simple _linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import pandas as pd\n",
    "from sklearn import linear_model\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Creatig independent varaiable \n",
    "x_values = np.array(range(10)).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [1],\n",
       "       [2],\n",
       "       [3],\n",
       "       [4],\n",
       "       [5],\n",
       "       [6],\n",
       "       [7],\n",
       "       [8],\n",
       "       [9]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Creatig dependent varaiable \n",
    "y_values = np.array([k**0.5 for k in range(10)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  1.        ,  1.41421356,  1.73205081,  2.        ,\n",
       "        2.23606798,  2.44948974,  2.64575131,  2.82842712,  3.        ])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#LinearRegression model\n",
    "lr = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Train LinearRegression\n",
    "lr.fit(x_values, y_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Predict value of Y \n",
    "y_predicted = lr.predict(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.54210217])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_predicted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
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mtwOH3f00M7sR+DHwpbYoeP6aAv73L1vYU1JBbIwRG2NtcRkRkYgWSs99CpDr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\nhRTuIiJRSOEuIhKFFO4iIlHo/wEMNnANGgCfrwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c11db3b390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#visualize actual data\n",
    "plt.scatter(x_values, y_values)\n",
    "plt.plot(x_values, y_values)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZPUAmEAO86O5rzOznQJa7zwPuNbMrgWpgL3BHM84sIiJNMHcPZMPp6emelZUV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\nEoUU7iIiUUjhLiIShf4HsRUyhl4bquoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c11dbb5eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#visualize results\n",
    "plt.scatter(x_values, y_values)\n",
    "plt.plot(x_values, lr.predict(x_values))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$y = \\beta_0 + \\beta_1x_1 + \\beta_2x_2 + ... + \\beta_nx_n$\n",
    "\n",
    "- $y$ is the response\n",
    "- $\\beta_0$ is the intercept\n",
    "- $\\beta_1$ is the coefficient for $x_1$ (the first feature)\n",
    "- $\\beta_n$ is the coefficient for $x_n$ (the nth feature)\n",
    "\n",
    "The $\\beta$ values are called the **model coefficients**:\n",
    "\n",
    "- These values are estimated (or \"learned\") during the model fitting process using the **least squares criterion**.\n",
    "- Specifically, we are find the line (mathematically) which minimizes the **sum of squared residuals** (or \"sum of squared errors\").\n",
    "- And once we've learned these coefficients, we can use the model to predict the response.\n",
    "\n",
    "![Estimating coefficients](data/images/estimating_coefficients.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.612098323517\n",
      "[ 0.29300038]\n"
     ]
    }
   ],
   "source": [
    "print(lr.intercept_)\n",
    "print(lr.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}