Code-Example-011-Linear-Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 31 entries, 0 to 30\n",
      "Data columns (total 3 columns):\n",
      " #   Column  Non-Null Count  Dtype  \n",
      "---  ------  --------------  -----  \n",
      " 0   name    31 non-null     object \n",
      " 1   hours   31 non-null     float64\n",
      " 2   score   31 non-null     int64  \n",
      "dtypes: float64(1), int64(1), object(1)\n",
      "memory usage: 872.0+ bytes\n"
     ]
    }
   ],
   "source": [
    "students = pd.read_csv(\"./datasets/students.csv\")\n",
    "students.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "hours = students[\"hours\"]\n",
    "exam_score = students[\"score\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.scatter(hours, exam_score, c=\"red\", alpha=0.9, marker='*',label=\"Score\")\n",
    "plt.xlabel(\"Hours of Study\")\n",
    "plt.ylabel(\"Exam Score\")\n",
    "plt.legend(loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>hours</th>\n",
       "      <th>score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>hours</th>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.88351</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>score</th>\n",
       "      <td>0.88351</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         hours    score\n",
       "hours  1.00000  0.88351\n",
       "score  0.88351  1.00000"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pearson's Correlation Coefficient \n",
    "students.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[8.  ]\n",
      " [2.  ]\n",
      " [9.  ]\n",
      " [9.  ]\n",
      " [7.  ]\n",
      " [6.5 ]\n",
      " [4.  ]\n",
      " [1.  ]\n",
      " [7.  ]\n",
      " [0.  ]\n",
      " [1.  ]\n",
      " [1.5 ]\n",
      " [4.5 ]\n",
      " [4.  ]\n",
      " [3.5 ]\n",
      " [3.  ]\n",
      " [3.  ]\n",
      " [3.  ]\n",
      " [4.  ]\n",
      " [6.  ]\n",
      " [5.  ]\n",
      " [0.5 ]\n",
      " [5.  ]\n",
      " [2.25]\n",
      " [2.  ]\n",
      " [3.5 ]\n",
      " [3.5 ]\n",
      " [9.  ]\n",
      " [1.  ]\n",
      " [4.75]\n",
      " [4.  ]]\n"
     ]
    }
   ],
   "source": [
    "# Scikit-learn for Linear Regression. \n",
    "# https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html\n",
    "\n",
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# Prepare the data in higher dimentions, List of Lists, Array of Arrays\n",
    "my_X = np.vstack((hours, )).T\n",
    "print(my_X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.01211837]\n",
      "51.51467443328784\n"
     ]
    }
   ],
   "source": [
    "\n",
    "reg = LinearRegression().fit(my_X, exam_score)\n",
    "\n",
    "print(reg.coef_)\n",
    "print(reg.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.01211837] 51.51467443328784\n"
     ]
    }
   ],
   "source": [
    "print( reg.coef_, reg.intercept_)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([91.61162142, 61.53891118, 96.62373979, 96.62373979, 86.59950304,\n",
       "       84.09344386, 71.56314793, 56.52679281, 86.59950304, 51.51467443,\n",
       "       56.52679281, 59.03285199, 74.06920711, 71.56314793, 69.05708874,\n",
       "       66.55102955, 66.55102955, 66.55102955, 71.56314793, 81.58738467,\n",
       "       76.5752663 , 54.02073362, 76.5752663 , 62.79194077, 61.53891118,\n",
       "       69.05708874, 69.05708874, 96.62373979, 56.52679281, 75.32223671,\n",
       "       71.56314793])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Our Predictions\n",
    "reg.predict(my_X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7805900600660101"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.score(my_X, exam_score)\n",
    "\n",
    "# Return the coefficient of determination R^2 of the prediction.\n",
    "# help(reg.score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.scatter(hours, exam_score, c=\"red\", alpha=0.9, marker='*',label=\"Exam Score\")\n",
    "plt.scatter(hours, reg.predict(my_X), c=\"blue\", alpha=0.9, marker='*',label=\"Prediciton of Score\")\n",
    "\n",
    "plt.xlabel(\"Hours of Study\")\n",
    "plt.ylabel(\"Exam Score\")\n",
    "plt.legend(loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.scatter(hours, exam_score, c=\"red\", alpha=0.9, marker='*',label=\"Exam Score\")\n",
    "plt.plot(hours, reg.predict(my_X), c=\"blue\", alpha=0.9, marker='*',label=\"Prediciton of Score\")\n",
    "\n",
    "plt.xlabel(\"Hours of Study\")\n",
    "plt.ylabel(\"Exam Score\")\n",
    "plt.legend(loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}