{ "metadata": { "name": "", "signature": "sha256:2df71f183fc4894b48e69dfe04b31f3a3a64336f8f51cdf74438340a1a8c6642" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Deconvolution" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "A tutorial by Jan Willem de Gee (jwdegee@gmail.com)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Deconvolution is equivalent to selective averaging with correction for overlap between temporally adjacent responses (Dale, 1999), based on the assumption that hemodynamic / pupil responses superimpose linearly over time (Boynton et al., 1996). This analysis is implemented in for example Donner, Sagi, Bonneh & Heeger, JoN, 2008." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is Python, so let's start with importing some modules:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import os\n", "import numpy as np\n", "import scipy as sp\n", "import scipy.stats as stats\n", "import scipy.signal as signal\n", "import matplotlib.pyplot as plt\n", "from sympy import *\n", "import math" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 48 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's do inline plotting:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 49 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's first create and plot the true pupil response to a transient input. This is called an \"Inpulse Response Function\" (IRF)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# define an Impulse Response Function:\n", "def pupil_IRF(timepoints, s=1.0/(10**26), n=10.1, tmax=0.93):\n", " \n", " \"\"\" pupil_IRF defines the IRF (response to a transient input) of the pupil.\n", " \n", " Parameters\n", " ----------\n", " t: IRF is defined with respect to 't'\n", " s: scaling factor\n", " n: sets the width\n", " tmax: sets the time to peak \n", " IRF_len: function is evaluated for t = [0:IRF_len]\n", " \n", " Returns\n", " -------\n", " y: IRF evaluated for t = [0:IRF_len]\n", " yprime: IRF first derivative evaluated for t = [0:IRF_len]\n", " \n", " \"\"\"\n", " \n", " # in sympy:\n", " t = Symbol('t')\n", " y = ( (s) * (t**n) * (math.e**((-n*t)/tmax)) )\n", " yprime = y.diff(t)\n", " \n", " # lambdify:\n", " y = lambdify(t, y, \"numpy\")\n", " yprime = lambdify(t, yprime, \"numpy\")\n", " \n", " # evaluate:\n", " y = y(timepoints)\n", " yprime = yprime(timepoints)\n", " \n", " return (y, yprime)\n", "\n", "# create the IRF:\n", "sample_rate = 10\n", "IRF_len = 3.0 # in seconds\n", "timepoints = np.linspace(0,IRF_len,IRF_len*sample_rate)\n", "\n", "IRF, IRF_prime = pupil_IRF(timepoints=timepoints)\n", "IRF = IRF / IRF.std()\n", "IRF_prime = IRF_prime / IRF_prime.std()\n", "\n", "# plot the IRF:\n", "fig = plt.figure()\n", "plt.plot(timepoints, IRF, color='r')\n", "# plt.plot(timepoints, IRF_prime, color='g')\n", "plt.legend(['IRF'])\n", "plt.title('Impulse Response Function')\n", "plt.xlabel('time (s)')\n", "plt.ylabel('a.u.')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 50, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 50 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's simulate convolved timeseries data based on this IRF." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# input:\n", "duration = 35 # in seconds\n", "times = np.array([1,6,11,11.5,16,16.5,21,22,26,27])\n", "input_signal = np.zeros(duration * sample_rate)\n", "for i in times:\n", " input_signal[i*sample_rate] = 1\n", "\n", "# convolve inputs with IRF: \n", "convolved_signal = (sp.convolve(input_signal, IRF, 'full'))[:-(IRF.shape[0]-1)]\n", "\n", "# let's add some noise:\n", "convolved_signal_noise = convolved_signal + np.random.normal(0,0.25,len(convolved_signal))\n", "\n", "timepoints = np.linspace(0,duration,duration*sample_rate)\n", "# plot simulated convolved signal with noise:\n", "fig = plt.figure()\n", "plt.plot(timepoints, convolved_signal_noise)\n", "for i in times:\n", " plt.axvline(i, color='r', alpha=0.5)\n", "plt.legend(['pupil time series'], loc=1)\n", "plt.title('simulated pupil time series, with measurement noise')\n", "plt.xlabel('time (s)')\n", "plt.ylabel('a.u.')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 53, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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DNm/2mkmqaW8HgoMtP/P3p89aW71jk0DgboQQCDyOdVgIICHYsgXo6fGKSaqx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\nFbx//9v1pa374hEAlCeYPRsYPZpccn7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Eedv5wnM9PTQr9fBh2x7Bd98Bv/sd2XruuVKB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\n+PDDDzF69Gj4+/tj79693jBBIBAIBL/hFSEYO3YsPvnkE0y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"text": [ "" ] } ], "prompt_number": 53 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's epoch the data and compute mean response." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# times for epoching:\n", "epoch_times = [0, 3] # in seconds\n", "\n", "# mean response:\n", "epochs = np.vstack([convolved_signal_noise[i+(epoch_times[0]*sample_rate):i+(epoch_times[1]*sample_rate)] for i in times*sample_rate])\n", "mean_response = np.mean(epochs, axis=0)\n", "\n", "# plot mean response versus IRF:\n", "timepoints = np.linspace(0,3,3*sample_rate)\n", "fig = plt.figure(figsize=(6,6))\n", "timepoints = np.linspace(epoch_times[0],epoch_times[1],(epoch_times[1]-epoch_times[0])*sample_rate)\n", "fig.add_subplot(211)\n", "for data in epochs:\n", " plt.plot(timepoints,data, color='b')\n", "plt.title('epoched responses')\n", "plt.xlabel('time from event (s)')\n", "plt.ylabel('a.u.')\n", "fig.add_subplot(212)\n", "plt.plot(timepoints, mean_response, color='b')\n", "plt.plot(timepoints, IRF, color='r')\n", "plt.legend(['mean epoched response', 'true response'])\n", "plt.title('mean response')\n", "plt.xlabel('time from event (s)')\n", "plt.ylabel('a.u.')\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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9oMXs3YtCfzY22O7SJaIWLZCj7+lT1I/y9CQqVgzBzo6OyGR+/z40qmLFoJVZ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UBphJKq/tWoMvz8ADs7YMGCYgoQAc2bA5s3FxMfSUP47TfOi3X+fLFGFABH4TAyApYvr0LZBAIN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\nQmCC\n", "text": [ "" ] } ], "prompt_number": 54 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is obviously not good... what we need to do is to is correct for for overlap between temporally adjacent responses...\n", "\n", "We'll have to try deconvolution.\n", "\n", "First make a design matrix:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# make design matrix:\n", "nr_samples = 3 * sample_rate # here we define the length of the deconvolution response we're interested in (30 samples = 3-s in our case).\n", "designMatrix = np.zeros((nr_samples, duration*sample_rate))\n", "for i in (times*sample_rate):\n", " for j in range(int(nr_samples)):\n", " designMatrix[j,i+j] = 1\n", "\n", "# plot design matrix:\n", "fig = plt.figure()\n", "plt.imshow(designMatrix.T, cmap='gray')\n", "plt.xticks([0,nr_samples])\n", "plt.title('design matrix')\n", "plt.xlabel('nr samples')\n", "plt.ylabel('length run')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 66, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 66 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's do deconvolution. \n", "\n", "For every regressor (in the above example, we have 30 regressors (the duration in samples of the response we are interested in) we want to find an associated scalar value (the \"beta\", $b$) that we can use to scale that particular regressor with, such that it best describes the measured data. In a deconvolution analysis, with a procedure called \"multiple regression\" we look for betas that minimimize the sum of squares of errors across all $k$ regressors in our design matrix at the same time.\n", "\n", "To do so, we set up the following equation (for a derivation, see all the way below):\n", "\n", "$ b = (X'X)^{-1} X'y $\n", "\n", "In which,\n", "\n", "$b$ is a vector containing the betas (size: number of regressors; in the above example: 30). In the case of deconvolution, this vector is the actual deconvolved response to some input;\n", "\n", "$X$ is the design matrix (size: length measured time series x number of regressors);\n", "\n", "$y$ is the measured BOLD timeseries." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# deconvolution:\n", "designMatrix = np.mat(designMatrix).T\n", "deconvolved_response = ((designMatrix.T * designMatrix).I * designMatrix.T) * np.mat(convolved_signal_noise).T\n", "deconvolved_response = np.array(deconvolved_response)\n", "\n", "# plot deconvoled response versus true response:\n", "timepoints = np.linspace(0,3,3*sample_rate)\n", "fig = plt.figure(figsize=(6,6))\n", "fig.add_subplot(211)\n", "plt.plot(timepoints,deconvolved_response, color='b')\n", "plt.xlim(xmax=3)\n", "plt.ylim(ymin=-0.5, ymax=3.5)\n", "plt.legend(['deconvolved response'])\n", "plt.title('deconvolved response')\n", "plt.xlabel('time (s)')\n", "plt.ylabel('a.u.')\n", "fig.add_subplot(212)\n", "plt.plot(timepoints,IRF, color='r')\n", "plt.xlim(xmax=3)\n", "plt.ylim(ymin=-0.5, ymax=3.5)\n", "plt.legend(['true response'])\n", "plt.xlabel('time from event (s)')\n", "plt.ylabel('a.u.')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 67, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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+PaKjo5GQkIA5c+YgISGhwnY8TqN6li4F0tOBzz+XO5K6tXo1cPIksGeP3JEw\npn8MbuU+XZZ7BYAZM2YgJiYGZmZm2Lp1K3x9fSvsi5OG7u7fF72LfvxRTIPekN29K0a5nzwpBjAy\nxv5mcEmjNnHS0N22bcDOnWKp1MZg4UIxC+6nn8odCWP6hZOG4RejzhEBvr7AihWih1FjkJ0NdO4s\nphixsZE7Gsb0B08jwqoUFwcUFwPPPit3JPXHwQEYM0ZMysgYe3xc02hERo0SNYxp0+SOpH5duiRG\nvaekAKamckfDmH7gmgZ7pGvXgPh4sZxrY9Oxo5iUccsWuSNhzPBxTaORmDVLzDP1/vtyRyKPEyfE\n6PerVxvmgEbGqosbwg2/GHWmoEB0PTXE9b9r0zPPABMmAJMmyR0JY/Lj01PsoTZvBoYMadwJAwAW\nLRI9x8rK5I6EMcPFSaOBKysD1q1rWGtm1JS/P+DoyCPEGXscNUoaw4YNq+04WB35/nvAxQXo1Uvu\nSPTDokXA8uWAWi13JIwZpholjc8b+qRFDUj5mhlMeOYZwNJSTNjIGKu+GiUNR0fHWnnxSZMmwd7e\nHt26dav08djYWFhaWsLHxwc+Pj6IiIiolddtLBITgcxMoJIJhBsthULUNiIixHK3jLHqqbL3lEcl\nM70pFAr8+eefj/3ix48fR4sWLfDCCy/g/PnzFR6PjY3FmjVrcODAgUfuh3tPVW7CBDEt+BtvyB2J\nfiECevYUyYMTKmusavq9WeV6GidPnpSul5SUYN++ffjrr7+q/UKV6d+/P1JSUh65DSeDmsnIEGuA\nR0bKHYn+USiAd94Bli0To+R5XS/GdFfl6SkbGxvp4uzsjDlz5uDQoUP1ERsUCgXi4+Ph5eWFoUOH\nIjk5uV5etyHYsAEICxPn71lFo0YBpaXA4cNyR8KYYamypnH69GlpvQuNRoNTp05BXU9dT3x9fZGe\nng5TU1McPnwYwcHBuNKQl5urJYWFwBdfAJWsV8X+n5HR37WNoCCubTCmqyqTxhtvvCElDWNjY7i7\nu+Orr76q88AAwNzcXLoeFBSEV199FXl5ebC2tq6wLS/3+rcvvwT69gXatpU7Ev32/PPA4sXATz+J\nXlWMNWQGv9xruZSUFIwYMaLShvDc3FzY2dlBoVAgMTERISEhlbaBcEO4Nl9fYOVK/iLUxZdfilpZ\nXJzckTBWv+qsIbwyp0+fRo8ePWryVC2hoaGIi4vD7du34eLigiVLlkClUgEQy73u27cPkZGRMDY2\nhqmpKfaGHCz3AAAgAElEQVTwUN4qXbgA3LwJBAbKHYlhCA0FliwBjh0T06czxh6tRjWNKVOm6NUA\nP65p/G3BAtGl9MMP5Y7EcGzeLKYW+eEHuSNhrP7U6Sy3eXl5uHr1Ku7fvw9AdIP19/evfpR1hJOG\noNEAbm6iR1DXrnJHYzhKS4H27UXiePJJuaNhrH7U2empzz//HOvWrUNGRga8vb2RkJCAp556Cj//\n/HONAmV1JzZWrIPNCaN6mjYF5s8XPanqqTc5YwarynEan3zyCRITE+Hm5oajR48iKSkJltz5Xy99\n+aUYm8Gq76WXgLNngdOn5Y6EMf1WZdJo1qwZmjdvDkCMCO/YsSMuX75c54Gx6ikqEjPahobKHYlh\natYMmDdPzEnFGHu4KpOGi4sL8vPzERwcjEGDBmHkyJFwd3evh9BYdezfD/j5AQ4OckdiuKZMEQMi\nz52TOxLG9Fe1ek/Fxsbi7t27GDJkCJrq0ULL3BAODB0qJiicOFHuSAzbRx8Bp04Be/fKHQljdYvX\nCDf8YtRYbi7QoYOYBt3MTO5oDJtSKdZTj4sDOnWSOxrG6g6vEd6I7d4NjBzJCaM2tGgBzJ4t1hJn\njFXESaMB4F5TtWvGDDHWhXtSMVYRJw0Dl5wM5OQAAwbIHUnDYWkJbNokFmjKyJA7Gsb0i2xJo6ql\nXgFg1qxZaNeuHby8vJCUlFSP0RmOL78UDeBNmsgdScMyZgwwcyYwYoRo52CMCbIljZdeegkxMTEP\nfTw6OhrXrl3D1atX8dlnn2H69On1GJ1h0GiAnTv51FRdmTdPLAsbGgrU0xIyjOk92ZJG//79YWVl\n9dDHDxw4gPDwcACAn58fCgoKkJubW1/hGYS4OMDKCujeXe5IGiaFAvjPf4DiYuD11+WOhjH9oLdt\nGpmZmXBxcZFuOzs7I4NPMGvhBvC6Z2IC7NsnZsBdv17uaBiTn94mDQAV+hAreE1OSVER8N13oj2D\n1a2WLcVEhsuX84SGjNVoEab64OTkhPT0dOl2RkYGnJycHrp9Y1vu9cABoFcvwNFR7kgaBw8P4Ntv\ngVGjRK3Dy0vuiBirngax3OujlnqNjo7G+vXrER0djYSEBMyZMwcJCQmV7qcxjggfNgwYP55PT9W3\nr74SDeQnTnDCZoatXpd7rQ1VLfU6dOhQREdHw9PTE2ZmZti6datcoeqdmzeBX3/l+ZHkEBICXLsm\nuuIeO8aj8Fnjw3NPGaB164CTJ0VDOKt/RGL9jYIC4JtveIwMM0w891Qjwr2m5KVQAJ99Bty5A7z5\nptzRMFa/OGkYmEuXxGy2AwfKHUnj1rSpqGUcOgRs3Ch3NIzVH73tPcUq9+WXYoQynxKRn7W1SBr9\n+olG8ZEj5Y6IsbrHbRoGRKMRXT/37we8veWOhpWLjxfjZezsgNdeA8aNE8vHMqbPuE2jETh+HLCw\n4DEC+qZPH+D6deDdd4E9ewAXF9HWceOG3JExVvs4aRiQ8gZwHhivf5o0AYYPF+twnDghaoW9ev19\nn0Yjd4SM1Q4+PWUgiosBJyfg3DnA2VnuaJguiopEzWPDBtE9d/p0YNIk0RbCmNz49FQD99//Ar6+\nnDAMiampSBKnTgG7domE37atGOORmip3dIzVDCcNA8FjMwyXQgH4+QHbtwNXrgBubuLU1fbtYqAg\nY4aET08ZgMxMoEsXID0dMDeXOxpWG86eFT8C2rUTS8va2MgdEWtsDPL0VExMDDp27Ih27drhww8/\nrPB4bGwsLC0t4ePjAx8fH0RERMgQpbwKC8XMqvPmccJoSLy8gMREoE0bcT06Wu6IGNONbDUNtVqN\nDh064Mcff4STkxN69eqF3bt3o1OnTtI2sbGxWLNmDQ4cOPDIfTXUmoZaDTz3HNCqFbBlC/eaaqji\n4oDwcGDIEGDVKqBFC7kjYo2BwdU0EhMT4enpCXd3d5iYmGD8+PHYv39/he0aYjLQBREwZ47ogbNp\nEyeMhszfX5yuKikBfHyAh6wAwJhekC1pVLaca2ZmptY2CoUC8fHx8PLywtChQ5GcnFzfYcrmk0+A\no0fFUqNNm8odDatrlpZAVBTw4YdAcDCwaBHw/ysFMKZXZEsauizd6uvri/T0dJw9exYzZ85EcHBw\nPUQmv2+/BT76SMxr1LKl3NGw+jR6NPD778CZM8CTTwIXL8odEWPaZJuw8J/Luaanp8P5H4MQzB9o\n+Q0KCsKrr76KvLw8WFcyOqqhLPf622/A1KlATIzomskan9atgYMHgc8/B55+GliyBHj1VbmjYobO\n4Jd7LSsrQ4cOHfDTTz/B0dERvXv3rtAQnpubCzs7OygUCiQmJiIkJAQpKSkV9tVQGsL//BPo21d8\nWQwfLnc0TB9cuyZOVz37rKh9GvHIKlZLDG65V2NjY6xfvx7PPvss1Go1Jk+ejE6dOmHTpk0AxJKv\n+/btQ2RkJIyNjWFqaoo9e/bIFW6dy8sDhg4V57I5YbBynp5iosoRI4AXXhC96LiNi8mJB/fpgfv3\ngcGDxSjhVavkjobpo+JiYPx40cNq3z4es8Men8F1uWUCkZifyNYWWLlS7miYvmreXKwU6OoKDBgA\n3Lwpd0SsseKkIbN33xVtGV9+yeer2aMZG4u1yYcMEasF8nodTA683KuMtmwBdu8WK781by53NMwQ\nKBTAsmWih1W/fqJbNq/iyOoTt2nI5MgR0bB57BjQvr3c0TBD9PXXYnnZr74CDLSHOZMRt2kYkAMH\ngH/9S/zTc8JgNTV2LLB3LxASIhrHGasPnDTq2RdfiMF70dFA//5yR8MMXWAg8L//AbNnA//5j9zR\nsMaA2zTqCREQESHmFzp2TKyjwFht8PERYzmefRbIzgaWLuUJLlnd4TaNeqBWAzNnAidOAIcPi0ZM\nxmrbzZvAyJHAyZNienVz86r/2tqKMUL8I6bxqen3JieNOlZSItovCgqA774DLCzkjog1dCqVWLzr\n3j1AqRSX8uv/vC8jQ5wqbdlSJJyRI8XStE2ayF2K+kEE5OeL9yE9XfzNyRE90gYObNhrm3DS0MNi\nFBSIVfccHIBt24AnnpA7IsYq0miA06eB/ftFJ43cXDGVzciRwKBBgKmp3BH+jUhM5vjppyI5tmih\n26WsTDsxlP/NyABMTAAXF8DZWfy1sRGrKv72m5hpeOhQcWnfvmGd9jPIpBETE4M5c+ZArVbj5Zdf\nxvz58ytsM2vWLBw+fBimpqaIioqCj49PhW30MWlkZgJBQWL07po1PHCPGY4bN0TyOHBAnOoKCBAJ\nZPhw+U6tEgE//CDmZisqAt56C7C3/7vW9LBLYaH4a2SknRjK/zo5PXxKlnv3gJ9+EjWx6Gjxo688\ngQQEGP7Yqhp/b5JMysrKqG3btnTjxg0qLS0lLy8vSk5O1trm0KFDFBQURERECQkJ5OfnV+m+ZCxG\npS5eJHJzI/rwQyKNRu5oGKu5vDyinTuJxo0jsrQkeu45omvX6jeG2Fii/v2JOnQg2r2bSK2u39cn\nEv/HZ88Svf++iMXcnGjYMKL164lSU+s/ntpQ0+9NvV7u9cCBAwgPDwcA+Pn5oaCgALm5uXKEq7OE\nBPErZOlS4M03G1Z1ljU+VlbAhAnAnj3iXH+vXqLNY/584O7dun3tEyeAZ54BXnoJmDwZ+OMPMWmj\nHLV2hQLo3h1YsED0fkxNFYNzT54EfH1FZ4KvvhKTjzZ0er3ca2XbZGRk1Pg1icSlrhw8KKrxW7eK\nDxRjDUmzZsDChcD588CtW0CHDmLckVpdu69z5gwwbBgwbpwYuHj5MhAeLube0hdWViK2qCjRPvLi\ni8DGjeKU1xtvAI+7MjURcPWqSEr6RrbDoMtyrwAqnHN72POIRMPzwxq7yq8DQNeugJfX35fu3as/\n1XR+PnDhgrj88Yf4e/GiSBy9e1dvX4wZEgcHMW/a6dNiUOGGDcDHHwP+/o+33/PngcWLRW194UIx\nq2+zZrUTc11q3lzUxiZMEItmbdkiakgeHsDLL4vkYmb26H2UlIj389dfxVx08fGi7EZG4vtqzRr9\nmT1Cr5d7/ec2GRkZcHJyqnR/TzzxHhQK0aXVwyMA3bsHwMVFTOpW3vDl7CySy7lzwNmzQFKS+KVw\n4YJo4HswkXh5Ae7uojEsObligrh3D+jcGejSRRzUESOAnj2BSlaiZaxB6tFDDCr86itRs+7VS6wu\n6OGh2/NzcsQpqIQE8ffyZWDePGDHDv3qsVUdnp7AihViid7oaFETe+MNkTheflm8ZwqF6KEWH/93\nkjh7FujUCejTBwgNFb3DXFzE6a5PPxX3v/CCmBW7ZcuaxdYolnuNjo7G+vXrER0djYSEBMyZMwcJ\nCQkV9qVQKHDnDtV4DIRaLaqCv/8uDl75paBAPN6pk0gO5QmiSxexrgG3VzAmFBcDq1cDa9cCr7wi\nejc9WHsvLRX/Xw8mibt3RfvIU0+Jrq19+1b9i9wQZWaKH6ebN4vyFRcDt2+LcvftKy69ej16TEhu\nrug5duCASEgvv/z4Y2kMssvt4cOHpS63kydPxsKFC7WWewWAGTNmICYmBmZmZti6dSt8fX0r7Keu\nutzeuSMOZGMZ6MTY48rMFAnjhx+A118X05okJIiE4ekpkkN5kmjfvnF1RddoRK2iZUtxlqImZf/9\nd2DOHHF6/OOPxdxjNWWQSaO26OM4DcYas8REMYFiu3YiSfTqxUvU1hYi4Ntvgblzxbxjq1YBbdpU\nfz+cNAy/GIwxprOSEtFAvmYNMGVKxVOCgDgtmJcH/PWXuJRfz8sD3nyTk4bcYTDGWL3LyhIJ48gR\n0d76YHIoKRGdc6ytgVatxKX8+urVnDTkDoMxxmRz/rxoQ3owQZibP7zDDp+eMvxiMMZYveHlXhlj\njNU5ThqMMcZ0xkmDMcaYzjhpMMYY0xknDcYYYzrjpMEYY0xnssxym5eXh3HjxiE1NRXu7u746quv\n0LKSqRvd3d1hYWGBJk2awMTEBImJiTJEyxhjrJwsNY0PPvgAgwYNwpUrVzBw4EB88MEHlW6nUCgQ\nGxuLpKSkRpswamMqY33G5TNsXL7GR5ak8eAyruHh4fj+++8fum1jH7TX0D+0XD7DxuVrfGRJGrm5\nubC3twcA2NvbP3Tdb4VCgWeeeQY9e/bE559/Xp8hMsYYq0SdtWkMGjQIOTk5Fe5fvny51m2FQvHQ\nJVx//fVXODg44NatWxg0aBA6duyI/v3710m8jDHGdEAy6NChA2VnZxMRUVZWFnXo0KHK57z33nu0\natWqSh9r27YtAeALX/jCF77oeGnbtm2Nvr9l6T01cuRIbNu2DfPnz8e2bdsQHBxcYZuioiKo1WqY\nm5ujsLAQR44cweLFiyvd37Vr1+o6ZMYYY5Bpltu8vDyEhIQgLS1Nq8ttVlYWpkyZgkOHDuHPP//E\n6NGjAYj1xP/1r39h4cKF9R0qY4yxBzSIqdEZY4zVD4MZER4TE4OOHTuiXbt2+PDDDyvdZtasWWjX\nrh28vLyQlJRUzxE+nqrKFxsbC0tLS/j4+MDHxwcREREyRFkzkyZNgr29Pbp16/bQbQz52FVVPkM+\ndgCQnp6OwMBAdOnSBV27dsW6desq3c4Qj6EuZTPk41dSUgI/Pz94e3ujc+fODz1bU61jV6OWkHpW\nVlZGbdu2pRs3blBpaSl5eXlRcnKy1jaHDh2ioKAgIiJKSEggPz8/OUKtEV3Kd/ToURoxYoRMET6e\nY8eO0ZkzZ6hr166VPm7Ix46o6vIZ8rEjIsrOzqakpCQiIrp37x61b9++wfz/6VI2Qz9+hYWFRESk\nUqnIz8+Pjh8/rvV4dY+dQdQ0EhMT4enpCXd3d5iYmGD8+PHYv3+/1jYPDhj08/NDQUHBQ8d/6Btd\nygfAYAc69u/fH1ZWVg993JCPHVB1+QDDPXYA0Lp1a3h7ewMAWrRogU6dOiErK0trG0M9hrqUDTDs\n42dqagoAKC0thVqthrW1tdbj1T12BpE0MjMz4eLiIt12dnZGZmZmldtkZGTUW4yPQ5fyKRQKxMfH\nw8vLC0OHDkVycnJ9h1lnDPnY6aIhHbuUlBQkJSXBz89P6/6GcAwfVjZDP34ajQbe3t6wt7dHYGAg\nOnfurPV4dY+dLF1uq+thg//+6Z+/BnR9ntx0idPX1xfp6ekwNTXF4cOHERwcjCtXrtRDdPXDUI+d\nLhrKsVMqlXj++efxySefoEWLFhUeN+Rj+KiyGfrxMzIywu+//447d+7g2WefRWxsLAICArS2qc6x\nM4iahpOTE9LT06Xb6enpcHZ2fuQ2GRkZcHJyqrcYH4cu5TM3N5eqmUFBQVCpVMjLy6vXOOuKIR87\nXTSEY6dSqTBmzBhMnDix0nFVhnwMqypbQzh+AGBpaYlhw4bh1KlTWvdX99gZRNLo2bMnrl69ipSU\nFJSWlmLv3r0YOXKk1jYjR47E9u3bAQAJCQlo2bKlNL+VvtOlfLm5udKvgcTERBBRhXOThsqQj50u\nDP3YEREmT56Mzp07Y86cOZVuY6jHUJeyGfLxu337NgoKCgAAxcXF+OGHH+Dj46O1TXWPnUGcnjI2\nNsb69evx7LPPQq1WY/LkyejUqRM2bdoEAJg6dSqGDh2K6OhoeHp6wszMDFu3bpU5at3pUr59+/Yh\nMjISxsbGMDU1xZ49e2SOWnehoaGIi4vD7du34eLigiVLlkClUgEw/GMHVF0+Qz52gJgDbseOHeje\nvbv0hbNixQqkpaUBMOxjqEvZDPn4ZWdnIzw8HBqNBhqNBmFhYRg4cOBjfXfy4D7GGGM6M4jTU4wx\nxvQDJw3GGGM646TBGGNMZ5w0GGOM6YyTBmOMMZ1x0mCMMaYzThqM/cOdO3cQGRkp3c7KysLYsWPr\n5LUOHjyI995776GPnzt3DpMnT66T12asJnicBmP/kJKSghEjRuD8+fN1/lqBgYHYs2fPI0fgBgQE\n4KuvvoKdnV2dx8NYVbimwdg/LFiwANevX4ePjw/mz5+P1NRUaYGlqKgoBAcHY/DgwfDw8MD69eux\natUq+Pr64qmnnkJ+fj4A4Pr16wgKCkLPnj3x9NNP4/LlyxVeJz09HaWlpVLC+Prrr9GtWzd4e3vD\n399f2i4oKAhff/11PZScMR3UwhofjDUoKSkpWgsq3bhxQ7q9detW8vT0JKVSSbdu3SILCwvatGkT\nERH9+9//po8//piIiAYMGEBXr14lIrGwzYABAyq8zu7du2nGjBnS7W7dulFWVhYREd25c0e6/+ef\nf6aQkJBaLiVjNWMQc08xVp+oijO2gYGBMDMzg5mZGVq2bIkRI0YAALp164Zz586hsLAQ8fHxWu0g\npaWlFfaTlpYGBwcH6Xbfvn0RHh6OkJAQjB49WrrfwcEBKSkpj1kqxmoHJw3GqumJJ56QrhsZGUm3\njYyMUFZWBo1GAysrK53WyX4wQUVGRiIxMRGHDh1Cjx49cPr0aVhbW4OIDGptCtawcZsGY/9gbm6O\ne/fuVft55QnA3NwcHh4e2Ldvn3T/uXPnKmzv5uaGnJwc6fb169fRu3dvLFmyBLa2ttLqadnZ2XBz\nc6tJURirdbIljZKSEvj5+cHb2xudO3fGwoULK2wTGxsLS0tL+Pj4wMfHBxERETJEyhqbVq1aoW/f\nvujWrRvmz58PhUIh/dJ/8Hr57Qevl9/euXMnNm/eDG9vb3Tt2hUHDhyo8Dp9+/bFmTNnpNtvvvkm\nunfvjm7duqFv377o3r07ALGGw9NPP10nZWWsumTtcltUVARTU1OUlZWhX79+WLVqFfr16yc9Hhsb\nizVr1lT6D8dYQzBgwADs3LlTq23jn7jLLdMnsp6eKl9CsbS0FGq1utLVsGTMaYzVublz52Ljxo0P\nffzcuXPw9PTkhMH0hqw1DY1GA19fX1y/fh3Tp0/HypUrtR6Pi4vD6NGj4ezsDCcnJ6xatQqdO3eW\nKVrGGGOy1jSMjIzw+++/IyMjA8eOHUNsbKzW476+vkhPT8fZs2cxc+bMShd9Z4wxVn/0ZhqRZcuW\noXnz5pg7d+5Dt/Hw8JC6IT7I09MT169fr+sQGWOswWjbti2uXbtW7efJVtO4ffs2CgoKAADFxcX4\n4YcfpIXdy+Xm5kptGomJiSCiSts9rl+/DiJqkJfFixfLHgOXj8vH5Wt4l5r+0JZtcF92djbCw8Oh\n0Wig0WgQFhaGgQMHYtOmTQCAqVOnYt++fYiMjISxsTFMTU2xZ88eucJljDEGGZNGt27dtPqol5s6\ndap0/bXXXsNrr71Wn2Exxhh7BB4RrucCAgLkDqFOcfkMG5ev8dGbhvDHoVAo0ACKwRhj9aam35s8\nYSFjjYS1tbW03gdrPKysrJCXl1dr++OaBmONBP+fNE4PO+41/TxwmwZjjDGdcdJgjDGmM04ajDHG\ndMZJgzHGmM44aTDG9IK7uzt+/vlnucNgVeCkwRjTC1X15ikrK6vT16/r/TcUer3cKwDMmjUL7dq1\ng5eXF5KSkuo5SsZYfQgLC0NaWhpGjBgBc3NzrFq1CikpKTAyMsKWLVvg5uaGZ555BnFxcXBxcdF6\nrru7O3766ScAYtG2Dz74AJ6enrCxscG4ceMeOjYlNjYWzs7OWLlyJRwcHDB58uRHPr+kpAQTJ06E\njY0NrKys0Lt3b9y6dQuAGDm+cOFC+Pn5wdLSEsHBwVqve+DAAXTp0gVWVlYIDAzEpUuXtOJfvXo1\nvLy80LJlS4wfPx73798HICZ2HT58OKysrNCqVSs8/fTTUmLNysrCmDFjYGdnhzZt2uDTTz+tpaNR\nBZJRYWEhERGpVCry8/Oj48ePaz1+6NAhCgoKIiKihIQE8vPzq3Q/MheDMYOg7/8n7u7u9NNPP0m3\nb9y4QQqFgsLDw6moqIiKi4vp6NGj5Ozs/NDnffzxx/TUU09RZmYmlZaW0tSpUyk0NLTS1zt69CgZ\nGxvTggULqLS0lIqLix/5/I0bN9KIESOouLiYNBoNnTlzhu7evUtERP7+/uTk5EQXLlygwsJCGjNm\nDE2cOJGIiC5fvkxmZmb0448/UllZGa1cuZI8PT1JpVJJ8fv5+VF2djbl5eVRp06daOPGjUREtGDB\nApo2bRqVlZVRWVkZ/fLLL0REpFarydfXl5YtW0YqlYr+/PNPatOmDf3vf/+rUM6HHfeafh704lNU\nWFhIPXv2pAsXLmjdP3XqVNqzZ490u0OHDpSTk1Ph+fr+z8CYPtDp/wSonUsNPCxp3LhxQ7qvqqTR\nqVMnrX1kZWWRiYkJqdXqCq939OhRatq0Kd2/f1+672HPLysroy1btlCfPn3o3LlzFfYVEBBACxcu\nlG4nJydT06ZNSa1W09KlS2ncuHHSYxqNhpycnCguLk6Kf+fOndLjb775Jk2bNo2IiN59910aNWoU\nXbt2Tev1EhISyNXVVeu+FStW0EsvvVQhttpOGrK2aWg0Gnh7e8Pe3h6BgYEVlnLNzMzUqoo6Ozsj\nIyOjvsNkrPGorbRRi/55OupRUlJS8Nxzz8HKygpWVlbo3LkzjI2NkZubW+n2tra2aNq0aZXPv3nz\nJsLCwvDss89i/PjxcHJywvz587XaQR6M09XVFSqVCrdv30Z2djZcXV2lxxQKBVxcXJCZmSnd17p1\na+l68+bNoVQqAQDz5s2Dp6cnBg8ejLZt2+LDDz8EAKSmpiIrK0uK08rKCu+//z5u3ryp83tVU3q9\n3CuACg1jCoWinqJjj4UI2L4d6NkT2LgR4EZGVoWH/W8/eL+ZmRmKioqk22q1WmpXAMSXdUxMDPLz\n86VLUVERHBwcdHrNRz3f2NgY7777Li5cuID4+HgcPHgQ27dvl56blpamdd3ExAS2trZwdHREamqq\n9BgRIT09HU5OTlXG1KJFC6xatQrXr1/HgQMHsGbNGvz8889wdXWFh4eHVpx3797FwYMHK91nbdKL\n3lOWlpYYNmwYTp06pXW/k5MT0tPTpdsZGRkPfaPfe+896VJZ8mH16No1YNAg4OOPgfnzgb17AR8f\n4Mcf5Y6M6TF7e/sqV5Nr3749SkpKEB0dDZVKhYiICKnRGACmTZuGt956S/oCv3XrFg4cOKBzDI96\nfmxsLM6fPw+1Wg1zc3OYmJigSZMmAEQi2LFjBy5evIiioiK8++67GDt2LBQKBcaOHYtDhw7h559/\nhkqlwurVq9GsWTP06dOn0hge/KF88OBBXLt2DUQECwsLNGnSBE2aNEHv3r1hbm6OlStXori4GGq1\nGn/88UeF79AHxcbGan1P1liNTmrVglu3blF+fj4RERUVFVH//v3pxx9/1NrmwYbwEydOcEO4vist\nJXr/faJWrYhWrSL6/4Y+0miIvvuOqG1bohEjiC5fljfORkrf/0/2799Prq6u1LJlS1q9ejXduHGD\njIyMKrRHREVFkYODA9nZ2dGqVavIw8NDaofQaDS0Zs0a6tChA5mbm1Pbtm3p7bffrvT1jh49Si4u\nLlr3Per5u3fvpg4dOpCZmRnZ29vT7NmzpdjK2zR69+5NFhYWNHLkSPrrr7+k/X733XfUuXNnsrS0\npICAAEpOTpYe+2dbznvvvUdhYWFERLR27Vpyd3cnMzMzcnZ2poiICGm7rKwsCg0NpdatW5OVlRU9\n9dRTWvsp97DjXtPPg2yz3J4/f77Ccq/z5s3TWu4VAGbMmIGYmBiYmZlh69at8PX1rbAvnr1TD/z2\nG/DKK4CjI/Cf/wAeHhW3uX8f+PRT4MMPgbAwYNEiwMqq/mNtpPj/pO4EBgYiLCwMkyZNkjuUCmp7\nllueGp09nnv3gLffBr7+GlizBhg/Hqiq3enmTeDdd4HvvhN/p04FjHlpl7rG/yd1JzAwEBMnTsTk\nyZPlDqUCnhqd6Y///hfo0gUoLAQuXABCQ6tOGABgZycax3/4QSQOLy/gf/+r+3gZq0ONpZMO1zRY\n9WVnA7NmAWfPAps2AYGBNd8XkUg+b7wBtG8vTl+1aVN7sTIJ/580TlzTYPL673+B7t2Bjh2Bc+ce\nL7JKHw4AACAASURBVGEAomYycqSoqfTpAwQFAf/fR50xpn+4psF0V1gItGsnutD27183r/Hii0CT\nJsDmzXWz/0aM/08aJ65pMPl88gnQr1/dJQxAnJ46dgz46qu6ew3GWI1xTYPp5q+/gA4dgBMnRG2j\nLp06BQwdCiQmAu7udftajYi1tfVDZ3xlDZeVlRXy8vIq3M9dbg2/GPpt7lxxeioysn5e76OPgO+/\nB+LiuDsuY3WAk4bhF0N/paWJaUD++AN4yBw+tU6jAZ59FujbF3icKQ8YY5XipGH4xdBfL70kRnov\nX16/r5udDfj6ivaNumxHYawR4qRh+MXQTxcuiG61V68Clpb1//oHDwKvvQb8/jtPOcJYLTK43lPp\n6ekIDAxEly5d0LVrV6xbt67CNrGxsbC0tISPjw98fHwQEREhQ6SN3FtviZlq5UgYADB8ODBqlJjX\nin8YMCY72WoaOTk5yMnJgbe3N5RKJXr06IHvv/8enTp1kraJjY3FmjVrqpzamGsadeTXX4EJE4DL\nl4FmzeSLo6QE8PMDZs4EXn5ZvjgYa0AMrqbRunVreHt7AxALjXTq1AlZWVkVtuNkIBMiYMECYMkS\neRMGIF5/925g4ULg0iV5Y2GskdOLwX0pKSlISkqCn5+f1v0KhQLx8fHw8vLC0KFDkZycLFOEjdCh\nQ0B+vpjCXB907gxERIhJER9YdIcxVr9kbwhXKpUICAjAO++8g+DgYK3H7t27hyZNmsDU1BSHDx/G\n7NmzceXKlQr74NNTtUytBry9RW+pkSPljuZvRMDzzwNubmIadsZYjdX0e1PWUVMqlQpjxozBxIkT\nKyQMADA3N5euBwUF4dVXX0VeXh6sra0rbPvg8oUBAQEICAioi5Abh507RcP3iBFyR6JNoQA+/1wk\ntMGDgSFD5I6IMYMRGxtbK0thy1bTICKEh4ejVatWWLt2baXb5Obmws7ODgqFAomJiQgJCUFKSkqF\n7bimUYtKSsR0ITt3inmm9FFcnDhNlZQE2NvLHQ1jBsngahq//vorduzYge7du8PHxwcAsGLFCmlB\n96lTp2Lfvn2IjIyEsbExTE1NsWfPHrnCbTwiI8XU5/qaMADA3x+YNAkIDwcOH9Zt4SfGWK2QvU2j\nNnBNo5bcuSMWQvrpJ6BrV7mjeTSVCnjqKeDf/wb+9S+5o2HM4PCIcMMvhvwWLQLS04GoKLkj0c2J\nE8DYsaIbbosWckfDmEHhpGH4xZBXTo5Y7/vMGdE7yVBMnCjire95sRgzcJw0DL8Y8nrtNeCJJwyv\nK2tmJuDlJdbe4LXFGdMZJw3DL4Z8rl0DnnxSnOaxsZE7mupbsUIs3PTtt3JHwpjB4KRh+MWQT2io\nODX1zjtyR1IzJSVixPjnnwMDB8odDWMGgZOG4RdDHpcviy6s168DZmZyR1Nz330nGvJ//51X+mNM\nBwY3YSHTE1u2iPEOhpwwACA4GGjdGti4Ue5IGGvQuKbRmKlUgKsrcPQo0LGj3NE8vj/+AAYMAC5e\nBFq1kjsaxvQa1zRY9R0+DLRt2zASBiAGJI4bB7z7rtyRMNZgcU2jMRs1SlwmTZI7ktqTlwd06gT8\n8IOYDoUxVimDq2nostwrAMyaNQvt2rWDl5cXkpKS6jnKBiwnBzh2DAgJkTuS2mVtDSxeDMyZw8vD\nMlYHZEsaJiYmWLt2LS5cuICEhARs2LABFy9e1NomOjoa165dw9WrV/HZZ59h+vTpMkXbAG3fDowe\n3TCn33jlFeD2bR63wVgd0OvlXg8cOIDw8HAAgJ+fHwoKCpCbm1vvsTY4RKLXVEM6LfUgY2Pgk0+A\nuXOB4mK5o2GsQdGLhvCHLfeamZkJFxcX6bazszMyMjLqO7yGJz5e/O3TR9446lJgINCjB7B6tdyR\nMNagyJ40lEolnn/+eXzyySdoUcmpkn821Ch47YTHV17LaOjv5apVwMcfA/xDg7Fao9fLvTo5OSE9\nPV26nZGRAScnp0r3xcu96ujePXGu/x/tRw2Suzvw6qvA/PliJULGGrFGsdxrdHQ01q9fj+joaCQk\nJGDOnDlISEiosB13ua2GLVuA/fvFpTEoLBRdcHfvBvr2lTsaxvSGwc099csvv+Dpp59G9+7dpVNO\n/1zuFQBmzJiBmJgYmJmZYevWrfD19a2wL04a1dC3r/jlPXKk3JHUn927xamqxESgSRO5o2FMLxhc\n0qhNnDR0dOmSaCBOSwNMTOSOpv4QAf37Ay++CLz8stzRMKYXOGkYfjHq3vz54u+HH8obhxySkoCg\nINGWY2UldzSMyY6ThuEXo241tMkJa+LVV8XpqU8/lTsSxmRncNOIsHrW0CYnrImICODrr8WaG4yx\nGuGk0Vhs3txwR4DrytoaWLYMmDGD56VirIY4aTQGDXVywpqYNAm4fx/YsUPuSBgzSJw0GoOGPDlh\ndTVpAqxfLzoF3L0rdzSMGRxuCG/oiMTgti1bGvZcU9X18suAhQWwZo3ckTAmC24IZ5Urn5zwqafk\njUPf/F979x4XZZX/AfwzMChxiYslcstxgRAEhkGULAlRiUAxuoiamSFpZt52u6j72l/prrX68u5S\nZG5e0tKSSmhFcjNH3XghXpBa3U1J0eEiiogCScDM+f1xlpGRgRmQmWeeme/79XpeczvM8z0cmO88\n53nOOX/9K++iOnNG6EgIEZUeJY1x48b1dhzEVLZsATIyrH9ywu568EG+WBOdFCekW3rUPVVZWQkf\nHx9TxNMj1D3Vifp6PjbjP/8BBgwQOhrL09oKREcDS5bwtcUJsSFm7Z7qrYQxY8YMeHl5ITw8XO/r\nSqUSbm5uUCgUUCgUWL58ea/s12bs2QPExVHC6IxUCrz/Pl+sqaFB6GgIEQWDRxqDBg3q+EMSCS5c\nuHDPOz969ChcXFzw4osv4qeffurwulKpxNq1a5Gbm9vl+9CRRidscXLCnnjxRcDHB1ixQuhICDGb\nnn5uGlxP4/jx49r7TU1NyM7OxvXr17u9I31iY2NRVlbWZRlKBj303/8CFy4AyclCR2L5Vq4EIiKA\n9HQgOFjoaAixaAa7px544AHt5ufnh4ULF2Lfvn3miA0SiQQFBQWQy+VITk7G2bNnzbJfq7BlC/8G\nLRV0nS1x8PYG/vhHYN48OilOiAEGP1FOnjypXe9Co9HgxIkTUKvVJg8MAKKioqBSqeDk5IT9+/cj\nNTUV586dM8u+Ra2lhQ/oO3xY6EjEY+5cPtXK11/zgZCEEL0MJo3XX39dmzSkUilkMhm++OILkwcG\nAK6urtr7SUlJmDNnDmpra+Hp6dmhLC332k5eHhAYSF0t3eHgwGe/TU8HnnwScHISOiJCepXol3tt\nU1ZWhpSUFL0nwqurq9G/f39IJBIUFRUhLS1N7zkQOhF+l5QU/m05PV3oSMRn8mQgKIhPbEiIFTPr\nehonT57E0KFDu72zu02ZMgWHDx9GTU0NvLy8sGzZMrS0tADgy72+//77yMrKglQqhZOTE9auXYtH\nHnmkYyUoadxx+TKgUPBbZ2ehoxGf8nIgMhIoLORHa4RYKbMmjZkzZ2Lz5s3d3pmpUNJo5//+D7h5\nE9i4UehIxGvlSuDoUeAf/xA6EkJMxqRJo7a2FufPn8dvv/0GgF8GGxcX1/0oTYSSxv+0tAADBwLf\nfQeEhgodjXg1NwNyObB0KY0UJ1bLZOM0Nm/ejI0bN6K8vByRkZEoLCzEiBEj8P333/coUGJCOTm8\nP54Sxr3p04dffTZuHB8g6ecndESEWAyD4zQ2bNiAoqIiDBw4EIcOHUJxcTHc3NzMERvprg8/BGbP\nFjoK6zBsGLBgATB9OqDRCB0NIRbDYNJwdHTEfffdB4CPCB88eDB+/vlnkwdGuuncOeCnn2iMQW9a\nvJiv8rdundCREGIxDHZP+fv748aNG0hNTUVCQgI8PDwgk8nMEBrplk2b+CW2ffsKHYn1sLcHduwA\nhg8Hxo7l5zkIsXHdunpKqVTi1q1bePLJJ9GnTx9TxtUtNn8i/PZtPgX6sWPA734ndDTW55NP+BVV\nJ04A/zvqJkTszHrJraWx+aSxYwfw2WfA/v1CR2KdGOOD/gYMADZsEDoaQnoFLfdqy7Ky6AS4KUkk\n/Hf89dfAt98KHQ0hgqKkIXYlJYBKxS8PJabj6Qls2wbMmAHU1AgdDSGCoaQhdps2ATNn0hTo5jB6\nNPD88/z3bcvdocSmCZY0DC31CgDz589HUFAQ5HI5iouLzRidSNTXA7t3AxkZQkdiO5YvBy5e5OuV\nEGKDBEsa6enpyM/P7/T1vLw8lJaW4vz58/joo4/w6quvmjE6kfjsM2DUKMDXV+hIbEffvsCnn/Ix\nHOfPCx0NIWYnWNKIjY2Fh4dHp6/n5uZi+vTpAICYmBjU1dWhurraXOFZPsboBLhQhgzhE0O+8AKf\n74sQG2Kx5zQqKirg7++vfezn54fy8nIBI7Iwx44BDQ180Bkxv7lzAQ8P3l1FiA2x2KQBoMM1xG0r\nCBLweaZeeQWws+gmtF52dsDWrfxChIICoaMhxGws9pIbX19fqFQq7ePy8nL4dtF3b1PLvdbWAnv3\nAqtWCR2JbfP25l2E06YBp08D7ZYnJsTSWMVyr10t9ZqXl4fMzEzk5eWhsLAQCxcuRGFhod73sbkR\n4evX8yktdu4UOhICAC+/zKdy2bmTDwQkRAREN42IoaVeAWDu3LnIz8+Hs7Mztm7diqioKL3vZVNJ\ngzEgJAT4+9+BkSOFjoYAQGMjkJAAPPooP/qjxEFEQHRJozfZVNI4dAiYN49Pg04fTpajthaIi+OD\n/5YsEToaQgwy2cp9xMJ8+CHw6quUMCyNpyefl2rkSKBfP2DWLKEjIsQk6EhDTK5c4V1TZWUArZ5o\nmUpL+RHH+vXAxIlCR0NIp+hIwxZs2QI89xwlDEsWGAjk5QFPPAG4u/NzHYRYETrSEAu1GggIAL78\nEhg6VOhoiCH/+hdfevebb4CYGKGjIaQDWk/D2uXnA/37U8IQi5Ej+eC/p54CzpwROhpCeg0lDbH4\n8EOaZ0psxo0D1qwBnnySn4cixApQ95QYlJbyLo7LlwFnZ6GjId21cSOQmQkcPQp4eQkdDSEA6ES4\n9WIMeO014K23KGGI1fz5wPXr/IhDqaQLGYioUfeUpfvsM36p7R/+IHQk5F4sXQo89hgwYQKfcoQQ\nkaLuKUt2/TpfuyE3Fxg+XOhoyL3SaPgaHA0N/Co4BwehIyI2TJRXT+Xn52Pw4MEICgrCypUrO7yu\nVCrh5uYGhUIBhUKB5ba2dsGbbwKTJlHCsBZ2dsD27fx2zBigslLoiAjpNsHOaajVasydOxffffcd\nfH19MWzYMEyYMAEhISE65eLi4pCbmytQlAL6/nvgu+/ock1r4+AAfPUV8N57QHQ0nxl39GihoyLE\naIIdaRQVFSEwMBAymQwODg6YPHkycnJyOpSzym4nQ27f5gssvf8+rdFgjezsgD/9CfjkE2DqVJ5A\nNBqhoyLEKIIlDX3LuVZUVOiUkUgkKCgogFwuR3JyMs6ePWvuMIXx7rtAZCSQkiJ0JMSUxo7l66Lk\n5fG2vn5d6IgIMUiwpGHM0q1RUVFQqVQoKSnBvHnzkJqaaobIBPbvf/MlRDdsEDoSYg6+vny6+5AQ\nPtq/qEjoiAjpkmDnNO5ezlWlUsHPz0+njGu7rpmkpCTMmTMHtbW18PT07PB+VrHcq0bDp9T+y18A\nHx+hoyHm4uAArF7NL8kdPx545x1gzhya/p70KtEv99ra2org4GAcPHgQPj4+GD58OHbt2qVzIry6\nuhr9+/eHRCJBUVER0tLSUKZnOgarueQ2K4ufGD16lPd7E9tTWsqnVB88GPjoIzqnRUxGdCPCpVIp\nMjMzkZiYCLVajYyMDISEhGDTpk0A+JKv2dnZyMrKglQqhZOTE3bv3i1UuKZXUQG8/TYfMUwJw3YF\nBgIFBXwU+bBhfDzHkCFCR0WIFg3usxTPPss/HP78Z6EjIZZi+3bgjTeAlSuBl16iLxOkV9Ea4WKu\nxt69wKJFQEkJ4OgodDTEkvz0E/Dyy8Cvv/KpSJ5+mpIH6RWUNMRajVu3+BHGjh2AGE/eE9NjDNi/\nn3dftrYCy5bxOazoRDm5B5Q0xFqN+fOBxkbg44+FjoRYOsb4SoBvvw1IpTx5JCdT8iA9QklDjNU4\ndgxITeVThei5jJgQvTQa3qX5zjuAkxM/D/bEE5Q8SLdQ0hBbNVpa+GCuJUuAKVOEjoaIkUYDZGfz\ncx0eHjx5jB5NyYMYhZKGmKrBGO9iaJtCgv7Jyb1Qq4HPP+fJw9sbmDsXSEoCXFyEjoxYMEoaYqlG\naSnw6qtATQ2QkwM89JDQERFr0doK7N7NB4gWFADx8cAzz/B5raj7k9xFlOtp2JTmZj6b6SOP8GU/\njx+nhEF6l1TKF3nKzwcuXeIjy3NyAJkMSEjgMw5UVQkdJRE5OtIwhx9+4FOdDxzIpzuXyYSOiNiS\nxkbg22/56PK8PCA0lA8mffppYNAgoaMjAqHuKUusRl0dsHgxv0xy/Xrguefo/AUR1m+/8QW+vvqK\nH4UMGMBXhlQogKgoICICcHYWOkpiBqLsnjK03CsAzJ8/H0FBQZDL5SguLjZzhD3EGD8xGRrKk8SZ\nM7yrgBIGEVrfvvwk+ebNvKtq82Z+Fd/p08C8ecCDD/K/26lTgTVreIK5cUPoqIkFEexIQ61WIzg4\nWGe517tnuc3Ly0NmZiby8vJw7NgxLFiwAIWFhR3ey6KONC5eBF57Dbh8mc9S+uijQkdEiPFaWoCz\nZ4HiYuDUKX57+jTwwAP8SCQ4GPD3B/z8+K2/Pz/JTl+IREd0s9y2X+4VgHa51/ZJIzc3F9OnTwcA\nxMTEoK6uDtXV1fDy8hIi5M6p1fxb265dfHK511/nW58+QkdGSPc4OAByOd9eeok/p9Hwq/5OneK3\np0/zLtfyckCl4hd5+PnpJpK2x56egLs7H0fi7k5zq1kBwZKGvuVejx07ZrBMeXm5+ZNGUxP/57h0\n6c52+fKd+xUV/J8jJoaP8g4IMG98hJiSnR3w8MN806ehgf9/tCURlYpfHbh3L+/aqqvj240b/Iik\nfRJpv7m6AvfdxzdHxzv3O3vs4NBxk0rv3Le3N+/vyUYIljSMWe4VQIfDp05/LjHRuB0zxr85aTT6\n77d/ru0IoraWL8s5cOCd7fHH+SWzAwfyb1b0DYrYKhcXvlxtu16CTjU16SaS9lt9PXD7Nr9/+zbf\nmpru3L97a23l3Wlt292PgTtJRCrlScTOjm9t9+++bbsvkfD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"text": [ "" ] } ], "prompt_number": 67 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Derivation of the multiple regression equation:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In raw form the regression equation is:\n", "\n", "$ y = a + b_1X_1 + b_2X_2 + ... + B_kX_k + e $\n", "\n", "This says that y, our dependent variable, is composed of a linear part and error. The linear part is composed of an intercept, a, and k independent variables, $X_1 ... X_k$ along with their associated regression weights $b_1 ... b_k$.\n", "\n", "In matrix terms, the same equation can be written:\n", "\n", "$ y = X b + e $\n", "\n", "If we solve for the $b$ weights, we find that\n", "\n", "$ b = (X'X)^{-1} X'y $\n", "\n", "To give you an idea why it looks like that, first remember the regression equation:\n", "\n", "$ y = X b + e $\n", "\n", "Let's assume that error will equal zero on average. Now we can simply drop the error term, in order to sketch a proof:\n", "\n", "$ y = Xb $\n", "\n", "Now we want to solve for $b$, so we need to get rid of $X$. First we will make $X$ into a square, symmetric matrix by premultiplying both sides of the equation by $X'$:\n", "\n", "$ X'y = X'Xb $\n", "\n", "And now we have a square, symmetric matrix that with any luck has an inverse, which we will call $(X'X)^{-1}$. Multiply both sides by this inverse, and we have:\n", "\n", "$ (X'X)^{-1} X'y = (X'X)^{-1} (X'X)b $\n", "\n", "It turns out that a matrix multiplied by its inverse is the identity matrix $(A^{-1}A=I)$:\n", "\n", "$ (X'X)^{-1} X'y=Ib $\n", "\n", "and a matrix multiplied by the identity matrix is itself $(AI = IA = A)$:\n", "\n", "$ (X'X)^{-1} X'y=b $\n", "\n", "which is the desired result." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }