.8  1.1.4              TRUE\n",
      "clock      0.6.0  0.7.0              TRUE\n",
      "hardhat    0.2.0  1.3.0             FALSE\n",
      "lifecycle  1.0.1  1.0.4             FALSE\n",
      "purrr      0.3.4  1.0.2              TRUE\n",
      "ggplot2    3.3.5  3.4.4             FALSE\n",
      "recipes    0.2.0  1.0.9             FALSE\n",
      "caret     6.0-92 6.0-94              TRUE\n",
      "\n",
      "  Binaries will be installed\n",
      "package 'cli' successfully unpacked and MD5 sums checked\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"cannot remove prior installation of package 'cli'\"\n",
      "Warning message in file.copy(savedcopy, lib, recursive = TRUE):\n",
      "\"problem copying C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\00LOCK\\cli\\libs\\x64\\cli.dll to C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\cli\\libs\\x64\\cli.dll: Permission denied\"\n",
      "Warning message:\n",
      "\"restored 'cli'\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "package 'tibble' successfully unpacked and MD5 sums checked\n",
      "package 'tzdb' successfully unpacked and MD5 sums checked\n",
      "package 'rlang' successfully unpacked and MD5 sums checked\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"cannot remove prior installation of package 'rlang'\"\n",
      "Warning message in file.copy(savedcopy, lib, recursive = TRUE):\n",
      "\"problem copying C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\00LOCK\\rlang\\libs\\x64\\rlang.dll to C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\rlang\\libs\\x64\\rlang.dll: Permission denied\"\n",
      "Warning message:\n",
      "\"restored 'rlang'\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "package 'vctrs' successfully unpacked and MD5 sums checked\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"cannot remove prior installation of package 'vctrs'\"\n",
      "Warning message in file.copy(savedcopy, lib, recursive = TRUE):\n",
      "\"problem copying C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\00LOCK\\vctrs\\libs\\x64\\vctrs.dll to C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\vctrs\\libs\\x64\\vctrs.dll: Permission denied\"\n",
      "Warning message:\n",
      "\"restored 'vctrs'\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "package 'dplyr' successfully unpacked and MD5 sums checked\n",
      "package 'clock' successfully unpacked and MD5 sums checked\n",
      "package 'purrr' successfully unpacked and MD5 sums checked\n",
      "package 'caret' successfully unpacked and MD5 sums checked\n",
      "\n",
      "The downloaded binary packages are in\n",
      "\tC:\\Users\\banog\\AppData\\Local\\Temp\\Rtmp6LhMqb\\downloaded_packages\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "installing the source packages 'pillar', 'gtable', 'hardhat', 'lifecycle', 'ggplot2', 'recipes'\n",
      "\n",
      "\n",
      "Warning message in install.packages(\"caret\"):\n",
      "\"installation of package 'hardhat' had non-zero exit status\"\n",
      "Warning message in install.packages(\"caret\"):\n",
      "\"installation of package 'lifecycle' had non-zero exit status\"\n",
      "Warning message in install.packages(\"caret\"):\n",
      "\"installation of package 'pillar' had non-zero exit status\"\n",
      "Warning message in install.packages(\"caret\"):\n",
      "\"installation of package 'gtable' had non-zero exit status\"\n",
      "Warning message in install.packages(\"caret\"):\n",
      "\"installation of package 'recipes' had non-zero exit status\"\n",
      "Warning message in install.packages(\"caret\"):\n",
      "\"installation of package 'ggplot2' had non-zero exit status\"\n",
      "Warning message:\n",
      "\"dependencies 'emmeans', 'pbkrtest' are not available\"\n",
      "also installing the dependencies 'xfun', 'bslib', 'stringr', 'htmltools', 'knitr', 'rmarkdown', 'cli', 'lifecycle', 'htmlwidgets', 'gtable', 'rlang', 'vctrs', 'car', 'DT', 'ggplot2'\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "  There are binary versions available but the source versions are later:\n",
      "            binary source needs_compilation\n",
      "xfun          0.30   0.41              TRUE\n",
      "bslib        0.3.1  0.6.1             FALSE\n",
      "stringr      1.4.0  1.5.1             FALSE\n",
      "htmltools    0.5.2  0.5.7              TRUE\n",
      "knitr         1.38   1.45             FALSE\n",
      "rmarkdown     2.13   2.25             FALSE\n",
      "cli          3.2.0  3.6.2              TRUE\n",
      "lifecycle    1.0.1  1.0.4             FALSE\n",
      "htmlwidgets  1.5.4  1.6.4             FALSE\n",
      "gtable       0.3.0  0.3.4             FALSE\n",
      "rlang        1.0.2  1.1.2              TRUE\n",
      "vctrs        0.4.1  0.6.5              TRUE\n",
      "car         3.0-12  3.1-2             FALSE\n",
      "DT            0.22   0.31             FALSE\n",
      "ggplot2      3.3.5  3.4.4             FALSE\n",
      "FactoMineR     2.4    2.9              TRUE\n",
      "\n",
      "  Binaries will be installed\n",
      "package 'xfun' successfully unpacked and MD5 sums checked\n",
      "package 'htmltools' successfully unpacked and MD5 sums checked\n",
      "package 'cli' successfully unpacked and MD5 sums checked\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"cannot remove prior installation of package 'cli'\"\n",
      "Warning message in file.copy(savedcopy, lib, recursive = TRUE):\n",
      "\"problem copying C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\00LOCK\\cli\\libs\\x64\\cli.dll to C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\cli\\libs\\x64\\cli.dll: Permission denied\"\n",
      "Warning message:\n",
      "\"restored 'cli'\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "package 'rlang' successfully unpacked and MD5 sums checked\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"cannot remove prior installation of package 'rlang'\"\n",
      "Warning message in file.copy(savedcopy, lib, recursive = TRUE):\n",
      "\"problem copying C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\00LOCK\\rlang\\libs\\x64\\rlang.dll to C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\rlang\\libs\\x64\\rlang.dll: Permission denied\"\n",
      "Warning message:\n",
      "\"restored 'rlang'\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "package 'vctrs' successfully unpacked and MD5 sums checked\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"cannot remove prior installation of package 'vctrs'\"\n",
      "Warning message in file.copy(savedcopy, lib, recursive = TRUE):\n",
      "\"problem copying C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\00LOCK\\vctrs\\libs\\x64\\vctrs.dll to C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\vctrs\\libs\\x64\\vctrs.dll: Permission denied\"\n",
      "Warning message:\n",
      "\"restored 'vctrs'\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "package 'FactoMineR' successfully unpacked and MD5 sums checked\n",
      "\n",
      "The downloaded binary packages are in\n",
      "\tC:\\Users\\banog\\AppData\\Local\\Temp\\Rtmp6LhMqb\\downloaded_packages\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "installing the source packages 'bslib', 'stringr', 'knitr', 'rmarkdown', 'lifecycle', 'htmlwidgets', 'gtable', 'car', 'DT', 'ggplot2'\n",
      "\n",
      "\n",
      "Warning message in install.packages(\"FactoMineR\"):\n",
      "\"installation of package 'knitr' had non-zero exit status\"\n",
      "Warning message in install.packages(\"FactoMineR\"):\n",
      "\"installation of package 'lifecycle' had non-zero exit status\"\n",
      "Warning message in install.packages(\"FactoMineR\"):\n",
      "\"installation of package 'car' had non-zero exit status\"\n",
      "Warning message in install.packages(\"FactoMineR\"):\n",
      "\"installation of package 'bslib' had non-zero exit status\"\n",
      "Warning message in install.packages(\"FactoMineR\"):\n",
      "\"installation of package 'stringr' had non-zero exit status\"\n",
      "Warning message in install.packages(\"FactoMineR\"):\n",
      "\"installation of package 'gtable' had non-zero exit status\"\n",
      "Warning message in install.packages(\"FactoMineR\"):\n",
      "\"installation of package 'rmarkdown' had non-zero exit status\"\n",
      "Warning message in install.packages(\"FactoMineR\"):\n",
      "\"installation of package 'ggplot2' had non-zero exit status\"\n",
      "Warning message in install.packages(\"FactoMineR\"):\n",
      "\"installation of package 'htmlwidgets' had non-zero exit status\"\n",
      "Warning message in install.packages(\"FactoMineR\"):\n",
      "\"installation of package 'DT' had non-zero exit status\"\n",
      "Warning message:\n",
      "\"dependency 'pbkrtest' is not available\"\n",
      "also installing the dependencies 'pillar', 'tibble', 'cli', 'lifecycle', 'dplyr', 'purrr', 'stringr', 'broom', 'car', 'gtable', 'rlang', 'vctrs', 'viridis', 'ggrepel', 'ggsci', 'tidyr', 'cowplot', 'ggsignif', 'rstatix', 'ggplot2', 'dendextend', 'ggpubr'\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "  There are binary versions available but the source versions are later:\n",
      "           binary source needs_compilation\n",
      "pillar      1.7.0  1.9.0             FALSE\n",
      "tibble      3.1.6  3.2.1              TRUE\n",
      "cli         3.2.0  3.6.2              TRUE\n",
      "lifecycle   1.0.1  1.0.4             FALSE\n",
      "dplyr       1.0.8  1.1.4              TRUE\n",
      "purrr       0.3.4  1.0.2              TRUE\n",
      "stringr     1.4.0  1.5.1             FALSE\n",
      "broom       0.8.0  1.0.5             FALSE\n",
      "car        3.0-12  3.1-2             FALSE\n",
      "gtable      0.3.0  0.3.4             FALSE\n",
      "rlang       1.0.2  1.1.2              TRUE\n",
      "vctrs       0.4.1  0.6.5              TRUE\n",
      "viridis     0.6.2  0.6.4             FALSE\n",
      "ggrepel     0.9.1  0.9.4              TRUE\n",
      "ggsci         2.9  3.0.0             FALSE\n",
      "tidyr       1.2.0  1.3.0              TRUE\n",
      "cowplot     1.1.1  1.1.2             FALSE\n",
      "ggsignif    0.6.3  0.6.4             FALSE\n",
      "rstatix     0.7.0  0.7.2             FALSE\n",
      "ggplot2     3.3.5  3.4.4             FALSE\n",
      "dendextend 1.15.2 1.17.1             FALSE\n",
      "ggpubr      0.4.0  0.6.0             FALSE\n",
      "\n",
      "  Binaries will be installed\n",
      "package 'tibble' successfully unpacked and MD5 sums checked\n",
      "package 'cli' successfully unpacked and MD5 sums checked\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"cannot remove prior installation of package 'cli'\"\n",
      "Warning message in file.copy(savedcopy, lib, recursive = TRUE):\n",
      "\"problem copying C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\00LOCK\\cli\\libs\\x64\\cli.dll to C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\cli\\libs\\x64\\cli.dll: Permission denied\"\n",
      "Warning message:\n",
      "\"restored 'cli'\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "package 'dplyr' successfully unpacked and MD5 sums checked\n",
      "package 'purrr' successfully unpacked and MD5 sums checked\n",
      "package 'rlang' successfully unpacked and MD5 sums checked\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"cannot remove prior installation of package 'rlang'\"\n",
      "Warning message in file.copy(savedcopy, lib, recursive = TRUE):\n",
      "\"problem copying C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\00LOCK\\rlang\\libs\\x64\\rlang.dll to C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\rlang\\libs\\x64\\rlang.dll: Permission denied\"\n",
      "Warning message:\n",
      "\"restored 'rlang'\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "package 'vctrs' successfully unpacked and MD5 sums checked\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"cannot remove prior installation of package 'vctrs'\"\n",
      "Warning message in file.copy(savedcopy, lib, recursive = TRUE):\n",
      "\"problem copying C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\00LOCK\\vctrs\\libs\\x64\\vctrs.dll to C:\\Users\\banog\\anaconda3\\Lib\\R\\library\\vctrs\\libs\\x64\\vctrs.dll: Permission denied\"\n",
      "Warning message:\n",
      "\"restored 'vctrs'\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "package 'ggrepel' successfully unpacked and MD5 sums checked\n",
      "package 'tidyr' successfully unpacked and MD5 sums checked\n",
      "package 'factoextra' successfully unpacked and MD5 sums checked\n",
      "\n",
      "The downloaded binary packages are in\n",
      "\tC:\\Users\\banog\\AppData\\Local\\Temp\\Rtmp6LhMqb\\downloaded_packages\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "installing the source packages 'pillar', 'lifecycle', 'stringr', 'broom', 'car', 'gtable', 'viridis', 'ggsci', 'cowplot', 'ggsignif', 'rstatix', 'ggplot2', 'dendextend', 'ggpubr'\n",
      "\n",
      "\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'lifecycle' had non-zero exit status\"\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'car' had non-zero exit status\"\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'pillar' had non-zero exit status\"\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'stringr' had non-zero exit status\"\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'gtable' had non-zero exit status\"\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'broom' had non-zero exit status\"\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'ggplot2' had non-zero exit status\"\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'viridis' had non-zero exit status\"\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'ggsci' had non-zero exit status\"\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'cowplot' had non-zero exit status\"\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'ggsignif' had non-zero exit status\"\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'rstatix' had non-zero exit status\"\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'dendextend' had non-zero exit status\"\n",
      "Warning message in install.packages(\"factoextra\"):\n",
      "\"installation of package 'ggpubr' had non-zero exit status\"\n"
     ]
    },
    {
     "ename": "ERROR",
     "evalue": "Error: package 'ggplot2' required by 'caret' could not be found\n",
     "output_type": "error",
     "traceback": [
      "Error: package 'ggplot2' required by 'caret' could not be found\nTraceback:\n",
      "1. library(caret)",
      "2. .getRequiredPackages2(pkgInfo, quietly = quietly)",
      "3. stop(gettextf(\"package %s required by %s could not be found\", \n .     sQuote(pkg), sQuote(pkgname)), call. = FALSE, domain = NA)"
     ]
    }
   ],
   "source": [
    "# Installing necessary packages\n",
    "install.packages(\"MASS\")\n",
    "install.packages(\"caret\")\n",
    "install.packages(\"FactoMineR\")\n",
    "install.packages(\"factoextra\")\n",
    "\n",
    "# Loading the packages\n",
    "library(MASS)\n",
    "library(caret)\n",
    "library(FactoMineR)\n",
    "library(factoextra)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "710c1358",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set seed for reproducibility\n",
    "set.seed(123)\n",
    "\n",
    "# Generate random indices for train and test split\n",
    "indices <- sample(1:nrow(nhanes_data), 0.8 * nrow(nhanes_data))\n",
    "\n",
    "# Create training and testing sets\n",
    "train_data <- nhanes_data[indices, ]\n",
    "test_data <- nhanes_data[-indices, ]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "35c19552",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        \n",
      "         Adult Senior\n",
      "  Adult    364      8\n",
      "  Senior    11     73\n",
      "Accuracy: 0.9583333 \n"
     ]
    }
   ],
   "source": [
    "# Fit LDA model\n",
    "lda_model <- lda(age_group ~ ., data = train_data)\n",
    "\n",
    "# Make predictions on the test set\n",
    "lda_predictions <- predict(lda_model, newdata = test_data)\n",
    "\n",
    "# Create confusion matrix manually\n",
    "conf_matrix_lda <- table(lda_predictions$class, test_data$age_group)\n",
    "print(conf_matrix_lda)\n",
    "\n",
    "# Calculate accuracy\n",
    "accuracy_lda <- sum(diag(conf_matrix_lda)) / sum(conf_matrix_lda)\n",
    "cat(\"Accuracy:\", accuracy_lda, \"\\n\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04b7dfa8",
   "metadata": {},
   "source": [
    "The confusion matrix you provided for the LDA model results in a classification accuracy of approximately 95.83%, which indicates that the model performed well in distinguishing between the \"Adult\" and \"Senior\" age groups. In the confusion matrix:\n",
    "\n",
    "- True Positives (Adult): 364\n",
    "- True Negatives (Senior): 73\n",
    "- False Positives: 8\n",
    "- False Negatives: 11\n",
    "\n",
    "The high accuracy suggests that the LDA model effectively captured the underlying patterns in the dataset related to age groups. The small number of misclassifications (8 cases of Adult misclassified as Senior and 11 cases of Senior misclassified as Adult) indicates a strong overall performance. However, it's essential to consider other metrics such as precision, recall, and F1 score, especially when dealing with imbalanced datasets. Further analysis and potentially fine-tuning the model could enhance its performance, but the initial results are promising for distinguishing between adult and senior age groups based on the given features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "145f5a40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mWvQAAhQQAhQQAhQQAhQQAhQQAhQQAh\nQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAh\nQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAh\nQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAh\nQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAh\nQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAh\nQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAh\nQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAhQQAh8VTp\nlmefqQFaPM+MSPrvuxYPykznufV/XyhFSDWNoFlCqmkEzRJSTSNowc3HFYRU0whakP53g5Bq\nGkELhFT9CFogpOpH0AIhVT+CFgip+hG0QEjVj6AFQqp+BC0QUvUjqMzt516FdMNu0R3+XE5S\nmr5nGkGzbuXxn5Bu2HYp7Xfd6V+aaZYRtEtI95qn2e7wx3x7aGqeFjlG0C4h3X26tDv/cbiV\nl7ocI2iXkO4+3fGEXbr4S/gI2iWke83TZr9fHv84XiP99U5Si8vCY4R0r03qFpv9rDuUtJqk\nVY4RtEtId1t1f54fWOYZQbOE9Avv88mxotlym20EjRJSmyOojJDaHEFlhNTmCCojpGEb8TwS\nV4Q0bCPftuI3rb62UiHV85vD3bQjg2Ih3dpixsv1l3MyihFURkhtjqAyQrrfejnrb5HOFutc\nI2iVkO61m1zcu/PGPq4J6V6L1L33L/3eb1edN/ZxTUj36k7voOhtvLGPa0K6+3Tpp7+EjaBd\nQrqXayT+Qkj3OtxHWp3ePuE+Et8I6W7Ti0ftJrssI2iWkO63XvTPI3WzpeeR+EJIbY6gMkJq\ncwSVyRDS3b9OXEiMRo6Q7t2kkBgNIbU5gsoIqc0RVEZIbY6gMkJqcwSVEVKbI6iMkNocQWWE\n1OYIKvNgSDcJKf8IKvNgSPf+oJAYNyFFbfbpv/mSZxJSmyOojJDaHEFlhNTmCCojpDZHUBkh\ntTmCygipzRFU5qkhPeVDk4REBk8N6eYPZr/EuQcI6RUJqc0RVEZIbY6gMkJqcwSVEVKbI6iM\nkAZs4V+bENLrEdKALQiJr4R09+nuf7pLSK9HSPdad0LiR0K6226Wpv0njblpxzdC+oX3lN73\nQuIGIf3GdppmOyHxnZB+Z5m6lZD4Rki/tJn8+xXqQno9Qvq1uZD4RkhtjqAyQmpzBJUR0rCN\neEKWK0IatpFvW/GbVl+bkNocQWWE1OYIKiOkNkfwRA99mJGQ9uvlrF+y2WKdawQtuP9gFtJ3\nu8nFPz/TLCNog5D6VRh4ukXq3jf9V9tVlxY5RtAGIfWrMPB0Xdp8fr1JXY4RtEFI/SoMPV36\n6S9hI2iDkPpVGHg610icCalfhYGnO9xHWvXvNHcf6dUJqV+FoSecXjxqN9llGUEThNSvwuBT\nrhf980jdbOl5pJcmpH4Vcg8Q0tgJqV+F3AOENHZC6lch9wAhjZ2Q+lXIPUBIYyekfhVyDxDS\n2AmpX4XcA4Q0dkLqVyH3ACGNnZD6Vcg9QEhjJ6R+FXIPENLYCalfhdwDhDR2QupXIfcAIY2d\nkPpVyD1ASGMnpH4Vcg8Q0tgJqV+FTJv1m1ZfhpD6Vcg9wDXS2AmpX4XcA4Q0dkLqVyH3ACGN\nnZD6Vcg9QEhjJ6R+FXIPENLYCalfhdwDhDR2QupXIfcAIY2dkPpVyD1ASGMnpH4Vcg8Q0tgJ\nqV+F3AOENHZC6lch9wAhjZ2Q+lXIPUBIYyekfhVyDxDS2AmpX4WhJ9zNU5quzhvx+UgvTEj9\nKgw83a47fRLzaSNCemFC6ldh4OkW6e1Q01vXfw6zkF6ZkPpVGHi67nTCbTfZCum1CalfhaGn\nO59wN50K6bUJqV+FgaebpI9P6ZtMhfTShNSvwsDTvaX5+attmgrplQmpX4WhJ1x81rP6x+83\nEdK4CalfhcGn3Mw+vtrOhfTChNSvQu4BQho7IfWrkHuAkMZOSP0q5B4gpLETUr8KIRtxH+mF\nCalfhZCNfNuKX1n8OoTUr0LuAa6Rxk5I/SrkHiCksRNSvwq5Bwhp7ITUr8LgU66Xs9Nbkhbr\nXCNogZD6VRh4ut3k4tGEaZYRtEFI/SoMPN0ide+b/qvtqkuLHCOoTrpJSPtH3ti3+fx6k7oc\nI6jOgwezkG6cLv30l7ARVEdIPy/NwNO5RnpFQvp5aQae7nAfabXtv3If6XUI6eelGXrC6cW9\nzcnubz8ppNEQ0s9LM/iU60X/PFI3W3oe6VUI6eelyT1ASCMipJ+XJvcAIY2IkH5emtwDhDQi\nQvp5aXIPENKICOnnpck9QEgjIqSflyb3ACGNiJB+XprcA4Q0Ig2HdEvo0kRu7GkjKKPhkG79\nYOjSRG7saSMoQ0g/L03kxp42gjKE9PPSRG7saSMoQ0g/L03kxp42gjKE9PPSRG7saSMoQ0g/\nL03kxi426zetjpGQfl6ayI09bQRlCOnnpYnc2NNGUIaQfl6ayI09bQRlCOnnpYnc2NNGUIaQ\nfl6ayI09bQRlCOnnpYnc2NNGUIaQfl6ayI09bQThbv92YiH9uF6RG3vaCMIVOpiFVNUIwgnp\nl+sVubGnjSCckH65XpEbe9oIwgnpl+sVubGnjSCckH65XoNP6aMvR01Iv1yvgafz0ZcjJ6Rf\nrtfA0/noy5ET0i/Xa+DpfNDYiNz7ybBC+ssaDl77n/4SNoJSnngwv3xIrpFGREgBazjwdD76\nckSEFLCGQ0/ooy/HQ0gBazj4lD76snK3X7998yeF9PhqR27saSO44fYBde9PCumXqx25saeN\n4AYhCYkAQmouJM8j1UhIIwjprt+0evveMBQScex/HsyRG4NXJSQIICQIUOCNfTB+Bd7YB+NX\n4I19MH4F3kZxmgOFDDykH1PgjX0PzfmlcY0Z2cUZ15igqb++Rho455fGNWZkF2dcY4Km/uKN\nfQ/N+aVxjRnZxRnXmKip97+x77E5vzOuMSO7OOMaEzb17jf2PTjnV8Y1ZmQXZ1xjnjR1XIto\n1Yx50tRxLaJVM+ZJU8e1iFbNmCdNHdciWjVjnjR1XIto1Yx50tRxLaJVM+ZJU8e1iFbNmCqm\nwsgICQIICQIICQIICQIICQIICQIICQIICQIICQIICQIICQIICQIICQIICQIICQKUDGmdf9hu\nntJ88++fe9TbJHWLf/9azIhJuRdt0RW6KNkvST+k2I75omBIuy7/sK7/za/ZS1r0Y7oCO2yT\n+8MVTr8xd5J3yFH2S3JUbsd8VTCkWf6VXKT58Y9Z5jGbNN8d/4WdZ55zmNRlXrR16jbHKdk/\ndTH7JemHFNsx35QL6b3AJ9d06fhvUfY5s9OA/JfnLU0zD1mk1f64b5ZZp5S4JEfFdsx3xUZu\ni6xk745PmYmZk/3ypEXuIbN0/EyRTfYr8fyX5HLYmEOapm2hy7dIb0Xm7PJ/du4m+0GRCv0b\nnv+S/FFgx3xX6sIt03uZlTzcgiz0ibZv/a2i3EYSUqEZvTI75otCF66/7VBkJd9mXfYb/L1t\nl/vmUE9Iv1Vox3xR6MJNjo9IllrJeYnbdruuzO0HIf1SqR3zReYLd/6Y6Xl/ZZtvJa8/zXqX\n69GGyzHTjE+9XM7JfPh1owsp5475izIh5f7o9i/bzj9mO5lu88y4npP98Ds9arfN/qjdvlBI\neXfMX5T5VyJ3SB9OzyNtsz9Rvyr3uFDmJVv2txVWJR6gKRFSwR3zRclH3Au9smE3y30faVtw\nd43llQ1FQiq5Y74YV0jn19rlXs15mevXXu4hkyIrdlRguUrumC9GFtLxtcyT7I/ZFbqhep6V\nd/u7/tXfeWecFFiukjvm6+jyI2F8hAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQB\nhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQBhAQB\nhAQBhAQBhAQBhNS03WKS0vTnjyh8xmfXvSYL3bLd6TNzU7f74QeEVIqFbtk8Tbf7/XaainwI\nLH8hpJal1F8V7VzxPJ09UIVFd7hSOeZwSGOSZofvvE3OH89+iuT03/aL608gvw7ocJLufJLt\nLHXLzx+42NZ560QTUg2mxzs681Mss3S8odZ/J0331yEtP755tkjz7edfZhcn6e87Lc8nvtzW\naeuEE1IFVqnb7DfdKZbp8dba+/k779chfX7zw6GRyWJ93sjhlLtpWp038pYmp5NdbWv608MS\nPEZIFZgdj/5DCX0s68vvTK9DOn3z8rbZan580G7Vn+TYyO74X08bOd8avN7Wuuwlex1CqsD5\nrs7HkX/rO9//26f1sjv2kT58Pcn3rRPPylbgsZD2+83pVpyQnsjKVmBoSJ9ffYlESOVZ2Qpc\n3Ue6+s7s/J31n/tPqzT/c7rTi4N2qfs4Se86pK/bIgcrW4GrR+3671w80jY51LKbXj5q9xnM\nIa+33eH/pseg+pPs3/708rG5b48AkoGVrcH0y92by+d+3o5fzM4Pjfdf/znd4ny66Z+TdNtv\ntwa/PidFBla2CosuTddX92LeuvOrEfbL7nBj7vzfZh/fPNvMD9dj0/MTS2+TdHqC9uvdqs9t\nCSkbK1uPy9cs3Pzvdla97JsKpOP9l93sXy/eEVLF7JsKLM/vKvrHjwmpYvZNDd7618z966eE\nVDH7BgIICQIICQIICQIICQIICQIICQIICQIICQIICQIICQIICQIICQIICQIICQIICQIICQII\nCQIICQIICQIICQIICQIICQIICQIICQIICQIICQL8HwWPt40IrWu+AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot LDA results\n",
    "lda_plot <- plot(lda_model, col = c(\"red\", \"blue\"))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6b653e7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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f3Ek0Vkh5VSjrxfRjGeIqSW+VTL/O4V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\nICRAgJAAgX9O2vmz4IiCwwAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Scree Plot\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wANw07GOAM7eYwdJy4RjWFcQd+0plkllofuaRKpBIPBptlLPR4PB3ZiTq7cgMfk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\nQfw/sYDG8SdOBkYAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "nhanes_data$age_group <- as.factor(nhanes_data$age_group)\n",
    "\n",
    "# Extract features for PCA\n",
    "pca_data <- nhanes_data[, -which(names(nhanes_data) == \"age_group\")]\n",
    "\n",
    "# Standardize the data\n",
    "pca_data_std <- scale(pca_data)\n",
    "\n",
    "# Perform PCA\n",
    "pca_model <- prcomp(pca_data_std, center = TRUE, scale. = TRUE)\n",
    "\n",
    "# Extract the results\n",
    "pca_results <- summary(pca_model)\n",
    "\n",
    "# Plot scree plot\n",
    "plot(1:length(pca_results$sdev), pca_results$sdev^2, type = \"b\", \n",
    "     xlab = \"Principal Component\", ylab = \"Variance Explained\", \n",
    "     main = \"Scree Plot\")\n",
    "\n",
    "# Visualize the first two principal components\n",
    "biplot(pca_model, scale = 0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "050869c6",
   "metadata": {},
   "source": [
    "# Machine learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c3e85528",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "               \n",
      "svm_predictions Adult Senior\n",
      "         Adult    374     11\n",
      "         Senior     1     70\n",
      "Accuracy: 0.9736842 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Setting levels: control = Adult, case = Senior\n",
      "\n",
      "Setting direction: controls < cases\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cross-validated Accuracy: 0.9732234 \n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Plot with title \"ROC Curve for SVM\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load necessary libraries\n",
    "library(e1071)\n",
    "library(pROC)\n",
    "\n",
    "nhanes_data$age_group <- as.factor(nhanes_data$age_group)\n",
    "\n",
    "nhanes_data_selected <- nhanes_data\n",
    "\n",
    "# Split the data into training and testing sets\n",
    "set.seed(123)\n",
    "indices <- sample(1:nrow(nhanes_data_selected), 0.8 * nrow(nhanes_data_selected))\n",
    "train_data <- nhanes_data_selected[indices, ]\n",
    "test_data <- nhanes_data_selected[-indices, ]\n",
    "\n",
    "# Train SVM model\n",
    "svm_model <- svm(age_group ~ ., data = train_data)\n",
    "\n",
    "# Make predictions on the test set\n",
    "svm_predictions <- predict(svm_model, newdata = test_data)\n",
    "\n",
    "# Evaluate performance\n",
    "conf_matrix_svm <- table(svm_predictions, test_data$age_group)\n",
    "accuracy_svm <- sum(diag(conf_matrix_svm)) / sum(conf_matrix_svm)\n",
    "\n",
    "# Print confusion matrix and accuracy\n",
    "print(conf_matrix_svm)\n",
    "cat(\"Accuracy:\", accuracy_svm, \"\\n\")\n",
    "\n",
    "# ROC curve\n",
    "svm_roc <- roc(test_data$age_group, as.numeric(svm_predictions))\n",
    "plot(svm_roc, main = \"ROC Curve for SVM\", col = \"blue\", lwd = 2)\n",
    "\n",
    "# K-fold Cross-Validation\n",
    "set.seed(123)\n",
    "folds <- cut(seq(1, nrow(nhanes_data_selected)), breaks = 5, labels = FALSE)\n",
    "cv_svm <- lapply(1:5, function(i) {\n",
    "  test_indices <- which(folds == i, arr.ind = TRUE)\n",
    "  test_data <- nhanes_data_selected[test_indices, ]\n",
    "  train_data <- nhanes_data_selected[-test_indices, ]\n",
    "  \n",
    "  svm_model <- svm(age_group ~ ., data = train_data)\n",
    "  svm_predictions <- predict(svm_model, newdata = test_data)\n",
    "  \n",
    "  conf_matrix <- table(svm_predictions, test_data$age_group)\n",
    "  accuracy <- sum(diag(conf_matrix)) / sum(conf_matrix)\n",
    "  \n",
    "  return(accuracy)\n",
    "})\n",
    "\n",
    "# Print cross-validated results\n",
    "cat(\"Cross-validated Accuracy:\", mean(unlist(cv_svm)), \"\\n\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1725070",
   "metadata": {},
   "source": [
    "The confusion matrix for the Support Vector Machine (SVM) model shows that it performed exceptionally well on the provided dataset. With an accuracy of approximately 97.37%, the model correctly classified 374 instances of the \"Adult\" age group and 70 instances of the \"Senior\" age group. The minimal misclassifications, with only 1 instance of \"Senior\" incorrectly predicted as \"Adult\" and 11 instances of \"Adult\" incorrectly predicted as \"Senior,\" underscore the robustness of the SVM model. This high accuracy indicates the effectiveness of the SVM algorithm in discerning patterns within the features to accurately classify individuals into their respective age groups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a6d946da",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.0.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}