{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Ordinary Least-Squares with Measurement Error\n", "====\n", "\n", "## Unit 12, Lecture 4\n", "\n", "*Numerical Methods and Statistics*\n", "\n", "----\n", "\n", "#### Prof. Andrew White, April 24 2018" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Goals:\n", "---\n", "\n", "0. Be able to plot with error bars\n", "1. Be able to choose the appropiate case for OLS with measurement error\n", "2. Are aware of attenuation error and its effect on independent variable measurement error" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from math import sqrt, pi, erf\n", "import seaborn\n", "seaborn.set_context(\"notebook\")\n", "seaborn.set_style(\"whitegrid\")\n", "import scipy.stats" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Plotting with Error Bars\n", "===\n", "\n", "Error bars are little lines that go up and down or left and right in graphs to indicate the standard error of a measurement. They may also indicate a confidence interval or standard deviation, however that will usually be specified in the figure caption. The code to make error bar plots is shown below with a constant y-error bar. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.array([1,2,4,4.5,7,10])\n", "y = 3 * x + 2\n", "\n", "#yerr=1 means constant standard error up and down of 1\n", "#fmt is for lines/points and color. capthick is necessary to make the small dashes at the top and bottom\n", "plt.errorbar(x,y, yerr=1, fmt='o', capthick=2) \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Somtimes you have x-error and y-error. You can do that too:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.errorbar(x,y, yerr=1, xerr=0.5, fmt='o', capthick=2) \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "You may have a different error value at each point. Then you pass an array instead:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#THIS IS NOT PART OF PLOTTING ERROR BARS\n", "#DO NOT COPY FOR HW/TEST\n", "#THIS IS TO CREATE FAKE DATA FOR PLOTTING\n", "#create some random numbers to use for my error bars\n", "#squre them to make sure they're positive\n", "yerror = 5*np.random.random(size=len(x))**2\n", "#END\n", "\n", "plt.errorbar(x,y, yerr=yerror, xerr=0.5, fmt='o', capthick=2) \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "If you do quantiling or some other technique that is non-parametric, you often can have error bars that are asymmetric. Then you need to pass in a 2xN array that has the distance up in the first row and distance down in the second row." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#THIS IS NOT PART OF PLOTTING ERROR BARS\n", "#DO NOT COPY FOR HW/TEST\n", "#THIS IS TO CREATE FAKE DATA FOR PLOTTING\n", "#create some random numbers to use for my error bars\n", "#squre them to make sure they're positive\n", "yerror_up = 2.5*np.random.random(size=len(x))**2\n", "yerror_down = 2.5*np.random.random(size=len(x))**2\n", "#END\n", "\n", "yerror = np.row_stack( (yerror_up, yerror_down) )\n", "\n", "plt.errorbar(x,y, yerr=yerror, xerr=0.5, fmt='o', capthick=2) \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Ordinary Least-Squares (OLS) Regression with Measurement Error\n", "====\n", "\n", "We're going to return to regression again. This time with error in both our independent and dependent variables. Here is the list of cases we'll consider:\n", "\n", "1. OLS with constant $y$ uncertainty in 1D\n", "2. OLS with constant $x$ uncertainty in 1D\n", "2. OLS with constant $x,y$ uncertainty in 1D\n", "2. OLS with multiple $y$ values in N-dimensions" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Case 1 - OLS with constant $y$ uncertainty in 1D\n", "===\n", "\n", "In this case we have some constant extra uncertainty in $y$, so that when we measure $y$ we don't get the actual $y$. We get some estimate of $y$. For example, if I'm weighing out a powder and the balance is only accuarate to $2$mg, I don't get the true mass but isntead some estimate with an uncertainty of $2$ mg. That means our measurements for $y$ do not contain the *true* value of y, but are instead an estimate of $y$. We're doing regression and our equation looks like this for the *true* y values:\n", "\n", "$$(y + \\eta) = \\alpha + \\beta x + \\epsilon$$\n", "\n", "where $\\eta$ is the extra uncertainty in $y$. We have measured $(y + \\eta)$ and $x$ for our regression. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We can rearrange the equation a little bit and get:\n", "\n", "$$y = \\alpha + \\beta x + \\epsilon_1$$\n", "\n", "where $\\epsilon_1 = \\epsilon - \\eta$. The $_1$ stands for case 1. Notice that since $\\eta$ and $\\epsilon$ are normally distributed and centered at $0$, we don't actually get a smaller error term for $\\epsilon_1$ than $\\epsilon$. Since we've arraived at the same equation as the usual OLS regression with a slope and intercept, we can use the same equations. EXCEPT, our standard error of $\\epsilon_1$ is slightly different. The standard error is:\n", "\n", "$$ S^2_{\\epsilon_1} = S^2_{\\epsilon} + \\sigma_{\\eta}^2 = \\frac{\\sum_i (y_i - \\hat{y}_i)^2}{N - 2} + \\sigma_{\\eta}^2 $$\n", "\n", "where $S^2_{\\epsilon}$ was our previously used standard error term. The $-2$ term is for the reduction in degrees of freedom \n", "\n", "and $\\sigma_{\\eta}^2$ is the squared error in our measurement. Notice \"error\" here generally means an instrument's stated precision." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### All Equations for Case 1" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "$$\\hat{\\beta} = \\frac{\\sigma_{xy}}{\\sigma_x^2}$$\n", "\n", "$$\\hat{\\alpha} = \\frac{1}{N }\\sum_i (y_i - \\hat{\\beta}x_i)$$\n", "\n", "$$ S^2_{\\epsilon_1} =\\frac{SSR}{N-2} + \\sigma_{\\eta}^2 $$\n", "\n", "$$SSR = \\sum_i (y_i - \\hat{\\beta}x_i - \\hat{\\alpha})^2$$\n", "\n", "$$S^2_{\\alpha} = S^2_{\\epsilon_1} \\left[ \\frac{1}{N - 2} + \\frac{\\bar{x}^2}{\\sum_i\\left(x_i - \\bar{x}\\right)^2}\\right]$$\n", "\n", "$$S^2_{\\beta} = \\frac{S^2_{\\epsilon_1}}{\\sum_i \\left(x_i - \\bar{x}\\right)^2}$$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Case 1 Example \n", "---\n", "\n", "The Gibbs equation for a chemical reaction is:\n", "\n", "$$\\Delta G = \\Delta H - T \\Delta S$$\n", "\n", "where $\\Delta G = -RT\\ln Q$ and $Q$ the equilibrium constant. We can measure $\\Delta G$ by measuring $Q$ and due to instrument precision, we know that the precision (generally 1 standard deviation) of $\\Delta G$ is 2 kcal / mol. What is the change in entropy, given these measurements:\n", "\n", "* $T \\textrm{[K]}$ :300, 312, 325, 345, 355, 400\n", "\n", "* $\\Delta G \\textrm{[kcal/mol]}$: 5.2, 2.9, 0.4, -4.2, -13" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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R3SfgZ3IhsCkifhf4J+CCmuuRJB1GI8Jk8sT7lOm/A06rpxpJ0lw17jCXJKnzGCaSpGKGiSSpWCPOmSyglQBPPvnkkqxsYmJiSdazVLqpn27qBbqrn27qBbqjnyl/M1fO9zUa8Qn4hdJqtU4H7q67DknqUGf09/d/fT4LdtueyT3AGcCjwP4jzCtJqqwEXkT1N3ReumrPRJJUD0/AS5KKGSaSpGKGiSSpmGEiSSpmmEiSihkmkqRihokkqVi3fWhxwUTEVcC5wAHghsz8REScCXwCOBq4OTMvb897MvAp4LnAXwOXZGajngw5Qz+DwG+2x74NvCczn2x6P9P1MuV7lwLnZuaG9vQa4CbgBUACA5n50yUv+jBm2Davp3rU9THAfcCFnbptIuJNwMeoPhh3L/Cudi+N3zaTIuJa4PmZedFM26BT+jmkl3OA3wNWAA8CF2fmj+fTi3sm04iINwK/BrwGOAW4LCJ+CbgROAc4CTg1It7cXuQm4NLMPIFqo7x76aue2Qz9BPBfqZ4b8xqqn4X3tRdpbD+H6YWIeBXw24cs8sfAH2fmiVSBecUSlntEh/lZ+wIwmJmvbs/6n9v/78RtcwPwHzOzD+jl6YfdNXrbTIqIjVQP7Js00zZofD9Te4mI5wJ/ArwlM3+J6k3Lle1Z59yLYTKNzLwL+NX2O74XUO3BHQt8PzMfbI/fBJwXEWuBozNze3vxzcB5NZQ9oxn6+Rnw3sz8SWYeAMaANU3vZ4ZeHo+IHuBPgQ9PzhsRq4B/BdzaHtpMg3qBGfs5GfhmZt7Xnu0y4LZO3TZUeyTPjYiVwC8AT3TCtgGIiOcBw8BH2tPTboNO6OfQXoBVwPsy85H29H1UfwPm1YthMoPM3BcRvwf8PbAVeDHVPb8mPQq89DDjjTJNPzsz806AiDgOuBT4Ih3QzzS9PAJ8lGrP8R+nzPp84CdTDgM1rheYtp/jgZ9GxOcj4rtUhyH+mc7dNu8FtgE/oNomt9Ih24bqDcoQ8OP29EzboBP6OaiXzPxhZt4GEBFHU+3V/y/m2YthchiZ+bvAccDLgBOojgNPWgE8RfVvON144xzSz7sBIuIlVL/0N2TmNjqkn0N6GQTWZOafHTLbob1AA3uBZ/TzC8C/AX4H6Ad+keoXvRO3zRXANUAf1Y0Et1Odd2z8tomIdwEPZ+bWKcMzbYNG9zNDL5PfWw18GfheZn6aefZimEwjIk5sn2QjM/dSHb/eQPXLMOl4qndau2YYb4wZ+nlNRJwIfAP4dGZe3Z690f3M0MvrgFe338V/CjglIm4G/glY3T68AlVfjekFZuznt4Ht7UOq+4G/AF5LZ26b84HxzPyHzHwK2ET1u9T4bUNV+5vaP1dXAWcD72L6bdD0fp7RS0RcFxEvonpsx31UvcE8ezFMpvcKYFNE9ETEUVQn3f8UiIh4Zfsf+Z3AVzJzB/CziHhDe9lfB75SS9Uzm66fbwF3AJdn5scnZ+yAfqbr5Y7MPCkzT6b6hfh2Zp6fmfuoflHOby97Ac3qBabvZxDoj4iXted5K9Dq0G1zE/DaiHhhe55zgHs6Ydtk5r/OzL72z9WHgS9l5sVMsw2a3s90vQAfArYAf5GZv9U+d8p8ezFMppGZf0m12/cdoAV8IzM/D1wE/E+q48H38/QJqgHguoi4H3gO8AdLXfPhTNcP1XHRFwIfjIjvtv+7qr1IY/s5zLaZyXuBwYj4e6pn3Vy++FXO3gz9/DnwHmBLexs8j+qcEHTetvko1aGur0XEfVRXeX2ovUijt81hzLQNOq2fs4FfBs6d8jfgU+3vzbkXn2ciSSrmnokkqZhhIkkqZphIkooZJpKkYoaJJKmYdw3WshcRf0B1LyKAV1HdPfWJ9vTrM/OJKfNeSXVDzG9m5tmHvM424A8z89b29EuAO6nuMPBf2h/am27966g+2PeciLgEODYzr5lHH38GvBm4NTMvnevyUgnDRMteZv7m5NcR8RDV7ba/fZhFbj7SH+uIeCVVkIy0P2sx21o+Odt5p1n24nbYPX++ryHNl2EiLbD2LeRvB4Yy8zNTxl8C/CGwhuqOrZ/PzI8csuyVVGHwJeDjmbm+PX4s1R7TK6g+FLgZ2Nh+rc9kZuNud67lxXMm0sJ6A9UdcndR3Upkqj8HbszMfqp7bZ0ZEW+f4XXuBJ4TEae0p98BfDkzJ+9e+5zMPIPqeTQfioiXL2AP0pwZJtLC+k/Av6N6CNTw5GBE/CLwRuDq9s32tlPtVZw83Yu075N0I9UtfAAuprpJ4qQvtud7hOrGfM9byCakuTJMpIX1W+2HRJ0HvDci/kN7fCXV7cpPy8yT2zfc+xWeflDRdG6kevDSyVQn5e+a8r0npnx9oP3aUm0ME2lhTQBk5gNUd//dHBEnZeZPqPZGPgD//xzI31DdRXda7b2Ov6W6Y/WnZppPagLDRFokmXkz1XmS29rP234n8CsRMUb1CIDPZeboEV5mE/AvgU8varFSIe8aLM3B5NVWTf0cR9PrU/dyz0Sau/Mj4kt1F3Go9ocWL6m7Di1P7plIkoq5ZyJJKmaYSJKKGSaSpGKGiSSpmGEiSSpmmEiSiv0/tvmDMqkPBscAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "T = np.array([300., 312, 325, 345, 355, 400])\n", "DG = np.array([5.2, 2.9, 0.4, -4.2,-5, -13])\n", "\n", "plt.errorbar(T, DG, yerr=2, fmt='go', capthick=3)\n", "plt.xlim(290, 420)\n", "plt.xlabel('T [ Kelivn]')\n", "plt.ylabel('$\\Delta G$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We can use our equations above to find the entropy, which is the negative of the slope:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.18243128145567172 kcal/mol*K\n" ] } ], "source": [ "cov_mat = np.cov(T, DG, ddof=1)\n", "slope = cov_mat[0,1] / cov_mat[0,0]\n", "DS = -slope\n", "print(DS, 'kcal/mol*K')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Now if we want to give a confidence interval, we need to get the standard error first. Let's start by checking our fit and we'll need the residuals" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "59.652086720867224\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "intercept = np.mean(DG - T * slope)\n", "print(intercept)\n", "\n", "plt.errorbar(T, DG, yerr=2, fmt='go', capthick=3)\n", "plt.plot(T, T * slope + intercept, '-')\n", "plt.xlim(290, 420)\n", "plt.xlabel('T [ Kelivn]')\n", "plt.ylabel('$\\Delta G$')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "residuals = DG - T * slope - intercept\n", "sig_e = np.sum(residuals**2) / (len(T) - 2)\n", "#this is where we include the error in measurement\n", "s2_e = sig_e + 2.0 ** 2\n", "s2_slope = s2_e / (np.sum( (np.mean(T) - T)**2 ) )" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Now we have the standard error in the slope, which is the same as entropy. Now we get our confidence interval" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.07134356636346217\n" ] } ], "source": [ "T = scipy.stats.t.ppf(0.975, len(T) - 2)\n", "slope_ci = T * np.sqrt(s2_slope)\n", "\n", "print(slope_ci)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Remember, the slope is the negative change in our entropy. So our final answer is\n", "\n", "$$\\Delta S = 0.18 \\pm 0.06 \\frac{\\textrm{kcal}}{\\textrm{mol}\\cdot\\textrm{K}}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Case 2 - OLS with constant $x$ uncertainty in 1D\n", "====\n", "\n", "\n", "Now we have a measurement error in our independent variables. Our $x$ values are just our best esimiates; we don't know the true $x$ values. Our model equation is:\n", "\n", "$$y = \\alpha + \\beta(x + \\eta) + \\epsilon$$\n", "\n", "where our measurements are $y$ and $(x + \\eta)$. Once again we can rearrange our model equation into:\n", "\n", "$$y = \\alpha + \\beta x + \\epsilon_2$$\n", "\n", "where $\\epsilon_2 = \\beta \\eta + \\epsilon$. Everything is the same as before, except that our extra variance term depends on the slope. That changes our standard error equation to:\n", "\n", "\n", "$$ S^2_{\\epsilon_2} = \\frac{SSR}{N - 2} + \\hat{\\beta}^2\\sigma_{\\eta}^2 $$\n", "\n", "and $\\sigma_{\\eta}^2$ is again the squared error in our measurement. Note that this is an approximate method." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### All Equations for Case 2\n", "\n", "\n", "$$\\hat{\\beta} = \\frac{\\sigma_{xy}}{\\sigma_x^2}$$\n", "\n", "$$\\hat{\\alpha} = \\frac{1}{N}\\sum_i (y_i - \\hat{\\beta}x_i)$$\n", "\n", "\n", "$$ S^2_{\\epsilon_2} = \\frac{SSR}{N-2} + \\hat{\\beta}^2\\sigma_{\\eta}^2 $$\n", "\n", "\n", "$$S^2_{\\alpha} = S^2_{\\epsilon_2} \\left[ \\frac{1}{N-2} + \\frac{\\bar{x}^2}{\\sum_i\\left(x_i - \\bar{x}\\right)^2}\\right]$$\n", "\n", "$$S^2_{\\beta} = \\frac{S^2_{\\epsilon_2}}{\\sum_i \\left(x_i - \\bar{x}\\right)^2}$$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Case 2 - Example\n", "---\n", "\n", "Repeat the case 1 example, except with an error in temperature measurement of 5 K. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "T = np.array([300., 312, 325, 345, 355, 400])\n", "DG = np.array([5.2, 2.9, 0.4, -4.2,-5, -13])\n", "\n", "plt.errorbar(T, DG, xerr=5, fmt='go', capthick=3)\n", "plt.xlim(290, 420)\n", "plt.xlabel('T [ Kelivn]')\n", "plt.ylabel('$\\Delta G$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Our slope and intercept are unchanged, but our standard error is different. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.03616816441646756\n" ] } ], "source": [ "#Now we use the independent variable measurement error\n", "s2_e = sig_e + slope**2 * 5.0 ** 2\n", "s2_slope = s2_e / (np.sum( (np.mean(T) - T)**2 ) )\n", "T = scipy.stats.t.ppf(0.975, len(T) - 2)\n", "slope_ci = T * np.sqrt(s2_slope)\n", "\n", "print(slope_ci)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "With the new measurement error, our new confidence interval for entropy is:\n", "\n", "$$\\Delta S = 0.18 \\pm 0.03 \\frac{\\textrm{kcal}}{\\textrm{mol}\\cdot\\textrm{K}}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Case 2 - Attenuation Error\n", "---\n", "\n", "There is an interesting side effect of independent measurement error. Let's look at some plots showing increasing uncertainty in $x$, but always with a slope of 3" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(24, 12))\n", "\n", "rows = 2\n", "cols = 3\n", "N = 1000\n", "\n", "for i in range(rows):\n", " for j in range(cols):\n", " index = i * cols + j + 1\n", " fig = plt.subplot(rows, cols, index)\n", " err = scipy.stats.norm.rvs(loc=0, scale = index - 1, size=N)\n", " x = np.linspace(0,5, N)\n", " y = 3 * (x + err)\n", " plt.plot(x, y, 'o')\n", " plt.xlim(-2, 7)\n", " plt.title('$\\sigma_\\eta = {}$'.format(index))\n", " \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Notice that as our error in our measurement gets larger, the slope becomes less and less clear. This is called **Attenuation Error**. As uncertainty in $x$ increases, our estimates for $\\alpha$ and $\\beta$ get smaller. We usually don't correct for this, because all our hypothesis tests become *more* conservative due to attenuation and thus we won't ever accidentally think there is a correlation when there isn't. But be aware that when the uncertatinty in $x$ becomes simiar in size to our range of data, we will underestimate the slope." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Case 3 - OLS with constant x,y uncertainty in 1D\n", "===\n", "\n", "As you may have expected, the standard error in $\\epsilon_3$ is just a combination of the previous two cases:\n", "\n", "$$S^2_{\\epsilon_3} = \\frac{SSR}{N} + \\hat{\\beta}^2\\sigma^2_{\\eta_x} + \\sigma^2_{\\eta_y}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### All Equations for Case 3\n", "\n", "\n", "$$\\hat{\\beta} = \\frac{\\sigma_{xy}}{\\sigma_x^2}$$\n", "\n", "$$\\hat{\\alpha} = \\frac{1}{N}\\sum_i (y_i - \\hat{\\beta}x_i)$$\n", "\n", "$$S^2_{\\epsilon_3} = \\frac{SSR}{N - 2} + \\hat{\\beta}^2\\sigma^2_{\\eta_x} + \\sigma^2_{\\eta_y}$$\n", "\n", "$$S^2_{\\alpha} = S^2_{\\epsilon_3} \\left[ \\frac{1}{N - 2} + \\frac{\\bar{x}^2}{\\sum_i\\left(x_i - \\bar{x}\\right)^2}\\right]$$\n", "\n", "$$S^2_{\\beta} = \\frac{S^2_{\\epsilon_3}}{\\sum_i \\left(x_i - \\bar{x}\\right)^2}$$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Case 3 - Example\n", "----\n", "\n", "Repeat the Case 1 example with an uncertainty in $\\Delta G$ of 2 kcal/mol and $T$ of 5K" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "temperature = np.array([300., 312, 325, 345, 355, 400])\n", "DG = np.array([5.2, 2.9, 0.4, -4.2,-5, -13])\n", "\n", "plt.errorbar(temperature, DG, xerr=5, yerr=2, fmt='go', capthick=3)\n", "plt.xlim(290, 420)\n", "plt.xlabel('T [ Kelivn]')\n", "plt.ylabel('$\\Delta G$')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.18243128145567172 kcal/mol*K\n", "59.652086720867224\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cov_mat = np.cov(temperature, DG, ddof=1)\n", "slope = cov_mat[0,1] / cov_mat[0,0]\n", "DS = -slope\n", "print(DS, 'kcal/mol*K')\n", "intercept = np.mean(DG - temperature * slope)\n", "print(intercept)\n", "\n", "plt.errorbar(temperature, DG, xerr=5, yerr=2, fmt='go', capthick=3)\n", "plt.plot(temperature, temperature * slope + intercept, '-')\n", "plt.xlim(290, 420)\n", "plt.xlabel('T [ Kelivn]')\n", "plt.ylabel('$\\Delta G$')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.04191610991258184\n" ] } ], "source": [ "residuals = DG - temperature * slope - intercept\n", "sig_e = np.sum(residuals**2)\n", "\n", "#The only new part\n", "#-------------------------------------\n", "#Now we use both the dependent and the independent variable measurement error\n", "sig_total = sig_e + slope**2 * 5.0 ** 2 + 2.0**2\n", "#-------------------------------------\n", "\n", "\n", "s2_e = sig_total / (len(temperature) - 2)\n", "s2_slope = s2_e / (np.sum( (np.mean(temperature) - temperature)**2 ) )\n", "T = scipy.stats.t.ppf(0.975, len(temperature) - 2)\n", "slope_ci = T * np.sqrt(s2_slope)\n", "\n", "print(slope_ci)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "With the both measurement errors, our confidence interval for entropy is:\n", "\n", "$$\\Delta S = 0.18 \\pm 0.04 \\frac{\\textrm{kcal}}{\\textrm{mol}\\cdot\\textrm{K}}$$\n", "\n", "which is a slightly larger confidence interval than for case 1" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Case 4 - OLS with multiple y values in N-dimensions\n", "===" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Sometimes you'll see people have multiple measurements for each $y$-value so that they can plot error bars. For example, let's say we have 3 $x$-values and we have 4 $y$-vaules at each $x$-value. That would give enough samples so that we can compute a standard error at each $y$-value:\n", "\n", "$$S_y = \\sqrt{\\frac{\\sigma_y^2}{N}}$$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.array([2, 4, 6])\n", "\n", "y_1 = np.array([1.2, 1.5, 1.1, 0.9])\n", "y_2 = np.array([2.6, 2.2, 2.1, 2.5])\n", "y_3 = np.array([3.0, 2.9, 3.3, 5])\n", "\n", "y = np.array([np.mean(y_1), np.mean(y_2), np.mean(y_3)])\n", "#compute standard error\n", "yerr = np.sqrt(np.array([np.var(y_1, ddof=1), np.var(y_2, ddof=1), np.var(y_3, ddof=1)])) / 4.0\n", "\n", "plt.errorbar(x, y, yerr=yerr, fmt='o', capthick=3)\n", "plt.xlim(0, 10)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "How would we do regression on this? Well, it turns out you don't do anything special. You just treat the 12 $y$-values as equivalent and use the normal regression equations. I know this seems obvious, but it's a common question." ] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 1 }