Manasi Kulkarni_Lab2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import sklearn.linear_model as lm\n",
    "import statsmodels.formula.api as smf\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pclass</th>\n",
       "      <th>survived</th>\n",
       "      <th>name</th>\n",
       "      <th>sex</th>\n",
       "      <th>age</th>\n",
       "      <th>sibsp</th>\n",
       "      <th>parch</th>\n",
       "      <th>ticket</th>\n",
       "      <th>fare</th>\n",
       "      <th>cabin</th>\n",
       "      <th>embarked</th>\n",
       "      <th>boat</th>\n",
       "      <th>body</th>\n",
       "      <th>home.dest</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Allen, Miss. Elisabeth Walton</td>\n",
       "      <td>female</td>\n",
       "      <td>29.0000</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>24160</td>\n",
       "      <td>211.3375</td>\n",
       "      <td>B5</td>\n",
       "      <td>S</td>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>St Louis, MO</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Allison, Master. Hudson Trevor</td>\n",
       "      <td>male</td>\n",
       "      <td>0.9167</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>113781</td>\n",
       "      <td>151.5500</td>\n",
       "      <td>C22 C26</td>\n",
       "      <td>S</td>\n",
       "      <td>11</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Montreal, PQ / Chesterville, ON</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>Allison, Miss. Helen Loraine</td>\n",
       "      <td>female</td>\n",
       "      <td>2.0000</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>113781</td>\n",
       "      <td>151.5500</td>\n",
       "      <td>C22 C26</td>\n",
       "      <td>S</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Montreal, PQ / Chesterville, ON</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>Allison, Mr. Hudson Joshua Creighton</td>\n",
       "      <td>male</td>\n",
       "      <td>30.0000</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>113781</td>\n",
       "      <td>151.5500</td>\n",
       "      <td>C22 C26</td>\n",
       "      <td>S</td>\n",
       "      <td>NaN</td>\n",
       "      <td>135.0</td>\n",
       "      <td>Montreal, PQ / Chesterville, ON</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>Allison, Mrs. Hudson J C (Bessie Waldo Daniels)</td>\n",
       "      <td>female</td>\n",
       "      <td>25.0000</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>113781</td>\n",
       "      <td>151.5500</td>\n",
       "      <td>C22 C26</td>\n",
       "      <td>S</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Montreal, PQ / Chesterville, ON</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   pclass  survived                                             name     sex  \\\n",
       "0       1         1                    Allen, Miss. Elisabeth Walton  female   \n",
       "1       1         1                   Allison, Master. Hudson Trevor    male   \n",
       "2       1         0                     Allison, Miss. Helen Loraine  female   \n",
       "3       1         0             Allison, Mr. Hudson Joshua Creighton    male   \n",
       "4       1         0  Allison, Mrs. Hudson J C (Bessie Waldo Daniels)  female   \n",
       "\n",
       "       age  sibsp  parch  ticket      fare    cabin embarked boat   body  \\\n",
       "0  29.0000      0      0   24160  211.3375       B5        S    2    NaN   \n",
       "1   0.9167      1      2  113781  151.5500  C22 C26        S   11    NaN   \n",
       "2   2.0000      1      2  113781  151.5500  C22 C26        S  NaN    NaN   \n",
       "3  30.0000      1      2  113781  151.5500  C22 C26        S  NaN  135.0   \n",
       "4  25.0000      1      2  113781  151.5500  C22 C26        S  NaN    NaN   \n",
       "\n",
       "                         home.dest  \n",
       "0                     St Louis, MO  \n",
       "1  Montreal, PQ / Chesterville, ON  \n",
       "2  Montreal, PQ / Chesterville, ON  \n",
       "3  Montreal, PQ / Chesterville, ON  \n",
       "4  Montreal, PQ / Chesterville, ON  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Loading the dataset and lookig at the head to get an idea of the columns and variables\n",
    "titanic_data=pd.read_csv('/Users/manasi/Desktop/titanic.csv')\n",
    "titanic_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Developing a model \n",
    "mod = smf.ols(formula='survived~C(pclass)+sex', data=titanic_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               survived   R-squared:                       0.341\n",
      "Model:                            OLS   Adj. R-squared:                  0.340\n",
      "Method:                 Least Squares   F-statistic:                     225.5\n",
      "Date:                Wed, 11 Apr 2018   Prob (F-statistic):          7.79e-118\n",
      "Time:                        19:20:19   Log-Likelihood:                -639.22\n",
      "No. Observations:                1309   AIC:                             1286.\n",
      "Df Residuals:                    1305   BIC:                             1307.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==================================================================================\n",
      "                     coef    std err          t      P>|t|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------\n",
      "Intercept          0.8990      0.025     35.398      0.000       0.849       0.949\n",
      "C(pclass)[T.2]    -0.1577      0.032     -4.872      0.000      -0.221      -0.094\n",
      "C(pclass)[T.3]    -0.2926      0.027    -10.957      0.000      -0.345      -0.240\n",
      "sex[T.male]       -0.5049      0.023    -21.974      0.000      -0.550      -0.460\n",
      "==============================================================================\n",
      "Omnibus:                       60.055   Durbin-Watson:                   1.760\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               67.798\n",
      "Skew:                           0.557   Prob(JB):                     1.90e-15\n",
      "Kurtosis:                       2.961   Cond. No.                         5.25\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "res = mod.fit()\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.89898393,  0.39411348,  0.89898393, ...,  0.10147811,\n",
       "        0.10147811,  0.10147811])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Predicting the res values\n",
    "yhat=res.predict()\n",
    "yhat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.89898393224477124"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10147811470358525"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 1, ..., 0, 0, 0])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Making an array of 0 and 1 for predicted values\n",
    "new=(yhat > 0.5)+0\n",
    "new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.77998472116119177"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Calculating the accuracy score which comes up to 78%\n",
    "accuracy_score(titanic_data['survived'],new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.77998472116119177"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mod1 = smf.ols(formula='survived~C(pclass)*sex', data=titanic_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               survived   R-squared:                       0.370\n",
      "Model:                            OLS   Adj. R-squared:                  0.368\n",
      "Method:                 Least Squares   F-statistic:                     153.2\n",
      "Date:                Wed, 11 Apr 2018   Prob (F-statistic):          4.02e-128\n",
      "Time:                        19:57:27   Log-Likelihood:                -609.86\n",
      "No. Observations:                1309   AIC:                             1232.\n",
      "Df Residuals:                    1303   BIC:                             1263.\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================================\n",
      "                                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------------------\n",
      "Intercept                      0.9653      0.032     29.974      0.000       0.902       1.028\n",
      "C(pclass)[T.2]                -0.0785      0.049     -1.587      0.113      -0.176       0.019\n",
      "C(pclass)[T.3]                -0.4745      0.042    -11.414      0.000      -0.556      -0.393\n",
      "sex[T.male]                   -0.6245      0.043    -14.436      0.000      -0.709      -0.540\n",
      "C(pclass)[T.2]:sex[T.male]    -0.1161      0.064     -1.801      0.072      -0.243       0.010\n",
      "C(pclass)[T.3]:sex[T.male]     0.2859      0.054      5.340      0.000       0.181       0.391\n",
      "==============================================================================\n",
      "Omnibus:                      113.251   Durbin-Watson:                   1.746\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              142.526\n",
      "Skew:                           0.805   Prob(JB):                     1.12e-31\n",
      "Kurtosis:                       3.136   Cond. No.                         13.3\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "res1 = mod1.fit()\n",
    "print(res1.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coeeficients of base intercept =0.9653\n",
    "Probability of Class 1 female surviving is 0.9653\n",
    "Probability of Class 2 female surviving is Intercept-0.0785\n",
    "Probability of Class 3 female surviving is Intercept-0.4745"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.96527778,  0.34078212,  0.96527778, ...,  0.15212982,\n",
       "        0.15212982,  0.15212982])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat1=res1.predict()\n",
    "yhat1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 1, ..., 0, 0, 0])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new1=(yhat1 > 0.5)+0\n",
    "new1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.78304048892284184"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The accuracy comes up to 79%\n",
    "accuracy_score(titanic_data['survived'],new1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The accuracy improved by 0.4 percent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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