Theory_of_Linear_Model.ipynb

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  "metadata": {
    "colab": {
      "name": "Theory of Linear Model.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true,
      "authorship_tag": "ABX9TyMtYTffhqzknB5bv8Ppo7JE",
      "include_colab_link": true
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    "kernelspec": {
      "name": "ir",
      "display_name": "R"
    }
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  "cells": [
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      "cell_type": "markdown",
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        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/yain22/Theory-of-Linear-Models-in-R-and-Python/blob/master/Theory_of_Linear_Model.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
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        "id": "Q1E_4bL6hP-2",
        "colab_type": "text"
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      "source": [
        "# Theory of Linear Model\n",
        "\n",
        " $$y = X\\beta  +  \\epsilon, \\quad \\epsilon \\sim N(0,\\sigma^2 I),\\quad X \\in R^{n \\times p} $$\n",
        "\n",
        " $$\\hat{\\beta} = [X^{\\top}X]^{-1}X^{\\top}y \\in R^p$$\n",
        " $$P_X = X[X^{\\top}X]^{-1}X^{\\top} \\in R^{n \\times n}$$\n",
        " $$\\hat{\\sigma}^2 = \\frac{y^{\\top}[I - P_X]y}{n-p} = \\frac{\\|[I - P_X]y \\|^2}{n-p} $$\n"
      ]
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qqwXOMcjjJr37xJ4kl0TwzqerHaBY2ktxtx97YpYDkjrjHUV84fs0ac1/431jWLjfK9tabPMc5+eV85J65IRvzNZLGQlTlUitEV7JqSi+p9TaZZadoOkWumackdvaWkSxRRrj5VA/n79zUzX8C9CW+grKorzpZlUfwpI3WHj1Mr4h6Ha+OPAupaHNbq0k0Ra2dyB5U6jMbZ7c4Bx1BI718J3FvLaXMtvcxtFNC5SRGGCrA4IP41+gNfI/x78Kr4d+JM13bIwttYT7YDjgSliJBnvz83/AxXRgsXOrNxqP0IrUlFXifSfwt1mK++Ffh19OaJIY7GOFkiHCug2uPXO4HOf1614H8bvETfEX4lWHh7w7AL6WwLW0c8RD+fI+0sAQPupjHoMMelct4a+Jmq6D8O9T8I6ZCxm1GceTPH9+NXG2RRjkk4UD0y3tXvnwd+FUHgjSE1PVokk167jBkJGfsqkf6pff+8R1PHQZKm5YaUqlSTfZXBWqJRivU2Pht8NNM+H+ixokcdxq0qg3V6VyS3dUJ5CD079TXbUUV485ynLmk9TrSSVkcN8aP+SO+IP8Arin/AKNSq/wK/wCSK6F/28f+lElWPjR/yR3xB/1xT/0alV/gV/yRXQv+3j/0okrp/wCYT/t79DP/AJe/I9BooorkNTnPHng2z8c+EbvSLxUWVlL2s5GTBKPusPbPBx1BIryf9nfxlcxXF74H1t3Wa2LSWaS9UKn95F+B+YD/AHq97r5X8XS/8IP+07/aFsRDC1/DcuQDykyjzvXruk6Z6/hXfhf3sJ0X6r1MKnuyUj6oooorgNwriPif8SrL4d6D522O61S4+W0sy+N3q7Y5Cj9TgcZyO3r5NPm/Gj48iKaZ200zMq7mAKWcRJ2jHQtz64L55xmuvC0Y1JOU/hWrMqknFWW7Lvhj4deL/jJff8JH4q1SWDT3JCXEy7mcA8rDHwFXOeeBnPBOa1vi58J/DHgX4bQ3mkQTyX/2uKF7qeZizKVcn5RhRnA7dvrX0Va2sFlZw2tpEkNvBGscUSDCoqjAUDsABivK/wBpD/klkf8A2EYv/QXrop4qdStGK0jfYzlTjGDfU53wN8FPCfjD4W6VqVyl1aaldQOXuYJycsJGAJVsr0AGBjj35rl9T0Lx/wDALUE1PRNV+06RNLhmjDGCQ9AJojwrHsQT7Nmvavgv/wAkd8P/APXF/wD0a9dfqem2msaVc6dqMKzWt1GYpY2HVSKX1ypSrSTd1dj9lGUF3M34dfFDT/iD4aXUbSHyLmI+Xd2pfLQvjP4qex789wQOwXUISPmDL+FfIHgG5vfhX8eG8P3kzfZp7kWE47SK+DDJjoOWQ57AsO9fVdbYjE1qM/dd09URCnCa13NlbmF/uyL+JxUoORkc1g05WZDlWK/Q0o5nL7URvDroziv2i7m3g+COrRz48y4mt44cj+MTKx/8dVq+W7WLUPhn4v8ADGuPvZngttWiUDYZIXJyn0IDLnuDXs37TusT3OmeHvD0TtLJdXTXPlADOVXYnvz5jD8D7VX/AGifCSQeA/Dd/ZxL/wASRE02Ro0xmEoAhPXADJgD1kr0IYqnJRb05tjndOSb8j6TtrmG8tYrm1kWWCZBJHIpyHUjII9iDXnfx/vI7P4I675hG6YQxRqTjcTMn8gCfwqn+z/4wj1/4T2FtcysbrSSbGQsuAVXmPHsIyo+orlv2qtbKeFdD0O2k3PfXjTskZJLLGuADg9CZAcEclR6V0KcW7J6kWe5037OGgLo3whtbtows+qzyXTkj5tudiDPphMj/e969XrK8LaOnh7wjpOjxqFFjZxQHGOSqAEnAAJJySe5NatUI8r+PHxNPgLwkLLSpmj1zVFK2roAfIQEb5D6HBwvvz/CarfAv4XW3hjw7b+Jdag8/wAR6khneaYh2t0fJAU9mZSCx65JHavI9Tc/FT9qpLK7Iu9Ot782yxnBQ21vuZl4J+VirnOed/bOK+uaACq2o6dZ6vps+n6nbR3VpcIY5YZVyrqexqzRQB+fPjbwvceDfGmp6Ddhs2kxWN2/5aRnlG/FSDX1D+zBqVndfCqSytwi3VnfSfaFDZZt+GVyO2R8v/AK4r9qrwgsN9pXiyzgIFwDZ3rqONyjMRPuRvGf9la8u+G3xP1L4atrMmlxpK2o2ojRZBlUlVvkkPrtDPx3JFAHr37T/jSyvYbLwNp6fatRS6S6uQqEmE7CI0HqzCTP0x610XwM+CqeELWPxF4otlfXplzBC/IskI/9GHuew4HfOV8DfhRfyaofiD48V5dSumM9nBcgFgzcmdwRw390duvpj6AoARlV1KuoZWGCCMgivmb4seF7n4OeONO+IHgSNLWxuJvKuLKNSsKORkoQD/q3APyjAUrx2x9NVzHxH8Pp4o+HGuaU8ayPNaO0IYdJVG5CORzuA70AXfCHiiy8Z+E7DXtMyILyPdsY5aNgcMh9wQRW1XzX+yh4llM+ueGZnZo9i39uuRhCCEk9+cx/kfWvpSgAooooAKKKKACiiigAooooAK8v+Kfxv0X4exSWFl5eqa8V+W0R/kgJ6GUjp67fvHjoDmvSru3F3ZT2xllhE0bRmSFyjpkYyrDoR2PY14H4m/ZVsL2ea68O+I7q3lkcuY9QQTAknJ+cYPc8kMfX1oA4P4UfFHU7346Q614u1KWcX1tNasdrMsSkb1SONeg3IoAAOSfU5r6Zbxqkw/4lPh/X9SyRjy7A24I6ZBuDGCPx9+lfNei/Bbx94A8f6HrEumJqNnZ38Uk02nS+biMN8/yYEn3d38J9O+D9c0Acx/aPjO8jb7JoGm6dnO1tQ1Eu47AmOJCD648z0Hfhw0bxXdFjf+K4rYE5C6XpiRlRjpumaXP1wPp2rpaKAOb/AOEHsJ+dV1DWNTbv9o1KVUP/AGzjKp04+7/M5u6b4T8PaPL5ulaJp9pKessNsiuenVsZPQd+w9K16KACiiigAoorg/ix4t8V+C/DTax4W0az1K3t0Zrx7h2JgGVCsI1wWXkk88AZ6AmgDvKRmVFLOQqqMkk4AFfO/wAHPi54o+InxLSx8Qavb2VpDaSTR2NpbogupBgbSWDNgKWbAYfdHoag/aD0VvE3xO8OeGfDtzdPq2poz3dqZ3MCIMBJNhO0EKkpOOcKD35APZPFPgzwv8SobePWHa+g0+ZgY7W8ZU3HaSjhDycBevIzxjNeXfFb4e+FPAVn4W1/QdEt7O3sNagjviS0ge3bO4SBydw+XHJz83vXsXhDwlpXgnw1baLodusUEKgyPtAeeTADSOR1Y4HPsAMAAVzvxu0n+2Pgz4ihAYtDbi6Xb1HlMJD+GFNAHdQwxW8KxW8aRRoMKiKFCj2Ap9YXgjVv7d8A6FqhKl7rT4JJNvQOUG4fg2R+FbtABRXlXw8+JXifxV8UPEPh/W9CSw0/TkkMEqxSBlZZQgV2PDFlYngD7vAr1WgDgfidpHjDxP8A2d4b8MTR6dpOobxq2ph/3kMQx+7VePvgnp1xg7RnPkvhfw9b/Cz9qmw0LT3lXTtQ08RI8zHc4MOSSejbpoTwOATxjFfTFfPn7Qh/4R34m+BPFqqmIZhHKTgErFKr4OexDv8ATmgD6DooryTxF8D7zxT4ovb/AFjx9rh024nMsOmwuQtupIJRSzsuOOMKMYHXFAHoOr+M/DOgbxrWv6bZNH96Oa6RX+m3OSfwp/hrxXonjDTZL/w3fpf2scxheVFZQHADEfMAejA/jXC6P+zr8O9J2tNpc+pyLjD3tyzcjPVU2qc57jHFeg6NoOk+HbD7FoOm2unW27cYrWFYwzYA3HHVsADJ5OBQBx3x10n+1/gtr8ahfMt4kukLfw+W6u347Qw/Gk+BOrnWPgvoMjgB7aJrVgP+mblV/wDHQprX8a+KvCNhouo6V4l17TrT7TbSQS28twvmbXTGNgy3Rh27ivnj4JfGjRvh94Qv9I1u21G6mkvPPtY7SNXDblVSvLDHK5/H1oA+sq534g6ONf8Ahzr+mFC7T2EojAGTvClk/wDHgK0PDmsr4h8N2OrLaz2Yu4RJ9nuFxJGT1UitKgDyT9mnWDqfwfhtXcM2m3k1sBnkKSJBn/v4R+HtXOfHD/infjX8PvFR/wBWZVtpm64RJQW64AO2Zsc9vau9+FPwu/4VlDrECap9ugv7lZYY/KKeSq5AB+Y5JBGTx0rpfE/gzw/4zt7WDxNpqX8VpN58KO7qFfGOdpGR7HIPpQBrXtpDf2FxZ3K7obiJopF9VYYI/I14t+zVY6lpGheJvD+r2E9ulrqO5TcQMgkLLsbGRg/6ocAnr78+30UAeB6f8LPiV8Ntcv4vhjqumz6JfybxDqGN8RGMFvl6gEjKnkDJAOK0pfgBP4mt4tT8e+Jri98TtcRyTX1so8uKJFIEMSEBQNxDbivUdBk59qooA4v4waSdb+D/AIlswNzLZNcKATyYiJQOO+U6d65z4DSWHib4MaMuo2VvdSaZJNbAzxB9pDEjbuzj5GUcV6rJGk0TRyorxupVkYZDA9QR3FVdK0fTdDsFsdFsLawtUJKw20SxoCepwB1PrQBbVVRQqAKqjAAGABXnnxp+Hl78SPBdvpukyWsN9bXqXEclySq7drKw3BSQMNngc7RXolFAFPSLWey0SxtbyYT3EFvHHLKOjuqgFvxIzVyiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiqN3c7v3cZ47n1pN2Qm7Bc3e4FIjx3PrVSiiudttmbdwooopCCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACuc8VeC7Pxc9sNSvLuKG3DbIrdlUFjjLHKnPAxXR0VMoqStI6MPiKuGqKrRlaS2Z88/EPwpY+EtYtbTTZbiWOaDzGM7KSDuI4wBxxWr8PPAOl+LdHurvUp7yKSGfy1EDqARtB5yp55q38bQP7b0w4GTbsCf+BVsfBIn+w9TGTgXCkD/gNeVGnD6y4NaH6liMwxS4bhiozanpr1+Kx3Hhzw9a+GNL/s+wmuJYAxdRO4YqT1xgD61rUUV6ySirI/KqtWdao6lR3k92FFFFMyCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACvkn4q/wDJylz/ANftj/6Khr62rNufDeh3uqJqV5o2n3F+mNl1Lao0q46YcjIx9aqLsxp2L1xBFdW0tvcxrLDMhSRGGQykYIP4V8RfEPwhc+BPGt9o8m8W7HzLVyf9bAzHaT64IwfdTX3DVDVNB0jXERNa0qx1FUOUW7tklCn23A46miMrDTseVfsx/wDJM9Q/7C8n/omGvIfiXo2ofDf4xPqljEUia8GpWEjqTG/zBynGMhWypGc4x619c6fptjpNmtnpVlb2VshJWC2iWNFJOThVAHWodY0LS/EFibPW9Pt7+3Jz5c8YYA+oz0PuKalrcL6njN3+1Bo/9h77DQr7+1Wj/wBVMyeQj4/vhtzAHH8K5HpXEfATwhfeJPiEviW+hZ7HTnad5pAQJZ2B2gepB+Y46YGeoB9vi+CPw7huDMnhqIsTnD3MzL1z90uR+ldtZWNpptnHaadaw2ltEMRwwRhEQZzwo4HJo5kloF10PnH9qP8A5GPQf+vST/0MV33/AAmF34F/Z38Pa5Y2kd28VrZo8cpIUo2A3I6HHAPYkcHpXo+qeH9G1zy/7b0ix1Hy/ufa7ZJdn03A4qR9I02TRzpL2FsdOMXk/ZPKXytn93bjGPalzKyQX0PDNY/aL8La74Qu7HUfDN5NdXEDJ9ll8t4NxGP9ZkNwe4XPHaua/Zp0e8ufHt3q0QK2dlaNHK/Zmcjav/jpP4V7RJ8E/h5Ldm5bw1CHPZZ5lTpj7gfb+nvXY6XpVhomnRWGkWcNlaRDCQwIFUepwO56k96fMrWQXVtD5M+JOlaj8NvjQ+r2kcixSXv9pWUrZ2yZbeyZ7gElSPQjPWvUrX9p/wAMvZK19ourQ3O35o4RFIgOOgcupI99teu6xoWl+ILE2et6fb39uTny54wwB9RnofcVx6/A34dLN5o8NpuyTg3c5Xn/AGd+KOZNahdPcX4ZfFOD4lS6sLXS5LCPTvJw0kwcyeZv7ADGNnqevtz87fEXTNU+HfxouNRiVQ32/wDtSxkIJR1aTeAeckA5UjjOD2Ir6y0Dwvonha1e38P6Zb2EchBfyUwXI6bm6n8TR4h8L6L4r08WXiHTob+AElRIOUJGMqwwVOO4IoUkmF7M8P8AFH7Rset+GTpnhLR76HWL9fILShWERbj93tJLtzgcDnBwelcl+z3DJbfGIQToUlitZ0dT1UjAIr6J8N/DTwh4Rvje+H9EhtbrBUTNI8rqDwcF2JH4VrWfhvQ9O1KTUNP0bT7W9l3eZcwWqJI+45bLAZOTyfWjmVrILroadc98Qf8Akmfif/sEXf8A6JauhpskaSxtHKiujgqysMhgeoIqBHzJ+y//AMjvrH/YO/8Aai19AeNfD/8AwlPgjVtFDbXvLZkibOAJByhPtuAz7VZ0vwzoOhzvNouiadp0si7HktLSOJmXOcEqBkZrUqnK7uDep8b/AA18fXnwm8U6hHqemzSxzL5F3aFvLeN0bhsEdRlhg/3jzXrt1+0/4XSEmx0bV5pMcLMsUYz9Q7fyr0jxF8P/AAr4smE3iDRLa7nC7fPwUkI6YLqQxA7c8dqx7P4KfDyxmEkPhqBmBziaeWUfk7kVTlF6sd0xmsfEW7t/gmfHOnadGLhoIpltJXMiqGlVDlgFJwCTnjpXCy/tKeFtU8Pz22teGL2WWZCr2ZMcsEg9C5IOP+AV7dHpljFpa6bHZwLYpGIltvLHlhAMbdvTHtXGz/BP4eXFyJ5PDUIcY4jnmReP9lXA/SpTj1DQ8H/Z50i81H4rw6lar5drpsMslwRnbh0ZFT82zz/dNN/aL/5K3L/15Q/yNfVGj6Jpnh/T1sdEsILG1UlvKgQKCT1Jx1PHU18r/tF/8lbl/wCvKH+Rq4u8hp3Z1/hv9pEaT4VNh4n0i6n1uzQwxvEFVJiowPMyQUPGDgHucDpXBfC3Q7/x/wDF+HUrmN2jivDqV/MgIVTvLgZ5xufjHXGfTNfSeq/DTwh4ujtb3xBokN1deQimZZHidgFwMlGBP41v6F4d0fwzp/2LQNOt7C33bikKY3H1Y9WPucmlzJLQV0eC/tM+EZxqFh4rtIXeBoha3jKMiNgSUY+mdxXPso78yeCP2jNN0bwXZ6Z4i0u+mvrCEW8UtpsZJkUYQsWYFTgAH73TPfA+hJ7eG6t3guoo5oZBteORQysPQg8GuIufgp8PLq7+0y+GoFfOcRTyxp/3wrhf0pKStZhdW1PnC6bV/jb8WmltLRoReSKu0ElbWBBjLNj0BPuxwByBXufx/tobP4Lva2qCOGCe3jjQdFUHAH5CvQ9B8M6J4YtDbeH9LttPibG/yYwGkxnBZurEZPJJq5fafZ6pZva6laQXls/34biISI31UjBoctUFzxv9mD/kRdW/7CR/9FJXLftR/wDIx6D/ANekn/oYr6I0vRdL0OB4NF02z06J23vHaQLErNjGSFAycAc0zVPD+ja55f8AbekWOo+X9z7XbJLs+m4HFHN71wvrc840rxNd+D/2ZtO17TreO5uLOyhKxSg7SGlVTnHPAYn8K56X9pTwtqnh+e21rwxeyyzIVezJjlgkHoXJBx/wCvb102xTTRpyWdutisflC1ESiIJ027cYx7Vxk/wT+HlxcieTw1CHGOI55kXj/ZVwP0pJrqGnU8H/AGedIvNR+K8OpWq+Xa6bDLJcEZ24dGRU/Ns8/wB00nxr0DUPBvxabXrNZEgvZ0v7S45wswILLn1DjOPQivqfR9E0zw/p62OiWEFjaqS3lQIFBJ6k46njqadqukadrmnvY6xZQX1rJ96GeMOufXB6Edj1FPn1uHNqeOWH7UHh17ANqmiapDd45jt/Lkjzj+8zKevtXV/Dn4uWvxH1rUbOw0qazhs4VkEs0wLSZbGNoGB+ZqVvgb8Omm80+G03ZBwLucLx/s78V0+geEtA8LJIvh7Sbaw80BZGhTDOBnG5up6nrSfL0DQ8j+O/xP8AFHg3xLp+leGrlbGOW0FzJOYEkLku67RvUgY2g+vI6d/VPAWr3uv+ANF1XVNpu7u0SSUqm0MSOuO2evpzWhqnh/Rtc8v+29IsdR8v7n2u2SXZ9NwOKvRxpFGscSKiIAqqowFA6ACk2rWF0HUUUUhBRRRQAUoJUgg4IpKKANG3uhKAr8P/ADqxWMDg5FaNrceau1z84/WtoyvozRMsUUUVoUFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFQ3dzHZWU91PkRQRtI+Bk4UZP8qmrhvjPrY0H4PeIbkSbJJrU2seCMlpSI+ORyAxPHIAJ7UAfEGrajNrGtXup3X+vvbiS4k5z8zsWP6mvX9PvPjR8O/hjaXWkwJZeHfJW6S4igtpXRZTv3OCC/8QyWHAwOMV5Do+myazrthpkBIlvbmO3QhcnLsFHHfrX6FXOj2V3oEuizQ5sJrU2jxbjzEV2Fc9enFAHw7oNwnxH+IVrH8RvFN1bRXLbTeyjeFbPCDJCxqemcYHHGOR9j+B/h34d+H2mNaeHbQo8gHn3UxDTT4zjc2B6ngAD2r4Mv7OTTtSubKcES20zxOCMEFSQf5V93fCvW28Q/Cnw7qMsjSyvZJHLIxyXePMbE8nkshP8Ah0oAs/ETWv8AhHvhvr+qDh4LGXyv+ujLtTuONxHQ59K8X/Zg8L6Nq3gvxBcavZ2Woi4vo4XtrqJZQojTcrFWBHJkbB/2fave9e0DTPE+jTaVrtqLuxmKmSFnZQ+1gwztIPBAP4VieH/hf4N8K6sup+H9DisrxFZBKkshOCMEYLEUAaWi+DfDXhyZptB0HTtPmYYaW3tkRyPTcBnHtW1RRQAUUUUAFc3rvw88J+J9S+36/oVrf3ewR+bMCSFHQdenJ/Oukrxn4qa38XLDxkIfh7ZTT6T9lQsy2kcg83LbhlhnptoA7D/hTXw8/wChT0//AL5P+NH/AApr4ef9Cnp//fJ/xrxr/hKP2jP+gVcf+C+D/Cj/AISj9oz/AKBVx/4L4P8ACgD2X/hTXw8/6FPT/wDvk/40f8Ka+Hn/AEKen/8AfJ/xrxr/AISj9oz/AKBVx/4L4P8ACg+Kf2iwMnS7gD/sHwf4UAfSdhYWul6db2GnwJb2ttGsUMUYwqKBgAVYrnvC2qajJ4P0qXxErf2u9rG14u0LtlIywwOBz2FXZL+Z/ukIPauOpjaNPrf0NY0ZyNJ3VBl2Cj3NeDftTeIRF4J0rR7eQf6deGSTjlkjXoM/7TqfwHvXrzMWOWJJ9Sa+eP2pFmM/hliD5AW5AOOA2Y8/oBXPRx0q1ZQSsjSdFQg2dj+zbYNpfwve9QFZNSvJJC57qnyADtjKt+Z9q9XaR3++xb6muD+Cyhfg5oAUADypDgDuZXJruq8zE1ZzqSTelzopxSirBRWU/ifR4/FEfh1r5Dq0kXnLaqrMQmCckgYXoepHb1FatczTW5ocX8X5RD8IvELMCQbbbx6l1A/nXm/7Lcaix8SyAfO0lupPsBJj+Zr1b4k2Tah8MfEVvH986fK6jOMlVLY/SvHv2XL0Lc+I7FmXLpBMi5GeC4Y46n7y/Tj1rvpa4Oa81+hjL+Kj6HooorzzcK+dP2lPE2hajJp2h2rfaNW0+ZnllQ5WBGXBjP8AtEhD7bfeu8+MnxUh8E6O+maROra/dpiMKQfsqH/lowwRn0B+vQc8/wDBr4RQQ6QfEvi+3N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      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NQYFFJGff2l7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "outputId": "f21fe9d6-a32a-4b2d-8b9b-7e6f730a5646"
      },
      "source": [
        "install.packages(\"mvtnorm\")\n",
        "library(\"mvtnorm\")\n",
        "\n",
        "set.seed(1)\n",
        "n = 100\n",
        "p = 5\n",
        "X = matrix(data = rnorm(n = n*p), nrow = n, ncol = p)\n",
        "beta_0 = rnorm(n = p)\n",
        "sigma.sq_0 = 0.001\n",
        "y = c(rmvnorm(n = 1, mean = X%*%beta_0, sigma = sigma.sq_0*diag(n))) \n",
        "P.X = X%*%solve(t(X)%*%X)%*%t(X)\n",
        "\n",
        "\n",
        "# Estimators\n",
        "beta.hat = solve(t(X)%*%X)%*%t(X)%*%y\n",
        "sigma.sq.hat = (t(y)%*%(diag(n) - P.X)%*%y)/(n-p)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Installing package into ‘/usr/local/lib/R/site-library’\n",
            "(as ‘lib’ is unspecified)\n",
            "\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lL1OhGYtgJ9P",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "5d771589-40bf-4687-95a3-a8f36298bbc7"
      },
      "source": [
        "plot(x = beta_0, y = beta.hat, pch = 20  ) ; abline( a = 0, b = 1, col = \"red\", lty = 2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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/4gnb/46u3tPWPGjJZ8HDHgwbgUCwAW9s+XXx44dOimTZuqVq3ao0ePm2++2XQR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\nAwAAUATFDgAAQBH/D4oPic5kKvU6AAAAAElFTkSuQmCC",
            "text/plain": [
              "plot without title"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Du_elkHMgmZA",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 90
        },
        "outputId": "49aae6f2-6788-4451-de1b-c6f174631dc5"
      },
      "source": [
        "sigma.sq_0 ; sigma.sq.hat"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[1] 0.001"
            ],
            "text/latex": "0.001",
            "text/markdown": "0.001",
            "text/html": [
              "0.001"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "     [,1]        \n",
              "[1,] 0.0009039501"
            ],
            "text/latex": "A matrix: 1 × 1 of type dbl\n\\begin{tabular}{l}\n\t 0.0009039501\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA matrix: 1 × 1 of type dbl\n\n| 0.0009039501 |\n\n",
            "text/html": [
              "<table>\n",
              "<caption>A matrix: 1 × 1 of type dbl</caption>\n",
              "<tbody>\n",
              "\t<tr><td>0.0009039501</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qJWTacQJj1bu",
        "colab_type": "text"
      },
      "source": [
        "# F - test in linear model (Reduced vs. full model )\n",
        "\n",
        "Sources: [link text](https://dnett.github.io/S510/03ReducedVsFull.pdf), [link text](https://dnett.github.io/S510/stat510.html)\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NXLX66Qg9Go6",
        "colab_type": "text"
      },
      "source": [
        "Assume the linear regression with Gaussian error:\n",
        "$$ y = X \\beta + \\epsilon, \\quad X\\in R^{n \\times p}, \\quad \\epsilon \\sim N(0,\\sigma^2I).$$\n",
        "\n",
        "Suppose there is some matrix $X_1 \\in R^{n \\times p_1}$ such that $C(X_1) \\in C(X)$.\n",
        "\n",
        "The goal is to test:\n",
        "$$H_0: E[y] \\in C(X_1) \\text{   vs.   } H_a: E[y] \\in C(X) - C(X_1).$$\n",
        "\n",
        "The reduced (null) model corresponds to the null hypothesis. \n",
        "\n",
        "\n",
        "Example 1) \n",
        "Given full rank matrix $X$, devides $X$ into \n",
        "$\n",
        "X= \\begin{bmatrix} \n",
        "X_1 | X_2\n",
        "\\end{bmatrix} \\in R^{n \\times (p_1 + p_2)}$.\n",
        "\n",
        "\n",
        "Example 2) \n",
        "$X_1 = \\begin{bmatrix} \n",
        "1 \\\\ 1 \\\\ 1 \\\\ 1 \\\\ 1 \\\\ 1 \n",
        "\\end{bmatrix}$ and \n",
        "$X = \n",
        "\\begin{bmatrix} \n",
        "1 &0 &0 \\\\\n",
        "1 &0 &0 \\\\\n",
        "0 &1 &0 \\\\ \n",
        "0 &1 &0 \\\\ \n",
        "0 &0 &1 \\\\ \n",
        "0 &0 &1 \n",
        "\\end{bmatrix}.\n",
        "$\n",
        "\n",
        "Under null model is true, we have F-test statistics\n",
        "$$\n",
        "\\Large\n",
        "F = \\frac{y^\\top (P_X - P_{X_1})y/(Rank(X) - Rank(X_1))}{\n",
        "y^\\top (I - P_X)y/(n - Rank(X))}\n",
        " \\sim F_{(Rank(X) - Rank(X_1)),(n - Rank(X))}.\n",
        "$$\n",
        "\n",
        "Note that \n",
        "$$\n",
        "\\large\n",
        "F = \\frac{\n",
        "  \\frac{y^\\top (P_X - P_{X_1})y}{Rank(X) - Rank(X_1)}\n",
        "  }{\n",
        "\\frac{y^\\top (I - P_X)y}{n - Rank(X)}\n",
        "  }\n",
        "  =\n",
        "  \\frac{\n",
        "  \\frac{y^\\top \\{(I- P_{X_1}) - (I - P_X ) \\} y}{Rank(X) - Rank(X_1)}\n",
        "  }{\n",
        "\\frac{y^\\top (I - P_X)y}{n - Rank(X)}\n",
        "  }\n",
        "  =\n",
        "  \\frac{\n",
        "  \\frac{y^\\top (I- P_{X_1})y - y^\\top(I - P_X )y}{(n - Rank(X_1)) - (n -Rank(X))  }}{\n",
        "\\frac{y^\\top (I - P_X)y}{n - Rank(X)}\n",
        "  }\n",
        "  $$\n",
        "\n",
        "  $$\n",
        "  \\Large\n",
        "  F =\n",
        " \\frac{\n",
        "  \\frac{SSE_{reduced} - SSE_{full}}{DFE_{reduced} - DFE_{full}}}{\n",
        "\\frac{SSE_{full}}{DFE_{full}}\n",
        "  }.\n",
        "  $$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZDh4ZuTTCtB2",
        "colab_type": "text"
      },
      "source": [
        "## Example problem (Lack of Linear Fit): "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZzafXwHE4CzA",
        "colab_type": "text"
      },
      "source": [
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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WlbTq71gDFcl",
        "colab_type": "text"
      },
      "source": [
        "Let's generate some artificial response"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MwU8MjwZj6YF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "3a70672e-9cbd-47ff-e789-2cfadf1ea799"
      },
      "source": [
        "x=rep(1:3,each=3)\n",
        "y=c(11,13,9,18,22,23,19,24,22)\n",
        "plot(x,y,pch=16,col=4,xlim=c(.5,3.5), xlab=\"Fertilizer Amount\", ylab=\"Yield\",axes=F,cex.lab=1.5)\n",
        "axis(1,labels=1:3,at=1:3)\n",
        "axis(2)\n",
        "box()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "plot without title"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3jmveTu2DOc-",
        "colab_type": "text"
      },
      "source": [
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ww_uVMCUDzZ-",
        "colab_type": "text"
      },
      "source": [
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8VW0/4M2/jrwtFBMty0OyO8RmChn2upCsDuUgjr1Her3gjXfG/ibXH1jVdOs9M8KXNsX0+BmJu3yVKSP2AK7jjjGQPevMfG2labo37JEFroOozalpxuklt7meAws6tOW+4eQMk/XrX0NaKqWcKIAqrGoAHYYoA8Z8KfEH4lfEfS7weGbHQ9OaxupIZtQuxJ5bkH5Y0QFjuAwWY8fMMCmeGfiT8SPFt1qHhaw0bSbTxBpEzRajqVwz/ZYwDtXagyS7ENjnGBnvxp/s4/8k91T/sOXP8AJKPhH/yVL4o/9hWL/wBq0AXvh3448T3njnWvBPju2shqumQLcx3VgGEc0RK84P8Avr6dwRkVd8FeO9T8RzeN1vbe0jHh/U7i0tfJRhvSPdgvljk/KM4x9KxNE/5Oy8R/9i/F/wChQ1U+FX/H18V/+w/efzegCLwf4/8AiX8TfC0N74YstD0toS6Xd7erJ5csoY4SFAWIAQpuZieScdK6n4XePNY8T3GvaJ4tsbez1vw/OsNy1sT5Uqtu2sMk4+4e/cHjpVH9nRQPghpBAwTLcE+/756xvCNtPefEz4x21nxcTJBHFzj5zFKBz9TQBZtfHHxB+It5e3Hw0ttHsNAs5mgi1DVt5a8ZepVVBwv4fjnIG78PPiFqmua/qnhPxnpsOmeJdLUSyJbsTDcRHGJEySQPmXufvD3A87+C/hTXNe+GdpJovxD1DSEgmmim06C2jYW7+YxwSeckENz/AHq6jwX4bsLL41309z43vPEPiKx07ybqGWzCLHExUqDIvy5BI+Xr+VAHrN59p+wz/YfL+1eW3k+aCU34+XcAQcZxnkVwPgD4lzeI/hTfeKNdggtrzSzcrfQwBlRGiBfADEkfKV6k85r0Svl7xrdz+Edd+IXgazBV/FV1aXGmqOATPIPNAHvkr/wGgD1H4KfFDVPiNY6qviG0tLO/sXidUtY3RWhlTcjYZmPYnOcYIrm9S8c6p4++CnxE1G7gtItLt5ZbXTWgRg8kakHc5LEE4ZOgAzmsrx3eR/CD4hXdzZZitNY8JtZ256D7TAgSM/gqoP8AgVdDd+Hf+EX/AGRrnTnTZMdJ8+cEciSRg7A/Tdj8KAIPB+pfFPW/hvolx4OtdE03T7PToYIE1Iu896Y4whbj5UUlTtzgkck12PgH4mx+JvhldeKNet1059MaaPUUTJVGiUMxUHnkEccnPHNbXw4AX4W+FQowP7GtOn/XFK8Q8PWlze/sx/EKKyBMg1a6kIH9xDC7/wDjqtQB2Gm+KPi74207/hIvCmn6DpekSZaytNSLtPdICcMSvAzj/Z/Lmtvwt8QNf8c+DdUTQ7Cw03xhpVwLW7stTZzbxuG+Ykp82CofHowxyOTz3gXwX4i1rwDol/o/xR1OGzlsovLgitIisGFAMef9kgr+Favwg0XSbHxF4svtL8V3PiO8muI4NRmltfKUTR7+jD5X6nleOnrQBzn7N58Sf8K/l84aX/wjv+keUU8z7X5+5ev8GzG7pz0rH+Ceo+PdT+GcOl+BbbS7G3sZ5fP1LVS7CWRmLeXGig9AVyx9cDpXYfs6f8kR/wC3q5/nVr9m5QPgrYEDBNzcE+/7w0AaPww8da54j1LXvDvjCxtrXXNBlRJntCfKmVwdrAEnH3c+4YcDpWJD458e/ELVNQPwxt9IstDsJ2txqeq72N3IvXYqg4Xn06Y5zxUXhGGa5+NXxXgtjtmlgtkjOcYYwkDn61zHwU8J67rfw7j/ALI+IGoaMbW5lhuNOgto2EEm4nnPPIIPPr7UAejfD/4hatq3iXUfB/jfTYNO8SadGJ/9GYmG6hJA3pkkj7y8ZPXtggcvZ/FDx/4t1vxB4d8HaRph1DStUnge+nDJBBbK22PcCxLSMVfpxhenpd8J+GbGz+N8st945vfEHiPT9OKTwS2YQRwsRgM6/LnLg4681J8DlUa78RXAG4+JbgE+oDN/iaAPV7bzhaQ/atpn2L5mz7u7HOPbNeCePj45/wCGjPC/9njw/wDavLu/7H87ztnleU+/z8c7sbsbOM4r6AryXxl/yc18PP8Ar0vf/RMlAGF8R9X1XRfjx4IurbTk1LWG0uWFLWFykbzOHT7x5CAkkk84FaOu+NfiZ8PL7TdS8axaDqGhX12ltOumrIslqWzjBbrgA9c5xjjINW/FIB/al8EZGcaZdEe3yS0v7R3/ACTax/7DFt/7PQB0PxG8f3XhN9L0jw/py6r4i1qUxWNq7YQBcbnc/wB0Z9R35GDXJ6r4z+KHw6hh1rx1ZaJq2gtIiXjaTvWW0DHAPzYBGTjocnAyM5rP+KOm3lx+0R4RMWuTaCt7p0lta38aKxWYGQlQG4ywdF/4EKs+O/BF5png68l8b/FjVBo0m2KdZLGNvMywwoVfmJzzx6E9qAOj+JvxRm8EW/hm/wBLt4dQsNWuMS/IzSPFtDL5WCMMc8ZBHPSpdL8VeLPD/hjXvE/xStrDT7GCNJrOzsW3yRg5Bjc9CxJjAOcZJ6VyPxB06HTv+FOabFK9zBbarZwpJNHsaRVEQBZT0JA5Brof2i7S5uvgrqRtQSIJoJZQO6CQA/kSD+FAGbaa98atd0dPEuk6Z4dtLKaMTW2kXJka4ljIyMtwMkdOV+gruPhz47t/iD4UXVYrZrO5hla2vLRzkwTLjK57jBBH19RXJ6T4H8S6joVnqGn/ABZ1RrKe3SWJ1tIduwrkfpVr4J6Vo1lpGuXvh/xFceIIr7Une4uprUwgzADeV/vA7gcjigDuPFOpzaJ4P1nVbVI3nsbCe5jWUEqzJGzAEAg4yPUVwV58W7nSfgZpfjO9sIZ9T1IJFDaw7kiaZy2OpJCgKT15xjIzXY/EH/kmfif/ALBF3/6JavMdMTwdd/s1+FtM8f3L2thqCpBBNGjlkn3OVIZVIU4B5bjGc0AW9U8Q/Gfwnp6a/rWnaBq1iHT7TpmmrKbiJWIHynuRnGfmx7jmvXrS5W8soLqNXVJ41kVZF2sARnBHY89K8W17w98Rfhb4duda0Hx3/bOl6bH5j6frMAZjGP4RJkk8dgV9BXrPhTXP+Em8I6VrYgNv/aFpHcGInOwsoJGe49+9AGP8SfGV34K8MR3elaW+q6jd3KWlpbKDtLtk5bHRRj88DI61wuveI/jJ4K0OTxNrsXhjUNOt9r3dja+askaFgPlY8cZ65b6Guk+LHjXWvDbeH9E8LC2j1fxFe/ZYLq6GY7cAqCxHc5dfXvwa4j4q+C/EFh8LtX1Hxd8RtQ1Pyo1K2kcEdrBNIWAClV+8M849s0Ae36RqUWs6JY6pbBlhvbeO4jDdQrqGGfwNeb/tIf8AJFNR/wCvi3/9GCu08Af8k18M/wDYItf/AEStcX+0h/yRTUf+vi3/APRgoA1fF/jTUPDGveBtLsILWWHXbsW1y06MWRQE5QhgAfmPUGszxn8TPEGhfFi08HaDpFrqUmoaWJ7RX3KwnMjjLvuwIlRGY4XPHXmqPxS/5Hn4Uf8AYU/pFUmoqD+1zpRIyR4ZYj2/ey0AQ33jX4jeAvE2iL47i0TUdG1m8SzM2mLIjW0jdPvdR1PQ5CnkV0nxC8f6h4f1bS/DXhLTo9T8S6vuaCGZisUEYzmVyMHHB4yOh54AOH8f/wDkF+Dv+xntf/QXrA8b6Tf3f7TunxQ+IJ/D73+i7LO8hjVyzKzFogG4GcE/iPWgDV1Hxz8RvhvPZ33xGtNH1Lw/czLDPeaSHElmzdCQwGR17c+oOAeq+I3jfV/Dq6Np/hHSk1XV9bmMdsZc+REoxl3K9vmHccZOeK4f4h+CJdP8Iyr4++K2qNpFzKkTRPp6P5r7tygKnzE5XPHpW14w8SeI9N8SeFPhz4LvILO/vrLfLqt5DvMccakZVDwWIjY4Oew46gAztd8Z/FH4bQ2us+N4/D+q6HJcJDdf2cJElg3dxuAB/I56cZzXTfFj4jXfw6TQLi2tIrq3vr7ybpGRmk8sDJEeGHzHoM5HtXmHx08Iato3w7W+8TePdR1u4a7jSG0kjjt4XY5y3lr1IAPfiu2+OCq/iH4cI4DK3iW3BB7jetAHW+BLnx1fNqF348s9P0+Gby2sLO0cvJAPm3LI3Qn7nI756V19FFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFc54z8B+H/AB9paWPiOz84REtBPG2yWEnqVbt24OQcDI4ro6KAPJR+z7pcqC2v/F/iu904cCym1AeWR6Eben0xXomleF9F0Xwyvh/TdPih0sRNEbYDIdWB3bs8knJyTyc1rUUAeV2vwC0OyMlpbeIfEkWhyuXk0ZNRK2756qQBkqfrn3rU1PwTo3gv4aeNU0CFoItQsry6kiLZVGMLDCjHCgDgV6BUdxbw3drLbXUSTQTIY5IpFDK6kYKkHqCOMUAeD/Dr4P6T4h+GWh6xY6xrOgXt7abbx9KuzEt0AzAb1wRnA/xzXp2heBdD8A+Cr/TfD1uyJJDJJNNK2+WZ9hG5m/oMAeldNYWFnpdjFZabaw2lrCNscEEYREHXAUcCp3RZI2SRQyMCGVhkEelAHzv8IvhRpfij4V6TrVtqmraDqshninu9JuzC06CZwA45BwPp0FeweBvh5oXw/wBPmt9Djlea5YPc3dy++adh3ZuPU8AAcn1rf03S7DRrBLHSLK3sbSMkpBbRCNFycnCjgZJJq1QB534h+DOi6x4in17SdV1jw3qV1/x9TaPdeSJ/UsMdT7YyeTk1t+CPh5oXgG0uI9GSaW5u2D3V7dSeZNOf9pvxPAAHJrqaKAPNNX+CGj3fiC71nQdc13w3dXzl7pdJvPKSVjySRjIyST1xz0rovBPw90PwFb3S6OLia5vHD3V7eS+ZPORnG5uPU9AOtdTRQB5trXwS0W/1661jQ9Y1rw1d3pJu/wCx7vyUnJ6krjqevHHJ4rpPBXgLQ/AWmzWuhRSl7l/Mubq4fzJrhueXbv1PAAHJ9TXS0UAFctrXw68P6/420vxVqMMranpYUQMsmFO1iy7hjnBYkV1NFAHK+NPhz4f8fSaa/iKCWU6bIzw+XJtzu25Dccg7RxXR31ja6np89jqEEdxa3EZjlikGVdSMEEVPRQB5Of2fNCVHsrbxH4lttEkYs+kRah/o5z1GCOn1yfevS9G0bT/D+j22laPapa2VqmyKFOijr+JJJJJ5JOau0UAFctoHw68P+GvF2reJNKhlTUNWLG4LSZUbm3ttGOMtzXU0UAcqvw58Pp8R38cCCX+2Wj2FvM+T7nl52467RjNXdf8AB+l+JNW0XUdSExn0W5+02nlvtG/j7w7j5RW7RQBw3jP4UaJ4y1mDWmu9R0fWYE8tNQ0y48qQr2B4Occ8jB96b4T+EujeF9e/t64v9U13WghjS/1a5854lOQQvAxwSMnJ5Pqa7uigDC0zwfpek+LtX8SWgm+36wsa3RZ8phF2rtHbgUar4P0vWfFWj+ILwTfbtG8z7LsfC/OMNuHfit2igAriPGnwvsPGPiCx11dY1bRdVsoTAl1plwI2MZJO0nB/vN0x1Oc129FAHI+NfhroXjqG0bVTc299Y/8AHrqNnL5c8X0bHPIzyPpiszwz8HdF0DxFHr+o6lqviLVoRiC61e584wjp8ox19znHbFeg0UAFcv44+HuhfEDTYbXXYpVltnL213bvsmgY91bn0HBBHA9BXUUUAeWx/ALw3c2848SaprfiC4kj8qO51G9Mj2yZBxHxgZx154zjFdl4k8EaH4s8LroGuWv2iyjVRGd2HjKjAZWHQ4/PJB4NdBRQB5bZ/AXQxeWz69rviDxDaWbBraw1O98yBMdPlwM/TgeoNdh438E6Z498MPomrvPDCZFljltmCvG69CMgjuR0710VFAHL2/gOwk8Cv4W8Q3d74htJd3mT6nMZJmycj5xgjbxgjkYrkIv2ftCPlWuoeIvEmoaNC4aLSLjUM264OQNoA4+mD716vRQBz3ibwRovivwkPDeowvFpi+WEitW8vYE+6BxwBjpXQIoRFVeijApaKAMLwj4P0vwTpM2naIJhBPcvdP50m872xnn04FGg+D9L8Oa1rWqaaJhc63Os935km5dw3Y2jsPmNbtFAGFbeD9LtfHV34tiE39p3lqtpKTJ8nlgqRhfX5RzUeieCdI8PvrjaeJwddupLu88yTd8753beOByeK6GigDF8JeFdN8F+G7fQ9FEos7dnZPOfe2WYscn6k0zRvB+l6F4k1rXLATfbNbeN7ve+VygIXaO33jW7RQB5xrnwU0XUfEFzrWiavrPhq9vCTdto935Kzk9SRjqevHGcnGa6HwV4A0PwFYT2+hxytLdP5l1d3MnmTXDc4Ltx6ngADk+prpqKACuW134deH/EXjLSvE+pwytqWlbfs7JJhTtYuu4Y5wxJFdTRQByvjb4deH/iANPHiOGWX+z5Gkh8qTb97G4HjkHaOPatjxBoVn4l8PXmi6mH+yXkflSiNtrbfY9ulaVFAFTSNMt9F0Wx0qy3fZrG3jtod5y2xFCrk9zgCsvwr4M0nwfpd3p+kJKbe8upLqVZ335dwA3bphRxW/RQB5ZcfAPQlu7k6Fr/AIh0Gxu2LXGnabfeXA+evykHj2ORXd+FfCmkeDNAi0fw/ai2tIyWPOWkY9XY9ycfyHQVsUUAcL4L+FWn+BdSvZdH1nV30+6WQLpc9wGt4S5UllUAfMNuATzgnrW/4Q8JaZ4I8ORaJogmFnE7OvnPvbLHJ5+prbooAwtK8H6Xo3irWPEFmJvt2s+X9q3vlfkGF2jtxXL6/wDBfRdV8Q3GuaPq2seG9Ruzm6k0e68kTnuWGOp68Yyck816LRQBy/gn4faH4Cs7iPRUmluLt991e3cnmT3Dc4LNx6ngAdT61b8NeD9L8KXGrT6UJg+r3j3tz5sm794xyceg56Vu0UAFcZ44+Glh431HTdTfVNS0jUtM3i3vNNmEbhW6jJB/THU12dFAHON4I0yXxTo/iK4kup9T0i1a1glklzvVlKkuMfMx3E59am8XeD9L8baPHputiY28dwlwvkvsO9c459OTW7RQBgeMfBOieO9F/szxDbGWJX8yKSNtkkL/AN5W7H9D3FchpvwL0SHVLS81/XNd8SLYsGtbbVrzzYYiOny45+nT2r06igDC8ReD9L8T6ho15qgmMujXa3lr5cm0eYCCN3qOBxWxdWsF9ZzWt5Ck9vMhjlikXcrqRggjuCKlooA8nf8AZ90JPNtNP8ReJNP0adi0uk2+oYt2z1GCDwffJ969I0HQdN8M6HbaRolqlrZWy7Y4l5xzkkk8kkkkk9Sa0KKAKmq6bBrOjXumXm77Pe2728uw4Ox1KnB7HBrn7n4beHLz4ew+DLu2km0mBAsW+T95GQSQwb+8CT/LpXV0UAeUxfAHR5BFbax4n8TavpcLAx6Zd6hmDAPAIAHH0xXqVvbw2lrFbWsaxQwoI440GFRQMAAdgBUlFAHN+NvAmjePtHjsNbWZDBKJre5tpNksDj+JWwf1BH5CuXX4GaHeWssXijWte8SO0TRQvql+ZPs2RjdGvQMM9TmvTKKAMDwV4UTwX4ai0aHVL/UooW/dSX0gdo0wAEXAGFAHA+tSeL/CWmeNvDkuia2JjZzOrt5L7GypyOfqK26KAMDW/Bmla/qWh32oCbztCn8+z2SYG75fvDHI+UU6Xwfpc3jyHxc4m/tSCzNkhEnyeXuLfdx1yx5rdooAwvFPg/S/GEOnxawJiun3qXsHlPt/eIDjPqOTxVfxr4C0Lx9pcVnr8Em6B/Mt7mB9k0Deqt+XByOBxwK6WigDzbRvgno1jrlpq2uazrfiW5sW3Wi6veedHAR0IXHUY78cDitzxz8ONH8d/Yp76a8sNQsGLWmoWE3lTQ56gHB4yAfX0I5rraKAPL7v4C+HdV0q5g8Q6rretX0ybI9S1C9Ms1uMg/uwRtXoM8HIz610DfDfTbvS/DtrrGoalqcvh66W7tru5nzLJIrbhvOPmA4GPQCuwooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKK8X+JGr+LW+OOh+G/CerS2P9qaSysWJaKD53LTbOjOEU4z3xQB7RRXj/iq71f4T/D6x0LR9cutZ8Q69qQtbS+1N97RNJgM/OeF4wDnBbJz0qjq3w41/Q9Bn1zQ/ifrVz4itYjcMlzdhra5ZRuKCI9AcYGcjpxQB3Pxa8Z3/gH4f3Gu6TBbT3MU0UYS5VihDNg8KQf1rs4mLwo56soJxXgXxK8Wt44/ZVg1+WJYprmaFZo16LIkpRsexKkj2Ir0X4hWXjTVdL0fS/A9z/Z6XU6jUdRV1EltCAOUBIJJyT8vPy4yM0Ad1XOeN/Gth4D0SHVNVguZ4ZrqO1VbZVLBnzg/MQMcV478Q9EvvhHosXiLQPiNrdzqMNxGH0/Vb4TJdgnkCPjtz34zyOtaP7Ruky3/AIS0nWxqt/BG93bQfYEl/cZbe3m7cffGcZ9KAPUfGmo+J9NsdPfwdpcGpXEt/HFdpMeIrcht7j5l5BC+vXpXR1478TRq/gTwF4YtNO8SavczyeI4IZr24uSZpo3EpKMwxleBx7CrnxJ1/wAQav8AEDRvh34R1JtJmvoGvNR1GIZkhgG4AL6E7T0wcleQM0AerUV4V4u0HxJ8GtNh8XeHvFms63p9rNGup6dq9x5yyxs23cpx8pyQOmec5OMHU+L/AIp1621TwC/gq/aJ9YunSNS5EU29YxGZFH3lG/ODQB7DRXhPxE8F+IPAfg+48Z6T8QPEV1q2ntHJcJd3Aa3nDOqkCIDCjLZ2nIwMe9afxY8catbeG/BsNjqf/CPweJJYxfaqg/480KoSAe33yc5HCdRzQB7HXEeIvGuoaP8AFjwp4Xt4LZ7PWo7hp5JFYyIY0LDaQcDkc5Brko/h/wCJ/D17pWt/DvxtqfiGE3Ki/tNV1FZoZ4f4mVugPbuec545p/GCPWJvjZ4Ch8N3EdrqU0VzFFcSJvEIZdrSbe5VSzAHjIFAHuFc54i1HxPZ+JPD9v4f0uC80y6mddVuJD81sg27SvzDrluzdK8l+I/h3XfhTo1v4z0Lxv4g1C4gu41vLXU7rzYbhWPOFAAAzxjnAPBBFdh8Sda1LTviZ8ObTT7+4tra/vp0uoYpCqzqBHgMB1AyevrQB6bRXhXiC78Za/8AtCar4P0DxDdaXp0thDNcSxsWNtEFUsYhnCuzMo3Dnmm+JrDxB8EL3TfEen+KdW1zw9Ndpb6nZatP5zIGz+8VscdD0AOducgmgD3euIl8a6gnxwh8GCC2/s99H+3mba3m795XGc424Hpn3rtlYMoZSCCMgjvXgXj+21/UP2ndO07wtf8A9m3V7oSwy33l72t4fMkZ2Uf3sLge7duoAPfqK8G8ZeH/ABR8HbCHxh4d8XazrdjbTRrqen6vcecsqM23cD/DyQOmRnOeMV0PxD8Z6pqmteGfCHgrU10yfxBB9tn1M43W1pjIKg92w3PHQAdcgA9YrnPGHjWw8FQ6XJqcFzMNTv47CL7Oqna75wWyR8vHbJ9q8p8V+H9d+Fmi/wDCWeFPHmq6x9hdGv8ATtWvBPHcoWAYqOx5+uM4PHMHxvsf+Eh0/wAFeJLXWdTgttW1Cyjis0mAig8xWcTKMcSAHGaAPoCivHNefWPh58R/ACSeItV1LR755dNu/ttwX82VmYxu/QbsygA46Riuf+MPjzxFpHxUgk0K/uodH8NxWk+qwQylUlMsw+V1HBypUc+poA+g6K8r+JOt6ne/EfwJ4V8PalcWgv7lr29e1lKF7ZADgkdmAk/ECsvUb7WPij8Stb0C08S3Ph3w14eZbe4ewmEdxeTnO4b+wUqw7jgcHPAB7RRXiVrd618K/iVoGjyeJ7rxJ4a8Qym1QahMJZ7SbIC/P6EsPQY3cZAJt+JdV1nx/wDFS+8F6R4gl8PaJosCPqV3aSBJ7iVwCI1b+HAPb0bOeBQB7FRXhd7JrPwe8XaDJbeLL7xF4Y1e8WxubbU7gTS2zt911f06ngAcEHOQRd8cal4su/2gtP8AC/hvWptOtdQ0MGZwSy2482QvKqdPM2oEBPTcPSgD2eivCPFei618JfEXhnWNG8Ya7qlnqOqxWF9Z6vd+esu/PzDgAcBu2Qcc9q93oA5zX/Gth4d8U+H9BvILmS516SWO2eJVKIYwpO8kgj7w6A1l+KfGuoaH8TvCPhu1gtntNcNx9okkVjInlqCNpBAHXnINedfFrwrPdfGzwUV8R6xB/a9zOIxFOB9g2JECYOPl3dT1zUnxXsdZs/iR8MtO8P37PqiRT2sV/eDzXzsRGmcdGYDL+hIoA94orwP4keGde+F/h+PxpoXjnxBfXlrcxi7t9SuvMhuAzYICAAAZPTnjpgiuu+KnjDWLa48O+FfCd1HYat4jkIN6+D9kgUAu4B4zgnB/2TjnBAB6dRXhPifwhr3w+8PTeKfCfxE1fUr7T1+0Xdnql2J4bpB9/CduMnufQg817D4X1yPxN4T0vW4U8tb+1jn8vOdhZQSufY5H4UAatFch8SovGF34bisvADJBf3Vykc92zqDbQc7nXceT0HHOM45xXmHj/wAIX3w28KT+JNM+J2vtrNqUfyNQvw8d2SwBURHr1Jwd3T8aAPfqK8g+LXi/V7b4F6T4j0q5lsL67ezmY20hT76bimQc4OcVl+P/AAX4p0DwPdeNH8e62fEdii3E0Uc4Sz+8A0aRAYAGTjOc45HNAHudFeHnwb4o8X/DkeM9X8cazZa1PYf2haW2nT+RaQKU3omxeSSMZbOee+ObVv8AFbUtN/ZlsfGN4UudanQ2sJccSTCZ4g5A6nahcjuRjvQB7NRXjdv8IfFtzoa6refEbX4vFLxiXC3OLSOTGfLMY/hzwSMDvt7Uyx+Ier+I/wBnLxBq1xM9l4g0mKa0uZYDsZZkx84x90kMOnGc4oA9norn/AF3cX/w38N3d7M89zPpVtJLLI25pHMSksSepJOa88+HPiHWNQ+FHjy+vtTuri6s9R1GO2mllLPCqQIVCk9ACSR6UAex0V4T8PfC3iT4nfD3T9X8VeM9dsYTG0dnDpt15TOFYqZZnIJdiwOB2AHrWn8M5PEHiPQvGHgvXfEmoNcaLqX2SDWLeTbc7AxP3jnn5D1ycMRngUAegeCPGth480ObVNKguYIYbp7VluVUMWTGT8pIxzXR14X+zb4fmj0G81k61qTxrfXFt/Z7Sj7Ox+Q+aVx9/wB69s1G+h0vS7q/u22wWsLzSt6KqlifyFAFiivCvCHhvxL8YNIfxf4l8XazotreSyf2bp2j3HkpDGrFQWOPm5B7ZOM55wNjwHq3iFfE3if4Y+LNZnu7y0tTNYaxGdk7QOoXdn++u9SCcnOeTgUAamgeO/E/in4o6vpOkadpsXhzQ7o2l9cXDubmR8N/qwDtHzL3HTvmvSa8C+C/hSeP4j+Mbg+I9YcaTrLxSRNONl+fnG+cY+Zu+eOa93u4DdWU9us0kBljZBLEcOmRjcp7EdRQB55p/jvxP4i+LWqeH/D+naauh6DNHFqV1du/nuXBP7sA4HKnqD06jOK9Jr58+FnheSz+LHji4uPFOsiLQ72Fp2e4GL4bZCTPx82Me3U1c8N2es/GWC68T674x1Pw/pElw8el6ZpV0ICqKdu92/iOQeo6g4IGBQB7vRXknw61/XdC+JWpfDzxLrB16KO0F9pmpSHMrR5AKOecnk8k5+U9iMct4Us/GfxL1nxZo83i3UdK0XTNbuMz28jGeXLYWBWz8kaBM4HHzjg9gD2HxP410/wrq2g6ffwXMsuuXgs7doVUqjkgZfJGB8w6ZpPEeo+J7PxH4ft/D+lwXmmXU7rqtxIfmtoxt2svzDk5bs3SvJ/jR4Vnfx94GceIdXQahqcVqiLOALQqEXzYuPlc9Seea6Lxnc6r4Y8ZfC/RbTXNRmhnvJobuSac77wKI8ebjAbqfzoA6L/hNtQ/4Xj/AMIX5Ft/Z/8AY/2/ztrebv37cZzjbj2z71q+GtR8T3mva/B4i0uCy0+2uQmlTRH5rmL5ss3zHnhey9elcP8A83cf9yz/AO1as/DvU9U1vxv8StOvtUu3htb9YLTMpP2VWEg/d5+70B49BQB6lRXhnjvwvP4C8MTatqXxR8XyPny7W1S8G+5lP3UX+p7DJrT0bVfE3wu+A9/4g8cX8+qay58+GC8lZ2haTakcRJOeD8zAdMsO2aAPYKK8S074ceINd0KHWtd+J+s2niO5iEypa3YjtrZmGQhjGM4zg4IHWrXhvx7rmufBPxn/AGvP5fiLw5Be2k13bHbueOJisoIxg5B6d1z3oA9jorxf4V6J4s8Yab4e8ZeJvFWoRwW8YFtpcLnZOqgoZJmz87OQW5HAI57V7RQAUV5JceBPGHjPxLrN74z8Tar4e0aG4KaZZaReJFuiGcSOwzyRg4IzknoMVW+FusajpvxW8Q+B5PE83ibS7OzS6tru5lEssTZQNGXGc/fwRnjb0GSKAPZKK+fPC1v4x+I3jjxnolx4s1TTPD+l61cbpLSYi4fMjKkKOc7EVUJwPUcHPGzps3iD4UfFTRfDmpa/ea74a8Rb4rWTUX3zWs64wu7vklR2B3dBjkA9qorwGy/4TLxx8YPGPhi38UahpehWd0slxLbyHzo1xhYYmP8AqwxLEkf3fwq9Kuv/AAa8f6BBL4j1DXfCuvXIsnTVJfMltJmICsH9Oc8YGA2RnBoA7ix8bahc/HDUvBjwWwsLTSVvkmCt5pcui4JzjHzntnpzWr4V1HxPfahrsfifS4LG2tr94tMkiPNxbgna7fM3JGPTr0rh9J/5O213/sW0/wDRkNP+Hniy7juvibfa9qFxc2ei6xdGJZpCwghjLnauegwvQUAesUV4T4Y0DXfipow8WeKfHWqaIL13fT9N0m7ECW0YYhS3948fXGOecDX+H/jfVtC1XxZ4V8a6kNWbw3bG/h1MY3T2u3cd3qQCvPJySCTjNAHr9cRYeNdQuvjdqfg2SC2FhaaUt6kwVvNLlkGCc4x857fjXAeDvDHin4taSfGPiTxjrOiw3kjnTdP0i48lII1YqCf73IPbJABzzxD8MYNesv2lPEVh4qvRqN9Z6L5K3gj2G4i8yExuQOM7SAfcHr1oA98rnPDXjWw8Ua3r2mWMFzFNoV0LW4aZVCu3zcpgkkfKeuK27+1a+025tEuJrVp4XjE8DbZIiwI3KezDOQfWvCvg34Tnj+J/jKY+JNYcaRqvlyRtONt+SJBunGPmPftzQB77RXhuiQa98btc1rVJvE+p6H4WsL1rOwttJm8l7goOZGfHPBU8g9cDGOdPwlqXiDwJ8W4/AHiHWp9d0zU7RrnSb28OZ4yu4tGzfxcK35LjGSKAPX6KK8t1zwd4y8a+O9TGs6/qPh3wpaoi2MelXSxyXRx8zuwyRg54YdxgcE0AepUV4l4Nv7/wj8cl8FW/i268S6Peac1xi9uBPLaSqSdu8d8LnHHDjjgGvbaACivBA/jLxj8cPF/hSx8T32l6JC8M080Eh82FAgxFCeke8vkkf3PwNm/i1/4K+MtBm/4SXUdc8KazeLY3MWqy+bJayN0cP+Z4A4UgjoaAO6j8bag/xxl8FmC2/s9NH+3iba3m794XGc424Ppn3ruK8kh/5O4uP+xZH/o1ay9Oj1740+Ldem/4SXUtC8KaPeNY20Oky+VJdSL952fHTkHBB4YDAwSQD2+ucs/Gthe/EPUPB0cFyL+wtFu5JWVfKZW24AOc5+Ydq4Dw5f8AiD4dfFqy8E65rlzruia1bvJpl1fNumgkQElGf+LgY/FcY5Fc5oPgm5/4aT1mw/4SzXt9np8N0119pHm3A3RnynOOU5xj2FAH0LRRXmXirwr408ZeP5rSbW73w/4PtrZTHLplwsc93KcFskfMoGSORj5enOaAPTaK8M0We+8BfHHRPCun+Mr3xFpOsQTefa6hdC4ktHRGZTuHTJXpgZ568GrPiq/8Waj+0L/wivh/XLjTrK80VWndWLC2XzCWljQ8CQ7QgbtvJoA9qorwrX9I1r4T+N/Cd5pHi3W9V0/WdTj0+9s9XuvP3byBuBwADgk9M5A5wSK1PGmqeIfHHxZHw88M6xNodhYWYu9XvrU4mO7BWNT24ZOhH3iTnGKAOq+LXjXUPAPgf+2dJgtp7j7VFDsuVYphicn5SDnj1rt6+Y/jZ4O1/wAE+D7aK38T6lrfh+8vI0mg1WQTS28wyyMr4HykBgRwBx1zx9OUAFFFFABXkmv/APJ13hb/ALAc385a9bqs+nWUmox6hJZ273sSFI7lolMiKeqhsZA5PHvQB5N+0RoiXeieH9du7GTUNN0bUlk1K2jzlrZ8bzwQR90D/gWaw9Y039n7TPCcut21rpd/+6LQWcGoS+dM+OE2b9ykngkjjqa98dEljaORVdGBVlYZBB6giubtPhv4LsdVGpWnhfSorsNvWVbVfkbOcqMYU+4oA8m+JdlbWP7K8IstB/4R6KeaCcaaZ2mMG+TdyzAHJBBII4Jx2rU+MmoPJ4s8F+Hta1e40XwrqQkN/dQS+UJGVRtRn7LnaOePmyenHsd9p9lqlqbbU7OC8t2IJiuIlkQkdDggioNX0PStf042Gt6dbX9qTnybiIOoI6EA9D7igD5u+L+j/Cnw54BuLLwZDY3GtzPGRLa3DXTwxhwWd3LMEB4XtncK7X456hZ3vwW0S9s7qG4tTqVowmicMmArZ5HHFel2XgPwpp2kXOl2Ph7TobK7XbcQrbriYejdz+PSp18H+HV8Mjw6NGszo4ziyMQMYy27OD33HOfWgDzb48ahZ6n4N8K3Wm3cF5bt4otAstvIJEOElzgjiovHN6ngT9oHQvGGrho9D1HT20ye62krbyZZhnHQH5fwDHtXqFn4T8P2GkW+lWujWSWFtL50NuYFZI5OTvAOcNyeevNXtQ06y1Wxks9UtILy1kGHhuIw6N9QeKAPIPjZ460XXfAreE/CmoWut6xrs0MMFvYSrNtUSK5ZipIH3cc+uegNJ8RNP/sjxV8H9NL+Z9jv1t9/97YsK5/SvStC8C+FvDNy1zoOgWFhcMMGaGAB8egbqB7VrXOnWV7Pbz3lnb3Etq2+CSWJWaJvVSR8p4HI9KAOF+PP/JD/ABF/1zh/9Hx1j+J/FmiaD4N8FaV4y0KLUNA1i2hhuLyc5jtHESbSV2k55JBBBGCa9VvLK11C0e1v7aG6t5MB4Z4w6Ng55B4PIqG90fTdS0s6bqGn2t1YlQptpoVePA6DaRjjt6UAfN/jzSvBHgq3s9Z+D/iVrfxDNdRrb6fpmofakuAx5DJljj6nB6Y5477xiZG/aH+GpnUJKba8LqDkBvJbI/Ou80X4feEfDt79s0Tw7p1ndD7s8cC71+jHkfhWzLp1lcX0F7PZ28t1bgiGd4lMkWRg7WIyM+1AHl/7Sv8AyRm6/wCvuD/0Km/FX/krHws/7CFx/KKvUr7TrLVLU22p2dveQEgmK4iWRSR0OCCKLjTrK8uLe4u7O3nmtWLQSyxKzQk9SpIyp4HT0oA8Kv8Axjp/gz9rDVLjWpPIsL3TIbWS5YfLAxWNlZj2BK4z71b+Nni3SvGukad4E8HX9vrGqaxexbvsUgmSCNTkszKSB2OPQMTitmx0Br/9pLxS+q6U1xpN1okUW64t90EpzFlckbSeDx7V32g+CvDXhiWSXw/odjp8sgw8kEIDkem7rj2oA2YIhBbxxKSRGoUE+wxXhPjbxVaeD/2ptL1PVNyae2hrBdThSwgV5ZAHOOg37AT717zVK50bS72eSe8020uJZYfs8kksCszxZzsJI5XPOOlAHkfxq8e6Lr3gg+EfCd/ba5rGvSxQQQWEqzbV8xWLMVOB93HPrnoDWH8TvCWi+H/HHgjUvGlo1/4Xh0xNGvJfnCwvGG8t22EHktn6Ka9m0PwL4W8NXb3Wg6BYWFw4wZoYAHx6A9QPYVsXlla6jZyWmoW0N1bSjbJDPGHRx6EHg0AeA+LdN+CGgaXA+haDp/iXVLyVIrTTdP1ORnlLEDkq7bRj1HJ4+m58a4LbRPBfgKHyY9PtLHXbJDF5u5LdEjb5d56hQMZPpmvSNF8A+E/Dl8bzQ/D2n2V1zieKBQ6564bqPwrS1nQ9L8Raa2n65YW9/aMQxhuIwy5HQ89D70AcB8bbGLxL8HbvVNFuIrmTS5E1K1uLdw65iYhyGHHCl/xFcf4M0mT4l/Df4j+Ibi3K3Hiad0tYzyQsCAwj8GOP+A17fp+h6ZpWipo+n2EEGnIjItqqDy9rElhjuDk5+tT2VhZ6ZaLa6baQWluhJWGCMRouTk4A460AeC/AO6ufG/jGfxTqCMV0TRbXRrdn53Nty7fX5W/77qhB4Y8C6Z8aPFml/FOyhQ6ndnUNKvbuZ4YpEkZmdd4YAYLY57qR6Z+htP0rT9JieLSrC2so5G3ultCsYZvUhQMnjrVfXPDWi+JrVbbxBpVpqMSnKrcxB9h9QTyPwoA8b0/TPhYnxW0XRPAnha11i8if7Xcaja6jKYtP8shlbOWVzkdMjnA78ZmteHPBumfH/XY/ifZRnTtdjjudLvrmR4olcACRCysAOT36YHTIz7toXhjQ/DFs8Hh7SbPTo3OXFtCELntuI5P41JrOg6T4isTZ67ptrqFvnPl3MQcA+oz0PuKAPEbnSPhHB480LQPBvhaz8Q6jdzh5pbPU5THYxqQTKzBmBI5O325xkZ6PUP8Ak7jS/wDsWW/9Gy16HoPhLw/4XR18PaNZad5n+sa3hCs/1bqfxq+2nWTakuoNZ25vVj8pbkxL5gTOdobGccnigDy74/f8gzwd/wBjPa/yevWqrXmnWWorEuoWdvdCGQSxieJX2OOjDI4I9as0AeP/ABbvLbT/AIv/AAwur6eO2t47q73zTOFRcrEOSeB1p/jyeK5+O/wvntpUmhlF48ckbBldTGCCCOCCO9eka94Y0TxRaJbeIdLtdRhjbei3EYbYfUHqPwqaLQ9KgWxEWm2o/s6MRWZ8lSbdAAu1DjKjAA4oA86/aP8A+SKaj/18W/8A6MFc78bNE01PEngrxN4nsXvvDduGs9UVQ2IlcDY52kHAJJ4/ugc5xXt19p9nqdq1rqVpBeW7EForiISISORwRin3Frb3dq9tdQRTW8i7XikQMjD0IPBFAHgPivT/AIE+H/Dov9L0nTtevZiq2mnWOpSvLOzEADCuxXr3Ht14r27wvYRaX4U0yzt9OGlpFbJ/oIlMotyRkpvPLYJIz3qjpPw98IaFqP2/SPDem2l2DlZo7dQyf7p/h/DFdHQB5B8e9Vu7QeFdLk1O50jQdU1Ew6tfWz7GRBtwu7sCC59Pl5yBiuL+JehfCHw18Pb+Lwwlhfa7cxAWzwXbXko+YFpCdzBQFDHPHtX0RqelWGtafJY6vZW99aS/fguIw6N6cGsvSvAfhTRLW5ttK8PadbRXSGO4VLdf3qHqrE8kex4oA8e+J97a337Lnh17K5iuEQafG7ROGCusYBU46EHqO1ekfGj/AJIz4l/68/8A2Za3rLwd4c07Rf7ItNEsU07zfO+ymBWj3/3sHPPvWrdWlvfWsltewRXEEgw8UyB1cehB4NAHH+H/APkgumf9i1F/6SivH49Bvdc/Yz0d9Liaa5024kvhEi5Lql1MG49lYt/wGvpBLW3js1tI4I0tljESwqgCBMY2hemMcYptlY2mnWaWmn2sNpbR52QwRhEXJycKOBySfxoA4m0+NPgefwcuvza9ZxDyd8lmZV+0K+MmMR53Fs8ccHrnHNeceF9E1Nv2avGuqXVpJHceIHutSig28iIgEHHvtYj1GK9dk+G3gqXVv7Sk8LaU13u3mQ2qct64xjPviumCgKFAAUDAAHGKAPL/AAJ8TfB+m/BvRLm816yjbT9MhgntjMvniSOMKUEedxJI4454Ncr8IJZZ/gV4/muYWgmkv9RaSJxgxsbZCVPuDxXq9t8OvB1nrA1W18M6XDfK29ZktVBVv7wGMA+45rah0vT7a3uILextoobp2eeOOFVWVmGGLADDEjqT1oA4n4Ff8kR8Of8AXGT/ANHPWL8Hv+SgfE7/ALDv9ZK9UtLO20+0S1sLaG1t4xhIYYwiLzngDgc0y206yspriazs7e3luX3zvFEqtK395iB8x56mgDyX9nHUrH/hC9Q037ZB9uXVrmQ2vmjzQvyfNt64969S8RaYdb8L6rpSvsa+s5rYMf4S6Fc/rVWw8G+HNK16fWtN0WztdSuAwluYYgrPuOWzj1IyfWtugDxn4LeP9C0j4fxeGfFGo2uiaxoTy29zbX8qwnAdmDDcRng4OO49CKPh7dr44+PPiXxrpau2iWtiul21yUKrcPlGYjPUDafwZfWvRtc8B+FfEt2t1rvh/T764UY86WAFyPQt1I+tbFjYWemWUdnptrDaW0QxHDBGERR7AcCgDy34N/8AI9fE3/sPt/6FJXrVVrXTrKymnlsrO3t5Ll/MneKJUMrf3mIHzHnqas0AeN/DyzGo/Ej4vWLNsFzcwwlgPu7kmGf1riPhl4Z+F39j3GhfEixsbDxRpVxLFd/2hePb+au4lWUlwpGCBx2GehzX0lb6dZWdzcXFpZ28E90waeWKJVaYjoWIGWPJ6+tZeveCPDHiedJvEGhWN/Mgwss0ILgem7rj2oA84+F1v4EuviNqrfD/AMKpFZ6VD5R15LyVkmkfGYkRsgjGfmz2HGCDVn4E/wDH14+/7Ga5/nXqOm6XYaNYpZaRZW9jax/cht4hGi/gOKW006y08zGws7e1M8hlmMMSp5jnqzYHJ9zQB5T8bbmCz8XfDe6u5Ugt4deVpJZGCqigpkkngD3o+J9zBefE/wCFVxaTRzwSajOySxOGVhiLkEcGvTdc8O6P4msBZeINNttQtgwdY7iMMFb1HoeTyPWlt/D2jWtvYQQaXaLHpoxZgwqfs3+4SPl6DpQB5r/zdx/3LP8A7Vqr8OdTtdF8bfFzVNQcx2tnqAnmcAnaiiUk4HXgV65/Z1l/aX9ofY7f7b5flfafKXzNmc7d2M49qjGjaYovAunWgF9/x9gQL/pHUfPx83U9c9aAPAvCvjbwx408dP45+IGv2FlFYu0ehaNPMP8ARlB/1zjpvOOPfnoFrs/ijPp3xQ+DmuQ+C9Qh1eazaObZaHeSUYMVx67dxA7kV3f/AAhHhT/oWNG/8F8X/wATWhp2j6Zo8bppGnWlgkhy62sCxBj6kKBmgDwvQdM+AGp+D4dYvINLs3WANc209/Ks0bgfMvl79zc5xtBz2rT8OxaLN+z7401bw54Vbw3ZX1heeSj3LzNdRpCwWU7vu5ywwM9Opr0e7+G/gu/1U6leeF9Kmu2bc0j2qnefVhjBPua6GS0t5bNrSWCJ7Zo/KaFkBQpjG0r0xjjFAHH/AAd/5I54Z/68V/ma7WorW1t7K1jtrOCO3gjG1IokCKg9ABwKloA+bfA1n4Q8dz63q/xh1pJdat9QljOm6jqJt47SNcYCJuXjO4enHTPJu/DDUvCMH7RWsp4U+zWOkS6QLey/5ZrcuJI9xj3cvkhue+0mvY9U+H3hHW9U/tLVvDmm3d5kFppbZSz46buPm/HNWbnwh4du9WsdTuNFsnvdPAW0n8kBoQOQFI7DsO1AHivwr8eaP4a+KXj/AEfxDeRadHfa5cTWtzcMEiZ1lcOhc8A4KkZ9/bOn4n12x+JXxv8ABukeFLhNQtfD9w2o397bnfEmCpVQ44PKAZGRlx6Grvw18IW2qal8QrXxXoSz2lz4knmgS+tvlkXc2HTcP1FeoaH4a0XwzatbeH9KtNOiY5dbeIJvPqSOT+NAHiPhDxxpXhL9oXx5Za9cpZWuqXMYS7mO2NJUDbVZui5DtyePlq/8SPEOnfEfx54Q8H+EruLVDbakmo39zaMJI4I4/wDbHBOC347R1NafgjwtFqXxL+J8XiTRRcade3lq0QvbbMc2BNkqWGDjI5HTNekaD4U0DwvFJH4e0ez04SHMht4Qpf6nqfxoA870n/k7bXf+xbT/ANGQ1keBNIk1+1+MmkQttlvtXvbdCezN5gH6mvaV06yTUn1BLO3W9ePy3uREokZOPlLYyRwOPai106ysZJ5LKzt7Z7mQyztDEqGVz1ZiByfc0AfOnw10H4P3/hJLXxrZWGm+I9OLw6jDqN7JbuXViNwBcA8Yzjoc10fgbRfCHii28bW/w/8AC40yxksZtJh1r7VIwvDInzBY36AEKc56Y6ZxXqGteAfCniO9F5rnh7T725HHnSwKXI9Cep/GtqysbTTbOO0061htLaIYjhgjCIg9Ao4FAHkPwY+IugaZ8P4PDnifUrXRNY0JpLa5tr+VYThXJBG488HBA5yD7Vm/DnxNb+L/ANpvxJq+nK50+TRvLtJWQr5yJLEhcZ7FlbH+Ner614C8KeIr5b3XPD2n310vHnTQKWI9Ce4+tatvpGm2dytxaafawTrCIFlihVWEYOQmQM7fbpQBbrxz4TalY23xU+JFlc3kEN3cayDDBJKFeUAyZ2qeW/CvY6xG8G+HH8TL4hbRbP8AtdTkXoiAkzjbnPc44z6UAeUfBvxFpfw/k1/wH4tvoNJvbHUpJraS9cRJcwsBtZWY4/hz9GHoang1W2+I37SWlX3huQXmkeFrGX7RfRDMbyyKyhFbofvD67W7DNeo694P8O+KPL/4SHRbLUWj+488IZlHoG6ge1XNI0TS9AsFstE0+2sLZeRFbRBFz6kDqfegC9Xzvp1v4c8c/E7xfH8W9ZKPpl+0Gn6Td35toFgBO11G5dxwFPB75OcivoisDXPAvhbxLeJd69oFhf3KAATTQAuQOgJ6kexoA8P0C+8C6f8AtKaOngv7HZ6RFpstu1wjbYZ7g7ydrsfnOCozk8jAr6PrDvfBPhjUVsFvNB0+RdOObNfs6gQc5+UAcDIBx0rcoA+f9C8baX4R/aY8aQa9cJZ2epGGNbuXiOOVY1KqzdFBBfk+lXfir4j0z4jeJPC3gfwleQ6rMdVjvr24s3EsdvEgIJLjjo7H8AO4rV8K+GU1L4x/EhPEGjfaNMvTaeX9rtt0U2EOSpYYOPUdK9G0Hwj4e8LrIPD2jWeneb/rGt4QrP7E9SPagDzyH/k7i4/7Fkf+jVrJ+FHiDTfh34g8U+CPFl5DpU66rJfWc944iS5icAAhjx0QHHuR2Ne0DTrIakdQFnbi9MflG58pfMKZzt3Yzj2qhr3hLw/4ojRfEOjWeo+X9xriEMyfRuooA8ru9XtPiR+0R4d/4RmZb3TPC8Es95fQ/NF5jjAQN0PIXp1+bHSrOnalY6b+1b4i/tG8t7Tz9Fgji8+UJ5jZi+Vc9T7V6no2g6T4esRZ6Fp1rp9uDny7aIICfU46n3NVNV8G+HNc1a31PV9Fs7u+tSphuZYgXTByOfY8igDbr59u49E8afG7xRpfxU1l7ax0sxLpelT3ptreVCMl8gjJxtPBydx7Dj6CrD1/wV4a8USxy+IdDsdQliG1JZ4QXUem7rj26UAeDNdfD3Rf2gPByeCvsNpptn9pS7vYpP3DytEwC+axwxGV7kDeO5ruk/5O4f8A7Fn/ANqiu8v/AAJ4V1PS7XTb7w9p0tlZtut4Ps6hIieu0AcZ7+ta39nWX9pf2h9jt/tvl+V9p8pfM2Zzt3Yzj2oA8u+OX/IS+H3/AGM9t/MVm6jqtt8OP2lL7VvET/ZdH8UafGkV84/dxTRhF2s3YYTn03qema9ju9Osr9oWvrO3uTbyCWEzRK/luOjLkcH3FRavouma/YNZa3p9tf2rcmK4iDrn1weh96APCf2iPiBoeseFbTw/4ev7fVZ2u47q6ks5BLHbxLwNzLkAlnUD/wCuM/QlYOneBvC2k6dLYaf4e02G1mYPLELZSshHQtkc47Z6VvUAFFFFABRRXnnif4mLoPxT8OeGo7jTPsOoLP8Ab5ppfntiiEqM7gFycfeFAHodFeY+I9fv4v2gPBGnWWpSrpd9ZXUs0Ecv7qfEUhViBwcYBBrt7Hxb4c1PUm0/Tdf0y7vVJDW0F5G8gx1+UHPFAGvRTZJEhiaSZ1jjQFmZjgKPUmsrS/Fnh3W7prbRte0zUJ05aK1vI5WH4KSaANeiigkAEk4A6mgAorHs/F/hrUdSOn2HiHS7q9BINtDexvJkdRtBzWhLqFnBeRWk13BHczAmKB5QHk/3Vzk/hQBYoqveX9np1v5+oXUFrDkL5k8gRc+mTSSalYxXLW8t7bpMsRnaJpVDCP8Av4znb79KALNFZWleKfD+u3EkGia5puozRDLx2l2krKPUhSSK05ZY4IXlmdY40BZnc4Cj1J7UAOorJ0vxX4e1y5a30XXtM1CZBlo7S8jlYD1wpJrUkkSGNpJXVEQFmZjgKPUmgB1FZOl+KvD2uXL2+i67puoTxjLxWl3HKyj1IUk1yfiz4ljw/wDE7w14diuNM+x6iZxqEs0nz2xRQV53ALnP8Q5oA9CoqF7y2jsvtj3ES2oTzPPLgJtxndu6Yx3qhpPinw/r0rxaHrmm6lJGMulpdxylR6kKTQBq0VHcXMFnbSXF3NHBBGu55ZXCqo9STwBXnvxI8bWFx8JPEWoeDfEdrPd2cKET6beJI0JMijqhOOCaAPRqKx/CNxNeeCNDubqRpZ5tOt5JJHOWdjGpJJ9STWhJqFnFfRWUt3Al1MC0cDSASOBnJC5yeh/KgCxRUdxcwWdu9xdzRwQxjLySuFVR7k8Cq9xrGm2mmjUbvUbSCxKhhdSzqsRB6HeTjFAFyisvSPFGga+7poWt6dqToMutpdJKVHqQpOK4bxXrep2n7QPgfSba/ni0+8t7trm2RyI5SsTlSw74IFAHptFQJfWkt7LZxXUL3UIDSQLIC6A9CV6jOaJ760triCC5uoYZrgkQxySBWlI6hQeTjI6etAE9FQXt/aabZyXeo3UNpbRjLzTyBEUe7HgVV0jxFouvo76Fq9jqSx/fNncpLt+u0nFAGjRRUVzdW9layXN5PHbwRjc8srhVQepJ4FAEtFZekeJ9B195E0LW9O1Joxl1s7pJSv1Ck4rz743eLrzSLLRNE0PXY9Ju9W1OG2ublHXzbaBs5fBOVGcHPHTrzQB6rRWT4XtVsvDNlbprEutrGhA1CaUSPPyeSw4Pp+FaksscMTSzOscaDLO5wFHqTQA6isSx8aeF9UvhZab4k0m7uicCCC+jdyfQKGzW3QAUVBdXtrZLG17cw24lkEcZlkCb3PRRnqTjpWfJ4t8ORawNKl1/S01EttFo15GJd3psznPtigDXorgPjhq2oaH8HdZ1DR7yayvITB5c8DlXXM8YOCPUEj8a7DSLgv4dsbi5lyTaxvJI5/2ASSaAL9FY+neLvDesXzWek+INLvrpc5gtryORxjr8qkmub+LvxAm+H3guTUtMNjLqXmxrFbXbE71LYYhQwY49aAO8orzj4saheaj8NftPg3xGLS9N3GlvJYzbmupDkCBSh6ksD7BST0rudV1zSdCtxPrep2enQscLJdzrEpPoCxFAF6iqel6xpmt2v2nRtRtdQgzjzbWdZVz6ZUkVcoAKKr2d/Z6hE0lhdQXUaOUZ4JA4Vh1BI78jihr+zS/Sxe7gW7dN6W5kAkZeeQvUjg8+1AFiiuU+H1hf6fpF/HqniVPEcj6hLIlwkm/yEIXEOcnG3BOP9qtTUvFvhzR75bPV9f0yxunxtgubyONznp8rEGgDXoqlqVxjQbu4tpf+XZ3jkRv9kkEGuL+Bmr6hrvwg0nUNZvJr28lecPPO5Z2xM4GSfQACgD0GisiLxb4cn1c6VBr+mSaiG2mzS8jMufTZnOfbFcV8Ddb1PXfDGvTazfT3ssOvXMETzuWKRqseFGewyePegD0yiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAK8M+IXhDw/d/tDeC4bnSbWSPVlu3vlZOLhljO0t64wK9zrxz4s3cnh34s+BfFNzYXtzpdgLqO4ktIDKULptAIH+9n3wcdKAMz4neGLbXPjn4C8PKz2tjJYzxOkDlP3CIxaMEcgMilPoaZ8cfA/hzwl4N0zX/C2k2+kanp+pQCG4s08tiDn72PvcgHJ5468muk1uzvtX+PfgDXrLTrxtMXTrlpbk27bIN8L7Vc4wpO4DB7mp/j/AKRqOtfDRLXR7C5v7j+0IH8m1haR9oJycKCcD1oA5n47+JNMbxt4Z8J+KNRl07w3KrX2qtErsZ1BIjjwgLY3IRx/eB7CuQ8fa18GZfC/2r4fXqaV4k04pLp81lZ3ELOykfKxKAHIzyTnOOeoPqPxS0TWtO8YeHfiD4Y019VuNGElve2EWTJNbuCMoB1I3P6nJBxwazdU+MGteLLSLSPhj4b1iPWbh1WS71GyCQWS5+YuSSCcAjn8MnAoA9L8H6xJ4g8EaJq9xgTX1hDPKAMAOyAtj8Sa8z/aI8SJp+n+HvDt5qEumabrl4w1K6iUsy20ezeoABPO8cAc7cdCa9gtI5orKCO6m+0TpGqyTbQvmMBy2BwMnnFeefGDwzrGpW+heJfC9sLzV/DV79rjtM83ERx5iD3O1ePTOOcUAeW+KtQ+Al54MuLPw5cxafqttCXsLq3srpJRMoym5ynzZIAO4988da7G30i/+LXwG8Pa9FcGLxXpyNPYX2cMZ4pGQgn0fyxntnB7YqbUfjdf6xpL6b4M8H+IP+EnnXykiurLbHaOeC7sTjC9eQB64q/43fxtdeFdF8F2K3FxrWsxrFq2tw2xW3s48fvTuACgnkAdcDsSKAOa8GajefHfxTYatr1ultofhlYy1jvDC6vyOXI/uL2B+nOWpvj3wxH4w/ag0rR72WVNOl0JXvo4pChniSWRvLJHOC4TPtWld+C7r4ReM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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6BpAsHA8EeFO",
        "colab_type": "text"
      },
      "source": [
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Lw02RVrbFFJ-",
        "colab_type": "text"
      },
      "source": [
        "Note that \n",
        "\n",
        "(1) Number of observations $n = 9$;\n",
        "\n",
        "(2) $C(X_1) \\in C(X)$;\n",
        "\n",
        "(3) $rank(X_1) = 2$ and $rank(X) = 3$.\n",
        "\n",
        "\n",
        "Under null model is true, we have F-test statistics\n",
        "$$F = \\frac{y^\\top (P_X - P_{X_1})y/(3 - 1)}{\n",
        "y^\\top (I - P_X)y/(9 - 3)}\n",
        " \\sim F_{(Rank(X) - Rank(X_1)),(n - Rank(X))}.\n",
        "$$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gmJVAK-v5SLK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X1=model.matrix(~x) # Construct Design Matrices for linear model with (unspecified response) ~ (intercept) + x ; x = c(1:4), y = c(2:5), mat <- model.matrix(object = ~ x + y)\n",
        "X=model.matrix(~0+factor(x))\n",
        "X1 ; X"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j9fiTuOP8r42",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Define projection function\n",
        "proj=function(x){ x%*%ginv(t(x)%*%x)%*%t(x)} # ginv: generalized inverse matrix\n",
        "library(MASS)\n",
        "PX1=proj(X1)\n",
        "PX=proj(X)"
      ],
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UFD1gyd-8-Eu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 493
        },
        "outputId": "08a4dd47-005a-46cb-80d5-589db01e2142"
      },
      "source": [
        "# Method1: Direct calculation\n",
        "\n",
        "Fstat=(t(y)%*%(PX-PX1)%*%y/1)/(t(y)%*%(diag(rep(1,9))-PX)%*%y/(9-3))\n",
        "pvalue=pf(q = Fstat, df1 = 1,df2 = 6, lower.tail = FALSE)\n",
        "\n",
        "curve(df(x = x, df1 = 1,df2 = 6), xlim = c(0, Fstat+3 ))\n",
        "abline(v = Fstat, lwd = 3, col = \"red\")\n",
        "pvalue"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "     [,1]      \n",
              "[1,] 0.03348515"
            ],
            "text/latex": "A matrix: 1 × 1 of type dbl\n\\begin{tabular}{l}\n\t 0.03348515\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA matrix: 1 × 1 of type dbl\n\n| 0.03348515 |\n\n",
            "text/html": [
              "<table>\n",
              "<caption>A matrix: 1 × 1 of type dbl</caption>\n",
              "<tbody>\n",
              "\t<tr><td>0.03348515</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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t69e0tLS7Oysl5++eXQ0NC//e1v165d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",
            "text/plain": [
              "plot without title"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K0wDMt06G5Cm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 183
        },
        "outputId": "a02e4d8c-2e6e-4fa8-d9c2-1710ef812459"
      },
      "source": [
        "# Method2: \n",
        "reduced=lm(y~x)\n",
        "full=lm(y~0+factor(x))\n",
        "\n",
        "rvsf=function(reduced,full){\n",
        "  sser=deviance(reduced) \n",
        "  ssef=deviance(full)\n",
        "  dfer=reduced$df\n",
        "  dfef=full$df\n",
        "  dfn=dfer-dfef\n",
        "\n",
        "  #############################################\n",
        "  Fstat=(sser-ssef)/dfn/(ssef/dfef)\n",
        "  #############################################\n",
        "  \n",
        "  pvalue=1-pf(Fstat,dfn,dfef)\n",
        "\n",
        "  list(Fstat=Fstat,dfn=dfn,dfd=dfef,pvalue=pvalue)\n",
        "}\n",
        "rvsf(reduced,full)"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "$Fstat\n",
              "[1] 7.538462\n",
              "\n",
              "$dfn\n",
              "[1] 1\n",
              "\n",
              "$dfd\n",
              "[1] 6\n",
              "\n",
              "$pvalue\n",
              "[1] 0.03348515\n"
            ],
            "text/latex": "\\begin{description}\n\\item[\\$Fstat] 7.53846153846154\n\\item[\\$dfn] 1\n\\item[\\$dfd] 6\n\\item[\\$pvalue] 0.033485153201973\n\\end{description}\n",
            "text/markdown": "$Fstat\n:   7.53846153846154\n$dfn\n:   1\n$dfd\n:   6\n$pvalue\n:   0.033485153201973\n\n\n",
            "text/html": [
              "<dl>\n",
              "\t<dt>$Fstat</dt>\n",
              "\t\t<dd>7.53846153846154</dd>\n",
              "\t<dt>$dfn</dt>\n",
              "\t\t<dd>1</dd>\n",
              "\t<dt>$dfd</dt>\n",
              "\t\t<dd>6</dd>\n",
              "\t<dt>$pvalue</dt>\n",
              "\t\t<dd>0.033485153201973</dd>\n",
              "</dl>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}