Linear Regression in scikit learn

linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Regression in scikit learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ":0: FutureWarning: IPython widgets are experimental and may change in the future.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# use seaborn for plot defaults\n",
    "# this can be safely commented out\n",
    "import seaborn; seaborn.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Every (scikit-learn) algorithm is imported into Python as an 'Estimator' Object. Linear Regression is implemented thusly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8 9]\n",
      "[[0]\n",
      " [1]\n",
      " [2]\n",
      " [3]\n",
      " [4]\n",
      " [5]\n",
      " [6]\n",
      " [7]\n",
      " [8]\n",
      " [9]]\n",
      "[0 1 2 3 4 5 6 7 8 9]\n",
      "[ -0.48357077   5.69132151   4.76155731   3.38485072  15.17076687\n",
      "  18.17068478  12.10393592  19.16282635  28.34737193  26.28719978]\n"
     ]
    }
   ],
   "source": [
    "# create / get data\n",
    "x = np.array(range(10))\n",
    "print x\n",
    "X = x.reshape(10,1)\n",
    "print X\n",
    "print X.squeeze()\n",
    "np.random.seed(42)\n",
    "y = 3*X.squeeze() +2 - 5*np.random.randn(10)\n",
    "print y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb7fe3cc850>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb834342450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the data\n",
    "plt.plot(X.squeeze(),y,'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create a linear model (OLS Model)\n",
    "linear_model = LinearRegression(normalize=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=True)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the OLS model to the data\n",
    "linear_model.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.395563921381\n",
      "[ 3.03450186]\n",
      "117.518530099\n"
     ]
    }
   ],
   "source": [
    "# print out the parameters of the fit model\n",
    "print linear_model.intercept_\n",
    "print linear_model.coef_\n",
    "print linear_model.residues_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-5, 10)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WEewXzOPWFOaMnO0RxTARcV8KaZHr6LR39RTDHIaDO6NnkDJpOYMDdKUtEXE9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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb81c0b5d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Data used for predictions\n",
    "x_fit = np.linspace(-5,10,500)[:,np.newaxis]\n",
    "y_fit = linear_model.predict(x_fit)\n",
    "plt.plot(X,y,'o')\n",
    "plt.plot(x_fit,y_fit)\n",
    "plt.xlim(-5,10)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}