{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Models\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example uses the only the first feature of the diabetes dataset, in order to illustrate a two-dimensional plot of this regression technique. The straight line can be seen in the plot, showing how linear regression attempts to draw a straight line that will best minimize the residual sum of squares between the observed responses in the dataset, and the responses predicted by the linear approximation.\n",
    "\n",
    "The coefficients, the residual sum of squares and the variance score are also calculated.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn import datasets, linear_model\n",
    "from sklearn.metrics import mean_squared_error, r2_score\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the diabetes dataset\n",
    "diabetes = datasets.load_diabetes()\n",
    "\n",
    "# Use only one feature\n",
    "diabetes_X = diabetes.data[:, np.newaxis, 2]\n",
    "\n",
    "# Split the data into training/testing sets\n",
    "diabetes_X_train = diabetes_X[:-20]\n",
    "diabetes_X_test = diabetes_X[-20:]\n",
    "\n",
    "# Split the targets into training/testing sets\n",
    "diabetes_y_train = diabetes.target[:-20]\n",
    "diabetes_y_test = diabetes.target[-20:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: \n",
      " [938.23786125]\n",
      "Mean squared error: 2548.07\n",
      "Variance score: 0.47\n"
     ]
    }
   ],
   "source": [
    "# Create linear regression object\n",
    "regr = linear_model.LinearRegression()\n",
    "\n",
    "# Train the model using the training sets\n",
    "regr.fit(diabetes_X_train, diabetes_y_train)\n",
    "\n",
    "# Make predictions using the testing set\n",
    "diabetes_y_pred = regr.predict(diabetes_X_test)\n",
    "\n",
    "# The coefficients\n",
    "print('Coefficients: \\n', regr.coef_)\n",
    "\n",
    "# The mean squared error\n",
    "print(\"Mean squared error: %.2f\"\n",
    "      % mean_squared_error(diabetes_y_test, diabetes_y_pred))\n",
    "\n",
    "# Explained variance score: 1 is perfect prediction\n",
    "print('Variance score: %.2f' % r2_score(diabetes_y_test, diabetes_y_pred))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot outputs\n",
    "plt.scatter(diabetes_X_test, diabetes_y_test,  color='black')\n",
    "plt.plot(diabetes_X_test, diabetes_y_pred, color='blue', linewidth=3)\n",
    "\n",
    "plt.xticks(())\n",
    "plt.yticks(())\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "* [Generalized Linear Models](http://scikit-learn.org/stable/modules/linear_model.html)\n",
    "* [Linear Regression Example](http://scikit-learn.org/stable/auto_examples/linear_model/plot_ols.html#sphx-glr-auto-examples-linear-model-plot-ols-py)"
   ]
  }
 ],
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