GraduateAdmissions-LinearRegression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting Chance of admit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.model_selection import train_test_split\n",
    "import numpy as np\n",
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "df=pd.read_csv(\"Admission_predict.csv\")\n",
    "df2=pd.read_csv(\"Admission_Predict_Ver1.1.csv\")\n",
    "dataset=pd.concat([df,df2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#dataset- https://www.kaggle.com/mohansacharya/graduate-admissions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exploration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Serial No.</th>\n",
       "      <th>GRE Score</th>\n",
       "      <th>TOEFL Score</th>\n",
       "      <th>University Rating</th>\n",
       "      <th>SOP</th>\n",
       "      <th>LOR</th>\n",
       "      <th>CGPA</th>\n",
       "      <th>Research</th>\n",
       "      <th>Chance of Admit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>337</td>\n",
       "      <td>118</td>\n",
       "      <td>4</td>\n",
       "      <td>4.5</td>\n",
       "      <td>4.5</td>\n",
       "      <td>9.65</td>\n",
       "      <td>1</td>\n",
       "      <td>0.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>324</td>\n",
       "      <td>107</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.5</td>\n",
       "      <td>8.87</td>\n",
       "      <td>1</td>\n",
       "      <td>0.76</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Serial No.  GRE Score  TOEFL Score  University Rating  SOP  LOR   CGPA  \\\n",
       "0           1        337          118                  4  4.5   4.5  9.65   \n",
       "1           2        324          107                  4  4.0   4.5  8.87   \n",
       "\n",
       "   Research  Chance of Admit   \n",
       "0         1              0.92  \n",
       "1         1              0.76  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Serial No.</th>\n",
       "      <th>GRE Score</th>\n",
       "      <th>TOEFL Score</th>\n",
       "      <th>University Rating</th>\n",
       "      <th>SOP</th>\n",
       "      <th>LOR</th>\n",
       "      <th>CGPA</th>\n",
       "      <th>Research</th>\n",
       "      <th>Chance of Admit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>900.000000</td>\n",
       "      <td>900.000000</td>\n",
       "      <td>900.000000</td>\n",
       "      <td>900.000000</td>\n",
       "      <td>900.000000</td>\n",
       "      <td>900.00000</td>\n",
       "      <td>900.000000</td>\n",
       "      <td>900.000000</td>\n",
       "      <td>900.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>228.277778</td>\n",
       "      <td>316.621111</td>\n",
       "      <td>107.288889</td>\n",
       "      <td>3.102222</td>\n",
       "      <td>3.385556</td>\n",
       "      <td>3.47000</td>\n",
       "      <td>8.586433</td>\n",
       "      <td>0.554444</td>\n",
       "      <td>0.722900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>134.674991</td>\n",
       "      <td>11.369700</td>\n",
       "      <td>6.073968</td>\n",
       "      <td>1.143048</td>\n",
       "      <td>0.997612</td>\n",
       "      <td>0.91319</td>\n",
       "      <td>0.600822</td>\n",
       "      <td>0.497303</td>\n",
       "      <td>0.141722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>290.000000</td>\n",
       "      <td>92.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>6.800000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.340000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>113.000000</td>\n",
       "      <td>308.000000</td>\n",
       "      <td>103.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.500000</td>\n",
       "      <td>3.00000</td>\n",
       "      <td>8.140000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.640000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>225.500000</td>\n",
       "      <td>317.000000</td>\n",
       "      <td>107.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.500000</td>\n",
       "      <td>3.50000</td>\n",
       "      <td>8.570000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.730000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>338.000000</td>\n",
       "      <td>325.000000</td>\n",
       "      <td>112.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.00000</td>\n",
       "      <td>9.052500</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.822500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>500.000000</td>\n",
       "      <td>340.000000</td>\n",
       "      <td>120.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>9.920000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.970000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Serial No.   GRE Score  TOEFL Score  University Rating         SOP  \\\n",
       "count  900.000000  900.000000   900.000000         900.000000  900.000000   \n",
       "mean   228.277778  316.621111   107.288889           3.102222    3.385556   \n",
       "std    134.674991   11.369700     6.073968           1.143048    0.997612   \n",
       "min      1.000000  290.000000    92.000000           1.000000    1.000000   \n",
       "25%    113.000000  308.000000   103.000000           2.000000    2.500000   \n",
       "50%    225.500000  317.000000   107.000000           3.000000    3.500000   \n",
       "75%    338.000000  325.000000   112.000000           4.000000    4.000000   \n",
       "max    500.000000  340.000000   120.000000           5.000000    5.000000   \n",
       "\n",
       "            LOR         CGPA    Research  Chance of Admit   \n",
       "count  900.00000  900.000000  900.000000        900.000000  \n",
       "mean     3.47000    8.586433    0.554444          0.722900  \n",
       "std      0.91319    0.600822    0.497303          0.141722  \n",
       "min      1.00000    6.800000    0.000000          0.340000  \n",
       "25%      3.00000    8.140000    0.000000          0.640000  \n",
       "50%      3.50000    8.570000    1.000000          0.730000  \n",
       "75%      4.00000    9.052500    1.000000          0.822500  \n",
       "max      5.00000    9.920000    1.000000          0.970000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Serial No.           0\n",
       "GRE Score            0\n",
       "TOEFL Score          0\n",
       "University Rating    0\n",
       "SOP                  0\n",
       "LOR                  0\n",
       "CGPA                 0\n",
       "Research             0\n",
       "Chance of Admit      0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset=dataset.drop([\"Serial No.\"],axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GRE Score</th>\n",
       "      <th>TOEFL Score</th>\n",
       "      <th>University Rating</th>\n",
       "      <th>SOP</th>\n",
       "      <th>LOR</th>\n",
       "      <th>CGPA</th>\n",
       "      <th>Research</th>\n",
       "      <th>Chance of Admit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>GRE Score</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.831137</td>\n",
       "      <td>0.650135</td>\n",
       "      <td>0.613269</td>\n",
       "      <td>0.538649</td>\n",
       "      <td>0.829021</td>\n",
       "      <td>0.570726</td>\n",
       "      <td>0.806873</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TOEFL Score</th>\n",
       "      <td>0.831137</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.669767</td>\n",
       "      <td>0.650534</td>\n",
       "      <td>0.552455</td>\n",
       "      <td>0.818476</td>\n",
       "      <td>0.476830</td>\n",
       "      <td>0.791934</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>University Rating</th>\n",
       "      <td>0.650135</td>\n",
       "      <td>0.669767</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.730656</td>\n",
       "      <td>0.631142</td>\n",
       "      <td>0.723023</td>\n",
       "      <td>0.436357</td>\n",
       "      <td>0.699380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SOP</th>\n",
       "      <td>0.613269</td>\n",
       "      <td>0.650534</td>\n",
       "      <td>0.730656</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.692200</td>\n",
       "      <td>0.714796</td>\n",
       "      <td>0.424001</td>\n",
       "      <td>0.680378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LOR</th>\n",
       "      <td>0.538649</td>\n",
       "      <td>0.552455</td>\n",
       "      <td>0.631142</td>\n",
       "      <td>0.692200</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.651118</td>\n",
       "      <td>0.383256</td>\n",
       "      <td>0.655735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CGPA</th>\n",
       "      <td>0.829021</td>\n",
       "      <td>0.818476</td>\n",
       "      <td>0.723023</td>\n",
       "      <td>0.714796</td>\n",
       "      <td>0.651118</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.509915</td>\n",
       "      <td>0.878284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Research</th>\n",
       "      <td>0.570726</td>\n",
       "      <td>0.476830</td>\n",
       "      <td>0.436357</td>\n",
       "      <td>0.424001</td>\n",
       "      <td>0.383256</td>\n",
       "      <td>0.509915</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.548968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Chance of Admit</th>\n",
       "      <td>0.806873</td>\n",
       "      <td>0.791934</td>\n",
       "      <td>0.699380</td>\n",
       "      <td>0.680378</td>\n",
       "      <td>0.655735</td>\n",
       "      <td>0.878284</td>\n",
       "      <td>0.548968</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   GRE Score  TOEFL Score  University Rating       SOP  \\\n",
       "GRE Score           1.000000     0.831137           0.650135  0.613269   \n",
       "TOEFL Score         0.831137     1.000000           0.669767  0.650534   \n",
       "University Rating   0.650135     0.669767           1.000000  0.730656   \n",
       "SOP                 0.613269     0.650534           0.730656  1.000000   \n",
       "LOR                 0.538649     0.552455           0.631142  0.692200   \n",
       "CGPA                0.829021     0.818476           0.723023  0.714796   \n",
       "Research            0.570726     0.476830           0.436357  0.424001   \n",
       "Chance of Admit     0.806873     0.791934           0.699380  0.680378   \n",
       "\n",
       "                       LOR       CGPA  Research  Chance of Admit   \n",
       "GRE Score          0.538649  0.829021  0.570726          0.806873  \n",
       "TOEFL Score        0.552455  0.818476  0.476830          0.791934  \n",
       "University Rating  0.631142  0.723023  0.436357          0.699380  \n",
       "SOP                0.692200  0.714796  0.424001          0.680378  \n",
       "LOR                1.000000  0.651118  0.383256          0.655735  \n",
       "CGPA               0.651118  1.000000  0.509915          0.878284  \n",
       "Research           0.383256  0.509915  1.000000          0.548968  \n",
       "Chance of Admit    0.655735  0.878284  0.548968          1.000000  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['GRE Score', 'TOEFL Score', 'University Rating', 'SOP', 'LOR ', 'CGPA',\n",
       "       'Research', 'Chance of Admit '],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Train-Test Split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=dataset.iloc[:,:-1]\n",
    "y=dataset[\"Chance of Admit \"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "#normalisation\n",
    "u=np.mean(X_train,axis=0)\n",
    "std=np.std(X_train,axis=0)\n",
    "X_train=(X_train-u)/std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Train the data- Multivariate Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "m=X_train.shape[0]  #no. of training examples\n",
    "n=X_train.shape[1]  #no. of features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=X_train.values #obtaining a numpy array from the data frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.ones((m,1)) #generating bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_X=np.hstack((x,X)) #appending bias to each training example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hypothesis(X,theta):\n",
    "    return np.dot(X,theta)\n",
    "\n",
    "def error(X,y,theta):\n",
    "    e = 0.0\n",
    "    y_ = hypothesis(X,theta)\n",
    "    e = np.sum((y-y_)**2)\n",
    "    \n",
    "    return e/m\n",
    "    \n",
    "def gradient(X,y,theta):\n",
    "    \n",
    "    y_ = hypothesis(X,theta)\n",
    "    grad = np.dot(X.T,(y_ - y))\n",
    "    m = X.shape[0]\n",
    "    return grad/m\n",
    "\n",
    "def gradient_descent(X,y,learning_rate = 0.01,max_iters=300):\n",
    "    \n",
    "    n = X.shape[1]\n",
    "    theta = np.zeros((n,))\n",
    "    error_list = []\n",
    "    \n",
    "    for i in range(max_iters):\n",
    "        e = error(X,y,theta)\n",
    "        error_list.append(e)\n",
    "        \n",
    "        #Gradient descent\n",
    "        grad = gradient(X,y,theta)\n",
    "        theta = theta - learning_rate*grad\n",
    "        \n",
    "    return theta,error_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta,error_list = gradient_descent(input_X,y,0.01,500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot the error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x228cf910f88>]"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.plot(error_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Make Predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "#normalisation\n",
    "u=np.mean(X_test,axis=0)\n",
    "std=np.std(X_test,axis=0)\n",
    "X_test=(X_test-u)/std\n",
    "x=np.ones((X_test.shape[0],1))\n",
    "X_test=np.hstack((x,X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "preds=hypothesis(X_test,theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80.52399859232963\n"
     ]
    }
   ],
   "source": [
    "print(r2_score(y_test,preds)*100)"
   ]
  }
 ],
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