{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# scikit-learn-linear-reg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Credits: Forked from [PyCon 2015 Scikit-learn Tutorial](https://github.com/jakevdp/sklearn_pycon2015) by Jake VanderPlas\n",
    "\n",
    "* Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn; \n",
    "from sklearn.linear_model import LinearRegression\n",
    "import pylab as pl\n",
    "\n",
    "seaborn.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression\n",
    "\n",
    "Linear Regression is a supervised learning algorithm that models the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variable) denoted X.\n",
    "\n",
    "Generate some data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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W+tna3JhxRcCy0fGyNC5cvppr27sZZm+LtWvbuzl/6UqefMoGA0A7gpelcbPTvd3u9Rt5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\naEjwAkBDghcAGhK8ANDQ/wN7enEGMBOV0AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11006e550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create some simple data\n",
    "import numpy as np\n",
    "np.random.seed(0)\n",
    "X = np.random.random(size=(20, 1))\n",
    "y = 3 * X.squeeze() + 2 + np.random.randn(20)\n",
    "\n",
    "plt.plot(X.squeeze(), y, 'o');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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btjTjtvjUxsWnNvZG1c1q1iy8J3Nmx1Z7tu9MvwtAXU0dkeBxYlaYY119NNU1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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x103f774d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = LinearRegression()\n",
    "model.fit(X, y)\n",
    "\n",
    "# Plot the data and the model prediction\n",
    "X_fit = np.linspace(0, 1, 100)[:, np.newaxis]\n",
    "y_fit = model.predict(X_fit)\n",
    "\n",
    "plt.plot(X.squeeze(), y, 'o')\n",
    "plt.plot(X_fit.squeeze(), y_fit);"
   ]
  }
 ],
 "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": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}