{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.random.rand(100)\n",
    "y = X + 0.1 * np.random.randn(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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amrRw4UIFAgGtW7dOr776qldNNZZdHwYCAe3fv181NTWSxMElNuz6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\n/j+azSoqphjdPwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x23e35d74e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, y);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following the steps prescribed by Jake Vanderplas in his awesome text [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do). He has kindly provided all his codes on [github](https://github.com/jakevdp/PythonDataScienceHandbook) as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 1. Choose a class of model.\n",
    "\n",
    "In this case we are using `linear regression`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2. Choose model hyperparameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = LinearRegression(fit_intercept=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3. Arrange data into a features matrix and target vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = X.reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 1)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4. Fit the model to your data.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.97408915])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.022535905418693603"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you are statistically trained, you would normally dig into other information such as normality of the residuals and check for autocorrelation etc. You may also want to evaluation the parameters as well. Those are valid `statistical modelling` questions.\n",
    "\n",
    "Machine Learning focus is on `prediction`. You will not find these information with the `scikit-learn` package. Do take note of this key difference between statistics and machine learning.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 5. Predict labels for unknown data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.02040816,  0.04081633,  0.06122449,  0.08163265,\n",
       "        0.10204082,  0.12244898,  0.14285714,  0.16326531,  0.18367347,\n",
       "        0.20408163,  0.2244898 ,  0.24489796,  0.26530612,  0.28571429,\n",
       "        0.30612245,  0.32653061,  0.34693878,  0.36734694,  0.3877551 ,\n",
       "        0.40816327,  0.42857143,  0.44897959,  0.46938776,  0.48979592,\n",
       "        0.51020408,  0.53061224,  0.55102041,  0.57142857,  0.59183673,\n",
       "        0.6122449 ,  0.63265306,  0.65306122,  0.67346939,  0.69387755,\n",
       "        0.71428571,  0.73469388,  0.75510204,  0.7755102 ,  0.79591837,\n",
       "        0.81632653,  0.83673469,  0.85714286,  0.87755102,  0.89795918,\n",
       "        0.91836735,  0.93877551,  0.95918367,  0.97959184,  1.        ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_test = np.linspace(0, 1)\n",
    "x_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred = model.predict(x_test.reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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J39VebkYK/s9nVuDAJ5fRYjKjzxLcJhbeY/UtneOGyHVaFTavNmBD8Rz8r88v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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x23e375cde10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, y)\n",
    "plt.plot(x_test, y_pred);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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
}