polynomial regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 171,
   "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>Position</th>\n",
       "      <th>Level</th>\n",
       "      <th>Salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Business Analyst</td>\n",
       "      <td>1</td>\n",
       "      <td>45000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Junior Consultant</td>\n",
       "      <td>2</td>\n",
       "      <td>50000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Senior Consultant</td>\n",
       "      <td>3</td>\n",
       "      <td>60000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Manager</td>\n",
       "      <td>4</td>\n",
       "      <td>80000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Country Manager</td>\n",
       "      <td>5</td>\n",
       "      <td>110000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Position  Level  Salary\n",
       "0   Business Analyst      1   45000\n",
       "1  Junior Consultant      2   50000\n",
       "2  Senior Consultant      3   60000\n",
       "3            Manager      4   80000\n",
       "4    Country Manager      5  110000"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df = pd.read_csv('position_salaries.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m=len(df)\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure()\n",
    "plt.scatter(df['Level'], df['Salary'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "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>00</th>\n",
       "      <th>Position</th>\n",
       "      <th>Level</th>\n",
       "      <th>Salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>Business Analyst</td>\n",
       "      <td>1</td>\n",
       "      <td>45000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>Junior Consultant</td>\n",
       "      <td>2</td>\n",
       "      <td>50000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>Senior Consultant</td>\n",
       "      <td>3</td>\n",
       "      <td>60000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>Manager</td>\n",
       "      <td>4</td>\n",
       "      <td>80000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>Country Manager</td>\n",
       "      <td>5</td>\n",
       "      <td>110000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   00           Position  Level  Salary\n",
       "0   1   Business Analyst      1   45000\n",
       "1   1  Junior Consultant      2   50000\n",
       "2   1  Senior Consultant      3   60000\n",
       "3   1            Manager      4   80000\n",
       "4   1    Country Manager      5  110000"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.concat([pd.Series(1, index=df.index, name='00'), df], axis=1)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df.drop(columns='Position')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     45000\n",
       "1     50000\n",
       "2     60000\n",
       "3     80000\n",
       "4    110000\n",
       "Name: Salary, dtype: int64"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = df['Salary']\n",
    "y[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df.drop(columns = 'Salary')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\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>00</th>\n",
       "      <th>Level</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   00  Level\n",
       "0   1      1\n",
       "1   1      2\n",
       "2   1      3\n",
       "3   1      4\n",
       "4   1      5"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "X['Level1'] = X['Level']**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [],
   "source": [
    "X['Level2'] = X['Level']**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "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>00</th>\n",
       "      <th>Level</th>\n",
       "      <th>Level1</th>\n",
       "      <th>Level2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>16</td>\n",
       "      <td>64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>25</td>\n",
       "      <td>125</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   00  Level  Level1  Level2\n",
       "0   1      1       1       1\n",
       "1   1      2       4       8\n",
       "2   1      3       9      27\n",
       "3   1      4      16      64\n",
       "4   1      5      25     125"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = X/X.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0])"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "theta = np.array([0]*len(X.columns))\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hypothesis(X, theta):\n",
    "    y1 = theta*X\n",
    "    return np.sum(y1, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(X, y, theta):\n",
    "    y1 = hypothesis(X, theta)\n",
    "    return sum(np.sqrt((y1-y)**2))/(2*m) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradientDescent(X, y, theta, alpha, epoch):\n",
    "    J=[]\n",
    "    k=0\n",
    "    while k < epoch:\n",
    "        y1 = hypothesis(X, theta)\n",
    "        for c in range(0, len(X.columns)):\n",
    "            theta[c] = theta[c] - alpha*sum((y1-y)* X.iloc[:, c])/m\n",
    "        j = cost(X, y, theta)\n",
    "        J.append(j)\n",
    "        k += 1\n",
    "    return J, j, theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.array([0.0]*len(X.columns))\n",
    "J, j, theta = gradientDescent(X, y, theta, 0.05, 700)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-38494.26294331,  66878.12378747, 287369.29171661, 460744.26580885])"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat = theta*X\n",
    "y_hat = np.sum(y_hat, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure()\n",
    "plt.scatter(x=X['Level'],y= y)          \n",
    "plt.scatter(x=X['Level'], y=y_hat)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}