Regression Modelling 10. Removal of interaction terms.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression Modelling 10\n",
    "## Removal of interaction terms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Updating HTML index of packages in '.Library'\n",
      "Making 'packages.html' ... done\n",
      "Updating HTML index of packages in '.Library'\n",
      "Making 'packages.html' ... done\n",
      "Updating HTML index of packages in '.Library'\n",
      "Making 'packages.html' ... done\n"
     ]
    }
   ],
   "source": [
    "install.packages(\"tidyverse\")\n",
    "install.packages(\"gridExtra\")\n",
    "install.packages(\"nortest\")\n",
    "\n",
    "require(tidyverse)\n",
    "require(gridExtra)\n",
    "require(\"nortest\")\n",
    "\n",
    "homes <- read.table(url(\"http://jupyter-regressions.s3.eu-west-1.amazonaws.com/homes5.csv\"), \n",
    "                           sep=\",\", header = T, stringsAsFactors = F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "options(repr.plot.width=15, repr.plot.height=10)\n",
    "theme <- theme(\n",
    "        axis.text=element_text(size = rel(2)),\n",
    "        axis.title=element_text(size = rel(2)),\n",
    "        plot.title=element_text(size = rel(3))\n",
    "    )\n",
    "points <- geom_point(size=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Price</th><th scope=col>Floor</th><th scope=col>School</th><th scope=col>DHa</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>359.9  </td><td>2.200  </td><td>Redwood</td><td>0      </td></tr>\n",
       "\t<tr><td>249.7  </td><td>1.868  </td><td>Redwood</td><td>0      </td></tr>\n",
       "\t<tr><td>265.0  </td><td>1.875  </td><td>Redwood</td><td>0      </td></tr>\n",
       "\t<tr><td>349.0  </td><td>2.000  </td><td>Redwood</td><td>0      </td></tr>\n",
       "\t<tr><td>319.0  </td><td>1.855  </td><td>Harris </td><td>1      </td></tr>\n",
       "\t<tr><td>339.0  </td><td>1.928  </td><td>Redwood</td><td>0      </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llll}\n",
       " Price & Floor & School & DHa\\\\\n",
       "\\hline\n",
       "\t 359.9   & 2.200   & Redwood & 0      \\\\\n",
       "\t 249.7   & 1.868   & Redwood & 0      \\\\\n",
       "\t 265.0   & 1.875   & Redwood & 0      \\\\\n",
       "\t 349.0   & 2.000   & Redwood & 0      \\\\\n",
       "\t 319.0   & 1.855   & Harris  & 1      \\\\\n",
       "\t 339.0   & 1.928   & Redwood & 0      \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| Price | Floor | School | DHa |\n",
       "|---|---|---|---|\n",
       "| 359.9   | 2.200   | Redwood | 0       |\n",
       "| 249.7   | 1.868   | Redwood | 0       |\n",
       "| 265.0   | 1.875   | Redwood | 0       |\n",
       "| 349.0   | 2.000   | Redwood | 0       |\n",
       "| 319.0   | 1.855   | Harris  | 1       |\n",
       "| 339.0   | 1.928   | Redwood | 0       |\n",
       "\n"
      ],
      "text/plain": [
       "  Price Floor School  DHa\n",
       "1 359.9 2.200 Redwood 0  \n",
       "2 249.7 1.868 Redwood 0  \n",
       "3 265.0 1.875 Redwood 0  \n",
       "4 349.0 2.000 Redwood 0  \n",
       "5 319.0 1.855 Harris  1  \n",
       "6 339.0 1.928 Redwood 0  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(homes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0IIQE5caxSA0IQQgNCEEKhRs+++8Du3\nTUs9BZUvQQjv32uFvpteMLvcESEEOuuRj/UastUyK96Seg4qXq4hHHRc6831PQpPGx1W7p2Y\nhBDopH/2P2xyS8vMMxt+l2iAe7958Ek3vJfozlkcuYYwG9XS8kbf+m/8c/LNK2fXlTkohEAn\nHb5d8drGX9g8yd1PH9aw41H7LLthuVdMUyFyD+GPssIFR/+U7bbwz06bPM+FQgi077ejt9rp\ny090fG7AtcX1yew/3TtQ+w5Za3zr7eQ91p2Z4t5ZLLmH8IvZXwv7wQMW+smJ9dn7TFnS+wBq\nWdOYngd854xdG77X0cE52f3FzdvZ4909VDsm1P25sL4z4CcJ7p3Fk3sIj8iK701/QM+Ff/ap\nR+c51VeEQHu+178QmBsa/rejk/1uLK5/y17o3pHaddncN5o7YmSCe2fx5B7Cb2evFvY7rVjm\noO8RAu1pWvni4mbMLh0d3e/A4nrm2t050If51idLm1P2SHH3LJZ8Q1jfq1fP7J7Cfo0hZQ4K\nIdCeidnzxc0dvTs6+mjPc9ueLfOrxnJPzOs2//WR0mbkqBR3z2LJNYTrFZzbtn0sO6bMQSEE\n2vNkNrm4ub+u7GuR29y4zFqHHLlJw3e7e6Z2vdTwP4X1lWVuSHL/LI5UV5Z5eFy5718LIdCe\nN+sfKm6uWK3jw69dMuaw8/7evQN9qK8tf2fr7fhNt2lKNACLziXWgCqyywGFa3HM3Pj41JN0\nYM5XG1bbab36vd9IPQgdE0KgijzZ97AXW1qe2nH111NP0qHnrzn9Rx284xyVIU0IJ3fwMkEh\nBNr3yCbZistmu6Z4SQS1Kt8QPj9mxxMmtTyycVa3/YRy54QQ+BDN4395+/Oph6Cm5BrCSStl\nWTbk1UHZyj2yVd4qc1AIAchJriE8PTv098dme67xTMuU/bKzyxwUQgBykmsINx04u6V5razt\nZTVv9N6yzEEhBCAnuYaw/96tNyOK11jbtn+Zg0II0KFy32Fi0eUawqWGt94cXfzln2koc1AI\nAcp7YO2GrG7FS1OPUQtyDeFHd269Ob5PYb/zoDIHhRCgrGvrlh19xUlrZ4elHqQG5BrCPd53\nUaS1fI8QYElNb1yrcLXVw0rvY0An5BrCM7N/zd0+kX29zEEhBCjnvGxicdPnk+UP0rFcQzhn\nZvPc7UPfGV/moBAClPPppUubzcp9m4lF4lqjANVnnz6lzRYDk85RE4QQoPp8s/hCtJaWfluk\nHaQWCCFA9Xmrx5DCOjb7VeJJaoAQAlShcdlq5z10xVbZrqkHqQFCCFCNrl8hy7KlTkw9Ri0Q\nQoDqNPO+N1OPUBuEEIDQhBCA0IQQgNCEEIDQhBCA0IQQgNCEEIDQhBDgA5qe+8us1DN05Jkf\nHvfde5s7PkdHhBBgITNOWjbLGoY9n3qOct47qu7j+23RuO2/Uw9SA4QQYEGztl/9uhffvHun\nARNTT1LGlwY90Hr74tZDZqeepPoJIcCCLhrwStsye9e9Uk/y4Z7vcU9hndT/msST1AAhBNp1\n7yGbrnvgDSG/BbXZWcX1j/Wvpx2kjJ98tLQ57NCkc9QEIQTac2rDZy/+0eilh0f8h7e+dxTX\nd7M/ph2kjG9vU9qM3T3pHDVBCIF23Njrt23LXweck3qSBJa/qbhOyR5JO0gZV6xR2ow6OOkc\nNUEIgXZse1xx/dGAOWkHSWGXLxbXW3pPSztIGc/V31dYJy9/VeJJaoAQAh/U3Ouu4ubFrJKf\nOdlNbup1f9vy2seOST1JGUet+nDr7b+336jiX+9Y+YQQ+KDZdfcXN29kf0k7SRInNB5z/a1n\nrrTVlNSDlDHrc3VDDtp+qS3+lXqQGiCEQDtWv7y4/r7h7bSDpHHrnqssu/W4Cv9a6/ELjjn7\nrqbUU9QCIQTa8fV1C38I5+z2qdSTQHcTQqAdb633id+/O/vxT63w99STQHcTQqA9r42o79GY\n7fBs6jmg2wkh0L63Hrzn1dQzQA6EEKAazfrpwUP3+/ak1GPUAiEEqEKvb7b8kecfv+7Ah1IP\nUgOEEKAK7bZF2xXBZ48e+FbqSaqfEAJUn8fqJhTWWWtcmHiSGiCEANXnkg1Km2MOTDpHTRBC\ngOpz7talzSl7JJ2jJgghQPX52dy3Bdl/TNpBaoEQAlSfN/r8V2Ed33hX4klqgBACVKHv9/rS\n10Yc97VV9089SA0QQoAqNH3jrK5vfbZcxLfJ6mpCCFCFDl77yYeuvvu5fdaekXqS6ieEANXn\n2bqHC+vUQT9OPEkNEEKA6nP5OqXNkQclnaMmCCFA9Tl3m9Jm7O5J56gJQghQff571ebiZuSo\npHPUBCEEqD4v97ytuPb9ZeJJaoAQAlShU5ZrK+HTG3+yKfUk1U8IAapQ0yk9V9p+7bp930w9\nSA0QQoCq9NLPz/zJU6mHqAlCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhC\nCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghA\naEII80363R0Tm1MPAeRLCGGuSZ+tb1w22+RPqecAciWEUDJt48EPvNcy8fClH049CZAnIYSS\ncz76VmE9ZGjiQYBcCSGUbPKd4vpM9kLaQYBcCSGULHtbcZ1T//u0gwC5EkIoWfm64vpO9kja\nQYBcCSGU7H9Qcb2+78y0gwC5EkIoeaBH4UvCv61ycupJgDwJIcz1g4Y9zv3+4UsPm5V6ECBP\nQgjzPHHMNpscdINLy0AsQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQgip\nzU49AMQmhJDUddsu27jJGdNTjwGBCSEk1Dy699du+90FH910cupJIC4hhIR+3vvhtmXyx49I\nPQnEJYSQ0A7HF9df95qSdhAITAghof43F9ep2cNpB4HAhBASWub24jozeyjtIBBYF4TwhT++\n3UXDzCOEBLHF6cX1/h5vpB0EAut0CB/aJMvubmn5+Ya/77KZhJAwLl3++bZl1nbDEg8CgXU2\nhOP79B3WFsKpfb7UdUMJIVHM3n2lH49/4dYtV30x9SQQV2dDeHDjXya1hbDlU5t22UxCSByz\nzlwpy/oc8u/Uc0BgnQ3hoM+2FEN40gpdNpMQEsprzzWlHgFC62wIG04uhfDkxi6bSQgByE1n\nQzjg86UQ7r56V43UIoQA5KazIdxv0LuFEP6ublSXzSSEAOSmsyF8sH6v+7LbH/5Kz55Pdd1Q\nQghAXjr9OsLLG7I2Pa/uspFahBCA3HT+yjLPHLv5Gpse/UxXDVQghADkxLVGAQhNCAEIrbMh\nvGHHlwrrSzvc2EUTtRFCAHLS2RDuunlps+keXTJPkRACkJNOX2Lt6NLmyFW6ZJ4iIQQgJ50N\nYc9TS5uxLrEGQBXqbAhXGl7aDB/YJfMUCSEAOelsCD/T69nCOr7X/l00URshBCAnnQ3hH+uX\nv+QfM/5xyfL1i//7fDghBCAnnb/EWo/CJdZ6XN5lI7UIIQC56fwL6p86evAag4/5S1cNVCCE\nAOTElWUACE0IAQhNCAEIrTMhHDZsfOv/5unCqYQQgJx0JoRZ9kBLNl8XTiWEAOSkMyF86aVZ\nrf+bpwunEkIActLZ7xE+9ETXzTKfEAKQk86GsO7ArptlPiEEICedDeGKh3XdLPMJIQA56fRF\nt9eb03XDzCOEAOSksyH8+wrHTu+6aeYSQgBy0tkQjtopW3HXz41q02UzCSEAuelsCL2OEICq\n1tkQPjFf1w0lhADkxbVGAQitkyF8/pe/eqELp5lLCAHISedCeGJdltWd2JXzFAkhADnpVAiv\ny+o/sXl99rMunaiNEAKQk06FcKe6u1pa7sh27tKJ2gghADnpVAiX377tdtsVunCeIiEEICed\nCmH959tuP1/fhfMUCSEAOelUCLOj226P7vqXUwghADkRQgBC61wIG/u1asz6FXThVEIIQE46\nF8IFdOFUQghATjoVwpkL6MKphBCAnLjWKAChCSEAoQkhAKHlHcLmCbdfe83tE5rLnxJCAHKS\nbwhnnLNq8Rmmq50zo9w5IQQgJ7mGcNqWWf2QEWOOGjG4PttqepmDQghATnIN4anZIa8Udy+P\nzE4rc1AIAchJriFca/OmudumzdYpc1AIAchJriFsPGH+/vheZQ4KIQA5yTWEA4bN3+87qMxB\nIQQgJ7mGcGT91XO3V9YdXOagEAKQk1xDOLFfNmTsVbfcctXYwVn/iWUOCiEAOcn3dYRPD537\nVhVDny53TggByEneV5Z5bNzo4cNHj3us/CkhBCAnrjUKQGhCCEBoLroN1anpvh9+77dd+X7Y\nEJWLbkNVemz9nhtuttTKd6WeA6qfi25DNfrncgdPav0jdXLjg6kngarnottUpBf/nXqCCjdq\nu+KFe4/YJvEgUP0q56Lb713943kOEcLQJh/dL8tW/Fq5fzQIb4WfFdeH6yalHQSqX+VcdPtf\n6681z4rZlCW9D6rfpPU2+sVzf7tyjS2V8EO9m/2xuHkjK3ttCqBjLrpNxRmzceHhf221MxIP\nUsmWvq24js9eSjsIVD8X3abSvNv3xuLmkjXSDlLR9j6kuJ5Z7o09gUXhottUmueyfxU3D2Vl\nX2QT2x8avt/2atxbel2behKoei66TaV5IftncfNg3ay0k1S065be4Mhjtujx7dRzQPVz0W0q\nzewVrixuvr1B0jkq3UvnHzbi7PGpp4Aa4FqjVJyvf7TwctMJy12cehLI3dQfHLzt4T99N/UY\nsQghFWf6diude/ddp/fbf3bqSSBvz665ypizD19hk1dSDxJKmhBO7uBlgkIY26zvDunVZ+jl\nTR2fhNry7jrD2l4+++a2W3fwzgR0pXxD+PyYHU+Y1PLIxlnd9hPKnRPC8OaoIBFdu9w7hfWl\nnr9LPEkouYZw0kpZlg15dVC2co9slbfKHBRCIKKjh5c225yVdI5gcg3h6dmhvz8223ONZ1qm\n7JedXeagEAIRjTyqtPnUV5POEUyuIdx04OyW5rWyG1q3b/TessxBIQQi+vpOpc263086RzC5\nhrD/3q03I7JX2/bb9i9zUAiBrtf8zA2/Kvv0hOT+2OPRwvo/Dc8lniSUXEO4VNs/fx9d/OWf\naShzUAiBLvf44GzgCtk2FZ3Cw1a6o6ll9nX9Tkk9SCi5hvCjO7feHN+nsN/Zu08AeRrf76AX\nW1r+vs+gSn7DjlknNi69fq+lz/G06TzlGsI9Vpu/X8v3CIE87btX4bV57211ROpJynrtrh/d\nPTn1EMHkGsIz576tQEvLE9nXyxwUQqCLTe95d3Hz83JPUCCiXEM4Z+a8iyU89J1yVwsWQqCL\nTZz7F/HHs7fTTkKlca1RIIRXs9Kbv/1fvavYsgAhBGJY55zievxWaeeg4gghEMNPlv6/tuWW\nnremnoQKI4RAECf12Oes03ftcW7qOag0QghE8eAXd9zluMdST0HFEUIAQhNCAEITQgBCE0IA\nQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEIT\nQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IA\nQhNCAEITQgBCE0KgIkxtSj0BUQkhkN6/R6+W9d76V6nHICYhBJL7+0qfuOqR33yl8ZTUgxCS\nEALJfXKv99qWu3vcl3oSIhJCILW/Zn8rbg48NO0gxCSEQGo3DCxtLhqcdA6CEkIgtV+sVNpc\nvGnSOQhKCIHU/lL3z+LmoJFpByEmIQSS22K/wosIH2i4O/UkRCSEQHLPLL/9jc8+eEbvL6ce\nhJCEEEjvhYP6Zz02ujL1GMQkhEBF+PfM1BMQlRACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhAC\nEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQWu2F8B9Xnn7F\nX7pwFgBqWq2FcNbR9avvvE7d8CldOg8ANavWQjh65d+33j6+7l5dOQ4AtavGQvhMXfH/nH80\n/rYLxwGgdtVYCMdtXNrseUKXDQNALauxEJ70qdLm6IO6bBgAalmNhfDcLUqb/b7YZcMAUMtq\nLIR/qn+2sL7W98YuHAeA2lVjIWzZe8N/tt6+uu1mc7pyHgBqVq2F8O1dG3c5es8+n3i5S+cB\noGbVWghbmn9z2sEn3+LrQQAWTc2FEAAWhxACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhAClDUt\n9QB0MyEE+HD/OuIj2TI73Jl6DLqTEAJ8qKdX2OrqP9/xhYbvph6EbiSEAB+mefCBhQs23tjj\n8dSj0H2EEOZ76c4bnmlKPQQV5E/1pQv47/qltIPQnYQQ5vrPsLo+A7P17089B5XjJ+uUNmdt\nn3QOupUQQsmU9Yc+0tzyyjFLLf6fCWrVFeuWNudsm3QOupUQQsmZa04prEdsnngQKscDDa8X\nN/sclXYQupMQQsnGpScGjs+eTzoHFWTO+qOa29bf1v8x9Sh0HyGEkmVvK65N9b9POwgV5M99\n97zjH384rdcpqQehGwkhlKxybXF9O3sk7SBUkmeH9c16bPyz1GPQnYQQSg4cXlyvWebdtINQ\nWZpfmpl6BLqXEELJQz1+2rY8M+gbqScB8iSEMNcVPXc4/fyRvUbMTj0IkCchhHn+euIuWxxx\nW+opgHwJIQChCSEAoQkhAKEJIQChCSFUiab/OefYS8enngJqjxBCdXhucO9tD/h4/XHeLxG6\nmBBCVZi+9u6vtS6/W35s6kmg1gghVIWLV5lWWG9unJR4Eqg1QghVYe/ji+uc5X6VdhCoOUII\nVWHo+aXNxy9LOgfUHiGEqrCPrwihmwghVAXfI4TuIoRQFaavvfvrLZ41Ct1ACKE6eB0hdBMh\nhCrhyjLQPYQQgNCEEIDQhBCA0IQQgNCEEIDQhBCA0IQQgNCEEIDQhJD2TP3h53Ycc+17qccA\n6H5CSDv+uubKnz/j4H6feD31IADdTgj5oBlr7j+9dXlti51STwLQ7YSQD/qvAcX//z/XY/H/\n6wCKJv/mBzf/K/UQLAoh5IMOP6S02fy7SeeAKnZ+n6U2Wq7+iGmp56BjQsgHHfDl0ma3U5PO\nAdXr3D5XzmlpuW+tvZpTT/87yuIAABb7SURBVEKHhJAPOm6v0mbNy5POAVXr1aWuL6z/WOqO\nxJPQMSHkg/6v5zOF9daeLyaeBKrU1SuV3kH5wNFpB2ERCCHtOPAjd7e0zLl22W+kHgSq1Le3\nKW1O2TPpHCwKIaQdM7/QsOyGvZc+x3c3YMn8YP3SZsyIpHOwKISQdr1y26W/eTP1EFC1nqor\nfn9hxqo/SDwJHRNCgK73qU1ebr2dOXJVn8wqnxACdL3J2/Yd8c0jV/3IE6kHSWT6U6+mHmHR\nCSFAN5hzw9E7H3bJlNRjpPHwtvVZttql1fIsAyEEEnnpzpv/nnoGusPvGg/+w5vjL1jmi6kH\nWURCCCTxrz2zPstlmz2eeg663HtrHFdYH+zx+8STLCIhBFKYtMb2jze1TBy57NOpJ6Gr3dP4\nVnGz35FpB1lUQgikcMKGM9qW5mG7pZ6ErnbZBqXN2dslnWORCSGQwmo/Lq5/qJ+cdhC63E/W\nKW1O3znpHItMCIEEZtfdX9y8mT2VdhK63CN1zxc3n/xK0jkWmRACKfT+dXF9PpuYdhC6XPOW\ne77btv6k57OpR1k0QgiksNPRxfWSuW/TQO34x6obXnTXVZ9tuCL1IItICIEU7my4qW15dLlx\nqSeh6036yqaNqx/wUOoxFlXeIWyecPu119w+oYPrDQgh1Lzv9tjzW+d/tvEIXxCSWr4hnHHO\nqlnBaufMKHdOCKH2PfqFbT9xxJ2pp4B8Qzhty6x+yIgxR40YXJ9tNb3MQSEEICe5hvDU7JBX\niruXR2anlTkohADkJNcQrrX5vO8GNG22TpmDQghATnINYeMJ8/fH9ypzUAgByEmuIRwwbP5+\n30FlDgohADnJNYQj66+eu72y7uAyB4UQgJzkGsKJ/bIhY6+65Zarxg7O+pe7rJIQApCTfF9H\n+PTQrGRo2fcgE0IAcpL3lWUeGzd6+PDR4x4rf0oIAciJa40CEJoQAhCaEAIQWoIQ3r/XCn03\nvWB2uSNCSFLTLzlwk33OnpR6jFZvdPBGLVSyOdccNGS3k59PPQYdyjWEg45rvbm+R+Fpo8PK\n/QEXQlJ6aYOVjv3+SesNfDjxHE/s2z/ru+sDiadgSU3ZftkjLxq7RZ9bUw9CR3INYTaq9W+4\nfeu/8c/JN6+cXVfmoBCSUPNWO7zdurx3xMpTks5xV6/9bnn616N6XN3xUSrRoeu93HrbfFbv\n51JPQgdyD+GPssIFR/+U7VbmoBCS0H0N/yqsM1e5LOUYUwaeXFgvXvrllGOwpF6uv6+42erE\ntIPQodxD+MXsr4X94AEL/eSre+86zwZZ2r+KE9p5nyhtDj8s5RjXLf9uYW1ed1zKMVhSN/Uv\nff/nW1ulHYQO5R7CI7Lie9Mf0HOhn5z6zZPn2cNXhKRz+i6lzXH7pxxj7B6lzeGjUo7Bkrrm\no6XNDzZKOgcdyz2E385eLex3WrHMQf80SkI/Xa30N/ndk/6T1ilCWN3u6/l2cfPFT6UdhA7l\nG8L6Xr16ZvcU9msMKXNQCEnoP0tdW1gf6fFgyjGuXXFWYW1e//yUY7Ck3lvlm4X15X5Xph2E\nDuUawvUKzm3bPpYdU+agEJLSuKUuntLy7g0DDk86xTsDTiusl/Z+KekcLKmbG06d1DL7no9t\nPyf1JHQg1ZVlHh73eJmfFUKSumyFupUbep/6Xtopft04/I7x/3tkjyvTjsESu/Wj2aDGhiM9\n9a/iucQafNDMR65/4J3UQ7Q8utcyWe8d7009Bkts9pM33FMJFyiiA0IIlav5P02pR4DaJ4QA\nhJZvCJuuP/q4u4vbC/Yoc04IAchJriGcs0/b5bYPKHzvZVS530UIAchJriG8PBt03mVDs83f\nahFCACpDriHcumFCS0vTN7Oh7wghAJUh1xAus0Nh+UH2yWlCCEBFyDWEvYYX13HZTjOEEIBK\nkGsI19m6tDkj23OkEAJQAXIN4WcaS1djbzkx6yGEAFSAXEP4s+zyudsxmRACUAFyDeGUi26a\nu206/+QyB4UQgJy4xBoAoQkhAKEJIXTgzXtvHu+tVaF2CSGU9c7nG3oun639m9RzAN1FCKGc\n2Z9c9+73Wl7+SsNdqScBuokQQjk/Xv7fhfWra3qLXKhRQgjl7HZicX29/s9pBwG6ixBCOR+7\norQZeEPSOYBuI4RQzuDvFdemPr9OOwjQXYQQyjlmp+J6T4/X0g4CdBchhHLGN17Qtrz0sSNS\nTwJ0EyGEsn6+1LZnXDxm2R39Jwm1SgihvL+fuNPGI65yaRmoWUIIQGhCCEBoQghAaEIIQGhC\nCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCHSF6Y/c+NjM1EPAkhBCoPOa\nzlu2bkC2/MXNqQeBxSeEQOd9pd9/TWl559I+Z6UeBBafEAKd9nT9PYX1pp7/TDwJLD4hBDrt\nzKGlzXoXJp0DloQQAp12+KjSZv/jUo4BS0QIgU770gGlza5jk84BS0IIgU67dvniH9k3lr4t\n8SSw+IQQ6LQZa4yc1bbs+/H3Uo8Ci00Igc57cuWPff3Sr66x+t9SDwKLTwiBLvDGOXt9fJ/v\nvJ16DFgCQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBo\nQghAaEIIQIWa+uebn+7+97gUQgAq0nunLl2/XLbKdd19P0IIQEU6dOAvprW8/q2eV3Tz/Qgh\nAJXo/xoeL6yXLjO5e+9ICAGoRMfsW1xnL//z7r0jIQSgEu15cmmz9bnde0dCCEAlOuBLpc1G\nF3fvHQkhAJXo/LVnF9Z/1v+pe+9ICAGoRJOWO76pdXl7u+2au/eOhBCAinRv/8HfuOzElTd4\nuZvvRwgBqEwvn7LL+p++cHp3340QAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhAC\nEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCa\nEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhAC\nEJoQAhCaEEK1mPrn2/4+J/UQUHuEEKrDzK8uVdc3W/P21HNAzRFCqArNn171pmktL53ccGPq\nSaDWCCFUhZt7/62wnjVoZuJJoNYIIVSFgw4rrtOW+t+0g0DNEUKoClueV9qsf3nSOaD2CCFU\nhZ2+UdqsdnXSOaD2CCFUhVM2ay6sT2YTEk8CtUYIoWI99cMTv/+n0v7Fpc9qW97YfJ+EA0FN\nEkKoUDMPrdtw38H1+0wu/vDWpbc5+8cnDBw8Ke1UUHuEECrUIas/3Hr77EY7F/9NtGXiCdut\nt+8l7yadCWqREEJlerLu0cL6/FJ3JZ4EapwQQmU6b3Bps/fxSeeAmieEUJm+um9pc9TIpHNA\nzRNCqEznfqK02ffLSeeAmieEUJkeqX+6sL6y9G2JJ4EaJ4RQofZfd3zr7Yuf2Lop9SRQ24QQ\nKtTUT/fY+tDtGrd/LfUgUOOEECrWg9858uzfNqeeAmqdEAIQmhACEJoQAhCaEAIQmhACEJoQ\nAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQ\nmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQWt4hbJ5w\n+7XX3D6hufwpIQQgJ/mGcMY5q2YFq50zo9w5IQQgJ7mGcNqWWf2QEWOOGjG4PttqepmDQghA\nTnIN4anZIa8Udy+PzE4rc1AIAchJriFca/OmudumzdYpc1AIAchJriFsPGH+/vheZQ4KIQA5\nyTWEA4bN3+87qMxBIQQgJ7mGcGT91XO3V9YdXOagEAKQk1xDOLFfNmTsVbfcctXYwVn/iWUO\nCiEAOcn3dYRPD81Khj5d7pwQApCTvK8s89i40cOHjx73WPlTQghATlxrFIDQhBCA0Fx0G4DQ\nXHQbgNBcdBuA0Fx0G4DQKuii21Mmz3OhEAJL6N0fHrjhrmNfSj0G1aNyLro9sS57n2lLeh9A\nbK8NHvClS08d0u/u1INQNSrootvPPDrPf2ezlvQ+gNj22OKN1tumk/q9mnoSqkVlXnT7D0II\nLJGnsr8W1jkbnJ14EqpGZV50WwiBJfPjtUubr+yddA6qSGVedFsIgSVz0eDS5swdUo5BNanM\ni24LIbBkblm29NljxKikc1BFKvNao0JIjXvttu/d8FzqIWrT1OUuLKzje/068SRUDSGE3DV9\ns1e/zQbWf86rhLrDVQ1nT2qZefOq+6cehKohhJC7sf1+2dzS8uDa+6QepDb9fJVsxR69vvpu\n6jmoGvmGsOn6o48rvcr1gj3KnBNCatmLPW8vrH/vdVfiSWrU7KdufPCd1ENQRXIN4Zx92p4w\nekDhv9BR5X4XIaSW/Wj10ubTX0g4BVCSawgvzwadd9nQbPO3WoSQwL65U2lz4qeTzgEU5BrC\nrRsmtD1PIBv6jhAS2Pc2KW0O+1zSOYCCXEO4zA6F5QfZJ6cJIXE9Wje+sE4Z8NPEk1DxZpV7\n51a6SK4h7DW8uI7LdpohhMS19yZt7xE09dNrz0w9CRWt6ZKNe9atdbJ3petuuYZwna1LmzOy\nPUcKIWFN3m7p/b9+8IB1nk09CBVtzv7LffveP/9w7Y3eTD1Jrcs1hJ9pfLu0OzHrIYTE1XTT\nl/ca85MZqcegsl3ef0Lb8vaGo1NPUutyDeHPssvnbsdkQghQxmanF9fbevtGYffKNYRTLrpp\n7rbp/JPLHBRCILrmXr8pbt7I/pJ2kprnEmsAlai58bfFzZvZU2knqXlCCFCRBp9VXH+9lMuz\ndy8hBKhIlyxfeKuuqYNHJR6k5gkhQEV6b68BFz781FUbrPt66klqnRACVKbZ561dlw069q3U\nc9Q8IQSoWFPfSD1BBEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIUTTd\ndMxOn73AlUpgIUIIQUzdrffwM45ee+CDqQeBCiOEEMShH3u+9Xb2Mct7LwNYgBBCDC/UFb8U\nnLP+WYkngQojhBDDdSuVNifvlnQOqDhCCDFctkFp890tk84BFUcIIYbb+75b3Iw+MO0gUGmE\nEGKY2u/SwvpKv2sTTwIVRgghiB81XtL6NeGfNth2TupJoLIIIUTx4/6NGyxXd9BbqeeACiOE\nEMbU311+0wuph4CKI4QAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaE\nAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACE\nJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEVpkhfCQDgJw8stiZ6v4Qtjz5aO35SXb1tVS6ER9L\nPQEd23Sf1BPQsaUuTP05dzE8ufiVyiGEteiBbHbqEejQuVunnoCO7f311BPQsWVuTz1B9xLC\nJSKE1UAIq4EQVgMhpB1CWA2EsBoIYTUQQtohhNVACKuBEFYDIaQdQlgNhLAaCGE1EELaIYTV\nQAirgRBWAyGkHUJYDYSwGghhNRBC2iGE1UAIq4EQVgMhpB1CWA2EsBoIYTUQQtohhNVACKuB\nEFYDIaQdf+45J/UIdOiCHVJPQMf2+0bqCejYCv+beoLuJYRLpPm51BPQsRn/Tj0BHXt9SuoJ\n6NjzTakn6F5CCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEII\nQGhCCEBoQghAaEIIQGhCCEBoQriobjp2mz7ZZxf64D3DBjau9ul7U8xDe9p5lJpv3nnVpdb8\nzB8TTcQHTP3FQev3XvaTP1ngvV4nHjyo1zqnTU81Ewtr51Fq94GrDUK4qDbPll134RCekvXa\nYcROK5yWZiI+qJ1H6YtZv0OP36u+7qpEI7Gwi7LGrYZv35B9+n2fUJ/uX7fv8ZtlW81INxYL\naOdRau+BqxFCuKju/UfzHQt9iv3vbOuXW5emN9JMxAd98FF6Llvxldbl1uwjiUZiYTde9nbr\n7V8HZtfP/9jQ7MrWP0kjs3NSDcVC2nmU2nvgaoQQLoaFPsXOWqnPq6lG4UMt9Cjdk+3dtjQ1\n9E4zDh/mO9nR8/aPZYPblpfrV2tONg/tef+j9OEfqnpCuBgW+hR7V3bIzF9849v3+KNbURZ6\nlF7uMeA/hY/ul2gePsRl2XHz9uOysYV1cDYh1Ti06/2P0od/qOoJ4WJY6FPs2dlxH8tabe3r\nwkqy8D9gfyvrf9gJ+zTsMynRPLSveavs7nk/GJ0Vv4U7Irs91Ty0Z4FH6UM/VP2EcDEs9Cn2\n2KzHevdO/ctu2Y6pBqIdC4ew5fplW/+2sl7tfVujyp2RHTD/B8OzWwrrUdk1icahXQs8Sh/6\noeonhIthoU+xX8ganm1dpq2SPZJoINqxcAjPrPv689Mf2730b29UiB9km70z/0dzQzgmuzbR\nPLRnwUfpwz5UA4RwMSz0KfbUbKPCOiq7PMk4tGuhR+k32ci2ZcZHeryQZh7ac0G2+eT3/dA/\njVakhR6lD/lQLRDCxbDQp9irs20L6/HZRUnGoV0LPUrHZVcU1uHZrUnGoT1nZFu//f4fz32y\nzBBPlqkgCz9K7X+oJgjhYlj4+Yh1K77Xtu7sU2wlWehROib7VmHdPrsryTi048Rsx6kLfOCx\nbEjb8kr9qp6DXTE+8Ci1+6HaIISLYf6n2Csveq319oDsjMJHV5yWbiYWttCj9LNspZda97fX\nLV2Tf5OtRk1jsj3mX0Gm+GdpaHZ1608c4gX1FaOdR2nBD9UUIVxUN40atUu2xqhRX237wdqF\n58e8ska29Zc+Vd/TF4QV44OP0pydsj6fPW63zDdyK8b5Wf3IUW0uaPtR8c/S0/3qh52webZl\njX6erULtPEoLfqimCOGiOi0rWr3tB8U/vC2Tvrx6zxX295zRytHOozTrwqF9ewzY93dpB2O+\nk0sPUrZH249Kf5YmjhzQuNap/m2lYrTzKC34oZoihACEJoQAhCaEAIQmhACEJoQAhCaEAIQm\nhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQA\nhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQm\nhFBBXsqGpR4BwhFCSGxmVvJzIYQUhBASm5n1HFXwJyGEFIQQEpuZ9Zu3F0LInxBCYu2F8Ofb\nLrPURt95d6H9E9moiZ8dUPdQiimhdgkhJNZOCL+WDfzCSRtkO7y34P6JbOcV1jvsgCdSTQq1\nSQghsbnfI7ygZW4I78/WfL2lZfZe2bcX3D+RZcfOST0u1BwhhMTmPmt0j5a5ITw8u7LtJ8bX\nrbng/olsxenp5oRaJYSQ2Af/aXST7IXCj1bJ3lpg/0S2a4oBocYJIST2wRCunhWfJrN5awTf\nv38i+1yKAaHGCSEktjhfEY5KMB/UOiGExD4YwlHZVW0/mND2fcH374UQuoMQQmIfDOF92dpv\ntLTM3if71oJ7IYTuIISQWDuvI/xKNuhLX/t4tt2sBfdCCN1BCCGx9q4sc902fXtt+K2ZC+2F\nELqDEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQ\nmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQ\nAhCaEAIQmhACEJoQAhCaEAIQ2v8DETiTeUPib9gAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(Price~Floor, homes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in ggplot(modHomes, aes(x = Floor, y = Price, group = DHa, fill = DHa, : object 'modHomes' not found\n",
     "output_type": "error",
     "traceback": [
      "Error in ggplot(modHomes, aes(x = Floor, y = Price, group = DHa, fill = DHa, : object 'modHomes' not found\nTraceback:\n",
      "1. ggplot(modHomes, aes(x = Floor, y = Price, group = DHa, fill = DHa, \n .     colour = DHa))"
     ]
    }
   ],
   "source": [
    "lmHomes <- lm(Price~DHa+Floor+DHa*Floor, homes)\n",
    "\n",
    "predicted1 = predict(lmHomes, interval = \"confidence\")\n",
    "fortifyHomes1 = fortify(lmHomes)\n",
    "modHomes1 <- cbind(fortifyHomes1, predicted1)\n",
    "    \n",
    "ggplot(modHomes, aes(x=Floor, y=Price, group=DHa, fill=DHa, colour=DHa)) + \n",
    "    stat_smooth(aes(x=Floor, y=.fitted), se=FALSE) + \n",
    "    theme + points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "summary(lmHomes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**A P-Value of 0.91 on the Dha:Floor term confirms the visual interpretations that the slopes are the same for both neighbourhoods, therefor we can remove the interaction term.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "lmHomes2 <- lm(Price~DHa+Floor+DHa, homes)\n",
    "\n",
    "predicted2 = predict(lmHomes2, interval = \"confidence\")\n",
    "fortifyHomes2 = fortify(lmHomes2)\n",
    "modHomes2 <- cbind(fortifyHomes2, predicted2)\n",
    "    \n",
    "ggplot(modHomes2, aes(x=Floor, y=Price, group=DHa, fill=DHa, colour=DHa)) + \n",
    "    stat_smooth(aes(x=Floor, y=.fitted), se=FALSE) + \n",
    "    theme + points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "summary(lmHomes2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot(lmHomes2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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