PCA_LinearRegression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from sklearn.decomposition import PCA\n",
    "%matplotlib inline\n",
    "\n",
    "datum = np.loadtxt(\"women.tsv\", delimiter=\"\\t\", usecols=(1, 2), skiprows=1)\n",
    "weights = np.transpose(datum)[0]\n",
    "heights = np.transpose(datum)[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-22.82135677],\n",
       "       [-20.62293037],\n",
       "       [-17.46342139],\n",
       "       [-14.3039124 ],\n",
       "       [-11.14440342],\n",
       "       [ -7.98489444],\n",
       "       [ -4.82538545],\n",
       "       [ -1.66587647],\n",
       "       [  2.45471509],\n",
       "       [  5.61422407],\n",
       "       [  9.73481564],\n",
       "       [ 13.8554072 ],\n",
       "       [ 17.97599876],\n",
       "       [ 23.05767291],\n",
       "       [ 28.13934705]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components = 1)\n",
    "pca.fit_transform(np.transpose(np.array([weights, heights])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  18.66666667,   64.4       ],\n",
       "       [  64.4       ,  224.19555556]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.get_covariance()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.99936171])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.27626124,  0.96108258])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pca.components_[0]\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LfM+vA54FOjrnfvN7XQtgCnAFOVM2M4AmeV0ZFYwXTB3rLnnORugWDXVWwqxY\n7my1iSmTh3sdT0TKgeJcMFWY5ZVTgQVAUzPbbGb3AOOAGsAMM/vOzMYDOOdWAR8Aq4AvgYFBV81P\n4qHoHtTsewX0i4ANXeDlpYQfWMXIhP5eRxMRyZdaIBTCroO7SJqXxJvfv8nfGt/Br/+qyY6fq/h6\n0fRTLxoRKTNqgXCKHco8xMtLXmbM/DHc1Owmlj+4nLBaYXCz18lERApPhT4PWdlZTF4+mWEpw2hb\nty1f9/ua5uc09zqWiEixqND7cc4x7adpRCdHU7NqTabePJVrLrjG61giIiWiQu+zJH0JUclRbNu3\njaSuSdzY7EYtlRSRkBByhX7Dhk3Exk4iPT2bsLCCT5am/ZbG0FlDWbBlAfER8fRr049KFULuj0VE\nyrGQWnWTV4uC8PCcFgW5i/32fdsZMWcE7//4Po9f9TiPXvkof6r8p1OaR0TkVCuVdfTBJO8WBcOJ\njZ107DV7D+8lPiWeFuNbULVSVdYMWkPMn2NU5EUkZIXUHMUJLQoAqM7WrdlkZGXw+tLXGTl3JN0a\ndWPp/Uu58IwLPUgpIlK2QqrQh4VVAPZzfLHfR0bTVbQY34Lw2uFM6zONNnXbeJRQRKTshfYc/YVf\nUvWGATRpejYvXP8CXRt1PaW/T0SkrBVnjj6kCj3kFPtBCUksqpHMkZq/MarrcAZ1fpgKFlKnI0Sk\nnAq6k7F53aGpJDbv3kz8D8NY2uJT4vpE8tuIbTzSJVJFXkTKNU8r4JQpT9C9+7gSF/udB3fyxPQn\naPuPtjQ4vQGpkak8csUjVKlY5RQlFREJXh4f6p64/LEoDmYcZMy8MTR7uRn7j+xn5UMrGdF5BLWq\n1jq1MUVEglgArLrJWf5YFFnZWbz9w9vEpcRxRdgVzLtnHs3OblZK+UREglsAFPr9nH9+4f5h4Zzj\ni9QviJkZw5nVzuTD2z7kynpXlnI+EZHg5umqG9iXb4uC3BZuWUhUchQ7D+4kqVsS1ze5Xk3HRKTc\nCbobj/TpM5aEhJMX+bU71jJk1hCWpC9hRMQI7mp9FxUrVCzDlCIiwS1g19H/svcXhs8ZzserP+bJ\nq58ksn0k1SpXK8OEIiKBJ+iO6POy5/Aenpn/DOO/HU//Nv1ZO2gtZ1Y70+tYIiJBK2AK/ZGsI7z2\n7WuMmjuK6xpfx3f3f0eDM3TTbRGRkvK80Ge7bN5f+T5DZw3lorMvYsbfZ9Dq3FZexxIRCRmeFvrk\n9clEJUeX9dGTAAAFiklEQVRR0Soy4cYJdG7Y2cs4IiIhydOTsY1faszoLqO5tcWtWiopIlIIQde9\n8kjmESpXrOzJ7xcRCUZB171SRV5EpPSpf6+ISIhToRcRCXEFFnozm2Bm281sud/YrWa20syyzOzS\nXK+PMbM0M1ttZj1KI7SIiBReYY7oJwLX5hpbAfwPMMd/0MyaA7cDzYGewHgL0eU0KSkpXkcoEeX3\nVjDnD+bsEPz5i6PAQu+cmwfsyjW21jmXBuQu4r2A95xzmc65jUAa0P4UZQ0owf5lUX5vBXP+YM4O\nwZ+/OE71HH0YsMXvebpvTEREPKKTsSIiIa5QF0yZWQPgc+dcq1zjs4HHnXPf+Z5HA845N8b3/Csg\nzjm3OI/P9OZKLRGRIFdabYqNE+fj/bcd9RkwxcyeJ2fKpjGwJK83FTWoiIgUT4GF3symAhHAWWa2\nGYgj5+TsOOBs4AszW+ac6+mcW2VmHwCrgAxg4EnvLiIiIqXOs143IiJSNsrsZKyZbTSzH8zsezNb\n4htrY2YLj46Z2eVllaeozOx0M/vQdyHYj2Z2hZnVNrPpZrbWzP7PzE73Omde8sn+tO/5MjP72Mxq\neZ0zP3nl99v2uJllm1nA3oYsv/xmFukbW2FmSV7nzE8+35/WwbDvmllTX8bvfP+728weCaJ9N7/8\nRdt/nXNl8gOsB2rnGvs/oIfvcU9gdlnlKUb+ScA9vseVgNOBMcBg31gUkOR1ziJk7wZU8I0lAYle\n5yxC/lq+x/WAr4ANwJle5yxKfnKmQ6cDlXzjZ3uds4jfn6DZd/3+OyoAW4H6wbLvniR/kfbfslxe\naZz4L4hscr40AGeQs+4+4Pj+tvyzc24igMu5IGw3OReIve172dvATR5FzFd+2Z1zyc65bN/LFpFT\nNANOPvn3+DY/DzzpWbhCOEn+h8gpLpm+8R0exszXSb77QbHv5tINWOec20IQ7Lt5OJa/qPtvWRZ6\nB8wws2/M7D7f2GPAWN9J3qeBmDLMUxQNgR1mNtH3T6jXzexPwLnOue0AzrltQB1PU+Ytr+zVcr2m\nPzDNg2yFkeefvZndCGxxzq3wOmAB8vvuNAU6mtkiM5sdqFMf5P/9CZZ9119vYKrvcTDsu7n1Bt7N\nY7zA/bcsC/01zrlLgb8AA83sz+Qc1TzqnLuAnC/OW2WYpygqAZcCr/j+G/YD0eT85eUvEM9s585+\nAL+d0syGAhnOuan5vN9ref3ZxwNDyFkBdlSgLtfN77tTiZypzCuBwcAH3kU8qbzyxxA8+y4AZlYZ\nuBH40DcUDPvuMXnkPzpeuP3Xo7mmOOBxYFeu8d1ez4Plk/dcYL3f8w7AF8Bqco4MAOoCq73OWsjs\nn/se9wPmA1W9zlnE/MnANnLO+2wgZynvRqCO13mL8N35EujkN/4TcJbXeYuQPyj2Xb98NwJf+T0P\n+H33ZPl9Y4Xef8vkiN73T+0avsfVgR7kdMDcamadfONdgdSyyFNULuefeFvMrKlvqCvwIzkXiPXz\njd0N/Lvs051cPtlXmdl15Mxv3+icO+xZwALkk3+pc66uc66Rc64h8DPQ1jn3X8+C5uMk351/AV0g\nZ2UFUNk595s3KfN3kvxBse/6uYPjpz0Cft/N5bj8Rd1/y2QdvZk1BD4l559HlYApzrkkM7sGeBGo\nCBwi5wKr70s9UDGYWWvgTaAyOUeS95CT+wNyzoJvAm53zv3uWch85JP9W6AKcLS4LHLODfQm4cnl\nld/lnBA8un09cLlzbqdHEU8qnz//A+RMd7QBDpPTSmROvh/ioXzytyR49t0/kbN/NnLO7fWNnUkQ\n7LuQb/40irD/6oIpEZEQp+6VIiIhToVeRCTEqdCLiIQ4FXoRkRCnQi8iEuJU6EVEQpwKvYhIiFOh\nFxEJcf8Pw5x+fTkXMJkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114946b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(weights, heights, \"o\")\n",
    "plt.plot(weights, np.mean(heights) + s[1] / s[0] * (weights - np.mean(weights)), \"g\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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S+vfl8OHd9Gx6kgr3dWHWLcMoV6Scp5lFJHe7EDdMPQq8638cCqxM8lq0fywo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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119488650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha = -87.43\n",
    "beta = 3.45\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.plot(weights, heights, \"o\")\n",
    "plt.plot(weights, np.mean(heights) + s[1] / s[0] * (weights - np.mean(weights)), \"g\")\n",
    "plt.plot(weights, alpha + beta * weights, \"r\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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
}