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\n", " \n", "
\n", "\n", "# Exploratory Computing with Python\n", "*Developed by Mark Bakker*\n", "## Statistics Notebook 4: Linear regression and curve fitting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook we will perform linear regression on some of the data in the data set on wooden beams, and we perform do curve fitting on a data set of groundwater head observations" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Linear regression\n", "We apply linear regression to fit a straight line through a set of data. The function `polyfit` fits a polynomial of arbitrary degree through a set of data (`polyfit` is part of the `numpy` package). The input arguments are `x,y,degree`. When the degree of the polynomial is 1, it fits a straight line of the form $y=p[0]*x+p[1]$ and it returns the array of parameters `p`. The parameters are obtained by `polyfit` by minimizing the sum of the squares of the errors between the data (the $y$-values) and the fitted polynomial. For example, consider the `xdata` and `ydata` below. The slope and $y$-intercept of the best-fit line are computed and both the data and best-fit line are drawn." ] }, { "cell_type": "code", "collapsed": false, "input": [ "xdata = array([0.0,1.0,2.0,3.0,4.0,5.0]) # Observed value of x\n", "ydata = array([1.0,3.0,2.0,5.0,5.0,6.0]) # Observed value of y\n", "a,b = polyfit(xdata,ydata,1)\n", "print 'fitted slope: ',a\n", "print 'fitted y-intercept: ',b\n", "plot(xdata, ydata, 'bo', label='observed')\n", "yfit = a*xdata + b\n", "error = ydata - yfit # Error\n", "plot(xdata, yfit, 'r', label='fit')\n", "xlabel('xdata')\n", "ylabel('ydata')\n", "legend(loc='best')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "fitted slope: 0.971428571429\n", "fitted y-intercept: 1.2380952381\n" ] }, { "output_type": "pyout", "prompt_number": 9, "text": [ "" ] }, { "output_type": "display_data", "png": 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ViYhD9HO6NysogPffhwkTbL/6ypUQGel0VSLiARTu3mrVKtsBExAAb78NMTFO\nVyQiHkTh7m22brW96gcO2I0yevZU94uI/Irm3L3FgQN24+lOnWxr486dduVGBbuIXILC3dMdPw4j\nR0Lz5lC/PuzbB089BeXLO12ZiHgwhbunOncOpk+329kZA7t22W3ubrjB6cpExAso3D1Nbi689ZZt\na0xNhQ0bYN48qFnT6cpExIvohqqnMAY+/NA+dHTbbbBihd2MWkTkGijcPUFysm1rzM2FN96Adu2c\nrkhEvJzC3Unbt9u2xt277fx67962b11E5DopSZzw3Xd28+l27aBjR3uztG9fBbuIlBqlSVk6eRJG\nj4amTaFOHdvWOGKEXeRLRKQUuTXcDx06RNu2bbn77ruJjo5m8eLF7hzOc50/bzfJqF8fLlywXTBT\np0Llyk5XJiI+ymWMMe568aNHj3L06FEiIyM5ceIEUVFRbNu2jRtvvNEO7nLhxuGdl5cH8+fD5MnQ\nqpWdV69Xz+mqRMTLlSQ73XpDNTQ0lNDQUABq1KjB3XffzebNm2nbtq07h3WeMfDxxzB+PISEwNKl\nEBXldFUeLyFhNfPmJZGTE0hQUB4jRrSnc2ft8ypyLcqsW2b//v2kpqYS5esht2aNbWvMyrJrqnfs\nqPVfSiAhYTUjRyaSljaj8Fha2gQABbzINSiTG6pZWVn06tWLOXPmUMlXdwXauRMefhgeewz+8Ae7\neuODDyrYS2jevKQiwQ6QljaD+PhPHapIxLu5/co9NzeXHj160L9/fx5++OFffX7y5MmFv46OjiY6\nOtrdJZWuw4ft1nYrVtie9ffeg+Bgp6vyOjk5l/6rmJ1drowrEfE8ycnJJCcnX9XXuPWGqjGGgQMH\nUqNGDWbPnv3rwb35hmpmJrz0EvztbzB0KIwdC1WrOl2V1+rQ4XmSkqZf4vhEVq6c5kBFIp6rJNnp\n1mmZtWvXsmjRIj7//HOaNGlCkyZNWLlypTuHdL/sbHj1VdvWmJlpnzKdOVPBfp1GjGhPePiEIsfC\nw+MYPlxLMYhcC7deuRc7uDdduefnwz/+YZfdbdbMBnqDBk5X5VMSElYTH/8p2dnlCA7OZ/jwdrqZ\nKnIJJclOhXtxjIGEBDufXrUqvPKK7VkXEXGI433uXm/9etvWeOKEnV/v0kXdLyLiFbS2zKXs2QM9\netg9Sh9/3M6rd+2qYBcRr6Fw/7n0dNv5ct990KIF7N0LgwZBObXjiYh3UbgDnD4NEybAPfdAlSr2\nyn3sWKjNvNlbAAAIPElEQVRQwenKRESuiX+He04OvPaaXcwrIwO++cbeMK1e3enKRESui3/eUC0o\ngMWLYeJEe7X+2WfQsKHTVYmIlBr/CndjIDHRtjVWqAALFkAb9VGLiO/xn3DftMm2Naan240zunVT\n94uI+Czfn3Pfvx969bJh3qcP7NgBsbEKdhHxab4b7seOwR//CC1bQuPGdr/SIUMg0H9+WBER/+V7\n4Z6VZZfgjYiwG0/v3g1xcVCxotOViYiUGd8J94sX4fXXoW5d+PZbSEmxOyHVqOF0ZSIiZc775ygK\nCuD99+1DSPXq2W6Yxo2drkpExFHeHe6rVtkOmIAAePttiIlxuiIREY/gneG+davtVT9wwK6r3rOn\nul9ERH7Gu+bcDxyAfv2gUyfb2rhzp125UcEuIlKEd4T78eMwciQ0b263t9u3D556CsqXd7oyERGP\n5Nnhfu4cTJ9ut7MzBnbtstvc3XCD05WJiHg0zwz33Fx46y3b1piaChs2wLx5ULOm05WJiHgFz7qh\nagx8+KF96KhOHVixwm5GLSIiV8Vzwv3LL+0GGbm58MYb0K6d0xWJiHgt58N9+3YYP97Op8+YYRf5\nCvDM2SIREW/hMsYYxwZ3uTAhIfbp0qFD4Te/caoUERGv4XK5KC66nQ/306ehcmWnShAR8TreEe7O\nDS8i4pVKkp2a3BYR8UEKdxERH+TWcB88eDAhISHcc8897hxGRER+wa3hPmjQIFauXOnOIXxGcnKy\n0yV4DL0XP9F78RO9F1fHreHeunVrqlWrdsVzOnR4noSE1e4swyvoL+5P9F78RO/FT/ReXB3HH2JK\nSppOWtoEADp3buNwNSIivsEjbqimpc0gPv5Tp8sQEfEZbu9zP3jwIF27duU///nPrwd33QmkuXN4\nERGfEx4ezv79+694jqPTMsZcuTgREbk2bp2W6dOnD61atWLv3r3Url2bd955x53DiYjIfzm6/ICI\niLiHYzdUV69eTYMGDahbty7x8fFOleE4Pej1k0OHDtG2bVvuvvtuoqOjWbx4sdMlOSY7O5sWLVoQ\nGRlJy5YtmTNnjtMlOS4/P58mTZrQtWtXp0txVFhYGI0aNaJJkyZERUVd9jzHrtybNGnC3LlzqVOn\nDh06dGDNmjXUqFHDiVIc9dVXX3HDDTcwYMCAS9509idHjx7l6NGjREZGcuLECaKioti2bRs33nij\n06U54vz581SsWJGcnByaNWvGRx99xJ133ul0WY6ZPXs2KSkpZGVlsXz5cqfLccztt99OSkoK1atX\nv+J5jly5nz59GoA2bdpQp04d2rdvz4YNG5woxXEledDLX4SGhhIZGQlAjRo1uPvuu9m8ebPDVTmn\nYsWKAJw9e5a8vDyCgoIcrsg5hw8f5l//+hdPPPGEVpKFEr0HjoT7pk2buOuuuwp/HxERwfr1650o\nRTzU/v37SU1NveKPnb6uoKCAxo0bExISwrBhw6hdu7bTJTlm1KhRzJo1iwDt0obL5SImJoZu3bpd\n8ScYvVPicbKysujVqxdz5syhUqVKTpfjmICAALZt28b+/ft588032bp1q9MlOeKTTz6hZs2aNGnS\nRFftwNq1a9m2bRsvvvgizzzzDEePHr3keY6Ee/Pmzdm9e3fh71NTU2nZsqUTpYiHyc3NpUePHvTv\n35+HH37Y6XI8QlhYGJ06dfLbqct169axfPlybr/9dvr06cPnn3/OgAEDnC7LMbVq1QKgQYMGPPTQ\nQ6xYseKS5zkS7lWqVAFsx8zBgwf59NNPadGihROliAcxxvD73/+ehg0b8qc//cnpchx14sQJTp06\nBcDJkydJSkry23/sZs6cyaFDh/j2229ZsmQJMTExLFy40OmyHHH+/HmysrIAOH78OImJiXTs2PGS\n5zr2hOprr73G0KFDyc3NZcSIEX7ZKQP2Qa8vv/ySkydPUrt2baZOncqgQYOcLssRa9euZdGiRYVt\nXgAvvvjiZf/y+rKMjAwGDhxIfn4+oaGhjBkzpvCKzd+5XC6nS3DMsWPHiI2NBeCmm25i9OjRl70X\no4eYRER8kG6oioj4IIW7iIgPUriLiPgghbuIiA9SuIuI+CCFu4iID1K4iwCPP/44H3744RXPWbBg\nARkZGWVUkcj1UbiLYB+MKe7hmPnz55Oenl5GFYlcH4W7+LxNmzbRuHFjcnJyOHfuHA0bNmTHjh3E\nx8fTqFEjOnTowKlTpwoXpZo6dSpRUVE0b96cmTNnAvDBBx+wefNm+vXrR9OmTcnOzr7keSKeQk+o\nil+YOHEi2dnZXLhwgdq1a9OuXTuGDRvGypUrOXz4MM2aNePdd9+le/fuZGZmUq1aNfLz84mNjWXW\nrFnUr1+ftm3b8uc//5mmTZsCXPY8EU+gK3fxC5MmTSIpKYmUlBSeffZZ/v3vf9OzZ08qV65MRERE\nkYXrNm/eTI8ePWjUqBFbtmwhKSmp8HM/vxb65XmJiYll+v8kciWOLRwmUpZOnDjBuXPnyM/PJzs7\nG5fLVSSof5xvN8YwfPhwPvjgAxo2bMioUaPIzMy86vNEnKYrd/ELQ4cOZfr06fTt25fnnnuOBx98\nkGXLlnHmzBl27dpVuBNYTk4OWVlZhIWFceTIET7++OPC16hTpw7ff//9Zc/z59UKxfPoyl183sKF\nCwkKCqJ3794UFBTQqlUrYmNj6d27N/fddx+1atXiwQcfBCA4OJhx48YRFRVF9erV6dSpU+HrPPbY\nY0ycOJG4uDjWrVt32fNEPIFuqIqI+CBNy4iI+CCFu4iID1K4i4j4IIW7iIgPUriLiPgghbuIiA9S\nuIuI+CCFu4iID/r/Kg05f/h1/KUAAAAASUVORK5CYII=\n" } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Exercise 1. Straight line fit between `Edyn` and `Estat`\n", "The data set of experiments on wooden beams contains two measurements of the elasticity modulus. The column labeled `Estat` contains measurements of the elasticity modulus using a standard static bending experiment. The column labeled `Edyn` contains measurements of the elasticity modulus using a dynamic mechanical analysis where an oscillatory force is applied. The two experiments don't give exactly the same value. You are asked to determine the linear relationship between the two measurements. Let's first assume that the measurement of `Estat` is much more accurate than the measurement of `Edyn` (we will consider the reverse some other time).\n", "\n", "Plot the `Edyn` data on the $y$-axis vs. the `Estat` data on the $x$-axis using blue markers. Use `polyfit` to determine the parameters of the best-fit straight line. Add the best-fit straight line as a red line to the graph. Label the axes and add a legend." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from pandas import read_csv\n", "w = read_csv('douglas_data.csv',skiprows=[1],skipinitialspace=True)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "a,b = polyfit(w.Estat,w.Edyn,1)\n", "xfit = linspace(w.Estat.min(),w.Estat.max(),100)\n", "yfit = a * xfit + b\n", "plot(w.Estat,w.Edyn,'bo',label='observed')\n", "plot(xfit,yfit,'r',label='best-fit line')\n", "xlabel('Estat')\n", "ylabel('Edyn')\n", "legend(loc='best')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 5, "text": [ "" ] }, { "output_type": "display_data", "png": 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Qrx+8/jps2wb//S/4+NhG0DpCKZ16SqdOnfjqq6/q5NobNmygW7du3H777fz222+4u7tX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\nd2bOnElWVhYAWVlZjBs3Dnd3d0JDQ1FK6XZBJ0+eJDo6GmdnZyZNmqS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} ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Exercise 2. Error analysis of linear regression of `Edyn` and `Estat`\n", "Compute the difference between the fitted and observed values of `Edyn`; these are called the errors. Compute the mean and standard deviation of the error (if you have done the fit correctly, the mean should be very close to zero). Create a histogram of the errors. Add to the same graph the Normal distribution using the sample mean and sample standard deviation you just computed. On the same graph, add vertical lines for the 2.5 and 97.5 percentiles according to the Normal distribution." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.stats import norm\n", "error = w.Edyn - (a*w.Estat + b)\n", "mu = mean(error)\n", "sig = std(error)\n", "hist(error,normed=True)\n", "x = linspace(-6000,6000,100)\n", "y = norm.pdf(x,loc=mu,scale=sig)\n", "plot(x,y,'r')\n", "x025 = norm.ppf(0.025,loc=mu,scale=sig)\n", "x975 = norm.ppf(0.975,loc=mu,scale=sig)\n", "axvline(x025,color='k')\n", "axvline(x975,color='k')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 6, "text": [ "" ] }, { "output_type": "display_data", "png": 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zM0VE5NChQ7Jp0ybJysqShQsXNqjnkksukTVr1khZWZmkpqZKQUFBo1hb0BzV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\n2DFYsQKSk+HCC52/yIYMMTs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} ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Count how many data points fall outside the 95% interval according to the corresponding Normal distribution. The data points outside the 95% interval are potential outliers. Recreate the plot you made in Exercise 3, but now plot the data points inside the 95% interval with black circles and the data points outside the 95% interval with red circles (refer to Notebook 4 of quarter 1 if you forgot how to do that)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "print 'number of points outside 95 percentile: ',sum(abs(error)>x975)\n", "outside = abs(error)>x975\n", "plot(w.Estat[~outside],w.Edyn[~outside],'ko')\n", "plot(w.Estat[outside],w.Edyn[outside],'ro')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "number of points outside 95 percentile: 19\n" ] }, { "output_type": "pyout", "prompt_number": 7, "text": [ "[]" ] }, { "output_type": "display_data", "png": 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7hfOOHz+OzMxMREdHo6OjQxhvbW2FyWQCAJhMJrS2tiIpKQmXLl3CrFmzJEPw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\nAKdOnRL9rL+/HwcOHAAgHfr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} ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Exercise 3. Fit `Estat` vs `Edyn` or the other way around?\n", "In the previous two exercises, we assumed that `Estat` is more accurate than `Edyn` so we fit: `Edyn = a1 * Estat + b1`; let's call this line 1. Next, we assume `Edyn` is more accurate than `Estat` so we fit `Estat = a2 * Edyn + b2`; let's call this line 2. Plot the `Edyn` data on the $y$-axis vs. the `Estat` data on the $x$-axis using blue markers. Plot the two best-fit lines you computed using red (line 1) and green (line 2), label the axes and add a legend. Report the slope and intercept of the best fit lines as they are shown on the graph (Note: that requires a bit of algebra for line 2 as it needs to be reworked in the form `Edyn = slope * Estat + intercept`)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "a1,b1 = polyfit(w.Estat,w.Edyn,1)\n", "a2,b2 = polyfit(w.Edyn,w.Estat,1)\n", "print 'a1,b1: ',a1,b1\n", "print 'a2,b2: ',1.0/a2,-b2/a2\n", "plot(w.Estat,w.Edyn,'bo',label='observed')\n", "x1 = array([w.Estat.min(),w.Estat.max()])\n", "y1 = a1*x1 + b1\n", "plot(x1,y1,'r',label='line 1')\n", "y2 = 1.0/a2 * x1 - b2/a2\n", "plot(x1,y2,'g',label='line 2')\n", "xlabel('Estat')\n", "ylabel('Edyn')\n", "legend(loc='best')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "a1,b1: 0.836674348143 3010.55026869\n", "a2,b2: 1.11078518985 -625.844196038\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "" ] }, { "metadata": {}, "output_type": 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/+OADMXPmTPHgwQMxY8YM8dFHHwkhhIiPjxf29vbi6tWr4tChQ8LZ2Vl1zeDB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\n1yHTxo72gIA50rLlOOnR41GLIb/Vz2f5s9zCPPkzd8kBPOU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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Exercise 4. Error analysis of `Estat` vs `Edyn` and the other way around.\n", "In the previous exercise, two straight lines were fit of the form `Edyn = slope * Estat + intercept`. Compute and report the mean error and the square root of the mean squared error of both straight lines, where the error is defined as the measured `Edyn` minus the fitted `Edyn`. Plot the errors vs. `Estat` for the two fitted lines with red and green dots, respectively. Does either of the errors show a trend?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "error1 = w.Edyn - a1 * w.Estat - b1\n", "error2 = w.Edyn - 1/a2 * w.Estat + b2/a2\n", "print 'mean error line 1: ',mean(error1)\n", "print 'mean error line 2: ',mean(error2)\n", "print 'mean squared error line 1: ',sqrt(mean(error1**2))\n", "print 'mean squared error line 2: ',sqrt(mean(error2**2))\n", "#\n", "plot(w.Estat,error1,'ro')\n", "plot(w.Estat,error2,'go')\n", "title('Line 2 (green dots) shows a trend')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "mean error line 1: 8.57377589649e-12\n", "mean error line 2: 7.05113869914e-12\n", "mean squared error line 1: 1536.36115\n", "mean squared error line 2: 1770.23176695\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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bj74exMx8qU35bezR0hWR69PWLUtNJAHbgTcALl6EHTuaZc4aGxVFemoqM1at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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Curve fitting\n", "To be added" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }