{ "metadata": { "name": "inference_basics" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Inference basics and p-values" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pandas as pd\n", "import pandas.rpy.common as com\n", "\n", "galton = com.load_data('galton', package='UsingR')" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We fit a line to the `galton` data, and get the line parameters:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from statsmodels.formula.api import ols\n", "\n", "lm1 = ols('child ~ parent', galton).fit()\n", "\n", "plot(galton['parent'], galton['child'], 'ob')\n", "plot(galton['parent'], lm1.fittedvalues, 'r', linewidth=3);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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IejJepOwWfHpGnpa2HEVFpbq2LShYh/DwWejffw7Cw2ehoGCdl9O5LyLibphM6TCZHoDJ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\nzusyBQfvN6yYq3i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} ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "lm1.params" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 3, "text": [ "Intercept 23.941530\n", "parent 0.646291" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "# emulates abline function, only possible to basic line styles and width\n", "def abline(intercept, gradient, *args, **kwargs):\n", " a = gca()\n", " xlim = a.get_xlim()\n", " ylim = a.get_ylim()\n", " \n", " if args:\n", " sty = args[0]\n", " else:\n", " sty = 'r'\n", " \n", " if kwargs:\n", " lw = kwargs['linewidth']\n", " else:\n", " lw = 5\n", "\n", " a.plot(xlim, [intercept + gradient * x for x in xlim], sty, linewidth=lw)\n", " a.set_xlim(xlim)\n", " a.set_ylim(ylim);" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `galton` data is just a sample obtained from all possible child-parent population. \n", "\n", "Here we create a simulated population containing 1 million families, assuming a normal distribution.\n", "\n", "On top of the population distribution plot, we show the line that was fitted to our sample (i.e. the `galton` data)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "parent = np.random.normal(loc=galton['parent'].mean(), scale=galton['parent'].std(), size=1e6)\n", "child = lm1.params[0] + lm1.params[1] * parent + np.random.normal(scale=lm1.resid.std(), size=1e6)\n", "\n", "newGalton = pd.DataFrame({'parent' : parent, 'child' : child})\n", "\n", "hexbin(newGalton['parent'], newGalton['child'], cmap='PuBu')\n", "abline(lm1.params['Intercept'], lm1.params['parent'], 'r', linewidth=3);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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Lj3mGoyPscwrz69ZR/Fyz+9XLT3rIcv1GmgTJEzxufKvi2mnglnpxATXU8Yip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\n9cHDY/rwfYV8OYbpPCzYPQAVRyA4QI3VRNOkv4JLcG+M6oilcEpp51m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} ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose we take a sample from the population, and fit a line to this sample (in black):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import random\n", "\n", "random.seed(134325)\n", "\n", "idx = random.sample(np.arange(1e6), 50)\n", "sampleGalton1 = newGalton.ix[idx,:]\n", "\n", "sampleLm1 = ols('child ~ parent', sampleGalton1).fit()\n", "\n", "plot(sampleGalton1['parent'], sampleGalton1['child'], 'ob')\n", "plot(sampleGalton1['parent'], sampleLm1.fittedvalues, 'k-.', linewidth=3)\n", "abline(lm1.params['Intercept'], lm1.params['parent'], 'r', linewidth=3);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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LSUlBSkoKNm7ciNzcXADAqVOncOnSJYSGhgIAAgMD0apVKyxYsAAjR44EABQUFGDPnj0Y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\nSUVORK5CYII=\n" } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we take another sample:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "idx = random.sample(np.arange(1e6), 50)\n", "sampleGalton2 = newGalton.ix[idx,:]\n", "\n", "sampleLm2 = ols('child ~ parent', sampleGalton2).fit()\n", "\n", "plot(sampleGalton2['parent'], sampleGalton2['child'], 'ob')\n", "plot(sampleGalton2['parent'], sampleLm2.fittedvalues, 'k-.', linewidth=1)\n", "abline(lm1.params['Intercept'], lm1.params['parent'], 'r', linewidth=3);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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Eo0evQK0Ok+zBqzEfcHKssmHmwYHcxv3000/YuXMn3nzzTZw7dw5KpRIjR45E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\nxhiTOQ7kjDEmcxzIGWNM5jiQM8aYzP0/DTgphEEhPowAAAAASUVORK5CYII=\n" } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that every sampling produces different fitted line. If we do this 100 times and plot all the fitted lines:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "sampleLm = []\n", "\n", "for i in range(100):\n", " idx = random.sample(np.arange(1e6), 50)\n", " sampleGalton = newGalton.ix[idx,:]\n", " \n", " sampleLm.append(ols('child ~ parent', sampleGalton).fit())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "hexbin(newGalton['parent'], newGalton['child'], cmap='PuBu')\n", "\n", "for lm in sampleLm:\n", " abline(lm.params['Intercept'], lm.params['parent'], 'k', linewidth=1)\n", " \n", "abline(lm1.params['Intercept'], lm1.params['parent'], 'r', linewidth=3);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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O+w6f10eHDh0Y//hT2Ow2XnhxEoeLimjXpi1r1q+lX5++7Ny9C5fLjbvGzUMP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HAAAg\nAElEQVRfusTUzDQrKys+yMWiUWpra+k43MGxvn66u7opisW4NDrCi2dOc35ggJnZGb/d58EDB+nu\n7ubOk3dwrL+foz29dHZ0EgrtnFcGgdnLmAeHhpiYnKCluYW2tjaKY0Wk0ylm5+a4ODTo9taw2Ewk\nthUGb0RzlJeVccuJW3j3ux7i7rvu5o/+9I/4zve+y/LKiv8ieAXHcChEWVkZS0tL2HssILaS10i/\nGrfhXiiaG0U4FCYcifDBD/4y733kUQ4erATAchyurm3y9a98gc9/5q9obOngfY/+Ot19tzIzM8nf\nf+LPuPDSD/i5X/wIb3/oA5jua+VRGABJy2Yjl39uQRDYyCkDDOACqlu0k5KrmTx1pAU+sjtSFnyC\nMAOAF9FF3t4tVOc8LyoCXHfIlf95zydIWZSGtMB+GmH3OQlBQYEwKMkzdJFXf+A2bdoha9U0dyLM\nDjK8bR30An9zkOkIUidyh89SN9Jd7wrWAXDe563fmHhNgH3u3Dk+/OEP09PTw/nz57n11lv58z//\nc/7wD/+Qv/3bv6WsrIzbbruNP/7jP6a8vDy/qRAYhuHzsNFolPraOtra2ug/2sdbbn8Lvd2qw9yV\n+Dhf/dpXefrZHzA4NMTC4gKWZRGNRmlqbORY3zHedu+9nLz9LXQd6SpwGwYjm80ydnlsx4y5uamZ\n3p4euo90UVxUxObmJuMTcZ59/nkWlxbVeKxkilQ6VXhydlBzeNSHEIK62jpOnTzJe37+PdTX1vF/\n/7//jRdOn2ZjMy+A88ZsZTIZikuKSWxusuEqT/YSe3UbPksepINuw1cH0h7DqyISiXDoUDX/8T/+\nOg899AtEIlE/e02lknzxHz7D337qLzjS3c+/+6WP0tRxlOvXrvKFv/vvPPWdr/Lgw4/y0Hv/A5Fo\nkQ+8UFgkTNsOa1nb/+3B75s5lWFLwBQiX/BzAdvjuiGQVUqJTR7EdPIabVNTk8VB/TzicthCKHOM\nl6EbgoKeHsHpLUWBZk2hANcNEDKCw3D1gqw5OIPR3A2wReEIryBgC1GYbauf7QzYHpi/NsD2ds7f\n3Afq1y++/9STfP+pJ/37v/f//LdXD9hnzpzh1KlTPPvss9x+++187GMfo7S0lN/4jd+gslJlV7/z\nO7/D/Pw8n/jEJ/KbCsGn/sfHeevd99DS3IwQgtnZWc4NnOc7T3yXF06f5vLlMa4vK/tFWVkZh9va\nue3WW/npd/w097/tbYov3iGCwBzMmD1gVsXEHnp7eqirreX69WXOnH2JZ579AS+cfpFIJIJt26RS\nqR2zZ+lOfgn+LZ4Zpr21jXvfeg/ve+8jLC4u8kd//icMDQ/7vUZAdb5rbmzmwIEDnD13lkg4wvr6\n+k01WjpBHqS7d1nzerkNvdB1fdv5CIVC9PYc5Td+/be4794HkAgsW5KzHFKpBJ/73Kf49Kf/ihMn\nbudDv/y/Ut/azfLaGl/47F/z1S9/lnc8+DAf+Pe/Rln5QTZzlg+yOUfJ9QQSW0LGrTZajiTjOJia\nRkiDjaxNxpYIJJaEnOMQ0jV0FzUUOEs2cg4py/YnlWtASNfd/aXLQQuyUoJU/T5A4EiHmGFgauo5\n6EIQdsdoCXBHckFYF4QNxWfbDhiaRtTw6A+h6BUhkI70+WmlmVZWcw+ATZcakY5Ec3XVAlUcVH+L\nek66lp/FKHyALATNbSAe0Fh7a/KSvjxoi+Am7ATOr0yHvBLXvR+vPl5Thr2wsMCpU6eIx+MAPPPM\nM/zBH/wBX/va1/w1ExMTvPvd7+bChQv5TYXgz/7wT3juxec4+/LLTE5NuT2EbSoqKujqPMLdd97F\nQw++iztO3rEjz5zL5RQwu9myB9Dj8XGaGpv8IqIH0IfbD3P5ymWee+EFnv7BM3z/qSdZurpEOBwm\nnU7vKIvzsk+lg9UL1kTCEbq7u3nnAz/Fz777Z/ne97/HJz/9KSYmJ/x1QggOHjjAHS498/0nn+TM\n2ZfQNI1UKrXt9+36IgB3kAfp1l3WeW7Dx1GTWV6t2zAYwU9CXpimyf1vf4CPffR/4+jR4/4bKJez\nWVtf5+8+83E+/Xd/wx133M2vfuRjdHR2s7a+qQD8U3/BXW+9n1/58G9RX9dA1nHI2BKkMrgoAHb/\nHjt/cbQcSU6qY1JKkpZN1lG3daFoEF2A5XLcuhA4UrKRC65TempTE9hSyQHNQHZb5PLFliN9YPeO\nefZxXVN9QjSU/hsh3QuB6gHi7SeE6pQHAk1TTZqCtEVwYrlhaL7EzutLAiDcC8JO2bLXuGlrRisp\nHBxQaIzBB2r3ZgFlsi12zZZfAZH3s+w3LF5z0fGee+7h4x//OJ2dnfzu7/4uqVSK//yf/zM1NcoI\n8ad/+qecPn2av//7v89vKgThcJhYNEZ/Xx/33XMvb7v3Pm49cQvFxcUF+weB2bOFDw4P+cAczJh7\nu3vo7OgkEomwsrLC8y++wJNPP8W3v/ddLg5e9OkLz9K9m3IjGo2ChHQm7R8vLiri+LHjPPxzP8ft\nt9zG//zC5/jHr3yFpatLBcNma2tqee/D7+HdP/MQ3/ned/nCY//A9PQ0tu3s2s9jp/Dchg+jiod1\nu6x7Pd2GXnj8ZpAq8ZQpH3jkg3z0o79JQ30jjtuoH2B1bZX/8Td/wWc++wnuued+PvKRj3G4vRPL\nsnjsS5/jv//3P6Kn9xi/9mu/TVt7p79vxnZ8tYcjJdkAJ5Kx8hy25Sgg9tatBrjpEiPfUtRxqQ5w\nOex0fl25a1BRxwr/5rJwPiko+AQFPj0CUBrUaweoBD1IxUBBW1NDz09+EVBAZwQt5poo7HO9TZIX\nyJiDI728n21bB9uke0Gp3a4Gl4JjW05UAOC3nsP9zPqNj9cM2OfPn+dDH/oQ2WyW9vZ2PvnJT/LR\nj36Uc+fOIYSgtbWVv/7rv/YdhqDeDAsTMwU/y+VyXL5yOZ8xuwB9ZfwKjQ2N2zLmI51HiEQigGqo\nP3xpmO8+8T2+8a1vcfqlMyyvLBfMHdS8f+gtfG0sGqWkpJR0Js3GxoZ/vLysnLfcfjvvf+/7qKw8\nyN988hM89czTrK3lbd6madLW0sp//F9+iQ9/6Jd5/sUX+OKXH+OLj32JzcTmnp2KXnhuw4dRMrzK\nXdYF3YbfAvaeq2+PIIe9lc/2NcCxGL/2qx/lV3/5P1FUXOr/C0spWbp6jb/5xF/wmc/+Le+4/518\n5MMfo6WlDUc6fPObX+NP/+z3+f/bO8/AKKq2DV+zLb2SRgAhNEEUCAgoKE2xIYpKsYICiqCiIlJC\nL6GqIPLZG76vvb72rhSVDqH3DqGlENKzu/P9mJ3Z2d3ZZCkhBM/9AzY7p83ZzZ1n7vOUuLhEhj4+\nmubNW/vMX+Z0Umx3auOV6Ai71OHUfK8dLqlEwpewg80mgsy+hI0sc6LYrknuoa4AFmUM1z26mobb\nzJplqh0Au66p3iOglOdSSVVP2BJoxQfAs7KLW5v2JXOrxZ2XWpLQrHXl8/CvRXunNvX14PDVt/U3\nJekaG/GsewyDX3/tHMD/JYHKQZUFznz6/kceFrNKzN4Ws56YVZw8eZKffvmZb77/jmUrlrFn715N\nW1atZqvVit1u9yAgi8VCclJNJQIyO4ucnBwcDociXdSowTVXd+CO22+nqKiId95bSMaG9R76c3Bw\nMJdf1oyhg4fwwL33UVBQwPc//cDC/7zHb3/8gcPpOO0ah2q0YW/JxC2y86yiDY10ZiMEBysFCtT9\nklzaqApVq4+Pi2f0yLHc2/d+LFarZlHJsszRY0d55fUFfPDhe3S/5XYeHfwktWtfglOWWbLkT55/\nPh2H08Ezw8dx9dWdACVvtOxyvwP377uMTH6pA6esjG13ytpho8Pp9DmIdC1CkTqQNbKWZbema5eV\nOiomZAocThxOpZ4iuA8YVToyq37ekqs8loQroZOE1axILaqlHWSWsMvKHwY1MMYkKcTrlk1MLtc6\nZQbVuja7ai8qh5suNz1NspB8dGfls5A8CF27R53+rF5zk6Wvq58k+a+gaGRp68fy7Om5FuM+ApWF\nKiPsnrfdzmVNmnpYzEYeHk6nk0VLFvPl11+x9O+/2b5jOwUFBZqnSVlZGcHBwTidTspKy3SHJxJR\nUVFc1rQpsgy79+7m+PHjSoShZCIhIYFO117LdV2u4+Chg3zw8Uc+ASrh4eG0bX0lwx4bxm233ook\nSRw8eJBPPv+Ml19/ld27dxuesFeESKAH0Mdi4Xq7vcJowy9Qog2NqDg0JJTCosIK57RarERHR3P8\nxHHA2DtE1asb1G/A9KkzubHbTUiSklhJVmRmMo8c5qWXX+TTTz/kjp69GProkyQn10KWYV3GGmbO\nnsKhw4cYMTyNm2++DbOL/ItLHUoODFyh5C6vDvfjtfJeqS4vSJnTrWE7dBGNsqwSMto12Uue0HRg\nCc31TtWmVQpSs+0pfdz6s1OWPbRks9nkIm1Fj9b8miUJq9Wk1TvUZ8oD8Awl9yzVpaUwlTw1Z7Mu\nNF1dv4fmjHsuXStDC1vCTaKaC58By3rPZwzJ50fBz+cfF1TyJ1mWWb9xA59/+QV/LlnE5s1byMrO\nUjRvWxAOp0OxdGw2pYSV7jDMZrORUrceV17Zhqys46xas4asrCytaGzNmjXpcNXVtLmyjVZY4ITr\nurqm6OhormnfgWeGPU2njh21NW3ctJEXF7zER59+TEFhxeRohDjgLouFO4HOdvtZRRuGh4VRWFQU\nkDtendp1yMnJIb9AcRU0koasVqV+Y+vU1rwwZy6tU1t75NMoLXNw6NBB5v/fPD7/8hN697qHoYOH\nkZiYhCzDzp3bmf1cOqvXruKpYc/Sp/e9WCxWrb/TKVOkkzDK7Mbrll2yhzavw93O4ZQ1S1uWZQ+r\n2677ikqgWbqgpCl15wjxbKcnPb2vtSfReWrY+jBwi0Xy0KZNfnyjlXHcpOuvbJfemnb3069JN553\nHpBy5BEj0cPHT7pcApYCbCdQ2agywrbnF7N121Z++Pknfv39N9ZvWM+Ro0eRZZmgoCAsFgvFRUWE\nh4dTWlamhXir/WNiYmjTqjWtW7Vm5epVrFi5UksjajKZqJVcizatWtOwYUNWr1vL3//87TNGYkIi\nXTp1ZuTwEbRs0UJbn91u57sfvmfClEls2LTxtGUOFcnAA2Hh3FJUSAen86yiDVV3w0AqlYeGhlK/\nXgpbt2/z8FhRn0hUqETdtXNX5r/wEin1UgCFYNU73rd/L8/NfY7/ffMV99/bj0cffowacUoWwoOH\nDvDC3Nn89Mv3DBn8BP37DSIkRHle0G+ZU3ZSXOxOyKRa7N7wJmy7zg/bKcvYne52esJ2eAXBWHQa\nrj/CBk8L2GYyeXlXuNvZdL7RZp0VbTZJWtUX9WePg0EDwgZ8M+u5Dga1w0QD8pW8xtFb3t7j627f\n9dqvH4gHypc0jP8gCJxfVBlhqzqp2WwmJDiE4pJibFYrFquVwoJCjwooVquVenXrcVO3G6hRowY/\n/fIzGeszKHIRsMlkIjk5mSsua0ZcjThWrVnNth3bkSRJkzjMZjO1kmtxU7cbGPXMs9SvX99jTadO\nnWLUuDG8/9GH5OXlnfG9NTKbeSAsnG6n8riqnK1bhZuk/dU2NJlMSs3GAHOGNKjfgJzcHEpKSrSs\ngzabTSFCnWeMmh2wZ4+ezHv+ReJcEYmKLKGMtXPXTp6bO4fvfvyOAf0HMuSRocTEKElXs7OzmTv/\neT785L/0v/8hBj/8BJFRSmCUSop6vVt2/V9mdyI73T871PpcgFNHxmoUoqaeym5yzS+1u5NA4fKs\nkNBC1rW908siKLqypM4ryxqZ2qySkgLVZMLhOuRU+1lc9RUlSbHw9b7PZpPJ5baHtq+gDxlX53a/\nVi1okyRp8pDWV3Jb0WavDHvecwRK1ur8ap/yIMi6eqDKCNtqsRIaFkppaamPT3JERARtW19Jt+u7\ncejQIf5YvIhtOmsRICkxkQb1G2KzWcnYsF7z3lDbWC0W6taty+233saIp4ZrboZ6/PDTj4wal8am\nzZvOKiS7dUgIvU1mbijIDyja8EtgH8ovk7cGbjKZPLxbKkJISAi1a9Xm+PHjlNnLNKKOjorm1KlT\nmiuhyRVsYTaZ6Xd/P2ZOm0loaJjPeFu3bWX2C7P55bdfeGTgIwx+eAjRUTGAzKn8fF59/WVeef3/\n6HnbnTzz9EiSXLIIuMK9NcJ2u/zJsnpNaWd3OHE43e2UrZc1cvY94nJb1arWXWyXtQM4q1kiWJdD\nWtbp2+C2dMvsTuxO9QkLQoOtmiUty/rK8ZIHGethMbsjGBWL2ORxTa8Zm7yHcP0RMZn8W7zuA0bf\n/npill2bo3fu8+um5y1jBCp/BNxH4Hyhyghb/39SYhI3dutG/ZT6bN22lb+X/cP+Awc061mWZWJj\nYqhdqzYlpSXs3LVLe7xXiS0oKIiG9RvQt3dvHn/0MWJifKu6ZGZmMnrcWL785itOnTo7j+VO4eH0\nKCvjlpKScqMN/0QhaTXa0Mj322KxaE8CgW53QkICxcXFJCUmsnffPi2/dlJiEplHMn3GDg4O5okh\nTzB29FiCgoIAPKy8TZs3Mev5mSxavIghg4fy8MDBREVGAVBcXMK7/3mH5+fO5toOHRkzaiz1Uxog\ne5GrPueJQyd7yLKMTo6mpMx9fOp06kneV7NXSUKtfK6OV6TLKxIWZNb8sL33T6/9lpQ5NOvcYpYI\n1vtU6/ZC9eQwgmf6U08PDr0k4uNOp4PZS/bQ1urVx58ObrRH/jRs3zkCo121mY/WLVClqDLCfvLx\nYdisVjZs2sjqNWvIylYOAG1WGw6ng7DQUOLi4snLy+Nk3kmCgoIoKiryyD/StElT+t17HwMfHOAT\ncANKua93//Me819+iV27d5+VFS0B3cLDubmoiNsdDlL8tDOKNjQiaVU/Pp1cHmazmcjISEJDQgiP\niGDHjh04nU7MZjO1a9Vm3/59HuM77A4iIiIYNWIkTwx9AqtVOerUE2TGhgxmzpnJsuX/8MTQYQwa\nMIjw8HCcTnA47Hz6+aekz5pG44aNmTB2Epc3u0KbQ+M4WdERHDrSK4+wy+xu4lQsbC8ZRXfPKlk4\nZdnDKi+xu320gywmgqzuhE966CuneFvYYcHuvNSyTrc3mTwTOelhNXv6TXta2L5Vx40I0h9hK3N7\n6eg+XhyS8R81yfNw0a+x7XHBn6Of8duCuKseVSiJWLA7HISGhmK3K3kkIiMiyT2ZS2hoKLIsk5/v\nDj5RE/kP7P8Qd/fpa+gCWFZWxk+//sKCl/+PxUsXU1R85gWsACzATcHB3FxcTE8qjjb8AvgOyJck\nkH0d/ixmMw5X4YJA/KVVMg8KCkKSJNq1bcvOnbs4dPgQoOjTCfEJHDp8SPsQbTYbTqeT6KhoJo2b\nyID+D2GxWDy8PmRZZtWaVcycM5PVa9fw9BNPMaD/QMLCQjVJ4Ycff2DStImEhYUzYewkrml/rUd/\n2Ws8Far0IeNLng6XP7QkKV4qOgnb4zDYbne4Snwp18wmt3SkWnySSwdWnsJcJInb4tWPJ3t9Fnpf\nZrNZDd9W5jDjTlvq0Fn/arSiSfWh9nKl0+bVzeNtdavvSZKkNVTX51NMQGddS+ob6jWDedT7Pz3r\n2piwXV9fg/7+xxY4P6g6wrZaNSszNjaW4mLPSMOoqCjatL6SwYMe4bbutxqmR3U6naxes5o3332b\n/33zDUePHT3rtQUBN1ks9LDbTyvasNjAitbfa1lZWcByR3BwMMXFxdhsNpISk2japCl//fMX+fn5\nSJJESEgIFrOFgkJ3eleLxaJVY58+OZ27+/RVrD+d1SrLsGzFMqbPms6mLZsY8dQzPPjAg4SEhGie\nIX/98xcTJ0/g5MmTTBw3iVtuugUZz3uTVbEZvIjbTZRqEIwa4q5Zx+DStt3Hinr5wWM83Z7oNXFv\n6OcCdz5odf/dGq9/SUBdghrMYjY4UETSHWaWY0Er47nIU6dbe9yXrNy/XvNW1+ieV3uF7qX+Pw+U\nr2EbXZN92qktfb6qwsK+IFBlhB0VFcWpvDxNl6wRW4MOV7dnyODBXN/lOsOET7Iss2PnDj74+GM+\n/eJTtm7bdlYyB4BJMhEiO7nZZOIOp7Pc2obHUbToz1GiDe3lkHRkRCSn8t1/gMxmM06H02+gTWRk\npCb5WCwWunW9nqzsLFauXoXT6cRithASEkxJaamH14fZbCY0JIT4+ASmT57GnT3vQNIxluwiysVL\nFzN99gx27d7Ns8Of5YF7H3BZ7kq7tRnrmDh1Elu3bmHc6HH07X23VnVHL3X4Ercbeh3Yu49dp4nY\ndcSrWqFG4+l/dDplj/H1cDg9x9OTo55UAyFsUDVsfTkuY125ovGMtG5/3xd/43kQeID+0Po+slc/\nf9q0P61aaNgXFqqMsJNr1qTjNR159OHBXNO+vd+SXIcPH+Z/337Nh598zIpVKwOuuFLe3JIkEeF0\n0h0lA14gtQ3VaENZknz8eUEt75VITm6u5vUSFBREqYtgjWC1WqlVM5l9B5QM1YmJiXTt1IVFSxZz\nOPOw5pNutVgodVnoKlGbTCYiIyJJrlmTqROn0KN7D+WAFk+i/P2PP0ifNZ3DmYcYOXwU9959L1ar\nO6hl955dTEmfwh+L/uTZZ0YyoP8AgmxBHus8E8JW3PPcrx26YgQOp6ekonpklEfY5VvYnuPprWO9\nhh0oYSsati6QxlvS0L3nHeiiH8+D6F3SiDFh+1+j93ID0al9rxn3MfxaCkv6gsYFFekIio/vr7//\nxoeffsyixYs5mXfyrK1oq9WK0+kkxuHgNhSSvp6Kaxt+AaxQFgwYeCBIEvVTUsjPz+fY8ePIskxw\ncDB2ux2Hw39ekUaNGpGTnc2JrCxMJhNt27QlIS6eH3/5STuIDLLZcMoyNpuNwsJCj6LB0VFR1Klz\nCZPHTeTmG2/2ISGn7OTnX39m2szp5ORkM3rEKPr06qs9tcgyHDl6hJlzZvDp55/x2KOP8fiQxz0O\nblWNWH2tEq6ib7rlEM92qtcH2n7JWjtlXco1Xx1Y8xaRFJnEpDCXxx6qYfJuDVv9I6Drg57wVNlB\nxiSZPAhTJVSnrPpXq/k9FDlD1r0vSRKyU71/l8RhlrR2sm59eI3nHQijwXVQq7RDuwtJ+8e1Dl2q\nBT28pRNtDJ+p/BO80KmrH6qcsAsKCljy11K++OpLfvzlJw4dPuzhy3smCA4OxiSZKC4pJsnp5A6U\nDHid8F/bcBPukHA12tDIIpIkiaZNmuJw2Nm5cxcOpwObzUZwUBAFBYV+U6hGhEfQonlzlq9cQVlZ\nGZERkXTu1JHtO3aye89uLSeKJElaseCsE1naeOFh4YSGhlA/pT4Tx02gW9fr0cwhHUF++8N3TJuZ\nTlFhIWmj0+jV8y7MZqUgLLKSOOuF+XN57a3XeeDeB3j2mRHE1YhXDkndsrIynmvtTp1lKyNrpCJ7\nWcoKcSuDaJqyazyPg0mnPlGXa05XO71W63AYC0iqhq6c3SmBM2bdoZ9+TZoB7GI1lXT1h5Ku6bSf\n9WTtMQY6i1q3T2hEjfaZ+OSh1u2tt1UuqzeuO4h0b4OXtq2fV4fyibYcC9vjPrxbC1xoqDLCHv3s\nKL7+5mstItHpdJ6xJS1JEvFxcRQVFVNQWEBdp5M7UUi6fTn91GjDL4GturGMSLpxo8ZERUayfuMG\niouLMZvNxMbGkp2VXW6e6zatryS/oICt27YiyzL1U+rTtEkT/lj0J8hQVFxETEwMRYWFFJeUkJxU\nk8NHMrU1JMTHI5lMNGl8KeNGj6VLp86+FrXTyVff/I/0mdORZZm0UWn0vO12j0PHoqIiXnn9VZ6b\n9zy33tydcWPGUrt2HW0Mf14fgKcUIel0UFkNelHX4btvxuN5fc7euq3r/zLvdn5gMek1Yl+3QL1u\n6w8m7zV4yxm6pQYSoOJhWRt8n9w+1eX/eukJ289w2vXyRqmondCqqweqjLDNZiVoIdCIPm+EhoZS\nq2YyR48f49SpU1wqy9yFIndUFG34JfClJLFHtbIwjjislVyLhg0bsHbtWnJdkZQJ8fEUFBZSWFjo\nd+MiIiK4vksXfvvzT/Ly8rBYLLS4ogVFRYUcPpJJUVERZWVlJCUlceLECWRZJiE+nkOHD2tj1Luk\nLsUlJVzerBljR6XR8ZprfeZxOBx8/uUXpM+eTnBQMGNHpdH9lu4ehGIvs7Pw/feYNiOdNq2vZNKE\nyTRtfCngtkb1j9TgS7BOL0taMrnblU/YajvPdTudXrlE/BC2w+nEzzmjB0wSWlHaMyVsvS7tXpLy\ns9nkfl0eYXvLFBoxGxB2oOzo6+pXOYQtUD1QpZGOp4s6tWtTo0YNdu/ZQ15eHqm4q4RXFG34pcnE\nt2Yz+8tJnmQ2mwkPD6dNqyvZtGWzFjEYHR1NWGgohzMzy92sls2bExEewdJ//gaU+o1NL72Urdu2\nExMTw+HMw64D12QOHDxASEgIEeERHDnqrrjYtElTcnNzaNmiJeNGp3F1u6t8fkHtdjsff/YJ6bNm\nEBMdzbgxY7mp243ofzGdspMvvvqSCVMmkFyzFumTptKmTVvAM0gE/BOr5wGjp4Tg1P2x0x8oqjqw\nOyDFbUUa/VHwGE9n5ql34tRLDa5BZK2fGoKuJyTPajl6bVqVakAf8KLXA2RXLmw3UXuQruR5cKh/\nglDv2Udq0f73vWdv+BRQ0ElGniqKbzvv+/DcRXVvDKcVqEa4oAnbZrXS7LJm2IKC2LhpI4UFBQHX\nNvwF+Npi4UebjQPlpES1mC1YrBbatW3HwYMH2b1nN7Isazk69uzdU+5TQHBQMNd1vY6169ZyOPMw\nZrOZ+Lg4rFab8iRhMrF3/z4iwiOIjY1h7759xERHYzKZycrO0vajdWorDh46SNsr2zJ29BjatL5S\nm0P9AMpKy3j/ow+YPnsmyTVrMm70WK7r2tVthUkKQf72x2+MmTAWZJnpU6ZxXWTCFA0AACAASURB\nVJfrkEwSao0C7QNVyQ98LFlPjnTnrvbnJaJq5IrG7T5URLUIZZAll77toWHryUnVx9WbUfOFuA73\n1NcqpUrKmozc/dxE6SJa9T60MVyWsyKE+2jd+jHUiEPve1abe5u9nvK2P+tWHVt3Wmj0m+ZjjEue\nL/39dgpt+qLEBUfYMTExXNmqNfkFBaxZuwZ7SQkdUUg6kNqGPwQH83tICPtycvzOYZJMmC1mml9x\nBaUlpWzeukUpbGAykVIvhRMnTpB7Mrfce6hTuw716tbln+XLtL5JiYnknjxJaouW7Nq9i8wjR0hK\nTMJsNnPo8CFiY2MpKS4m35WgyWK2cFW7duzYuZMO7dszbtQYWrbwFXRKSkpY+N/3mPncbOqnpDB+\nzDg6Xnutjx/tylUrSZswjgMHDzJ1wmTu7HmnK+mTq42X+5tnhKLnnPqndu8oSfdrzz7espJHcQLd\n+/78qfVze49fngzgTztX2xiN55YslJ+9NWw99C56ToMxKlwg3mR9ptq0J1lLAfQR2vTFhSonbEmS\naFi/AS1btGT3nt2sW5+B2eE4rdqGv0VG8k9kJDsOHSr3ZiwWC/Xq1SMiIoKNGzciO2XsDjt1atVG\nMps44Eo45Q8mSaJ58xacOHGcg4cOERISgt1uJzQ0lJqJSTRo0IAlfy0lPz+flHr1yMnNJS8vj+jo\naPLy8rQ0qUE2G9dccw0bNm6kS8fOpI0czRWXX+EzX3FxMW8tfIfZz8/hsqZNGTc6jfZXeR2jSrB1\n6xbGT57E8pUrmJA2jn739fPwtVb2uXzCNtJ+tWv616dF2Mq/vqHhsiHR6NfqPb6hZWswnuSyutXm\n+qhHvO7Rp2Yikg+x6sfUnha8r/kVlrV/PPVt3b/uMQLVpgOjXyF/XJyoMsLu0qkzKXXrsfivpeza\nvYsQWeYmFJK+FYjy01eNNlwcF0dGTA027dpRrneJzWYjKiqKWsnJbN22DWSZ4pISoqOiSUxMYPee\nPRUWBQgJDiElpR7bXcmWQkNDKSsrQ5IkbrvlVvILC/nlt18AaNigIXv37cVutxMZGUlOTo6LUGRC\nQ0Pp0rETy1et5KZuNzLm2VE0bdLU55e1sLCQ199+k+fmPk+rlqmMG5NG2yvbAJ7tDhw8wOT0qXz7\nw3eMeGo4jw0equVY0ROYHrJsrE2rDZ2uMlr++MdTq3b30c+lv+ZPt1b3RK9hez/h6zVivb6radja\n4G75w+SVtc9IdvHR72VlDO2pQts0GSPClWU8DjPRWere+rMkeWrT3vuit7DBt50/PdofBFFf3Kgy\nwpYkiQhZ5lYqjjY8hOLVsSK5FptiY1m7cUO5iw4KCsJsNlO/Xgp79u3FJEkUFBYq76XU5+jRI5rX\nhz+YTWaioqIwmU1kZ2crhYBlKLOXUadOHe7p3YdFS5bwz/JlhASHcEmdOuzeuwfZ6SQkNFTLzy3L\nMhHh4XTt3JWl//xFj1tuJW3kKBo1bOQxn4ySXfCV11/jhflz6XBVe8aOGkNqy1RdC+XfEyeymPnc\nLBb+9z0GD3qEEU8OJzo6uoJd99aclTdkg0dr7QBQ2wu3COoRzej6x580AW69GAOCV7q7CE711NE9\nw6vE6D2eNrtOm6Yc61jVur21eJNJvXnfflpn2e13ri1K3Qzc5Ky+49FOCqzSi+d9nQZ8/64I+eMi\nR0WE7ZvQ4xzhW1muMNrwK5OJ9fUbsCk8jLXr1+M8dBAOHTRsr1ZWSalbj8yjR7BYLOzYuYOS0lLq\n1q1LRGQkhw8fZtv2bX7XJElKGa3IiEjyTuWRezKXmOgYTCYTZWVldL/pFjq0v5o33n6LGXNmE1ej\nBnUvuYQTWVns3rMbi8VKQXEBpWUnkWWZ6KgoOnfqzOKlS0hISGDFkr+pn1LfZ968vDwWvPoy8xbM\np2unLvz8zQ8GEolEfn4+c196kfkvv0Sfu3qzYeVaatasWa684PdeQSNrw2sGe6PA83CtPIYwJDKf\nuXzEXaOX+A4RQOJ+35Y+fVSpw6/mor8H3B4k2nj+ln8aBHymXlPamvx8jgL/PlQaYd9i8N4mFM+O\nHZdfwTqHk4xNG3Du3OF3DNWXOykxifz8fGxWK0ePHSM/P5/o6GiSk2ux/8B+9u3b59FPn4NakpRs\nerIsY7VYkWUnp/JPERUVRVZWFharhYlp45BlmRf/bwFff/cNtWvVIjY2lpCQEA4eOoQkSZSWliqJ\nmZCJi63BNe07sGjpEpJr1mTtspVcUucSn/Xn5OQw/+UFLHj1ZW68/gb+/Ok3mjbxdVAsKSnh9bff\nZMacmXTt1IVli/6iQf36LnnjtLb9jOB0ypoWHIBBWiECbWfQ02OMQOBPGvJp4HtBm6+yydBTAjmd\nfrrXgK9HicC/DZVG2CpWA98FBbEvtRUrTuWxafNm5HVr/bZXreCoyEgcTqeW//lU/ikkSeKSOnUo\ns5eRk5NDjs5TxGKxaO55qldHZESElnPbZrURHBxMaVkpxQUFNKzfgDdfeY1vv/+eabNm4HA4qHvJ\nJZSUlhAZEcmRo0fJyclxBYEovzkJ8Qm0a9uGpX//Td26ddkwdz61atXyuYesrCzmvvQir7zxGrd1\n78Ffvy/2kUiUdTr44OMPmTBlMpc1bcr3X35DyxYtdS2MJAj/HGTkqeBLaDKy9ljvOZM/svawWo00\nc307yVPf9ZhflnTCj6f6IOnI03s8ta3veO51e2rOfm4EkPwkc1K7aIZ3OX88yvP68GwTIL36IeLz\n8cdaoHqh0gh7UkQEe1q25J/DmezcvQt52T+A/8dDm82m5NC2WLDZbMTExLJ3rxJAk5iQoB3w7d6z\nR+tjNpmQXPUR7XY7ZrPZlY40lLxTecrBoclEXGwNjp84DhLc06cvA/o9yMRpU7jr7j7YbDZq1Uwm\nL/8UsTGx7N9/gE1bNnscnCUlJpLaMpVlK5bTuGFjXl/wqmENyWPHjvH8i3N58923uavnnaxc+g8p\n9XwlEhmZ777/jrSJ44mMiODdN9+mYwffSEd3eLP6r3E2uHJhQOKqOC3rmEcjmNMc30gykMGdsF9H\nRpp/tZE4ixfpeo1nUqMRJZBU9ta9lrTx3RNqP6uv/co2uPVo2XNNvrqNwWsjtcXgj6L+uno+UC6n\nG2+TwL8Y58UP21+ZrCBbEDKKd4XFbCGlXj127NxBUVExVpuVsNAwjh0/5kNSISEhWopTSZKwWa1E\nRESQX1BASUkJkRERlNntBNmCOJl3kuSaNRkzcjQ1k5IYO3E827ZvJyoqiiCbjdjYGsRER7N8xXLs\nDoc7R7TDQc2kmlzR7HJWrV3NIwMGMXzYU8THx/vcR2ZmJnPmPs+7/32Pe/vezcjhIzSJxHt3l/y1\nlDHj08g7dYrpk6dyqyvUPNBP4Vx8XOUN4TD4nM6IK7y+A4qM7FsZxruL37kMxjNupw5ezjWDt428\nXgymNZRe/LoCGlzTJPXylyTwL0WVHTqqVVgAD7JWU6GGhYZiNptpfkVz9u3fT+aRTNZmrCMuNk4h\n3vwS8vPztX4hISHYy+yU2csoKioiODgYWZaJiY7h6LGjnMrPx2QyERsTQ56rAG+LK5ozbdIU1mWs\nY+LUyWRnZ5MQn0B4eDht27Qh/1S+FhhjNpu1SjA1k5K4rMllrNuQQbu2bflg4X+oUaOGzz0eOHiA\n2S88x/sffUj/+x9g4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BYLXTt3YeqESbRu1dpn3OLiYt569x1mPT+Hy5o25b/vLKTD1e0r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\ngWqC/wcENWPFAnpSTAAAAABJRU5ErkJggg==\n" } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we plot the distribution of the line parameters:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "f, (ax1, ax2) = subplots(ncols=2)\n", "\n", "ax1.hist(map(lambda x: x.params['Intercept'], sampleLm))\n", "ax1.set_xlabel('Intercept')\n", "\n", "ax2.hist(map(lambda x: x.params['parent'], sampleLm))\n", "ax2.set_xlabel('Slope')\n", "\n", "f.tight_layout();" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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} ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the Central limit theorem:\n", "\n", "$$\\hat{b}_0 \\sim N(b_0, Var(\\hat{b}_0))$$\n", "$$\\hat{b}_1 \\sim N(b_1, Var(\\hat{b}_1))$$\n", "\n", "which can be estimated with:\n", "\n", "$$\\hat{b}_0 \\approx N(b_0, \\widehat{Var}(\\hat{b}_0))$$\n", "$$\\hat{b}_1 \\approx N(b_1, \\widehat{Var}(\\hat{b}_1))$$\n", "\n", "That is, we can estimate the variance of our estimates using its standard error: $\\sqrt{\\widehat{Var}(\\hat{b}_0)}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The estimate's standar error is computed by the `ols` function, and the value can be accessed in the resulting regression object." ] }, { "cell_type": "code", "collapsed": false, "input": [ "idx = random.sample(np.arange(1e6), 50)\n", "sampleGalton4 = newGalton.ix[idx,:]\n", "\n", "sampleLm4 = ols('child ~ parent', sampleGalton4).fit()\n", "\n", "sampleLm4.summary()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: child R-squared: 0.132
Model: OLS Adj. R-squared: 0.114
Method: Least Squares F-statistic: 7.330
Date: Sat, 23 Mar 2013 Prob (F-statistic): 0.00937
Time: 16:04:39 Log-Likelihood: -114.48
No. Observations: 50 AIC: 233.0
Df Residuals: 48 BIC: 236.8
Df Model: 1
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [95.0% Conf. Int.]
Intercept 32.4634 13.141 2.470 0.017 6.042 58.885
parent 0.5177 0.191 2.707 0.009 0.133 0.902
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 2.024 Durbin-Watson: 2.725
Prob(Omnibus): 0.364 Jarque-Bera (JB): 1.332
Skew: 0.111 Prob(JB): 0.514
Kurtosis: 2.232 Cond. No. 2.62e+03
" ], "output_type": "pyout", "prompt_number": 16, "text": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: child R-squared: 0.132\n", "Model: OLS Adj. R-squared: 0.114\n", "Method: Least Squares F-statistic: 7.330\n", "Date: Sat, 23 Mar 2013 Prob (F-statistic): 0.00937\n", "Time: 16:04:39 Log-Likelihood: -114.48\n", "No. Observations: 50 AIC: 233.0\n", "Df Residuals: 48 BIC: 236.8\n", "Df Model: 1 \n", "==============================================================================\n", " coef std err t P>|t| [95.0% Conf. Int.]\n", "------------------------------------------------------------------------------\n", "Intercept 32.4634 13.141 2.470 0.017 6.042 58.885\n", "parent 0.5177 0.191 2.707 0.009 0.133 0.902\n", "==============================================================================\n", "Omnibus: 2.024 Durbin-Watson: 2.725\n", "Prob(Omnibus): 0.364 Jarque-Bera (JB): 1.332\n", "Skew: 0.111 Prob(JB): 0.514\n", "Kurtosis: 2.232 Cond. No. 2.62e+03\n", "==============================================================================\n", "\n", "The condition number is large, 2.62e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] } ], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "# estimated vs real distribution --- very close\n", "import scipy.stats as sst\n", "\n", "hist(map(lambda x: x.params['parent'], sampleLm), normed=True, bins=10)\n", "xlabel('Slope')\n", "\n", "x = np.linspace(0.2, 1.4, num=100)\n", "y = sst.norm.pdf(x, loc=sampleLm4.params['parent'], scale=sampleLm4.bse[1])\n", "plot(x, y, 'r');" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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Sm1Kwi/jQcUK5CXidO9hEArfyptUtiQ0p2EUs8CyTGUQ6s5jOYsbpvu5iKgW7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\n" } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Standardised coefficients:\n", "\n", "$$\\frac{\\hat{b_0} - b_0}{S.E. (\\hat{b_0})} \\sim t_{n-2}$$\n", "\n", "and\n", "\n", "$$\\frac{\\hat{b_1} - b_1}{S.E. (\\hat{b_1})} \\sim t_{n-2}$$\n", "\n", "That is, the standardised coefficients have a Student's t-distribution with $(n-2)$ Degrees of Freedom.\n", "\n", "Degrees of Freedom $\\approx$ (number of samples - number of things you estimated)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "t-distribution (3 DoF in red, 10 DoF in black) vs normal distribution (the higher the DoF, the closer a t-distribution is to a normal distribution):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = np.linspace(-5, 5, num=100)\n", "plot(x, sst.norm.pdf(x), 'k', linewidth=3)\n", "plot(x, sst.t.pdf(x, 3), 'r', linewidth=3)\n", "plot(x, sst.t.pdf(x, 10), 'b', linewidth=3);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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wv7B5++1Uqm7doIU2eyVnzjCwzUG7wgGASfLwokpJgBduQesZe6MNkdQMrL8DSsaeBwdD\nu3aV2wgPD4c/Ip0Pr6Bly5KtZkA3CfCiSkmAF25BC5y90G4sgg4dIODnFbYKrr656Xrs56VZ+0Op\nPPzBgwc5ffp01bRF1HoS4EWNl5mZyfHjx9GGI2r696dq8+9lvc/69QzoZ7Er1NZmlV68qCo3DPDJ\nycmEhobSsWNHZs6cWao8KSmJiIgIIiMj6dWrF2vtvlQ3OlYIV7BduLQtbt0v6irY3zkaF1c1jQkJ\nQR8fmZ9P36Z77QolwIsqppwoKipSwcHBKiMjQ5nNZhUREaHS09Md6hQUFOjP09LSVHBwcLmPvcHb\nC1EuzzzzjAIUnFSgFCj1c+ImpW9061a1DXrsMf29zW+8rerWtTUFblP9+vWr2vYIt1Pe2OnlLPin\npqYSEhJCUFAQAGPGjCEpKYmwsDC9Tn27eT0KCgpoYR1FUJ5jAWbMmKE/j4uLI66qelrCbWg94vZA\na0C7obTLkeW2CpU9euZad9wBc+cC4L0phT59pmGbLTiW7duXcvXqVXx9fau2XaLGSklJuakZSZ0G\n+KysLAIDA/XtgIAA680kjhYtWsT06dM5efIkq6zzfpT3WPsAL0RFXbx40TrB2Bh9X2wsePxot7i2\n45XOyjdggO355s30faqY9etLsqF9uXr1e3bu3ElsbGyZhwtxrWs7v6+99lq5jnOagzeV866/++67\nj71797JkyRIeffRRWYZPVJkdO3ZgsViwz7/37VMEqam2SvYBtyq0b6+tGgVaHr51hl2h1s6yOjtC\nuJrTAO/v709mZqa+nZmZSYBtgo1SBgwYQFFREefPnycgIKBCxwpxM2yB0i7AN9sLV69qGx07QqtW\nVdsok8nhj0rspR/sCnsCdSTAiyrhNMBHRUVx4MABjhw5gtlsZuHChSQkJDjUOXTokN5j37lzJwDN\nmzcv17FC3CotUDYEugPavUZ9cuzmn6nq3nsZ79t852pCQ0u2fIBeEuBFlXCag/fy8mLOnDnEx8dj\nsViYMGECYWFhJCYmAjB58mS+//575s6di7e3Nw0aNOCbb75xeqwQrqQFyj6AJwDdu0Oj1DW2CtUg\nwLNhA31HKPbtK0l59iUj4x3OnDmDn5+fIc0TtYNJGZgwN5lMkq8XN+3EiRP4+/sDLwOvAzDlyWI+\n/Lop5OdrlQ4e1KYpqGrFxdC8OeTmAvD5X04y8U+trYWLgJEsWbKEEa5eH1bUCuWNnXInq6ixbGkO\n2x2s/QKO2YJ7mzbYLY5atTw8oJ+tXX2Lf7QrlAutompIgBc1lhYgTUCMvq+vOcVWYcCAyp3//Ubs\n0jSdDyyjWbOSrZZAiKzRKiqdBHhRY2kBPgxoDGiDZYJ+XWarYFT+vYz39/hxAzEx9oUxpKamygpP\nolJJgBc1ksViYfv27dj33mNiFKYf7eZ/NzrAR0VBnTra88OHiemab1cYQ35+Pvv37zekaaJ2kAAv\naqT09HQKCgpwCPAh5+DUKW2jcWNtAQ4j+fhAdLS+GeO9065Qa7fk4UVlkgAvaiRbYLQL8F7bbRX6\n9QNPz6ptVFnsfkX0Obvc7pJABFBXAryoVBLgRY1ku8GpK6ANWonKXmqrYDeCxVB27Wi8/Qdst4J4\nITc8icomAV7USFpg7E3JR7h7d2jw0zpbheoS4GNibCN59uwhplehfSFpaWlcunTJkKYJ9ycBXtQ4\nFy9e5Ndff8UhPRN5BdLTtQ0vL+jd25jGXatJE+iq/crAYiHG75BdYQwWi4Vdu3YZ0jTh/iTAixpn\n586d1uGFdhcwm9iNRomMhHr1qr5h12P3ayLmaopdgdb+n376qWrbI2oNCfCixknVpwK268Hbz9hY\nXdIzJeza0+XAYho0KNkKAPwlwItKIwFe1DhaQGyPdkeolgXptG+JrUI1DvCeWzfRp4/9HCIxdn+w\nhHAtCfCixtECvK33Ht2nGI+f7Eaj9O1b+iAjtW9vm5M+P5+YDmfsCmM4ePAgOTk5hjRNuDcJ8KJG\nOXv2LIcPH8YhwAeehMuXtY2gINtqStWFyeTQi4/22mFXqJ2HdleuEK4lAV7UKLZAaJd/97BLcVS3\n9EwJ+wB/xm68Pr0Ab0nTiEohAV7UKFog9AV66Pv6nEyyVagBAb7VzhW0b1+yVRcIlwutolJIgBc1\nihYII9GWvoOOHRXNd9gt0Vfd8u8lIiNtE49lZBAdftmuMFp68KJSSIAXNYZSyhoIbePfo7tehJMn\ntY2GDY2fYOx6fHwcbr6KbvqbXWE0J0+eJCsrq+rbJdzaDQN8cnIyoaGhdOzYkZkzZ5Yqnz9/PhER\nEYSHh9OvXz/S0tL0sqCgIMLDw4mMjKRPnz6ubbmodTIzMzl9+jQOAb7RXluF2NjqMcHY9djn4a+s\ntyuQG55E5XAa4C0WC1OnTiU5OZn09HQWLFjA3r17Hep06NCBDRs2kJaWxssvv8zvf/97vcxkMpGS\nksKuXbvkJ6i4ZbYAaH+D01pbheqanilh177Iw9/j7V2y1RloKt8R4XJOA3xqaiohISEEBQXh7e3N\nmDFjSEpKcqgTGxtL48baijrR0dEcP37coVwW1RauogVAP7SbnMDXF8L3/9tWobpeYC0RG6s/rbNr\nCxHd7Vdz6iM9eOFyXs4Ks7KyCAwM1LcDAgKcTm/6+eefc/fdd+vbJpOJwYMH4+npyeTJk5k0aVKp\nY2bMmKE/j4uLIy4urgLNF7WJFgBt6ZmeEUX4bLdO1OXhAdU9DdiiBXTuDPv3Q2Eh0UHZbN9ZMmY/\nmu3b30cphcnIdWRFtZSSkkJKSkqFj3Ma4CvyQVu3bh1ffPEFmzZt0vdt2rSJNm3acObMGYYMGUJo\naCgDrllGzT7AC3E9xcXF7NixA3hR3xcdkAWp1l5w9+7QqJExjauIvn21AA/EeO/gA2wBPjc3l4MH\nD9KxY0fj2ieqpWs7v6+99lq5jnOaovH39yczM1PfzszMJCAgoFS9tLQ0Jk2axOLFi2natKm+v02b\nNgD4+fkxcuRIyTGKm/bbb7+Rn5+PwwVWD7uURnVPz5RwuOHJboFwudAqKoHTAB8VFcWBAwc4cuQI\nZrOZhQsXkpCQ4FDn2LFjjBo1iq+++oqQkBB9/6VLl7hw4QKgzd+9atUqunfvXgmnIGoDLfCZAFsa\nJubUYluF6n6BtYRdO0P2fE+zZiXXqJoDIRLghUs5TdF4eXkxZ84c4uPjsVgsTJgwgbCwMBITEwGY\nPHkyr7/+Ojk5OUyZMgUAb2/ttuvs7GxGjRoFQFFREePGjWPo0KGVfDrCXWmBLxTQLui3bKlot2uR\nrUJN6cF37gzNmsH585jOnaXPgEskb6xvLYyWAC9cyqQMHOZiMplklI0ol9jYWLZuDQW+BOCeQXks\nXt9EK2zTBrKyoKZcnBwxApZp6ZkZ9+7itaSSaRdmU7fuNPLz8/Hyctr3ErVceWOn3Mkqqr3CwkJ2\n796N4w1O+2wV+vWrOcEdnNzwFMPly5dJL1l6UIhbJAFeVHu//PILV65cwWGK4Et2C2zXlPx7Cbv2\nRh/5xq4gAvCVNI1wGQnwotrTAl49QLtIbzJBn4Nf2yrUtADfu7e2MDjQbP9WOoVYrAU+QKQEeOEy\nEuBFtacFvChAm2emS6dCGh39WSusW1ebqbEmqVcPevbUN6PbnrQrjJEAL1xGAryo9q5doi/G33Zv\nBn36aDM11jR2efgYL/vVnGJIS0uzpqSEuDUS4EW1dunSJX755RfsL7DGmOymy+jfv+ob5Qp27Y45\nbbdgONEUFRWxZ8+eqm+TcDsS4EW1tnv3biwWC2CbqCv6pN3495oa4O168N3TF1KnTsmQtyCgtaRp\nhEtIgBfVmhboAgFt2osGDRRd9v5HKzSZHGZorFFatQLrnd/e5otEdbpgVyg3PAnXkAAvqrVr8+99\nQnLwVEXaRvfuYJ2qukayT9M0sRvXLxdahYtIgBfV2rVL9MU0/MVWWFPTMyXsA7z9wiVEs2/fPuvk\nakLcPAnwotrKycnhwIEDONzglL/aVqGmzD9zPfZ3tB6cb1fQG6U8rNMjC3HzJMCLamv79u2AN9BL\n3xd94CtbhZreg+/cGZo3ByAg9xf8WxVaCxoAXWV6bXHLJMCLaksLcOFAHQDa+1+l1aUjWmFgILRt\na1TTXMNkckzT+NsvdxktAV7cMgnwotoqdYNTqyO2wpqenilhf8OT/fh+YuVCq7hlEuBFtaX1YO3G\nvxdvthXW9PRMCfse/Mn/2BXEkJmZSXZ2dtW3SbgNCfCiWsrKyuLkyZOAbSKxvscW2iq4S4Dv1Qvq\naCmoXieW4OVVcsNTGNBUevHilkiAF9WS1ntvBbQHoI5vMRHnrUMJmzTRxsC7Ax8f/Watulwhst15\nu8IYycOLWyIBXlRLWs/Vlp7p3fYUPlhHmQwYAB5u9NEdOFB/2rfebruCvtKDF7fEjb4lwp1oPVdb\neibW225M+KBBVd+gymR3PrHnl9sVxJKamirLWoqbdsMAn5ycTGhoKB07dmTmzJmlyufPn09ERATh\n4eH069ePtLS0ch8rRFmKi4tL9eBjTyfZKtj1eN1CdDR4ewMQm/Vvu4I+5OTkc+jQIWPaJWo+5URR\nUZEKDg5WGRkZymw2q4iICJWenu5QZ/PmzSo3N1cppdSKFStUdHR0uY+9wduLWmrfvn0KvBVcVqAU\nKJVNS+1J/fpKFRYa3UTX69tXKVDFoPybXdLPGyLU119/bXTrRDVT3tjptAefmppKSEgIQUFBeHt7\nM2bMGJKSkhzqxMbG0tg64VN0dDTHjx8v97FClEVLz0RScoNTh5YXaMVprbBfP325O7di/VViAmKb\n7bcriGXbtm1lHiLEjTj9pmRlZREYGKhvBwQEOP2wff7559x9990VOnbGjBn687i4OOLi4srbduGm\ntm7din16pm/DXyiJ726XnikxcCC8/TYAfS+v4Tt6WAv6sm3bh8a1S1QLKSkppKSkVPg4pwHeZDKV\n+4XWrVvHF198waZNmyp0rH2AFwKwdgRe1Ldj81faCt3tAmuJfv20kUHFxcRmfQ+8YC2IZdeuSZjN\nZnxq4tKEwiWu7fy+9tpr5TrOaYrG39+fzEzb+peZmZkEBASUqpeWlsakSZNYvHgxTZs2rdCxQti7\nfPmydbk6uxE0Z6ypPV9f6N3bmIZVtkaN9MXDI9mJj5fFWhDC1auNZAk/cVOcBvioqCgOHDjAkSNH\nMJvNLFy4kISEBIc6x44dY9SoUXz11VeEWFeoKe+xQlxr165dFBW1QlvFCer7FtKdn7XCmBgtyLsr\na/rJFzNRrewWFpc8vLhJTgO8l5cXc+bMIT4+ni5duvDQQw8RFhZGYmIiiYmJALz++uvk5OQwZcoU\nIiMj6dOnj9NjhXBGy7/beu99mh/GC2tv1l3z7yXszi/W8qNdQT/r/xchKsZkHXJjzJubTHITh3Dw\n0EMP8e23/YBnAfhzsw954/zTWuG6deDOF+FzcrT54ZXiv6ZRjFLfWws2ERLyO+viJ0KUP3bKnayi\nWtFSEbaJxPqft+bf69TRUjTurGlT6NkTgP5qg11Bbw4ePM65c+eMaZeosSTAi2ojOzubo0fPAxEA\neJiKiWWLVtivnz7rolu74w4A/DhL56anrDt9gCiZeExUmAR4UW1ovfdYwBOAiKbHaMQFrdAa+Nye\n3Xn2xz4P31/y8KLCJMCLaqNUesa81lZYWwJ8//76nbr9c5bYF8hIGlFhEuBFtVEqwBcka08aNoSo\nKGMaVdUaNNAmH+PaHnw/tm3bLoMSRIVIgBfVgsViITV1NxCt7+uHdlc0Awe65/wz12P9tRLMIVrX\ny7PubEJu7m0ykkZUiAR4US3s3buXgoKOQD0A2tc/hT8ntMI77zSuYUawnq8J6O9htw4t/dmyZYsh\nTRI1kwR4US1s3rwZh/RM0XpbYW3Jv5eIidFHDOlpKm1LAryoEAnwolq4NsAPuLpae9K8ufusv1pe\nvr76ouLXjqTR/j8JUT4S4EW1sGnTNT34ksB2++3utf5qeVl/tUSwhwZel6072/Lzz3nk5eVd/zgh\n7NTCb46obs6ePcvBg15ACwCaeefTGeuiF0OHGtcwI1nP2wsLsSb78e8D5IYnUW4S4IXhtLxynL49\n0LIOD6waXbRyAAAgAElEQVTDAePjDWmT4SIjwc8PgIGFP9gVxEmaRpSbBHhhOC1gxenbccXWG5zC\nwqBtW0PaZDgPD70XH0eKXYEEeFF+EuCF4bT8e5y+rQe02tp7L2E9/978RF2PK9adIWzenInFYrn+\ncUJYSYAXhiosLGTbtnygJQDNPHJsC3wMG2Zcw6oDaw/eFzN91SZ9d0FBT9LT041qlahBJMALQ+3e\nvRuz2bbA9qBia/69Th33X+DjRlq10pfxu13ZzcsjaRpRThLghaFK5d9L0jMDB0LdukY0qXqxpmkk\nDy9uhgR4Yajr5t9re3qmhPX/Q29+oi4l4+FDWL/+sHFtEjWGBHhhGKUUGzacQc+/c45u/KIV1vYL\nrCViY6FBA3wopJ/dXa1Hj7bj9OnTBjZM1AQ3DPDJycmEhobSsWNHZs6cWap83759xMbGUqdOHd59\n912HsqCgIMLDwx0W4xaixNGjRzl1KlTfHsR6Lf8eEKANkRTg46NPPnZtmubHH38s8xAhSjgN8BaL\nhalTp5KcnEx6ejoLFixg7969DnWaN2/O7NmzeeGFF0odbzKZSElJYdeuXXL3nShlw4YNlJmeGTEC\nTCYjmlQ9DR8OlA7w2v8/Ia7PaYBPTU0lJCSEoKAgvL29GTNmDElJSQ51/Pz8iIqKwtvbu8zXkAUK\nxPVs2PAjZQb4hAQjmlN9jRgBlOThL1l3hvDDDzI3vHDO6SoKWVlZBAYG6tsBAQEVWjbMZDIxePBg\nPD09mTx5MpMmTSpVZ8aMGfrzuLg44uLiyv36omZbvfoUJfn35pzV8u/162sTjAmbNm2gTx98UlPp\nz4+sRhsf/+uvrcnLy6Nx48YGN1BUtpSUFFJSUip8nNMAb7rFn8mbNm2iTZs2nDlzhiFDhhAaGsqA\nAQMc6tgHeFF7ZGdnc+xYZ317MGu0/PvQofpc6MLOPfdAaipDWK0HeKWGsHnzZu666y6DGycq27Wd\n39dee61cxzlN0fj7+5OZmalvZ2ZmEhAQUO5GtWnTBtDSOCNHjpQ8vNBpFwiH6NtDWaU9kfRM2az/\nX4aw2m7nndY0lxBlcxrgo6KiOHDgAEeOHMFsNrNw4UISrvMFvDbXfunSJS5cuADAxYsXWbVqFd1r\n28IN4rrWrt0C2H7NDWG1dmHVekFRXKN7d2jXjnDSaMkp604/Vqw4aWizRPXmNEXj5eXFnDlziI+P\nx2KxMGHCBMLCwkhMTARg8uTJZGdn07t3b/Lz8/Hw8GDWrFmkp6dz+vRpRo0aBUBRURHjxo1jaG2d\n21uUsnLlRUBLxXRmH4Ech9i++hS54homE9xzDx5z5jCYNXzNOAB+/rk1ly9fpq7c9SvKYFIGDnMx\nmUwyyqYWys3NpWnTT4CXAJjKbGbzLLz9NkybZmzjqrPVq2HoUP7JeB7nn9ada0hJ8WbQoEFGtkxU\nsfLGTrmTVVS5TZs2Ifn3mzBoEDRseE0evj8//CDz0oiySYAXVW7Fih2ANkuiF4Xa+PdOnSA01Olx\ntZ6PDwwfjj8nCKNkuuA6LF0qa7SKskmAF1UuOblIfx7DVhpSAA8+KHevlseDDwKOo2l+/rk1ZrPZ\nqBaJakwCvKhSeXl5HDrUQd/WA9Xo0Qa1qIYZNgwaNHAI8EVFt1foBkRRe0iAF1UqJWUDYJspciir\noHNnbRiguLG6deGee4gjBW9Keu0RLFr0k6HNEtWTBHhRpb755jdAuwGuBWfozU9a713SM+U3ejQN\nuMhAbJONLV4sa7SK0iTAiyq1dq1tGoK7WIEnxXpeWZSTNU0zgqX6rkOHOnPx4kUDGyWqIwnwosqc\nOnWK06dt6wKMYKmWnunWzcBW1UDWNI19gFfqTtas2eTkIFEbSYAXVeY//9kC9AbAkyIt/y7pmZsz\nejQhHKIT+6076jN37jFDmySqHwnwososWJCrPx/ARpqQJ+mZmzVsGDRs6NCL37ixoYENEtWRBHhR\nZXbsaKM/H8FS6NFDRs/crLp1YfRohwB/5kw0586dN7BRorqRAC+qxP79R7h0qZ++PZxlMH68gS1y\nA+PH058faUTJnaxBzJ27w9AmiepFAryoEomJe4EGAARzkM4eB2HsWGMbVdP17493+0DiWanv+vbb\nAgMbJKobCfCiSixZYruQOpxlmO6+C1q2NLBFbsDDAx57TPs1ZLV7d1sDGySqGwnwotKZzUUcOhSu\nbyewWNIzrvLYY9zNcjzQbnS6cqUXP/542OBGiepCAryodF9+mY5StwHa4toDm6Rpa4yKW9ehA34D\nwrQZOa3+8Q8ZLik0EuBFpfvii3z9+X0swvvh0eDra2CL3Mz48TzAd/rmunVNDWyMqE5kRSdRqZSC\ner5ZXCn0B2AFwxj20/+DqCiDW+ZG8vM50TqCgMuHUHgAFg4fvkr79vWMbpmoJLKik6gWVq48qwf3\nJuQwqEeOBHdXa9SI28YPoz8/Wnd48ve/HzK0SaJ6uGGAT05OJjQ0lI4dOzJz5sxS5fv27SM2NpY6\nderw7rvvVuhY4f5mv5+lP09gMXWfm2Jga9zYlCkOaZpl/5HpH8QNUjQWi4XOnTuzZs0a/P396d27\nNwsWLCAsLEyvc+bMGY4ePcqiRYto2rQpf/zjH8t9rKRo3JtS4Fcvk3NXAgH4zud+7s/9SrsLU7jc\nr6GD6bZ/DQAeFHHqjCctWkigd0cuSdGkpqYSEhJCUFAQ3t7ejBkzhqSkJIc6fn5+REVF4e3tXeFj\nhXvbubNID+4NuED06KYS3CtRp+mPEsMWAIrx4pPEkwa3SBjNy1lhVlYWgYGB+nZAQEC5lwYr77Ez\nZszQn8fFxREXF1eu1xfV3/tvHAS0hbRHsBT/V14ytkFuznvMGIZPeJmtllgAvv0wh//7020Gt0q4\nQkpKCikpKRU+zmmAN93CNK7lPdY+wAv3YbHAiuW24Xr9m6/C1OlhA1tUC/j6EtX/BKb1xSg8SDsR\nRlYW+Psb3TBxq67t/L722mvlOs5pisbf35/MzEx9OzMzk4CAgHK98K0cK2q+dYvzOVPYCtCW5us5\npb3BLaodIt95jttZC4DCg89n7L/BEcKdOQ3wUVFRHDhwgCNHjmA2m1m4cCEJCQll1r024V+RY4X7\n+fT/0vXn8XxDzz9JeqYqtOrdmx4NFunbX3/liYxjqL2cpmi8vLyYM2cO8fHxWCwWJkyYQFhYGImJ\niQBMnjyZ7OxsevfuTX5+Ph4eHsyaNYv09HQaNGhQ5rHC/V08e5ll+2zL8Pl324lvnTpOjhCuFPK7\nRtSdc4nL1GP/lRD2LD5Kj3vbGd0sYQC5k1W43Pwn1vDIl4MBCGEvb87fzeixkn+vKocOHWJiyBZS\neASA57om849fhhncKuFKcierMIbFwr8W2IbMtjF9xV0JMrFYVQoODsan9Rp9+5tfe1CUKUMmayMJ\n8MKlTsz5Dz9c6a9vNxp0nAYNGhjYotopemJ7mqMF9VO0ZvUziw1ukTCCBHjhOmYzn804TjGeAASx\nlgfG325wo2qnB0aPpDHz9e3ExW3gmEwjXNtIgBcuU/Tpl3ySO1rfPm36hHtk3ndDdO/eHXPAcn17\niRrOsWkfGNgiYQQJ8MI1Ll9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} ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Confidence intervals: We have an estimate $b_1$ and we want to know something about how good our estimate is. One way is to create a \"level $\\alpha$ confidence interval\".\n", "\n", "A confidence interval
will include the real parameter
$\\alpha$ percent of the time
in repeated studies.
" ] }, { "cell_type": "code", "collapsed": false, "input": [ "sampleLm4.params" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 20, "text": [ "Intercept 32.463411\n", "parent 0.517689" ] } ], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "sampleLm4.conf_int()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
01
Intercept 6.041595 58.885228
parent 0.133226 0.902152
\n", "
" ], "output_type": "pyout", "prompt_number": 19, "text": [ " 0 1\n", "Intercept 6.041595 58.885228\n", "parent 0.133226 0.902152" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "How to report the inference? A one inch increase in parental height is associated with a 0.52 inch increase in child's height (95% CI: 0.13 - 0.92 inches)." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "
P-values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Most common measure of \"statistical significance\"\n", "* Commonly reported in papers\n", "* Used for decision making (e.g. FDA)\n", "* Controversial among statisticians\n", "\n", "Approach:\n", "\n", "* Define the hypothetical distribution of a data summary (statistic) when \"nothing is going on\" (null hypothesis)\n", "* Calculate the summary/statistic with the data we have (test statistic)\n", "* Compare what we calculated to our hypothetical distribution and see if the value is \"extreme\" (p-value)\n", "\n", "Our standardised slope parameter:\n", "\n", "$$\\frac{\\hat{b_1} - b_1}{S.E. (\\hat{b_1})} \\sim t_{n-2}$$\n", "\n", "Define the null hypothesis: \n", "\n", "$H_0$: There is no relationship between parent and child height\n", "\n", "That is, the distribution of the slope parameter under the null hypothesis (the null distribution):\n", "\n", "$$\\frac{\\hat{b_1}}{S.E. (\\hat{b_1})} \\sim t_{n-2}$$\n", "\n", "The alternative to the the null hypothesis (alternate hypothesis):\n", "\n", "$H_a$: There is a relationship, i.e. $b_i \\neq 0$\n", "\n", "This is a two-tailed test." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the null distribution together with the observed statistics (t-value):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# null distribution\n", "x = np.linspace(-20, 20, num=100)\n", "plot(x, sst.t.pdf(x, (928 - 2)), linewidth=3)\n", "arr = Arrow(lm1.tvalues[1], .25, 0, -0.25, lw=3, fc='r', ec='r')\n", "ax = gca()\n", "ax.add_patch(arr);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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} ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's obvious from the figure that in this case, the probability of obtaining such results, given the null distribution, is very low. So we reject the null hypothesis.\n", "\n", "How to compute p-values?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "lm1.summary()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: child R-squared: 0.210
Model: OLS Adj. R-squared: 0.210
Method: Least Squares F-statistic: 246.8
Date: Sat, 23 Mar 2013 Prob (F-statistic): 1.73e-49
Time: 16:41:26 Log-Likelihood: -2063.6
No. Observations: 928 AIC: 4131.
Df Residuals: 926 BIC: 4141.
Df Model: 1
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [95.0% Conf. Int.]
Intercept 23.9415 2.811 8.517 0.000 18.425 29.458
parent 0.6463 0.041 15.711 0.000 0.566 0.727
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 11.057 Durbin-Watson: 0.046
Prob(Omnibus): 0.004 Jarque-Bera (JB): 10.944
Skew: -0.241 Prob(JB): 0.00420
Kurtosis: 2.775 Cond. No. 2.61e+03
" ], "output_type": "pyout", "prompt_number": 22, "text": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: child R-squared: 0.210\n", "Model: OLS Adj. R-squared: 0.210\n", "Method: Least Squares F-statistic: 246.8\n", "Date: Sat, 23 Mar 2013 Prob (F-statistic): 1.73e-49\n", "Time: 16:41:26 Log-Likelihood: -2063.6\n", "No. Observations: 928 AIC: 4131.\n", "Df Residuals: 926 BIC: 4141.\n", "Df Model: 1 \n", "==============================================================================\n", " coef std err t P>|t| [95.0% Conf. Int.]\n", "------------------------------------------------------------------------------\n", "Intercept 23.9415 2.811 8.517 0.000 18.425 29.458\n", "parent 0.6463 0.041 15.711 0.000 0.566 0.727\n", "==============================================================================\n", "Omnibus: 11.057 Durbin-Watson: 0.046\n", "Prob(Omnibus): 0.004 Jarque-Bera (JB): 10.944\n", "Skew: -0.241 Prob(JB): 0.00420\n", "Kurtosis: 2.775 Cond. No. 2.61e+03\n", "==============================================================================\n", "\n", "The condition number is large, 2.61e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] } ], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [ "lm1.pvalues" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 24, "text": [ "Intercept 6.536845e-17\n", "parent 1.732509e-49" ] } ], "prompt_number": 24 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some typical values:\n", "\n", "* $P < 0.05$ (significant)\n", "* $P < 0.01$ (strongly significant)\n", "* $P < 0.001$ (very significant)\n", "\n", "In modern analyses, people generally report both the confidence interval and P-value. This is less true if many many hypotheses are tested.\n", "\n", "How to interpret the results: A one inch increase in parental height is associated with a 0.52 inch increase in child's height (95% CI: 0.13 - 0.92 inches). This difference was statistically significant $(P < 0.001)$" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }