Lab_8_Linear_Regression_Raw_Real_example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ae7b76bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "50b48e31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5,)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.array([1,2,3,4,5])\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "67ea77a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.array([3,4,2,4,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7528452b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5bba9db8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2387f265100>"
      ]
     },
     "execution_count": 5,
     "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(X,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ec353fe",
   "metadata": {},
   "source": [
    "# Linear Regression: fit a line through this data and plot the result"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25e54c0b",
   "metadata": {},
   "source": [
    "# Single variable y = ax+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3eea42d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize\n",
    "a = 0\n",
    "b = 0\n",
    "yp = 0\n",
    "lr = 0.01\n",
    "epochs = 15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5d4cb46c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.23200000000000004 0.07200000000000001\n",
      "0.40864 0.12864000000000003\n",
      "0.5430208 0.17354880000000003\n",
      "0.645143296 0.20949657600000005\n",
      "0.72264197632 0.23859804672000004\n",
      "0.7813448587264 0.2624675672064\n",
      "0.825700935774208 0.28233752433868803\n",
      "0.8591064784435609 0.2991487177054618\n",
      "0.8841541301236499 0.3136193546447389\n",
      "0.9028230602177626 0.3262977197444251\n",
      "0.9166241237851893 0.33760238173647084\n",
      "0.9267106736482594 0.34785288667463005\n",
      "0.9339631522451646 0.3572931885222419\n",
      "0.9390536674398938 0.3661095356170872\n",
      "0.942495288466092 0.3744441248583518\n",
      "7.374105786561548\n"
     ]
    },
    {
     "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": [
    "for i in range(epochs):\n",
    "    yp = a*X+b\n",
    "    da = (-2/len(X))*np.sum((y-yp)*X)\n",
    "    db = (-2/len(X))*np.sum(y-yp)\n",
    "    a = a - lr*da\n",
    "    b = b - lr*db\n",
    "    plt.scatter(X,y)\n",
    "    plt.plot([min(X),max(X)],[min(yp),max(yp)],color = 'red')\n",
    "    #plt.show()\n",
    "    print(a,b)\n",
    "print(np.sum((y-yp)**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "665270b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2387f414730>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3+usq5lJjNJAnkggffhgW05o/H845Bx54ADSTS2qYeugiu2PTJvjrX8M88jVrQo/82WdVzCUS6qGL7Kp33gmzVz77LNy+f/fdsP/+UaeSDKYeukhVrVsXCviJJ4bXEyeGXYRUzCViKugiVfHGG+EGoREjwlDLvHlwwglRpxIBVNBF4lNcHC52nn46HHhg2Kh5wADYe++ok4nsoIIusjPuYfph06bwyithWmJhIRx1VNTJRH5CF0VFSsmfvZwBBYtYsbaE1raRYVNHUH/y23D00TByJDQvdyFRkaSggi4Skz97Of1HF/H95i2cPbeA/u88xh7bt1N01c20vOdGqFUr6ogiO6WCLhIzoGARB3/9FXeNH0yHpfOZ2qgV13W9gu31/oupKuaSAlTQRQC2buXUgme5asozbK6VxTVdr+ClVieBGba2JOp0InFRQReZNw8uuojrCwt56/AO/O2k3qza98AdhxvkZEcYTiR+KuiSuX74Ae64Izzq1GHGXUO5ckMjSrZu39EkO6sW/bo0iTCkSPw0bVEy07RpYVXEW28NW8ItXEj7ay/lzt+0IjcnGwNyc7K588yWdG+bG3Vakbiohy6Z5bvvwqYTDz4Iubnw5pvQrduOw93b5qqAS8pSQZfM8c9/hsW0vvgCLrsM7rwT9tsv6lQiCaMhF0l/a9eG7d86dw7bwb37Ljz0kIq5pJ14Noney8xmmNlcM1tgZreU08bMbJCZLTazeWbWrnriilTRa6+FxbSeeAKuvRbmzoVf/SrqVCLVIp4hlx+AE919o5llAVPMbJy7TyvV5hTg8NjjaGBo7KtINL7+Gq64Al56CVq3DqskHnlk1KlEqlWlPXQPNsZeZsUeXqbZGcBTsbbTgBwzOySxUUXi4A5PPx165fn5cPvtYXs4FXPJAHGNoZtZLTObA6wCJrj79DJNcoGlpV4vi71X9uf0MrNCMyssLi7excgiFfjqKzj1VOjZE5o0gTlz4IYbICsr6mQiNSKugu7u29y9DdAQaG9mLco0sfK+rZyfM9zd89w9r572XJRE2b4dHn44rIT47rthSuLkyWHJW5EMUqVZLu6+FpgEdC1zaBlwaKnXDYEVuxNMJC6ffAKdOkGfPnDMMbBgQRg712JakoHimeVSz8xyYs+zgc7Ax2WavQ70jM126QCsc/eViQ4rssPWrWFT5latoKgIHn8cCgqgceOok4lEJp5ZLocAT5pZLcI/AC+5+xgzuxTA3YcBY4FuwGJgE3BBNeUVCWPjF10Es2bB//1fmFN+iK7Bi1Ra0N19HtC2nPeHlXruQJ/ERhMp4/vv4bbbQs+8bt2wJdxvfhN1KpGkoVv/JTW8/37olX/8MZx3HgwcCAccEHUqkaSiW/8luW3cGC5yHnssbNoE48eHuz5VzEV+QgVdktdbb0GLFjBkSJjFMn8+dOkSdSqRpKWCLslnzRq44IJQvPfaC957DwYPhn33jTqZSFJTQZfkMnp0uG3/6aehf/8wo+XYY6NOJZISdFFUksO//gWXXw6jRkGbNjB2LLT9yeQqEdkJ9dAlWu7hImezZjBmTNh0YsYMFXORXaAeukRnyRK45JJw8fPYY2HEiLColojsEvXQpeZt3x4ucrZoEeaXDxkSFtVSMRfZLeqhS836+OOwHdzUqWEWyyOPQKNGUacSSQvqoUvN2LIF7rgj7B700Ufw5JMwbpyKuUgCqYcu1W/WrHDb/pw5cNZZYYjl4IOjTiWSdtRDl+pTUhLmkrdvH6Yljh4NL7+sYi5STdRDl+oxZUrolX/yCVx4Idx7L9SpE3UqkbSmHrok1oYN4Qah446DzZthwgQYOVLFXKQGqKBL4owbF/b1fPhhuPLKsJNQ585RpxLJGCrosvtWr4aePaFbN6hdO0xJfOCB8FxEakw8e4oeambvmNlCM1tgZleW06aTma0zszmxx03VE1eSinu4yNmsGTz/PPztbzB7dtisWURqXDwXRbcCV7v7LDPbF5hpZhPc/aMy7Sa7+2mJjyhJaeVKuOwyyM+HI48Mt++3bh11KpGMVmkP3d1Xuvus2PMNwEIgt7qDSZJyh8ceg6ZNw+5B99wD06apmIskgSqNoZtZY8KG0dPLOXyMmc01s3Fm1ryC7+9lZoVmVlhcXFz1tBKtL76Ak08O0xFbt4a5c6FfP9hDs19FkkHcBd3MagOjgL7uvr7M4VlAI3dvDQwG8sv7Ge4+3N3z3D2vXr16uxhZaty2bfDgg2ExrenTYehQeOcdOOKIqJOJSClxFXQzyyIU82fdfXTZ4+6+3t03xp6PBbLMrG5Ck0o0PvooLG3bty8cfzwsWACXXgo/0wQpkWQTzywXA0YCC919YAVt6sfaYWbtYz93dSKDSg3bvBluuy1sNPHpp/DMM/Dmm3DooVEnE5EKxDP42RH4I1BkZnNi710PHAbg7sOAs4DeZrYVKAF6uLsnPq7UiMLCME4+bx706BGGWw46KOpUIlKJSgu6u08BrJI2Q4AhiQolESkpgZtvhvvug/r14bXX4PTTo04lInHS9AQJ3n03bDyxeDFcfHGYjpiTE3UqEakCXdnKdOvXQ+/e0KlT2Brun/+E4cNVzEVSkAp6JnvzzbCY1vDhcNVVYcz8xBOjTiUiu0gFPRN98w2cey6cdhrsv3/YqPm++2CffaJOJiK7QWPoaS5/9nIGFCxixdoSGuy/Fw/YIo6672ZYty5cAL3+evj5z6OOKSIJoIKexvJnL6f/6CJKtmzj4A3f8PdRQzlq8XTWNG9NnYkToWXLqCOKSAKpoKexAQWLKNm8lR5zC7j+ncfI2r6N20+4kILOPZisYi6SdlTQ09geX3zOc+MH88uv5vHBYS25ruuf+bJOA2z95qijiUg1UEFPR7HFtAoev57NVov+XS7nhdYn4xaugTfIyY44oIhUBxX0dDN/frhtf8YM1h7XmR5te7Ik+4Adh7OzatGvS5MIA4pIddG0xXSxeTPccgu0aweffw7PP0/9d9+i7/knkpuTjQG5OdnceWZLurfV/iQi6Ug99HQwY0bolc+fD+ecExbTqhtWL+7eNlcFXCRDqIeeyjZtgquvDpsyr1kDb7wBzz67o5iLSGZRDz1VvfNOWEzr88/hkkvg7rvDXZ8ikrHUQ08169ZBr15hzRWzUNiHDVMxFxEV9JTyxhvQrBmMHBk2Z543L6ySKCKCCnpqKC6Gs88Om00ceGDYqPmee2DvvaNOJiJJJJ49RQ81s3fMbKGZLTCzK8tpY2Y2yMwWm9k8M2tXPXEzjHu4yNm0KYwaBbfeGraHy8uLOpmIJKF4LopuBa5291lmti8w08wmuPtHpdqcAhweexwNDI19lV21dGnYeOLNN+Hoo8MwS/PmUacSkSRWaQ/d3Ve6+6zY8w3AQqDsxOYzgKc8mAbkmNkhCU+bCbZvDxc5mzcPFzzvvx+mTlUxF5FKVWkM3cwaA22B6WUO5QJLS71exk+LPmbWy8wKzaywuLi4ilEzwKefhtkrvXtD+/ZQVAR9+0KtWlEnE5EUEHdBN7PawCigr7uvL3u4nG/xn7zhPtzd89w9r169elVLms62boUBA6BVK5gzJwyvTJgAv/hF1MlEJIXEdWORmWURivmz7j66nCbLgENLvW4IrNj9eBlg7txw2/7MmXDGGfDww9CgQdSpRCQFxTPLxYCRwEJ3H1hBs9eBnrHZLh2Ade6+MoE5088PP8CNN4YZK0uXwksvwauvqpiLyC6Lp4feEfgjUGRmc2LvXQ8cBuDuw4CxQDdgMbAJuCDhSdPJBx+EXvnChfDHP4YLnwceGHUqEUlxlRZ0d59C+WPkpds40CdRodLWd9/BDTfAoEHQsCGMHQunnBJ1KhFJE1qcq6a8/TZcfDEsWQKXXQZ33gn77Rd1KhFJI7r1v7qtXRuGV046CbKy4L334KGHVMxFJOFU0KtTfn5YTOvJJ+G668KMluOOizqViKQpDblUh6+/hj//GV5+GVq3DqskHnlk1KlEJM2ph55I7vDUU2Exrddeg3/8Az78UMVcRGqEeuiJ8tVXYeeg8ePDlnAjR4bCLiJSQ9RD313bt4eLnM2bw+TJYUri5Mkq5iJS49RD3x2LFoV9PadMCbNYhg+Hxo2jTiUiGUo99F2xZQvcdVe44Dl/Pjz+OBQUqJiLSKTUQ6+q2bPDvPLZs+HMM8NwS/36UacSEVEPPW7ffx9u2z/qKFixAl55JWwLp2IuIklCPfR4TJ0aeuWLFsF558HAgXDAAVGnEhH5EfXQd2bjRrjiinB35/ffhymJTzyhYi4iSUkFvSIFBdCiBQwZApdfHi5+dukSdSoRkQqpoJf17bdw/vnQtSvstdd/5pbXrh11MhGRnVJBL23UqLCY1jPPwPXXh/09O3aMOpWISFx0URRg5cowrDJ6NLRtG8bK27SJOpWISJVkdg/dPVzkbNYM3nwz3Cw0fbqKuYikpHg2iX7MzFaZ2fwKjncys3VmNif2uCnxMavBkiXhIucFF4SLn3PnwrXXhk0oRERSUDw99CeArpW0mezubWKPW3c/VjXatg0GDw5F/IMPwp2e774LTZpEnUxEZLfEs0n0e2bWuAayVL+FC8NiWu+/H2axDBsGjRpFnUpEJCESNYZ+jJnNNbNxZta8okZm1svMCs2ssLi4OEEfHYctW8JmE23awMcfh00oxo5VMReRtJKIWS6zgEbuvtHMugH5wOHlNXT34cBwgLy8PE/AZ8eRbhZceGEYI//tb8Nwy8EH18hHi4jUpN3uobv7enffGHs+Fsgys7q7nWx3lZSEjZnbtw97fI4eDS+9pGIuImlrt3voZlYf+Nrd3czaE/6RWL3byXbH5MlhrPyTT8KiWgMGQJ06kUYSEalulRZ0M3se6ATUNbNlwM1AFoC7DwPOAnqb2VagBOjh7jUznFLW+vXQvz88/HDYbGLCBOjcOZIoIiI1LZ5ZLmdXcnwIMCRhiXbVuHFhk+Zly6BvX7j9dthnn6hTiYjUmNS/U3T1aujZE7p1CwtoTZ0K99+vYi4iGSel1nLJn72cAQWLWLG2hAb778X9P/uU9vfdBGvWwI03hh2F9twz6pgiIpFImYKeP3s5/UcXUbJlGwdtWM1No4fS/tNprGnaijpvvw2tWkUdUUQkUilT0AcULKJkyzY6ffYhg964l59v28IdnS5gfOezeU/FXEQkdQr6irUlAHxxQC6zGvw//t65F0sOyMU2bI44mYhIckiZgt4gJ5vla0v4sk4Dzv/dLT96X0REUmiWS78uTcjOqvWj97KzatGvi1ZJFBGBFOqhd2+bC/CfWS452fTr0mTH+yIimS5lCjqEoq4CLiJSvpQZchERkZ1TQRcRSRMq6CIiaUIFXUQkTaigi4ikCYtq6XIzKwa+3MVvrwt8k8A4iZKsuSB5sylX1ShX1aRjrkbuXq+8A5EV9N1hZoXunhd1jrKSNRckbzblqhrlqppMy6UhFxGRNKGCLiKSJlK1oA+POkAFkjUXJG825aoa5aqajMqVkmPoIiLyU6naQxcRkTJU0EVE0kRSF3Qze8zMVpnZ/AqOm5kNMrPFZjbPzNolSa5OZrbOzObEHjfVQKZDzewdM1toZgvM7Mpy2tT4+YozVxTnay8zm2Fmc2O5bimnTRTnK55cNX6+Sn12LTObbWZjyjkWyd9jHLmiPF9LzKwo9rmF5RxP7Dlz96R9AL8C2gHzKzjeDRgHGNABmJ4kuToBY2r4XB0CtIs93xf4BGgW9fmKM1cU58uA2rHnWcB0oEMSnK94ctX4+Sr12VcBz5X3+VH9PcaRK8rztQSou5PjCT1nSd1Dd/f3gG930uQM4CkPpgE5ZnZIEuSqce6+0t1nxZ5vABYCZRePr/HzFWeuGhc7BxtjL7Nij7IzBKI4X/HkioSZNQROBUZU0CSSv8c4ciWzhJ6zpC7occgFlpZ6vYwkKBYxx8T+2zzOzJrX5AebWWOgLaF3V1qk52snuSCC8xX7b/ocYBUwwd2T4nzFkQui+f16ALgG2F7B8ah+vx5g57kgur9HB94ys5lm1quc4wk9Z6le0K2c95KhNzOLsN5Ca2AwkF9TH2xmtYFRQF93X1/2cDnfUiPnq5JckZwvd9/m7m2AhkB7M2tRpkkk5yuOXDV+vszsNGCVu8/cWbNy3qvW8xVnrsj+HoGO7t4OOAXoY2a/KnM8oecs1Qv6MuDQUq8bAisiyrKDu6//93+b3X0skGVmdav7c80si1A0n3X30eU0ieR8VZYrqvNV6vPXApOArmUORfr7VVGuiM5XR+B0M1sCvACcaGbPlGkTxfmqNFeUv1/uviL2dRXwKtC+TJOEnrNUL+ivAz1jV4o7AOvcfWXUocysvplZ7Hl7wnleXc2facBIYKG7D6ygWY2fr3hyRXS+6plZTux5NtAZ+LhMsyjOV6W5ojhf7t7f3Ru6e2OgBzDR3c8t06zGz1c8uaI4X7HP2sfM9v33c+BkoOzMuISes6TeJNrMnidcoa5rZsuAmwkXiXD3YcBYwlXixcAm4IIkyXUW0NvMtgIlQA+PXdKuRh2BPwJFsfFXgOuBw0rliuJ8xZMrivN1CPCkmdUi/IG/5O5jzOzSUrmiOF/x5IrifJUrCc5XPLmiOl8HA6/G/i3ZA3jO3cdX5znTrf8iImki1YdcREQkRgVdRCRNqKCLiKQJFXQRkTShgi4ikiZU0EVE0oQKuohImvj/ZtcQu4N5ZTUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,yp)\n",
    "plt.plot([min(X),max(y)],[min(yp),max(yp)],color = 'red')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e9ca532",
   "metadata": {},
   "source": [
    "# Lets do real Example: How to use Linear Regression using sklearn API"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2e5eed53",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7736bc96",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_q = pd.read_csv('dataS.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7eb6b1d3",
   "metadata": {},
   "source": [
    "# Q_1: Apply linear regression on this data and find the best fitting line parameters a and b. Also compute the mse and show at what learning rate and number of epochs you get the lowest mse. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0f355fba",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('datasets_13720_18513_insurance_MAIN.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2af5dc6a",
   "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>gender</th>\n",
       "      <th>bmi</th>\n",
       "      <th>children</th>\n",
       "      <th>smoker</th>\n",
       "      <th>region</th>\n",
       "      <th>charges</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>19</td>\n",
       "      <td>female</td>\n",
       "      <td>27.900</td>\n",
       "      <td>0</td>\n",
       "      <td>yes</td>\n",
       "      <td>southwest</td>\n",
       "      <td>16884.92400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>18</td>\n",
       "      <td>male</td>\n",
       "      <td>33.770</td>\n",
       "      <td>1</td>\n",
       "      <td>no</td>\n",
       "      <td>southeast</td>\n",
       "      <td>1725.55230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>28</td>\n",
       "      <td>male</td>\n",
       "      <td>33.000</td>\n",
       "      <td>3</td>\n",
       "      <td>no</td>\n",
       "      <td>southeast</td>\n",
       "      <td>4449.46200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>33</td>\n",
       "      <td>male</td>\n",
       "      <td>22.705</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>northwest</td>\n",
       "      <td>21984.47061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>32</td>\n",
       "      <td>male</td>\n",
       "      <td>28.880</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>northwest</td>\n",
       "      <td>3866.85520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1333</th>\n",
       "      <td>50</td>\n",
       "      <td>male</td>\n",
       "      <td>30.970</td>\n",
       "      <td>3</td>\n",
       "      <td>no</td>\n",
       "      <td>northwest</td>\n",
       "      <td>10600.54830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1334</th>\n",
       "      <td>18</td>\n",
       "      <td>female</td>\n",
       "      <td>31.920</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>northeast</td>\n",
       "      <td>2205.98080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1335</th>\n",
       "      <td>18</td>\n",
       "      <td>female</td>\n",
       "      <td>36.850</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>southeast</td>\n",
       "      <td>1629.83350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1336</th>\n",
       "      <td>21</td>\n",
       "      <td>female</td>\n",
       "      <td>25.800</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>southwest</td>\n",
       "      <td>2007.94500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1337</th>\n",
       "      <td>61</td>\n",
       "      <td>female</td>\n",
       "      <td>29.070</td>\n",
       "      <td>0</td>\n",
       "      <td>yes</td>\n",
       "      <td>northwest</td>\n",
       "      <td>29141.36030</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1338 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      age  gender     bmi  children smoker     region      charges\n",
       "0      19  female  27.900         0    yes  southwest  16884.92400\n",
       "1      18    male  33.770         1     no  southeast   1725.55230\n",
       "2      28    male  33.000         3     no  southeast   4449.46200\n",
       "3      33    male  22.705         0     no  northwest  21984.47061\n",
       "4      32    male  28.880         0     no  northwest   3866.85520\n",
       "...   ...     ...     ...       ...    ...        ...          ...\n",
       "1333   50    male  30.970         3     no  northwest  10600.54830\n",
       "1334   18  female  31.920         0     no  northeast   2205.98080\n",
       "1335   18  female  36.850         0     no  southeast   1629.83350\n",
       "1336   21  female  25.800         0     no  southwest   2007.94500\n",
       "1337   61  female  29.070         0    yes  northwest  29141.36030\n",
       "\n",
       "[1338 rows x 7 columns]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "734aa363",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3f944ef7",
   "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>bmi</th>\n",
       "      <th>children</th>\n",
       "      <th>charges</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1338.000000</td>\n",
       "      <td>1338.000000</td>\n",
       "      <td>1338.000000</td>\n",
       "      <td>1338.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>39.207025</td>\n",
       "      <td>30.663397</td>\n",
       "      <td>1.094918</td>\n",
       "      <td>13270.422265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>14.049960</td>\n",
       "      <td>6.098187</td>\n",
       "      <td>1.205493</td>\n",
       "      <td>12110.011237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>18.000000</td>\n",
       "      <td>15.960000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1121.873900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>27.000000</td>\n",
       "      <td>26.296250</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4740.287150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>39.000000</td>\n",
       "      <td>30.400000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>9382.033000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>51.000000</td>\n",
       "      <td>34.693750</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>16639.912515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>64.000000</td>\n",
       "      <td>53.130000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>63770.428010</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               age          bmi     children       charges\n",
       "count  1338.000000  1338.000000  1338.000000   1338.000000\n",
       "mean     39.207025    30.663397     1.094918  13270.422265\n",
       "std      14.049960     6.098187     1.205493  12110.011237\n",
       "min      18.000000    15.960000     0.000000   1121.873900\n",
       "25%      27.000000    26.296250     0.000000   4740.287150\n",
       "50%      39.000000    30.400000     1.000000   9382.033000\n",
       "75%      51.000000    34.693750     2.000000  16639.912515\n",
       "max      64.000000    53.130000     5.000000  63770.428010"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f07ed57b",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_num = pd.read_csv('datasets_13720_18513_insurance_1.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "746203dd",
   "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>gender</th>\n",
       "      <th>bmi</th>\n",
       "      <th>children</th>\n",
       "      <th>smoker</th>\n",
       "      <th>region</th>\n",
       "      <th>charges</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>19</td>\n",
       "      <td>2</td>\n",
       "      <td>27.900</td>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>10</td>\n",
       "      <td>16884.92400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>18</td>\n",
       "      <td>8</td>\n",
       "      <td>33.770</td>\n",
       "      <td>1</td>\n",
       "      <td>22</td>\n",
       "      <td>20</td>\n",
       "      <td>1725.55230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>28</td>\n",
       "      <td>8</td>\n",
       "      <td>33.000</td>\n",
       "      <td>3</td>\n",
       "      <td>22</td>\n",
       "      <td>20</td>\n",
       "      <td>4449.46200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>33</td>\n",
       "      <td>8</td>\n",
       "      <td>22.705</td>\n",
       "      <td>0</td>\n",
       "      <td>22</td>\n",
       "      <td>30</td>\n",
       "      <td>21984.47061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>32</td>\n",
       "      <td>8</td>\n",
       "      <td>28.880</td>\n",
       "      <td>0</td>\n",
       "      <td>22</td>\n",
       "      <td>30</td>\n",
       "      <td>3866.85520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1333</th>\n",
       "      <td>50</td>\n",
       "      <td>8</td>\n",
       "      <td>30.970</td>\n",
       "      <td>3</td>\n",
       "      <td>22</td>\n",
       "      <td>30</td>\n",
       "      <td>10600.54830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1334</th>\n",
       "      <td>18</td>\n",
       "      <td>2</td>\n",
       "      <td>31.920</td>\n",
       "      <td>0</td>\n",
       "      <td>22</td>\n",
       "      <td>40</td>\n",
       "      <td>2205.98080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1335</th>\n",
       "      <td>18</td>\n",
       "      <td>2</td>\n",
       "      <td>36.850</td>\n",
       "      <td>0</td>\n",
       "      <td>22</td>\n",
       "      <td>20</td>\n",
       "      <td>1629.83350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1336</th>\n",
       "      <td>21</td>\n",
       "      <td>2</td>\n",
       "      <td>25.800</td>\n",
       "      <td>0</td>\n",
       "      <td>22</td>\n",
       "      <td>10</td>\n",
       "      <td>2007.94500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1337</th>\n",
       "      <td>61</td>\n",
       "      <td>2</td>\n",
       "      <td>29.070</td>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>30</td>\n",
       "      <td>29141.36030</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1338 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      age  gender     bmi  children  smoker  region      charges\n",
       "0      19       2  27.900         0      11      10  16884.92400\n",
       "1      18       8  33.770         1      22      20   1725.55230\n",
       "2      28       8  33.000         3      22      20   4449.46200\n",
       "3      33       8  22.705         0      22      30  21984.47061\n",
       "4      32       8  28.880         0      22      30   3866.85520\n",
       "...   ...     ...     ...       ...     ...     ...          ...\n",
       "1333   50       8  30.970         3      22      30  10600.54830\n",
       "1334   18       2  31.920         0      22      40   2205.98080\n",
       "1335   18       2  36.850         0      22      20   1629.83350\n",
       "1336   21       2  25.800         0      22      10   2007.94500\n",
       "1337   61       2  29.070         0      11      30  29141.36030\n",
       "\n",
       "[1338 rows x 7 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_num"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ec9b51c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df_num[['age','gender','bmi','children','smoker','region']].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3c219885",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1338, 6)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c8412f13",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = df_num['charges'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b401ce71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1338,)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08f2e330",
   "metadata": {},
   "source": [
    "# Split data into training and testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ab63ff62",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(936, 6)\n",
      "(402, 6)\n",
      "(936,)\n",
      "(402,)\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X,y, test_size = 0.3, random_state = 2)\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "print(y_train.shape)\n",
    "print(y_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "bc008906",
   "metadata": {},
   "outputs": [],
   "source": [
    "regressor = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "18c0ea28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regressor.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "236473b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_predict = regressor.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "28a8b058",
   "metadata": {},
   "outputs": [],
   "source": [
    "error = np.sum((y_test-y_predict)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "6626254a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(402,)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test.shape\n",
    "y_predict.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "278e0695",
   "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>Actual</th>\n",
       "      <th>Predicted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2395.17155</td>\n",
       "      <td>2026.089786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11286.53870</td>\n",
       "      <td>12050.784098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>9617.66245</td>\n",
       "      <td>10492.132951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1719.43630</td>\n",
       "      <td>2493.021730</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8891.13950</td>\n",
       "      <td>8319.412496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>397</th>\n",
       "      <td>23288.92840</td>\n",
       "      <td>4158.753605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>398</th>\n",
       "      <td>12479.70895</td>\n",
       "      <td>11431.257986</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399</th>\n",
       "      <td>40103.89000</td>\n",
       "      <td>33228.937538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>400</th>\n",
       "      <td>43578.93940</td>\n",
       "      <td>35935.918239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>401</th>\n",
       "      <td>5028.14660</td>\n",
       "      <td>7035.244026</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>402 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Actual     Predicted\n",
       "0     2395.17155   2026.089786\n",
       "1    11286.53870  12050.784098\n",
       "2     9617.66245  10492.132951\n",
       "3     1719.43630   2493.021730\n",
       "4     8891.13950   8319.412496\n",
       "..           ...           ...\n",
       "397  23288.92840   4158.753605\n",
       "398  12479.70895  11431.257986\n",
       "399  40103.89000  33228.937538\n",
       "400  43578.93940  35935.918239\n",
       "401   5028.14660   7035.244026\n",
       "\n",
       "[402 rows x 2 columns]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_result = pd.DataFrame({'Actual':y_test, 'Predicted': y_predict})\n",
    "df_result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "9a07f63d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Absolute Error: 4288.957513559822\n",
      "Mean Squared Error: 38010670.32913278\n",
      "Root Mean Squared Error: 6165.279420199281\n"
     ]
    }
   ],
   "source": [
    "print('Mean Absolute Error:', metrics.mean_absolute_error(y_test, y_predict))  \n",
    "print('Mean Squared Error:', metrics.mean_squared_error(y_test, y_predict))  \n",
    "print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(y_test, y_predict)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34f41749",
   "metadata": {},
   "source": [
    "# Lets test the model by asking some tough questions and give marks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "e97f15c0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Age of the Person being Insured\n",
      "55\n",
      "Age  55\n",
      "Gender of the Person being Insured\n",
      "2\n",
      "M?F  2\n",
      "BMI of the Person being Insured\n",
      "24\n",
      "bmi  24\n",
      "Number of childern for the person being Insured\n",
      "2\n",
      "Number of Childern  2\n",
      "Smoking Status of the Person being Insured\n",
      "11\n",
      "Y?N  11\n",
      "Region of the Person being Insured\n",
      "20\n",
      "Place  20\n"
     ]
    }
   ],
   "source": [
    "print('Age of the Person being Insured')\n",
    "X1 = input()\n",
    "print('Age  ' + X1)\n",
    "print('Gender of the Person being Insured')\n",
    "X2 = input()\n",
    "print('M?F  ' + X2)\n",
    "print('BMI of the Person being Insured')\n",
    "X3 = input()\n",
    "print('bmi  ' + X3)\n",
    "print('Number of childern for the person being Insured')\n",
    "X4 = input()\n",
    "print('Number of Childern  ' + X4)\n",
    "print('Smoking Status of the Person being Insured')\n",
    "X5 = input()\n",
    "print('Y?N  ' + X5)\n",
    "print('Region of the Person being Insured')\n",
    "X6 = input()\n",
    "print('Place  ' + X6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "00bd60c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_in = np.array([[X1], [X2], [X3], [X4], [X5],[X6]], dtype=float).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "a6b43de5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 6)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_in.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "5422f5dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_pred1 = regressor.predict(X_in)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "0ed9ed12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([33788.85083661])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_pred1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "c4c2e0b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[55.,  2., 24.,  2., 11., 20.]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_in"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32a82cf6",
   "metadata": {},
   "source": [
    "# Q_2: Build a dataset of CGPA vs Package for the last year placements of KLU. Feed your CGPA and predict the package. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "35cecb45",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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