Logistic Regression_Insurance_data.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7f696279",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9cc61147",
   "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>age</th>\n",
       "      <th>bought_insurance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>22</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>25</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>47</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>52</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>46</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age  bought_insurance\n",
       "0   22                 0\n",
       "1   25                 0\n",
       "2   47                 1\n",
       "3   52                 0\n",
       "4   46                 1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"insurance_data.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0d6e3843",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(27, 2)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6d5d0d19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x22b8ef2dfd0>"
      ]
     },
     "execution_count": 4,
     "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.scatter(df.age,df.bought_insurance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3c062fa7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c24f532d",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train,X_test,y_train,y_test = train_test_split(df[['age']],df.bought_insurance,train_size=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f027caf0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8e0ae3eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d2fe2d88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b5ae2036",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6b471c76",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "model = LogisticRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "731876e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "23dd15f2",
   "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>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    age\n",
       "5    56\n",
       "22   40\n",
       "13   29\n",
       "11   28\n",
       "2    47\n",
       "7    60\n",
       "21   26\n",
       "9    61\n",
       "0    22"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "70a64116",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 0, 0, 1, 1, 0, 1, 0], dtype=int64)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1f917db0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.14937311, 0.85062689],\n",
       "       [0.48639106, 0.51360894],\n",
       "       [0.75101656, 0.24898344],\n",
       "       [0.77018545, 0.22981455],\n",
       "       [0.31181011, 0.68818989],\n",
       "       [0.10332671, 0.89667329],\n",
       "       [0.80533737, 0.19466263],\n",
       "       [0.09396863, 0.90603137],\n",
       "       [0.86309796, 0.13690204]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict_proba(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a07f6fec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "088db9a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.10531732]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#model.coef_ indicates value of m in y=m*x + b equation\n",
    "\n",
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e48be048",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.15824364])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#model.intercept_ indicates value of b in y=m*x + b equation\n",
    "\n",
    "model.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85922838",
   "metadata": {},
   "source": [
    "# Sigmoid function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "afbee128",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + math.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f63da4f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def prediction_function(age):\n",
    "    z = 0.11 * age - 4.16 \n",
    "    y = sigmoid(z)\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "2c537092",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.42311473886795364"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age = 35\n",
    "prediction_function(age)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1adb08d9",
   "metadata": {},
   "source": [
    "### 0.42311473886795364 is less than 0.5 which means person with 35 age will not buy insurance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "317e0d0d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6878313305828404"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age = 45\n",
    "prediction_function(age)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47dd927f",
   "metadata": {},
   "source": [
    "### 0.6878313305828404 is greater than 0.5 which means person with 45 age will buy insurance"
   ]
  }
 ],
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