{ "metadata": { "name": "basic_least_squares" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Basic least squares" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pandas as pd\n", "import numpy as np\n", "import pandas.rpy.common as com" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "To do this exercise, let's load the `galton` data from R:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "galton = com.load_data('galton', package='UsingR')\n", "galton.head()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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childparent
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2 61.7 68.5
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" ], "output_type": "pyout", "prompt_number": 2, "text": [ " child parent\n", "1 61.7 70.5\n", "2 61.7 68.5\n", "3 61.7 65.5\n", "4 61.7 64.5\n", "5 61.7 64.0" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the histograms of the child and parent heights:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "f, (ax1, ax2) = subplots(ncols=2)\n", "\n", "ax1.hist(galton['child'], bins=100)\n", "ax2.hist(galton['parent'], bins=100)\n", "\n", "f.tight_layout();" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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8vDzYbDaUlJT0OX9YzylbAE7PQnLTYnoWItKGx5+DcjqdMBgMAACDwQCn0wkAquYPo8FP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\nMJvNIiEhQcyaNUu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} ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we only know the child data, the average is a good estimate, because if $C_i$ is the height of child $i$ then the average is the value of $\\mu$ that minimizes:\n", "\n", "$$\\sum_{i=1}^{928}{(C_i - \\mu)}^2$$\n", "\n", "Add a line to show the mean of the child height:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "f, ax = subplots(ncols=1)\n", "\n", "ax.hist(galton['child'], bins=100)\n", "\n", "meanChild = galton['child'].mean()\n", "\n", "ax.plot(np.repeat(meanChild, 100), np.linspace(0, 150, num=100), 'r', linewidth=5);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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} ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we plot child vs parent height:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(galton['parent'], galton['child'], 'ob');" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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otrAnsudU7EeuYiaiK1mHhXzOnDnIysrC559/jgMHDiAhIQEZGRk4dOgQKioq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\nTkRkcizkREQm9/8Bv/1lBKfIulkAAAAASUVORK5CYII=\n" } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some measurement points are stack up one after another, we can't see all of them in the plot. What we can do is to add some jitter:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def jitter(series, factor):\n", " z = float(series.max()) - float(series.min())\n", " a = float(factor) * z / 50.\n", " return series.apply(lambda x: x + np.random.uniform(-a, a))\n", " \n", "np.random.seed(1234)\n", "plot(jitter(galton['parent'], factor=1), jitter(galton['child'], factor=1), 'ob', alpha=.5);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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UjyAIm1CUQwSD/YyOWggGa4jHd7NpU8Wcb/GtVg2fr2vSiff2DiGKXmy2ryOKexEEfc47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} ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Fitting a line\n", "\n", "If $C_i$ is the height of child $i$ and $P_i$ is the height of the average parent, then we can imagine writing the equation for a line\n", "\n", "$$C_i = b_0 + b_1 P_i + e_i$$\n", "\n", "$e_i$ is everything we didn't measure (how much they eat, where they live, do they stretch in the morning...)\n", "\n", "We pick a line that minimises: \n", "\n", "$$\\sum_{i=1}^{928}{(C_i - (b_0 + b_1 P_i))^2}$$\n", "\n", "We compute this by using the `ols` (ordinary least square) function from `statsmodels`. \n", "\n", "Then we can plot the line the the 'residuals':" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from statsmodels.formula.api import ols\n", "\n", "lm = ols('child ~ parent', galton).fit()\n", "\n", "f, (ax1, ax2) = subplots(ncols=2)\n", "\n", "# plot fitted values\n", "ax1.plot(galton['parent'], galton['child'], 'ob')\n", "ax1.plot(galton['parent'], lm.fittedvalues, 'r', linewidth=3);\n", "\n", "# plot residuals\n", "ax2.plot(galton['parent'], lm.resid, 'ob')\n", "ax2.plot(galton['parent'], np.repeat(0, len(galton['parent'])), 'r', linewidth=3)\n", "\n", "f.tight_layout();" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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3XgB7msT6pjw5dbWntAfP5s2fq9rbsuVzTfbUUv/r3T/NjZkEHICZ1gONKl1j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\nty8jgNpedvvPqKys0p8rhpCbu5SAeR7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} ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }