Thursday Mar 26 2015 - Fitting and Visualizing Data.ipynb

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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from science import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Anscombe\u2019s quartet"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x1= array([ 10.,   8.,  13.,   9.,  11.,  14.,   6.,   4.,  12.,   7.,   5.])\n",
      "y1= array([  8.04,   6.95,   7.58,   8.81,   8.33,   9.96,   7.24,   4.26,\n",
      "        10.84,   4.82,   5.68])\n",
      "\n",
      "x2= array([ 10.,   8.,  13.,   9.,  11.,  14.,   6.,   4.,  12.,   7.,   5.])\n",
      "y2= array([ 9.14,  8.14,  8.74,  8.77,  9.26,  8.1 ,  6.13,  3.1 ,  9.13,\n",
      "        7.26,  4.74])\n",
      "\n",
      "x3= array([ 10.,   8.,  13.,   9.,  11.,  14.,   6.,   4.,  12.,   7.,   5.])\n",
      "y3= array([  7.46,   6.77,  12.74,   7.11,   7.81,   8.84,   6.08,   5.39,\n",
      "         8.15,   6.42,   5.73])\n",
      "\n",
      "x4= array([  8.,   8.,   8.,   8.,   8.,   8.,   8.,  19.,   8.,   8.,   8.])\n",
      "y4= array([  6.58,   5.76,   7.71,   8.84,   8.47,   7.04,   5.25,  12.5 ,\n",
      "         5.56,   7.91,   6.89])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Means:\",mean(x1),mean(y1)\n",
      "print \"Standard Deviations:\",std(x1),std(y1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Means: 9.0 7.50090909091\n",
        "Standard Deviations: 3.16227766017 1.93702421511\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What are the means, etc... for the other data?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Visualizing and Fitting"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(x1,y1,'o')\n",
      "result=fit(x1,y1,'linear')\n",
      "print result\n",
      "\n",
      "x=linspace(4,14,20)\n",
      "y=fitval(result,x)\n",
      "plot(x,y)\n",
      "title(result['label'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "{'type': 'linear', 'pandas_result': \n",
        "-------------------------Summary of Regression Analysis-------------------------\n",
        "\n",
        "Formula: Y ~ <x> + <intercept>\n",
        "\n",
        "Number of Observations:         11\n",
        "Number of Degrees of Freedom:   2\n",
        "\n",
        "R-squared:         0.6665\n",
        "Adj R-squared:     0.6295\n",
        "\n",
        "Rmse:              1.2366\n",
        "\n",
        "F-stat (1, 9):    17.9899, p-value:     0.0022\n",
        "\n",
        "Degrees of Freedom: model 1, resid 9\n",
        "\n",
        "-----------------------Summary of Estimated Coefficients------------------------\n",
        "      Variable       Coef    Std Err     t-stat    p-value    CI 2.5%   CI 97.5%\n",
        "--------------------------------------------------------------------------------\n",
        "             x     0.5001     0.1179       4.24     0.0022     0.2690     0.7312\n",
        "     intercept     3.0001     1.1247       2.67     0.0257     0.7956     5.2046\n",
        "---------------------------------End of Summary---------------------------------\n",
        ", 'params': [0.50009090909090936, 3.0000909090909058], 'label': 'y= 5.0009e-01 x + 3.0001e+00'}\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<matplotlib.text.Text at 0x1112aa310>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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IuB44EuhPKTX1Kitq01ZfccUVLFy4cCqbpymycuVKli5d2u5maII8fp3LY1d9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\nZJKkfRnMpJLVrSM7cD+OP7z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       "text": [
        "<matplotlib.figure.Figure at 0x1107eb410>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "what does it look like for the other data?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}