polynomial regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "     y =mx+c is linear equation and trying to predict the data on linear model comes under linear regression analysis\n",
    "\n",
    "    but what the trend is not linear , which happens in most of the cases.\n",
    "    For that we will work on polynomial regression\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "first order polynomial : y =mx+c\n",
    "\n",
    "second order polynomial: y =ax2+bx+c\n",
    "\n",
    "and so on "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np# importing numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "customer=np.random.randn(1,1000)# generating random data in normal distribution for getting a perfect fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import seaborn as sns # seaborn for plotting the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f3045952940>"
      ]
     },
     "execution_count": 41,
     "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": [
    "sns.distplot(customer.T) # histogram plot  to see the data distribution "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "purchases=(customer*50)**3+(customer*340)**2+(customer*889)*3+190  \n",
    "# generating a polynomial \n",
    "#dependent on customer data above so that we get the output as perfect degree three polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f30458dbe80>"
      ]
     },
     "execution_count": 40,
     "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": [
    "sns.distplot(purchases.T,bins=10,kde=1,color='r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "df=pd.DataFrame(customer.T,columns=['customers'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['purchases']=purchases.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "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>customers</th>\n",
       "      <th>purchases</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-1.206452</td>\n",
       "      <td>-54271.685527</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.380875</td>\n",
       "      <td>9037.320006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.605933</td>\n",
       "      <td>13208.170344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.044435</td>\n",
       "      <td>547.723563</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.019551</td>\n",
       "      <td>-14840.621440</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   customers     purchases\n",
       "0  -1.206452 -54271.685527\n",
       "1  -0.380875   9037.320006\n",
       "2  -0.605933  13208.170344\n",
       "3   0.044435    547.723563\n",
       "4  -1.019551 -14840.621440"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f3044c77860>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/9L0A+eS08uk3uP7cuYcsQFhbEae2ooyG6gTjqys1pHecFdWTMrMvAt8H2oDvAR8AvuruPx7G2ERE8rq70+zt7qEsDgSQCpwgnG7IcV7f2cHNT7zODeedxuUFSWmgYbzcbBArn36DG5bM5aqHN3Ljui35BQirymPEYsaEqoTecyqhYof7Pufu3zGzTwD1wEXAvYCSlIgMidz7SQZ0p7NDdWUxo7zMIMge4+6k0s7ejh6u6FOF94Pn3uGvPnEy8Ri9ktJAw3hBOG3p7vYkDXUVPPT5BaQzTqIsO32RElM0FJukcgX/fwTc6+6bzGzUvgRgZouA7wBx4Hvu/u0ShyRjQDKZpiOdJp12ArJ/6XoCJxM45fEYleVGW3eGqvI46SC7HEQ8LH3OuINDZSKGO+BkjwnPT8RjxGNGd0+GWMxIxGO4O93pgPKYUVEeo6snIGbgDhl3ymIxahJGe/JgwqhKxEj2HLy3GQQO5eHnnoyTcSduRiy3L270ZDy/nQmyiSAInLQ7lWUx8GzPKBM4ZvDNxzbz4827si/QXng6tZVx3t2f5KqHN3Lt2XO47rHNh1ThXXv2HK5es5F/Wr6gV1Iq7CkVvpR7QlVZfsmMynIjHjPqKhJ6vyliik1SG8zsx8As4GtmVkf+/21GFzOLA7cAfwg0A8+b2Vp331zayGQk6u5O09KVyn/JVydi9IRJCLKJJBM4VWUxMg4ZD+hMZehJBxzoTvf6Yl25dB6bt+9jVkMt//2hl3pNbFqViHPrU1v5n2fPwYFkT4aW9lSv82/6zGn83Y9+xe72JDcsmUt1Is431m5md3uSWy88nf/30nY+evIUrl6TPefzH5nJ2e9vzA+d5b7c//GJ1/IJ5Ppz53LPz97ikjNmMbE2wY3rtvTa98yWnfzxadP47pOvc/GHZ3H1mo001FbwlUUnc9XD2c/fOGcOnalMr1j//rzT8u8nXX7/C/xg+YL8/vFV5f0O3+XaO5M93Hrh6fme1u72JJNqE9x36XwCh0RZjNqKbLKdUltBRYXqx6Ks2P7spcBXgQ+6eyeQAC4ZtqhKaz6w1d3fdPcU8ACwuMQxSUQFgdPa0c1vWjvZsa+T37R28uu9HWxv7WTXgS7eaOnIP8D/7Kpn2b4vSWtXip0HunlrTwfnr3qWLz3wS97Y08F5t/+cTb9pY3trN7vaDiYYyH4JX3bfBj48uyGfoHLtVz28kdaOHs6dN51U2ulJO9tbuw85/78/9BKXLXxf/py9HT357Svuf4ElTTPyCQpgSdOMXs92cjMunDtven776jUbOXfe9Pzkqn33LWmawRX3v8C586bnr33ZwvflY7ts4fvY29FzSKxf/ueX8u8nNbd2Ebjn9+eG7wo11lfl23fsTzKuqowHVyzgJ1ct5MEVC6ivTmBmVJTFmFSVLYCYMq5KCWoEKPbfkANzgLOBvwVqgMrhCqrEpgHbCrabgQ8VHmBmK4AVADNmzDh+kUlJBYHT2pWkO5Ud/qooixE4JNMZ9rSlMIMvPfjLfG/glj87nVueev2QRHP3JfPZ25Hk2kdfobm1i2vPntOrl5DTX28hE3i/7dWJONXEyY1UDVQskLt+4Tm57XjMep3Td7vvNQq3+16v7zULez99Pw/0u+b25V6gzQ3h5arwckmvsEe3cuk8GmoTxGOWH1asDwsfJvX/r1Uirtie1K3A7wEXhNttZIfExiR3X+XuTe7e1NDQUOpwZJgEgdPS3s274ewEe9q7ae/OsGN/N9v2drLzQDefuf3n/MGNP6E9mc4nKMh+yV75Ty/kexY5za1dxKx3Ein80t7X1UNnKkNnKtNvbyEes37bO1MZ9nX1EHj2uc9A5+/r6jnknNx2JvBe5/Td7nuNwu2+1+t7zcLeT9/Ph4s190wqHWSyc+PVV/Hitn3c87O3uP8vPsQzX8n2lN47qZpv/MkpnDS+goa6SibVZXtKDXWVKoAY4Yr9t/chd78S6AZw91ayQ36j0Xag8JulMWyTUS4InN1tSXa3ZYfvfrO/k5aOFG/t6eBv/3UTO/YnufB7v2DJyp/z1R++nF0vqLYCGLjnkputICdXVVb4xVz4pb3y6Teorylncl0i/6WcO2/l0nn87PXd3PSZ0w6Z2LS+ppw1G7aRKMtWw02rrzzk/Js+cxorn34jf86EmvL89q0Xns7D63/d6z2hh9f/mtuW9p5E9bal81izYVt++/pz57JmwzZuWDKXafWVh+x7eP2vufXC01mzYVv+2rlChtznCTXlh8R6+0Xz+N1pJ/DgigVMGVdBTXkZ75tUwwMrFvDMVQv5m3NO5cTaCmZMqGFafTVTx1dzUn01E2o0setoU9Ty8Wb2C+DDwPPufrqZNQA/dvcPDHeAx5uZlQGvAWeRTU7PA3/m7pv6O17Lx49sQeDs706S6slWwgWBgxnffGwT586bTiIe49pHXzmkogyyX6bXnj2Hz9+7gdsvmtfv/tWfm8+yu57rVfxQHofuniBfLFBYSNDc2sXH50zmG+ecQtzskOq+9u4MlWF1XzoT5Cc2PVx1XxCePxzVfTGDzEDVfTEIgoLqvnD7cNV9uVhPqDQqyvR+0mg21MvH3ww8Akw2s28BS4D/eQzxRZa7p83sC8A6siXodw2UoGRkSibT7OnMVtyVx4y0O9vDYoLC6rLqRJzOVOaIFWXQf5nz9efO5cHn3uH+v/gQBsRiRk2uui8c3XpgxQKCIPtF/dDnF9CTycZUlYgxrvLQ9Ygm1ByPP6HexlUf/3uK5BSVpNz9fjPbQLZ3YcCn3P3VYY2shNz9R8CPSh2HDJ0gcPZ1pYibs62190J2qz83v9/qsu//+QfZ057q9Xykv0XuoPCF0N8jEwTELNuzmDlxFuVxI3D0gqjIIBQ7LdL7gLfc/RYzWwj8oZntcPd9wxqdyBAIAuftlg7aunsYX504ZB63vR2pfntJ7ck09eHzku//9K1DKspuv2geDTUJnrlqIfGYMbm2QvO6iQyxYof71gBNZvZbwO3AWuCfyM5AIRI5qVSa3R0HX6INPDuVTk/m0BLulo5Uv72kXW1J1mzYxjfOOYX/9SenEDd4cMUCMoFTFo8xuVY9I5HhVmySCsJnNX8KfNfd/9HMXhzOwEQGK5VKs2V3R6+ZElYuncf46nJ2tSUPSUhrNmzrNUNBrpdUX13OqSedwqTqhNYMEimRYv/m9ZjZBcAy4E/CtvLDHC9y3ASB09KRIggCMg7pTMCetiQNtRU0t3b1eon2tqe3HjJs94UzZxM34wfLF+CerS5LlBnjKlVdJlJqxSapS4DLgG+5+1tmNovsLOgiJRMEzoHuFNtbu/nOE6/l54YrrK67cd0WXty2j+bWLirLYyz/yHu54z/f5Nqz5zCxJkFDXQVV5THAmFR7aDWdiJRWUe9JycD0nlRp9PRk2NWeJHC44I5nj/geU2N9FQ+tWEA8ZvlJXeMxoyoRZ3yVZr4WOd6G9D0pM5sN/G+y8/fl5+xz9/cOOkKRQUom0+zuTJFKB5THYzTUVhz2PabcTAmTavRsSWSkKfZv7PeBrwM3AX9AdvhPg/Vy3PX0ZHhtT++iiBuWzCVw77dCb1p9FQ+uWECDEpTIiFRsoqly9yfIDg++4+7fAP54+MIS6S03r96u9uQhy0dc9fBGzKzXvHON9VXcsayJk8ZVMa2+WglKZIQq9m9u0sxiwOvhlEHbgdrhC0skKzdTxI593Xz+vg2s/tz8fof1po6rJGbZaYYMSJTFmVijZ00iI12xSeqLQDXwl8B1wJnAxcMVlEg6HbCrPUlPJjvF0HeeeC2/nlJ/w3rxmFFVHqO+WhV6IqNJsXP3PR9+bGf0rsgrEdHTk+FXu9p7PXe6/ty57G5Lccczbx7y4u1tS+fRUJ3QKqsio1Cx1X2/DVwFvKfwHHc/c5jikjGopyfD7o4Ugfshz52uXrMxX04OcPcl8ymPG2WaM09kVCu2cOKfgRfILs9xVcGPyJDI9Z4+c/vPSaWDwy4g+LM3W+jJBEyvr2ZafbUSlMgoVuz4SNrdbxvWSGRMyk1p1JlK56cyGui505QTKnn6rxZSXRFnUo2ePYmMBYdNUmY2Ifz4r2Z2BdmFD5O5/e6+dxhjk1EuCJwtO9tYvnp9r2dP//7yjn6fO9VVxjmhUhV7ImPJYadFMrO3ACe70GFfrhknNC3SYAWB8+6Bbj5z+8/7ncroic07WfH776M8bsRjxhQ9dxIZVYZkWiR3nzV0IYlk5XpQHcn0gFMZ/ezNFpZ9eCb11RUqKxcZw4oqnDCzK81sfMF2fTj8J1K03KwRzfs6eXd/N909mfwMETmFUxmdPLmWibWVSlAiY1ix1X3LC5eKd/dWYPnwhCSjUU9Phm2tnbzT0sGrO9r4wXPvUFtZxt+fd9qAUxlpeE9Eiq3ui5uZefgAy8ziQGL4wpLRJJ0O2LKrncv6vJx761NbueSMWfm1nU4aX8WJJ6jnJCIHFduTWgc8aGZnmdlZwA+Afx++sGQ02dWezCcoOPhy7rnzphMz47rHNlNTUaYEJSKHKLYn9RVgBXB5uP048L1hiUhGjdw7UD2ZgV/OnTqukkeuOEOTwYpIv46YpMKhvdXufiGwcvhDktGg8B2oa8+e0+/LuQ11FUwdV6XkJCIDOuJwn7tngPeYmZ5BSdFaOlL5l3RXPv3GIWs9rVw6j5M0vCciR1DscN+bwE/NbC3QkWt0938YlqhkxEulM/me04vb9nHjui1ce/YcfufEOsrjMSbXVlBWpsWdReTwiv2WeAN4LDy+ruBHpF+Jsnivd6Be3LaP6x7bTHWijJPGVylBiUhRil1P6m+GOxAZ2XJFEql0hkRZnPqqcu5Y1tRrXr47ljXlZzIXESlGsetJPUV2Dr9eBruelJndAPwJkCLbS7sk97KwmX0NuBTIAH/p7uvC9kXAd4A48D13/3bYPgt4AJgIbAAucveUmVUAq4F5QAvwWXd/ezD3kMPrb6LYO5Y1MbuhlkeuOCOfuFTBJyJHq9gxl7/i4BpS1wK/BI5lVtXHgVPdfS7wGvA1ADObA5wPnAIsAm41s3hYYXgL8ElgDnBBeCzA9cBN7v5bQCvZ5EP4z9aw/abwuMHeQ/rRd5qjhtoKIFtevnz1elq7emioq2BafTUNdZp/T0SOXrHDfRv6NP3UzJ4b7E3d/ccFm88CS8LPi4EH3D0JvGVmW4H54b6t7v4mgJk9ACw2s1eBM4E/C4+5B/gGcFt4rW+E7Q8D3zUzO9p7AJsH+3uOZgMts3Hjui28uG0fza1dpNKZUocpIiNcsRPMTij4mRQOi40bohg+B/xb+HkasK1gX3PYNlD7RGCfu6f7tPe6Vrh/f3j80d5D+lFYYg4HZ5G4bOH7gGyZeaJMc++JyLEptgR9AwefSaWBtzk4rNYvM/sP4MR+dl3j7o+Gx1wTXu/+IuOIBDNbQXYGDmbMmFHiaEqjsMQ8J7fMhookRGSoFJuk5gBXAP+VbLL6T47wTMrdP3a4/Wb258DZwFm5iWuB7cD0gsMawzYGaG8BxptZWdhbKjw+d61mMysj2/NrGcQ9+vvdVgGrILvo4eF+z9EqV2LedxaJxvoqTXMkIkOm2MKJe4D/AtwM/CPZpHXvYG8aDhd+BTjH3TsLdq0FzjezirBqbzbwHPA8MNvMZoUzX5wPrA2T21McfKZ1MfBowbUuDj8vAZ4Mjz+qewz2dxztJtYkuGNZ0yHLbEwdV6UiCREZMsX2pE5198JKt6fM7FgKCr4LVACPZ2sZeNbdL3P3TWb2ENlihTRwZTgtE2b2BbKzsceBu9x9U3itq4EHzOybwIvAnWH7ncC9YWHEXrJJh0HeQ/qIxYyTp9SpxFxEhpUdHGk7zEFm9wHfdfdnw+0Pkf1yXzbM8UVeU1OTr19/LNX4IiJjj5ltcPemIx1XbE9qHvAzM/t1uD0D2GJmLwMevu8ko1DfmSTUWxKR46nYJLVoWKOQSBpoJomTp9QpUYnIcVFU4YS7v3O4n+EOUkqjv3ehlq9eT0tHqsSRichYoamoZUADvQulmSRE5HhRkpIB9V1uAzSThIgcX0pSMqCB3oXSTBIicrwUWzghY5DehRKRUlOSksOKxYyGuopShyEiY5SG+0REJLKBzTPHAAAMWElEQVSUpEREJLKUpEREJLKUpEREJLKUpEREJLKUpEREJLKUpEREJLKUpEREJLL0Mu8Yo/WhRGQkUZIaQ7Q+lIiMNBruG0O0PpSIjDRKUmOI1ocSkZFGSWoM0fpQIjLSKEmNIVofSkRGGhVOjCFaH0pERholqTFG60OJyEii4T4REYksJSkREYksJSkREYksJSkREYksJSkREYmskiYpM/uymbmZTQq3zcxuNrOtZrbRzE4vOPZiM3s9/Lm4oH2emb0cnnOzmVnYPsHMHg+Pf9zM6gd7DxERKY2SJSkzmw58HPh1QfMngdnhzwrgtvDYCcDXgQ8B84Gv55JOeMzygvMWhe1fBZ5w99nAE+H2YO8hIiIlUMqe1E3AVwAvaFsMrPasZ4HxZjYV+ATwuLvvdfdW4HFgUbjvBHd/1t0dWA18quBa94Sf7+nTXvQ9hul3FxGRIpQkSZnZYmC7u7/UZ9c0YFvBdnPYdrj25n7aAaa4+47w87vAlEHeQ0RESmTYZpwws/8ATuxn1zXAX5Md6jsu3N3NzI98ZHHMbAXZoUJmzJgxVJcdNC1kKCKj1bAlKXf/WH/tZva7wCzgpbDGoRF4wczmA9uB6QWHN4Zt24GFfdqfDtsb+zkeYKeZTXX3HeFw3q6w/Wjv0d/vtgpYBdDU1DRkyW8wtJChiIxmx324z91fdvfJ7j7T3WeSHVY73d3fBdYCy8IKvAXA/nDIbh3wcTOrD4sZPg6sC/cdMLMFYVXfMuDR8FZrgVyF3sV92ou+x/D+aRw7LWQoIqNZ1CaY/RHwR8BWoBO4BMDd95rZdcDz4XF/6+57w89XAHcDVcC/hT8A3wYeMrNLgXeAzxzDPSJLCxmKyGhW8iQV9qZynx24coDj7gLu6qd9PXBqP+0twFn9tB/1PaIst5BhYaLSQoYiMlpoxokRTgsZishoVvKelBwbLWQoIqOZktQooIUMRWS00nCfiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhElpKUiIhEVsmSlJn9NzP7lZltMrP/U9D+NTPbamZbzOwTBe2LwratZvbVgvZZZvaLsP1BM0uE7RXh9tZw/8zB3kNEREqjJEnKzP4AWAyc5u6nADeG7XOA84FTgEXArWYWN7M4cAvwSWAOcEF4LMD1wE3u/ltAK3Bp2H4p0Bq23xQeN9h7iIhICZSqJ3U58G13TwK4+66wfTHwgLsn3f0tYCswP/zZ6u5vunsKeABYbGYGnAk8HJ5/D/CpgmvdE35+GDgrPP6o7jFMv7+IiBShVEnqt4GPhMNwPzGzD4bt04BtBcc1h20DtU8E9rl7uk97r2uF+/eHxx/tPQ5hZivMbL2Zrd+9e3fRv7SIiBydsuG6sJn9B3BiP7uuCe87AVgAfBB4yMzeO1yxDDV3XwWsAmhqavLBXCMInJaOFKl0hkRZnIk1CWIxG9I4RURGumFLUu7+sYH2mdnlwA/d3YHnzCwAJgHbgekFhzaGbQzQ3gKMN7OysLdUeHzuWs1mVgaMC48/2nsMuSBwtuxsY/nq9TS3dtFYX8Udy5o4eUqdEpWISIFSDff9C/AHAGb220AC2AOsBc4PK/NmAbOB54DngdlhJV+CbOHD2jDJPQUsCa97MfBo+HltuE24/8nw+KO6x3D88i0dqXyCAmhu7WL56vW0dKSG43YiIiPWsPWkjuAu4C4zewVIAReHCWSTmT0EbAbSwJXungEwsy8A64A4cJe7bwqvdTXwgJl9E3gRuDNsvxO418y2AnvJJh3cfTD3GFKpdCafoHKaW7tIpTPDcTsRkRHLsrlBBqupqcnXr19/VOfsbkvy6Vt/2itRNdZX8cgVZ9BQVzHUIYqIRI6ZbXD3piMdpxknSmBiTYI7ljXRWF8FkH8mNbEmUeLIRESipVTDfWNaLGacPKWOR644Q9V9IiKHoSRVIrGYaWhPROQINNwnIiKRpSQlIiKRpSQlIiKRpSQlIiKRpSQlIiKRpZd5j5GZ7QbeOYZLTCI7JdRIMZLiHUmxwsiKdyTFCop3OA021ve4e8ORDlKSKjEzW1/MW9dRMZLiHUmxwsiKdyTFCop3OA13rBruExGRyFKSEhGRyFKSKr1VpQ7gKI2keEdSrDCy4h1JsYLiHU7DGqueSYmISGSpJyUiIpGlJBUhZvZlM3Mzm1TqWAZiZteZ2UYz+6WZ/djMTip1TIdjZjeY2a/CmB8xs/GljulwzOw8M9tkZoGZRbK6y8wWmdkWM9tqZl8tdTyHY2Z3mdmucIHVSDOz6Wb2lJltDv8b+GKpYzocM6s0s+fM7KUw3r8ZjvsoSUWEmU0HPg78utSxHMEN7j7X3d8PPAb8r1IHdASPA6e6+1zgNeBrJY7nSF4B/hR4ptSB9MfM4sAtwCeBOcAFZjantFEd1t3AolIHUaQ08GV3nwMsAK6M+J9tEjjT3U8D3g8sMrMFQ30TJanouAn4ChDph4TufqBgs4box/tjd0+Hm88CjaWM50jc/VV331LqOA5jPrDV3d909xTwALC4xDENyN2fAfaWOo5iuPsOd38h/NwGvApMK21UA/Os9nCzPPwZ8u8DJakIMLPFwHZ3f6nUsRTDzL5lZtuAC4l+T6rQ54B/K3UQI9w0YFvBdjMR/iIdqcxsJvAB4BeljeTwzCxuZr8EdgGPu/uQx6tFD48TM/sP4MR+dl0D/DXZob5IOFys7v6ou18DXGNmXwO+AHz9uAbYx5HiDY+5huxwyv3HM7b+FBOvjF1mVgusAb7UZ+Qictw9A7w/fNb7iJmd6u5D+vxPSeo4cfeP9dduZr8LzAJeMjPIDke9YGbz3f3d4xhi3kCx9uN+4EeUOEkdKV4z+3PgbOAsj8A7F0fx5xtF24HpBduNYZsMATMrJ5ug7nf3H5Y6nmK5+z4ze4rs878hTVIa7isxd3/Z3Se7+0x3n0l2+OT0UiWoIzGz2QWbi4FflSqWYpjZIrLP+s5x985SxzMKPA/MNrNZZpYAzgfWljimUcGy/5d6J/Cqu/9DqeM5EjNryFXLmlkV8IcMw/eBkpQcrW+b2StmtpHsEGWky2SB7wJ1wONh2fzKUgd0OGb2aTNrBn4P+H9mtq7UMRUKi1C+AKwj+2D/IXffVNqoBmZmPwB+DpxsZs1mdmmpYzqMM4CLgDPD/1Z/aWZ/VOqgDmMq8FT4XfA82WdSjw31TTTjhIiIRJZ6UiIiEllKUiIiEllKUiIiEllKUiIiEllKUiIiEllKUiIjlJn9daljEBluKkEXGaHMrN3da4/j/coKJusVOS7UkxIpETNbFq5z9ZKZ3Wtmd5vZkoL97eE/p5rZM+HLna+Y2UfM7NtAVdh2f3jc/wj3v2JmXwrbZobrad1tZq+Z2f1m9jEz+6mZvW5m88PjasK1l54zsxfDSY8xsz83s7Vm9iTwRH+xHO8/Nxlb1JMSKQEzOwV4BPiwu+8xswnAPwCPufvD4THt7l5rZl8GKt39W+F6TtXu3lbYkzKzeWTXTloAGNnZs5cCrcBWsjNqbyI7M8BLwKXAOcAl7v4pM/s7YLO73xdOdfNceM55wDeBue6+d6BYhv0PTMYsTTArUhpnAv/s7nsAwgQw0LHPA3eFk4/+i7v/sp9j/ivwiLt3AJjZD4GPkJ1X7y13fzls3wQ84e5uZi8DM8PzPw6cY2Z/FW5XAjPCz4+7e25NpmJiERkyGu4TiY404d9JM4sBCcgv3PdRsrON321my47yusmCz0HBdsDB/1E14Fx3f3/4M8PdXw33deROHoJYRI6KkpRIaTwJnGdmEwHC4b63gXnh/nPIrnSKmb0H2OnudwDfA04Pj+kJezQA/wl8ysyqzawG+HTYVqx1wH8LZ+LGzD7Q30GHiUVkWGi4T6QE3H2TmX0L+ImZZYAXgauBR83sJeDfOdiDWQhcZWY9QDuQ672sAjaa2QvufqGZ3U32WRLA99z9xXCF12JcB/zf8Hox4C2ya3D1NVAsIsNChRMiIhJZGu4TEZHIUpISEZHIUpISEZHIUpISEZHIUpISEZHIUpISEZHIUpISEZHIUpISEZHI+v+o7IvZdKE0RgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(df.customers,df.purchases)# degree three equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "#importing polynomial features to fit out x data into polynomial function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "polynomial_features= PolynomialFeatures(degree=3)\n",
    "x_poly = polynomial_features.fit_transform(df[['customers']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "model = LinearRegression()\n",
    "model.fit(x_poly, df[['purchases']])\n",
    "y_poly_pred = model.predict(x_poly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f303f3f0a90>]"
      ]
     },
     "execution_count": 83,
     "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['customers'], df['purchases'], s=10)\n",
    "plt.plot(df['customers'], y_poly_pred, color='r')\n",
    "\n",
    "\n",
    "#this is exact fit data because we used 3 degree and our generated purchaes data is also degree three/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-54271.59868208]])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(polynomial_features.fit_transform([[-1.206452]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "score=model.score(x_poly,y_poly_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score# score is 1 giving perfect fit equation has been evaluated by the algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Shashank Shawak"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
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