sklearn - Simple Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import the relevant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For this model we will need NumPy, pandas, matplotlib and seaborn\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "\n",
    "# and of course the actual regression (machine learning) module\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1714</td>\n",
       "      <td>2.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1664</td>\n",
       "      <td>2.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1760</td>\n",
       "      <td>2.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1685</td>\n",
       "      <td>2.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1693</td>\n",
       "      <td>2.83</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "    SAT   GPA\n",
       "0  1714  2.40\n",
       "1  1664  2.52\n",
       "2  1760  2.54\n",
       "3  1685  2.74\n",
       "4  1693  2.83"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(r\"Simple_linear_regression_sk.csv\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create the regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Declare the dependent and independent variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# There is a single independent variable: 'SAT'\n",
    "x = data['SAT']\n",
    "\n",
    "# and a single depended variable: 'GPA'\n",
    "y = data['GPA']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(84,)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Often it is useful to check the shapes of the features\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(84,)"
      ]
     },
     "execution_count": 18,
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   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(84, 1)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In order to feed x to sklearn, it should be a 2D array (a matrix)\n",
    "# Therefore, we must reshape it \n",
    "# Note that this will not be needed when we've got more than 1 feature (as the inputs will be a 2D array by default)\n",
    "\n",
    "# x_matrix = x.values.reshape(84,1)\n",
    "x_matrix = x.values.reshape(-1,1)\n",
    "\n",
    "# Check the shape just in case\n",
    "x_matrix.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression itself\n",
    "Full documentation: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We start by creating a linear regression object\n",
    "reg = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The whole learning process boils down to fitting the regression\n",
    "# Note that the first argument is the independent variable, while the second - the dependent (unlike with StatsModels)\n",
    "reg.fit(x_matrix,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### R-squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.40600391479679765"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To get the R-squared in sklearn we must call the appropriate method\n",
    "reg.score(x_matrix,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00165569])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Getting the coefficients of the regression\n",
    "# Note that the output is an array, as we usually expect several coefficients\n",
    "reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2750402996602803"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Getting the intercept of the regression\n",
    "# Note that the result is a float as we usually expect a single value\n",
    "reg.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Making predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.15593751])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# There is a dedicated method should we want to predict values\n",
    "# Note that the result is an array, as we can predict more than one value at a time\n",
    "reg.predict([[1740]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1760</td>\n",
       "    </tr>\n",
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      "text/plain": [
       "    SAT\n",
       "0  1740\n",
       "1  1760"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To be in line with our knowledge so far, we can create a pandas data frame with several different values of SAT\n",
    "new_data = pd.DataFrame(data=[1740,1760],columns=['SAT'])\n",
    "new_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.15593751, 3.18905127])"
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     "execution_count": 32,
     "metadata": {},
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   ],
   "source": [
    "# We can predict the whole data frame in bulk\n",
    "# Note that the result is an array, this time with 2 elements\n",
    "reg.predict(new_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SAT</th>\n",
       "      <th>Predicted_GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1740</td>\n",
       "      <td>3.155938</td>\n",
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       "      <th>1</th>\n",
       "      <td>1760</td>\n",
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      "text/plain": [
       "    SAT  Predicted_GPA\n",
       "0  1740       3.155938\n",
       "1  1760       3.189051"
      ]
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     "execution_count": 33,
     "metadata": {},
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   "source": [
    "# Finally, we can directly store the predictions in a new series of the same dataframe\n",
    "new_data['Predicted_GPA'] = reg.predict(new_data)\n",
    "new_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1da92dba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# There are different ways to plot the data - here's the matplotlib code\n",
    "plt.scatter(x,y)\n",
    "\n",
    "# Parametrized version of the regression line\n",
    "yhat = reg.coef_*x_matrix + reg.intercept_\n",
    "\n",
    "# Non-parametrized version of the regression line\n",
    "#yhat = 0.0017*x + 0.275\n",
    "\n",
    "# Plotting the regression line\n",
    "fig = plt.plot(x,yhat, lw=4, c='orange', label ='regression line')\n",
    "\n",
    "# Labelling our axes\n",
    "plt.xlabel('SAT', fontsize = 20)\n",
    "plt.ylabel('GPA', fontsize = 20)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  },
  "pycharm": {
   "stem_cell": {
    "cell_type": "raw",
    "source": [],
    "metadata": {
     "collapsed": false
    }
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}