Simple Linear Regression- No. of Study Hours.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ashish Mahendra Deolikar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem Statement\n",
    "\n",
    "### 1. Predict the percentage of an student based on thr no. of study hours.\n",
    "### 2. This is a simple linear regression task as it involves just 2 variables.\n",
    "### 3. You can use R, Python, SAS Enterprise Miner or any other tool.\n",
    "### 4. What will be predicted score if a student studies for 9.25 hrs/day?\n",
    "### Data can be found at http://bit.ly/w-data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GzfdMfk10NE6"
   },
   "source": [
    "## **Linear Regression with Python Scikit Learn**\n",
    "In this section we will see how the Python Scikit-Learn library for machine learning can be used to implement regression functions. We will start with simple linear regression involving two variables.\n",
    "\n",
    "### **Simple Linear Regression**\n",
    "In this regression task we will predict the percentage of marks that a student is expected to score based upon the number of hours they studied. This is a simple linear regression task as it involves just two variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "V9QN2ZxC38pB"
   },
   "outputs": [],
   "source": [
    "# Importing all libraries required in this notebook\n",
    "import pandas as pd\n",
    "import numpy as np  \n",
    "import matplotlib.pyplot as plt  \n",
    "%matplotlib inline\n",
    "\n",
    "# to suppress warnings \n",
    "from warnings import filterwarnings\n",
    "filterwarnings('ignore')\n",
    "\n",
    "# display all columns of the dataframe\n",
    "pd.options.display.max_columns = None\n",
    "\n",
    "# display all rows of the dataframe\n",
    "pd.options.display.max_rows = None\n",
    " \n",
    "# to display the float values upto 6 decimal places     \n",
    "pd.options.display.float_format = '{:.6f}'.format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 376
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 2534,
     "status": "ok",
     "timestamp": 1544113345787,
     "user": {
      "displayName": "A M Aditya",
      "photoUrl": "https://lh3.googleusercontent.com/-WI8p7JNWLic/AAAAAAAAAAI/AAAAAAAAAfs/vS8ElgH0p0c/s64/photo.jpg",
      "userId": "15341571102300750919"
     },
     "user_tz": -480
    },
    "id": "LtU4YMEhqm9m",
    "outputId": "5b4b36af-1545-497e-a6dc-7658bab71dbc",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data imported successfully\n"
     ]
    },
    {
     "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>Scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.500000</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.100000</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.200000</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.500000</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.500000</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.500000</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>9.200000</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.500000</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8.300000</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2.700000</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Hours  Scores\n",
       "0 2.500000      21\n",
       "1 5.100000      47\n",
       "2 3.200000      27\n",
       "3 8.500000      75\n",
       "4 3.500000      30\n",
       "5 1.500000      20\n",
       "6 9.200000      88\n",
       "7 5.500000      60\n",
       "8 8.300000      81\n",
       "9 2.700000      25"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reading data from remote link\n",
    "url = \"http://bit.ly/w-data\"\n",
    "df = pd.read_csv(url)\n",
    "print(\"Data imported successfully\")\n",
    "\n",
    "df.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RHsPneuM4NgB"
   },
   "source": [
    "Let's plot our data points on 2-D graph to eyeball our dataset and see if we can manually find any relationship between the data. We can create the plot with the following script:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 294
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 718,
     "status": "ok",
     "timestamp": 1544113350499,
     "user": {
      "displayName": "A M Aditya",
      "photoUrl": "https://lh3.googleusercontent.com/-WI8p7JNWLic/AAAAAAAAAAI/AAAAAAAAAfs/vS8ElgH0p0c/s64/photo.jpg",
      "userId": "15341571102300750919"
     },
     "user_tz": -480
    },
    "id": "qxYBZkhAqpn9",
    "outputId": "37264af1-786d-4e0c-a668-383264d1ddd1"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the distribution of scores\n",
    "df.plot(x='Hours', y='Scores', style='o')  \n",
    "plt.title('Hours vs Percentage')  \n",
    "plt.xlabel('Hours Studied')  \n",
    "plt.ylabel('Percentage Score')  \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fiQaULio4Rzr"
   },
   "source": [
    "**From the graph above, we can clearly see that there is a positive linear relation between the number of hours studied and percentage of score.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WWtEr64M4jdz"
   },
   "source": [
    "### **Preparing the data**\n",
    "\n",
    "The next step is to divide the data into \"attributes\" (inputs) and \"labels\" (outputs)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "LiJ5210e4tNX"
   },
   "outputs": [],
   "source": [
    "X = df.iloc[:, :-1]  \n",
    "y = df.iloc[:, 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Riz-ZiZ34fO4"
   },
   "source": [
    "Now that we have our attributes and labels, the next step is to split this data into training and test sets. We'll do this by using Scikit-Learn's built-in train_test_split() method:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "a6WXptFU5CkC"
   },
   "source": [
    "### **Training the Algorithm**\n",
    "We have split our data into training and testing sets, and now is finally the time to train our algorithm. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Method-1 (Using OLS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "udFYso1M4BNw"
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split  \n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": false
   },
   "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>intercept</th>\n",
       "      <th>Hours</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>7.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>6.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.100000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    intercept    Hours\n",
       "22   1.000000 3.800000\n",
       "17   1.000000 1.900000\n",
       "24   1.000000 7.800000\n",
       "23   1.000000 6.900000\n",
       "14   1.000000 1.100000"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# convert the X_train to DataFrame\n",
    "X_train = pd.DataFrame(X_train)\n",
    "\n",
    "# insert a column of intercept to 'X_train'\n",
    "# create an array of ones with length equal to the total number of observations\n",
    "c = np.ones(X_train.shape[0])\n",
    "\n",
    "# A design matrix is a matrix of observations of independent variables whose first column is of ones\n",
    "# If there are 'm' observations and 'n' variables, then the dimension of a design matrix is m * (n+1) \n",
    "\n",
    "# add the intercept \n",
    "# pass location index of intercept to the parameter 'loc'\n",
    "# pass column name to the parameter 'column'\n",
    "# pass the column value to the parameter 'value'\n",
    "X_train.insert(loc = 0, column = 'intercept', value = c)\n",
    "\n",
    "# display the first five rows of design matrix\n",
    "X_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": false
   },
   "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>intercept</th>\n",
       "      <th>Hours</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>7.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.900000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    intercept    Hours\n",
       "5    1.000000 1.500000\n",
       "2    1.000000 3.200000\n",
       "19   1.000000 7.400000\n",
       "16   1.000000 2.500000\n",
       "11   1.000000 5.900000"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# convert the X_train to DataFrame\n",
    "X_test = pd.DataFrame(X_test)\n",
    "\n",
    "# insert a column of intercept to 'X_test'\n",
    "# create an array of ones with length equal to the total number of observations\n",
    "c = np.ones(X_test.shape[0])\n",
    "\n",
    "# A design matrix is a matrix of observations of independent variables whose first column is of ones\n",
    "# If there are 'm' observations and 'n' variables, then the dimension of a design matrix is m * (n+1) \n",
    "\n",
    "# add the intercept \n",
    "# pass location index of intercept to the parameter 'loc'\n",
    "# pass column name to the parameter 'column'\n",
    "# pass the column value to the parameter 'value'\n",
    "X_test.insert(loc = 0, column = 'intercept', value = c)\n",
    "\n",
    "# display the first five rows of design matrix\n",
    "X_test.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 Scores   R-squared:                       0.952\n",
      "Model:                            OLS   Adj. R-squared:                  0.949\n",
      "Method:                 Least Squares   F-statistic:                     353.5\n",
      "Date:                Sun, 28 Aug 2022   Prob (F-statistic):           2.79e-13\n",
      "Time:                        13:21:34   Log-Likelihood:                -62.686\n",
      "No. Observations:                  20   AIC:                             129.4\n",
      "Df Residuals:                      18   BIC:                             131.4\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "intercept      2.0182      3.057      0.660      0.517      -4.404       8.441\n",
      "Hours          9.9107      0.527     18.802      0.000       8.803      11.018\n",
      "==============================================================================\n",
      "Omnibus:                        4.659   Durbin-Watson:                   1.813\n",
      "Prob(Omnibus):                  0.097   Jarque-Bera (JB):                1.720\n",
      "Skew:                          -0.296   Prob(JB):                        0.423\n",
      "Kurtosis:                       1.691   Cond. No.                         13.9\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "# building a model on the train dataset with an intercept\n",
    "# fit() is used to fit the OLS model\n",
    "SLR_model = sm.OLS(y_train, X_train).fit()\n",
    "\n",
    "# print the summary output\n",
    "print(SLR_model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22   39.678655\n",
       "17   20.848407\n",
       "24   79.321281\n",
       "23   70.401690\n",
       "14   12.919882\n",
       "dtype: float64"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# predict the y_train_pred using 'predict()' on training data\n",
    "y_train_pred = SLR_model.predict(X_train)\n",
    "\n",
    "# display the first five predicted values \n",
    "y_train_pred.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5    16.884145\n",
       "2    33.732261\n",
       "19   75.357018\n",
       "16   26.794801\n",
       "11   60.491033\n",
       "dtype: float64"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# predict the y_test_pred using 'predict()' on training data\n",
    "y_test_pred = SLR_model.predict(X_test)\n",
    "\n",
    "# display the first five predicted values \n",
    "y_test_pred.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "scrolled": false
   },
   "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>Actual</th>\n",
       "      <th>Predicted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>20</td>\n",
       "      <td>16.884145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>27</td>\n",
       "      <td>33.732261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>69</td>\n",
       "      <td>75.357018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>30</td>\n",
       "      <td>26.794801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>62</td>\n",
       "      <td>60.491033</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Actual  Predicted\n",
       "5       20  16.884145\n",
       "2       27  33.732261\n",
       "19      69  75.357018\n",
       "16      30  26.794801\n",
       "11      62  60.491033"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({'Actual': y_test, 'Predicted': y_test_pred})  \n",
    "df "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 862,
     "status": "ok",
     "timestamp": 1544113370494,
     "user": {
      "displayName": "A M Aditya",
      "photoUrl": "https://lh3.googleusercontent.com/-WI8p7JNWLic/AAAAAAAAAAI/AAAAAAAAAfs/vS8ElgH0p0c/s64/photo.jpg",
      "userId": "15341571102300750919"
     },
     "user_tz": -480
    },
    "id": "KAFO8zbx-AH1",
    "outputId": "fcb3830f-3cda-4dcb-f122-84b71f101fae",
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No of Hours = 9.25\n",
      "Predicted Score = 93.6917324873754\n"
     ]
    }
   ],
   "source": [
    "# # You can also test with your own data\n",
    "hours = [1,9.25]\n",
    "own_pred = SLR_model.predict(hours)  # \"1\" refers to the intercept term\n",
    "print(\"No of Hours = {}\".format(hours[1]))\n",
    "print(\"Predicted Score = {}\".format(own_pred[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Method-2 (Using LinearRegression())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "udFYso1M4BNw"
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split  \n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, \n",
    "                            test_size=0.2, random_state=0) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 701,
     "status": "ok",
     "timestamp": 1544113358086,
     "user": {
      "displayName": "A M Aditya",
      "photoUrl": "https://lh3.googleusercontent.com/-WI8p7JNWLic/AAAAAAAAAAI/AAAAAAAAAfs/vS8ElgH0p0c/s64/photo.jpg",
      "userId": "15341571102300750919"
     },
     "user_tz": -480
    },
    "id": "qddCuaS84fpK",
    "outputId": "befbd977-772c-4bd1-bb48-ee5dd6bae73c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete.\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression  \n",
    "LinReg = LinearRegression()  \n",
    "LinReg.fit(X_train, y_train) \n",
    "\n",
    "print(\"Training complete.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 985,
     "status": "ok",
     "timestamp": 1544113360867,
     "user": {
      "displayName": "A M Aditya",
      "photoUrl": "https://lh3.googleusercontent.com/-WI8p7JNWLic/AAAAAAAAAAI/AAAAAAAAAfs/vS8ElgH0p0c/s64/photo.jpg",
      "userId": "15341571102300750919"
     },
     "user_tz": -480
    },
    "id": "J61NX2_2-px7",
    "outputId": "d20ec1fd-3e2d-4eae-84a2-a0df57d31009"
   },
   "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": [
    "# Plotting the regression line\n",
    "line = LinReg.coef_*X+LinReg.intercept_\n",
    "\n",
    "# Plotting for the test data\n",
    "plt.scatter(X, y)\n",
    "plt.plot(X, line);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "JCQn-g4m5OK2"
   },
   "source": [
    "### **Making Predictions**\n",
    "Now that we have trained our algorithm, it's time to make some predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 698,
     "status": "ok",
     "timestamp": 1544113363729,
     "user": {
      "displayName": "A M Aditya",
      "photoUrl": "https://lh3.googleusercontent.com/-WI8p7JNWLic/AAAAAAAAAAI/AAAAAAAAAfs/vS8ElgH0p0c/s64/photo.jpg",
      "userId": "15341571102300750919"
     },
     "user_tz": -480
    },
    "id": "Tt-Fmzu55EGM",
    "outputId": "46f1acf8-91ac-4984-cfbe-e614aa9ea849"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      Hours\n",
      "5  1.500000\n",
      "2  3.200000\n",
      "19 7.400000\n",
      "16 2.500000\n",
      "11 5.900000\n"
     ]
    }
   ],
   "source": [
    "print(X_test) # Testing data - In Hours\n",
    "y_pred = LinReg.predict(X_test) # Predicting the scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 204
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 753,
     "status": "ok",
     "timestamp": 1544113366918,
     "user": {
      "displayName": "A M Aditya",
      "photoUrl": "https://lh3.googleusercontent.com/-WI8p7JNWLic/AAAAAAAAAAI/AAAAAAAAAfs/vS8ElgH0p0c/s64/photo.jpg",
      "userId": "15341571102300750919"
     },
     "user_tz": -480
    },
    "id": "6bmZUMZh5QLb",
    "outputId": "8ea11a9e-c1b7-4fab-ab62-4dcbd2c8607b",
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Actual</th>\n",
       "      <th>Predicted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>20</td>\n",
       "      <td>16.884145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>27</td>\n",
       "      <td>33.732261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>69</td>\n",
       "      <td>75.357018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>30</td>\n",
       "      <td>26.794801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>62</td>\n",
       "      <td>60.491033</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Actual  Predicted\n",
       "5       20  16.884145\n",
       "2       27  33.732261\n",
       "19      69  75.357018\n",
       "16      30  26.794801\n",
       "11      62  60.491033"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Comparing Actual vs Predicted\n",
    "df = pd.DataFrame({'Actual': y_test, 'Predicted': y_pred})  \n",
    "df "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 862,
     "status": "ok",
     "timestamp": 1544113370494,
     "user": {
      "displayName": "A M Aditya",
      "photoUrl": "https://lh3.googleusercontent.com/-WI8p7JNWLic/AAAAAAAAAAI/AAAAAAAAAfs/vS8ElgH0p0c/s64/photo.jpg",
      "userId": "15341571102300750919"
     },
     "user_tz": -480
    },
    "id": "KAFO8zbx-AH1",
    "outputId": "fcb3830f-3cda-4dcb-f122-84b71f101fae"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No of Hours = [[9.25]]\n",
      "Predicted Score = 93.69173248737538\n"
     ]
    }
   ],
   "source": [
    "# You can also test with your own data\n",
    "hours = [[9.25]]\n",
    "own_pred = LinReg.predict(hours)\n",
    "print(\"No of Hours = {}\".format(hours))\n",
    "print(\"Predicted Score = {}\".format(own_pred[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "0AAsPVA_6KmK"
   },
   "source": [
    "### **Evaluating the model**\n",
    "\n",
    "The final step is to evaluate the performance of algorithm. This step is particularly important to compare how well different algorithms perform on a particular dataset. For simplicity here, we have chosen the mean square error. There are many such metrics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 834,
     "status": "ok",
     "timestamp": 1544113374919,
     "user": {
      "displayName": "A M Aditya",
      "photoUrl": "https://lh3.googleusercontent.com/-WI8p7JNWLic/AAAAAAAAAAI/AAAAAAAAAfs/vS8ElgH0p0c/s64/photo.jpg",
      "userId": "15341571102300750919"
     },
     "user_tz": -480
    },
    "id": "r5UOrRH-5VCQ",
    "outputId": "7b9ddcf1-2848-408f-d81f-7a60652c381e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Absolute Error: 4.183859899002975\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics  \n",
    "print('Mean Absolute Error:',metrics.mean_absolute_error(y_test, y_pred)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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