Prediction of Earth Quake.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "df <- read.csv(\"shanghai26.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>time</th><th scope=col>mag.vec1</th><th scope=col>mag.vec2</th><th scope=col>mag.vec3</th><th scope=col>mag.vec4</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1977.000</td><td>3       </td><td>3.00    </td><td>3       </td><td>3       </td></tr>\n",
       "\t<tr><td>1977.038</td><td>3       </td><td>5.45    </td><td>3       </td><td>3       </td></tr>\n",
       "\t<tr><td>1977.077</td><td>3       </td><td>3.00    </td><td>3       </td><td>3       </td></tr>\n",
       "\t<tr><td>1977.115</td><td>3       </td><td>3.00    </td><td>3       </td><td>3       </td></tr>\n",
       "\t<tr><td>1977.154</td><td>3       </td><td>3.00    </td><td>3       </td><td>3       </td></tr>\n",
       "\t<tr><td>1977.192</td><td>3       </td><td>3.00    </td><td>3       </td><td>3       </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       " time & mag.vec1 & mag.vec2 & mag.vec3 & mag.vec4\\\\\n",
       "\\hline\n",
       "\t 1977.000 & 3        & 3.00     & 3        & 3       \\\\\n",
       "\t 1977.038 & 3        & 5.45     & 3        & 3       \\\\\n",
       "\t 1977.077 & 3        & 3.00     & 3        & 3       \\\\\n",
       "\t 1977.115 & 3        & 3.00     & 3        & 3       \\\\\n",
       "\t 1977.154 & 3        & 3.00     & 3        & 3       \\\\\n",
       "\t 1977.192 & 3        & 3.00     & 3        & 3       \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "time | mag.vec1 | mag.vec2 | mag.vec3 | mag.vec4 | \n",
       "|---|---|---|---|---|---|\n",
       "| 1977.000 | 3        | 3.00     | 3        | 3        | \n",
       "| 1977.038 | 3        | 5.45     | 3        | 3        | \n",
       "| 1977.077 | 3        | 3.00     | 3        | 3        | \n",
       "| 1977.115 | 3        | 3.00     | 3        | 3        | \n",
       "| 1977.154 | 3        | 3.00     | 3        | 3        | \n",
       "| 1977.192 | 3        | 3.00     | 3        | 3        | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  time     mag.vec1 mag.vec2 mag.vec3 mag.vec4\n",
       "1 1977.000 3        3.00     3        3       \n",
       "2 1977.038 3        5.45     3        3       \n",
       "3 1977.077 3        3.00     3        3       \n",
       "4 1977.115 3        3.00     3        3       \n",
       "5 1977.154 3        3.00     3        3       \n",
       "6 1977.192 3        3.00     3        3       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GnFjwZHkOZaLht8LUiNux2AdPmuXbpb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\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(df$time, df$mag.vec1, type = 'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qSwSiIkUSsjHNbG90gSthiFFD3p3oex9UFKpz95Ro/PBgFKDsnFsSlIfjlnh1FB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\nD0OSaWr6m7GoAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(df$time, df$mag.vec2, type = 'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Wtf5LUnJO8BRVoYUpcO06+HtB56uw+J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\nQgIMEBJggJAAA4QEGCAkwMA/DFQLEU31wYAAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(df$time, df$mag.vec3, type = 'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mjxr4eU7ix6qV4cREhLElp87i3S4XKf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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(df$time, df$mag.vec4, type = 'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Gmsi+gRJI11ET2CpLEuokeQNNZF9AiS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\nRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"density.default(x = df$mag.vec1)\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(density(df$mag.vec1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mFq18cku5UTJK+iVKZ3dUyzW3sCQVK88mOUpnh1zOCs7t8RJK8i1KZ5dcxicwHs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\nQABBAgQQJEAAQQIEECRAAEECBBAkQMD/ZTDrTE02xacAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"density.default(x = df$mag.vec2)\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(density(df$mag.vec2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3kfqYyy/xEhIfFqfLIBAoQEAfeFNB/X\n/+2T4ST9O0lC4sXcE9JyuP8diqHP2vFPuyOkVVUG8/o3zZcfg/o/pB8kJF7MHSFNOse8h/V/\nSf/2Ea4tVUi8mDtCGpTD/tzyR28kCYl3c0dIRznc8Fm7ciwyKyHxHHoM6bMSEu+qx5DWq9H2\n6N7FK99c2aW5XD8THqnPkOq/kFk+brmykHgxd4X0843IclhGq1xIl68nJHrXc0j136+o5kLi\n3fT/WbvF4Hp1QuLF/MWHVsdC4t289qe/hcSTEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQI\nCQKEBAFCggAhQYCQIEBIECAkCBASBAgJAt4xJCXRu5cO6aurCYm+CQkChAQBQoIAIUGAkCBA\nSBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIE\nCAkChAQBQoIAIUGAkCBASBAgJAgQEgS8ckhfXktI9E1IECAkCBASBAgJAoQEAUKCACFBgJAg\nQEgQ8JYhKYm+CQkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBAS\nBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCDghUP67kpKol9CggAhQYCQ\nIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoKANw1JSfRLSBAgJAgQ\nEgQICQKEBAFCggAhQYCQIKDPkFbjUobz7SD3ZyAknkePIa2qUhu1gwiJd9JjSJMy29Q0q4bN\nIELinfQYUtXecFkNlkLizfQY0q6d1XB4KaTSdfc8hESvegxpUFa7U0NbJN5LjyHNynh7almG\nQuKt9Hn4e7KvZ35l701IvJhe35BdjHanluO7M/j+OkKiV6/7yQYh8USEBAFCggAhQYCQIEBI\nEPCuISmJXgkJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAh42ZCu\nXUVI9ElIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkC3jYkJdGnVw0pcQ2IERIE\nCAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCHjRkBK/Qgs5QoIA\nIUGAkCBASBDwviEpiR4JCQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAg4DVD\num0KSqI3QoIAIUGAkCBASBAgJAgQEgQICQLeOSQl0RshQYCQIEBIECAkCBASBAgJAl4ypFtn\nICT6IiQIEBIECAkC3jokJdEXIUGAkCBASBAgJAh4xZBun4CQ6ImQIEBIECAkCBASBLxgSD9Z\nvpLoh5AgQEgQICQIEBIECAkCXi+kHy1eSPRDSBDw5iEpiX4ICQKEBAFCgoCXC+mnS1cSfRAS\nBLx9SEqiD68W0s8XLiR6ICQIeLGQfrNsJfF4QoKAFwvpzweDi3oN6XM6KrXR5PNRi3j8aHBB\njyGtBuVg+JBF9DEaXNBjSJNSfSyaU8t5VSaPWEQ/w8GZHkOqymJ/elGqRyziy/GKll5T+dot\nN/39Mn98o18s5+c3aW9Xvvphe87Bf/Bi+gvpD7dI8GD9vkaaL5tTfb9Ggkfr8/D3sLPzNlg9\nZBHwN/p9H2nSvI9Ujaa9vo8ED/cPfLIBHk9IECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQI\nEBIECAkChAQBQoIAIUGAkCBASBDwpCHBi/nFWp4PJ+DBszK84d9mwd967Ufb8G87/BMu+Fuv\n/Wgb/m2Hf8IFf+u1H23Dv+3wT7jgb732o234tx3+CRf8rdd+tA3/tsM/4YK/9dqPtuHfdvgn\nXPC3XvvRNvzbDv+EC/7Waz/ahn/b4Z9wwd967Ufb8G87/BMu+Fuv/Wgb/m2Hf8IFf+u1H23D\nv+3wT7hgeCdCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkCniek\n1biU8aJ7zqQq1WT1qOF//Z9L/9Ln0WDR2Z8Nn539+WjR2Z8NH37sF/W/7bJzRvyxv+55Qqqa\nx7azqg+bMwYPGn4RD2lVdQfLzv50+Ozsz0eLzv5s+PBjP28Gqw7hxB/7GzxNSJMyrr+M9md8\nlmqxXlTl8zHDLzqnM0bdNSM7+7Phs7M/Gy07+7Phw499tZnsalQmu5/zj/0NniakqtTPKJ2V\nZVLmm68fZfqY4Wehgfc+jp5is7M/Gz47+7PRsrM/Gz47+48moVWpdmfEH/tbPE1IrcOjsXkG\nrvd6s09eneFnZRYceL1elmF3TU/P/mT47OzPRsvO/mz47OzHZXF8xiPWnKueK6RJ5xHerjfJ\nVzHd4UdlPt68Io2NPSzL45fT3W/x4bOzPxstO/uz4bOzH5T1tCrjw0ukB6w51z1TSJu9l4f9\nY54NP2pf7w5Dg0/Lx/qBIZ0On5392WjpkE6Gz86+lGa8qnNG91tPnimk2ajq7NfGH47T4T82\nO9aT0E5Gsx/xuJAuDJ+c/dlo2dlfGD47+/pgw/jwb/vPh7Su93cf9I95NnxrFTpIOqgPvj4u\npLPhW6nZn432iMf+bLKp2bdvaiwfO/vrs+hzYdd1jr1UD/nHrE7OyQw/bo4TdceKzv58+K3s\nunIY7RGP/flosQ3eyWgPmf3VWfS5sBsc7n177GWZPfbyoH/M878rH539l3+2/lFr+is99pvJ\nnoz2kNlf8zQhtW/0dDbQ0+ZpeF4yB3fOht+d8aA1PTr78+Gjsz8f7TGP/ejLM+7STnZ5OHaR\nnf2Nniak5qMHq9HhRcwDPtnQHX5SP86r9r27kMd+suFo+Ozsz0ZLP/Ynw2dnv3l2XNUHGz52\nZ/zbn2zYfhiueVppV5lB9Pj06fCr9ozks9bRznp29qfDZ2ffHe0Bsz8bPvzYTx+75tzmeUKq\nP7I7aDcY7cOxaj7D+9DhB9FPNxyFFJ79peFzs1899rG/OHzwsZ8Pd5N91GN/3ROFBK9LSBAg\nJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkC\nhAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIv1R2fwH127/N3f7tuFVzclzK\neNGePRvszr00cPN3G6/+AdQLy+2c1ZycX53f1mGWF8/4PAyxPbk6u8W/Tki/VEq1O/H1lZbt\nH0ut6j9X355sSpq0515eD3d/wHxxdQLfnVWfHJRr89saNgscfHXGqtoPsT3ZvV80hPRLm/Vo\nuj3x9ZXGzR8cbv6i+vbLaPPzoow3Dc3qMy4OvG5uc+1vCX8fSH1puTGks78CfnLG6DDE9mTn\nftES0i9tnrDLsj3x3ZX236qy2p0x6v5V5e9uc2UC1y69NaRJs5f6sX1iODvjo+yH2J28dY7/\nEA/FL232vZrNy7dr03afaLcX2D11NaTmmvPNJqD9+9ylLEelalftzQuUyeaMz3aLMG9frY03\nP5fOpe0+YjPeZHfDy0bNM8L27pydsSzD3Uz3J8/uF0L6pc0aNW72fQ49lL3dOdPtLtBuNZ6U\n2X6A1Rc7b7tdu1lz+8akObt5XVKP1LyCqXeyqs5+Vr1WNzfdX7oPaVSfmB3GP53l2fbl6Ixh\nWe4u2Z88vV8I6bc2a9SqeTn+XUjrWb32V9uV+KNNYnfR7rDf2cD7eDanP5qbNSeHq81tBvXP\n7SuYslmfP9a7wx71jlh9xcOl+1273Q2/muW3IdXL2P7cOXl0v1gL6dfqNWpWP89/+0Kh3aRs\nn7hno+rwHL6sRpdvsl3Lh4vOOc2X3eZv1Jyab04u643a52aLs2i2FieX7kM63m5evivrL0Jq\n9u/anzsnj+8XayH9WrNGDcrq21V0Vm9YVuPDftX+5Kr66qhcO958e8xsOZ8OtyHtLuys5sPN\n8iebF2vTtqmTS7sHBn4b0qA+SN/+3Dl5dr8Q0i81a1T9cv+7XbtBc6huddivWu1enw8779pc\nGLh+/q9LG+7HuxjSfJNQNVgPBu1e3k0hnc+yOg3pcMa42f9sLumcPL9fCOmX2jVqs1f13Sp6\nfpi4PbkcDL98L3N35fr7uAxm8+XXIa3L4HOzcZiUVbNq/zKk9iDd8vSoXX1G58rd2zn8fcZD\n8UvbIsrg+uHvZjPUvo+0bJ7E59+927odr7lRc/o0pFGzaWiPdU9KvaGYb76Ozy+9dddu2txk\nfjgScjjji5A694uWkH6p86r76ytNSv15tEm9ijYfA1iN6pcVy28/tdCOtxrWN6oPFCxOXyPN\nD8fl6mDaTdF+v2vePWq3XN8S0rVPNpxvUTv3i5aQfmm3clXf7t+0r3GG2ytuT47PjpIfD9yq\nVrsP5TXH3To9NO8LjXevVgbNYqoLlw7Kfqv2/V7Y4DDL3aj7M05uvD05PL4CQvqt3co1//6F\nQvMp6f3Jway96fWQth+tHtefA58fjju3X6fbzy6sd2+NTndvOx1d+jm4MaTVYZbb7WFn2utL\nIa2Pr4CQIEFIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBA\nSBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCgP8BTCj/lJdTLOkAAAAA\nSUVORK5CYII=",
      "text/plain": [
       "Plot with title \"density.default(x = df$mag.vec3)\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(density(df$mag.vec3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3H7NYVE5+7etHOwAYQEEe/4gqyS6JyQ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",
      "text/plain": [
       "Plot with title \"density.default(x = df$mag.vec4)\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(density(df$mag.vec4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "magnitude 3 & 4 seems too be of no use as values are mostly around 3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Proportion of values less than 3.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "i1 <- df$mag.vec1<= 3.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "i1_flag <- 1*i1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.640625"
      ],
      "text/latex": [
       "0.640625"
      ],
      "text/markdown": [
       "0.640625"
      ],
      "text/plain": [
       "[1] 0.640625"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(i1_flag)/length(i1_flag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "i2 <- df$mag.vec2<= 3.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "i2_flag <- 1*i2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.673076923076923"
      ],
      "text/latex": [
       "0.673076923076923"
      ],
      "text/markdown": [
       "0.673076923076923"
      ],
      "text/plain": [
       "[1] 0.6730769"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(i2_flag)/length(i2_flag)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us consider only the data points with magnitude greater than 3.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "f1 <- df$mag.vec1 >3.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>6.65</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>6.8</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>6</li>\n",
       "\t<li>6</li>\n",
       "\t<li>5.55</li>\n",
       "\t<li>7.2</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>7</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.45</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>6.4</li>\n",
       "\t<li>6</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>6.233333333</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.55</li>\n",
       "\t<li>6.233333333</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.85</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>6.05</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>6</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.54</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>6.35</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>6.2</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.85</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>6.6</li>\n",
       "\t<li>6.2</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>6</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>6.35</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>6.1</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.944444444</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.45</li>\n",
       "\t<li>5.566666667</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.35</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.533333333</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.75</li>\n",
       "\t<li>6.25</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>6.75</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>6.05</li>\n",
       "\t<li>6.085714286</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>6.05</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>6.2</li>\n",
       "\t<li>5.45</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.666666667</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>6.091666667</li>\n",
       "\t<li>5.566666667</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>6.133333333</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>4.6</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.35</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>6.05</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>6.2</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.35</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>6.1</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.75</li>\n",
       "\t<li>5.133333333</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.85</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.333333333</li>\n",
       "\t<li>6.3</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.45</li>\n",
       "\t<li>6.4</li>\n",
       "\t<li>5.55</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.575</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.566666667</li>\n",
       "\t<li>5.25</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.666666667</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>6.425</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.65</li>\n",
       "\t<li>6.4</li>\n",
       "\t<li>6.5</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.375</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.25</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.45</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.666666667</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.45</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>6.8</li>\n",
       "\t<li>5.325</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.333333333</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.65</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.433333333</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.033333333</li>\n",
       "\t<li>4.8</li>\n",
       "\t<li>5.75</li>\n",
       "\t<li>4.95</li>\n",
       "\t<li>4.7</li>\n",
       "\t<li>6.4</li>\n",
       "\t<li>4.7</li>\n",
       "\t<li>5.171428571</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>4.8</li>\n",
       "\t<li>4.8</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>5.45</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>4.8</li>\n",
       "\t<li>4.966666667</li>\n",
       "\t<li>4.8</li>\n",
       "\t<li>5.85</li>\n",
       "\t<li>5.45</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>5.866666667</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>5.433333333</li>\n",
       "\t<li>5.55</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.730769231</li>\n",
       "\t<li>5.45</li>\n",
       "\t<li>4.8</li>\n",
       "\t<li>4.8</li>\n",
       "\t<li>5.557142857</li>\n",
       "\t<li>5.15</li>\n",
       "\t<li>6.2</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.233333333</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.15</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>4.8</li>\n",
       "\t<li>5.616666667</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 6.65\n",
       "\\item 5.8\n",
       "\\item 5.8\n",
       "\\item 6.8\n",
       "\\item 5.5\n",
       "\\item 6\n",
       "\\item 6\n",
       "\\item 5.55\n",
       "\\item 7.2\n",
       "\\item 5.4\n",
       "\\item 5.2\n",
       "\\item 5.2\n",
       "\\item 7\n",
       "\\item 5.4\n",
       "\\item 5.3\n",
       "\\item 5.8\n",
       "\\item 5.9\n",
       "\\item 5.5\n",
       "\\item 5.9\n",
       "\\item 5.5\n",
       "\\item 5.8\n",
       "\\item 5.9\n",
       "\\item 5.6\n",
       "\\item 5.45\n",
       "\\item 5.8\n",
       "\\item 5.5\n",
       "\\item 5.2\n",
       "\\item 5.2\n",
       "\\item 6.4\n",
       "\\item 6\n",
       "\\item 5.9\n",
       "\\item 5.4\n",
       "\\item 5.8\n",
       "\\item 6.233333333\n",
       "\\item 5.9\n",
       "\\item 5.55\n",
       "\\item 6.233333333\n",
       "\\item 5.1\n",
       "\\item 5.2\n",
       "\\item 5.6\n",
       "\\item 5.3\n",
       "\\item 5.9\n",
       "\\item 5.2\n",
       "\\item 5.6\n",
       "\\item 5.85\n",
       "\\item 5.5\n",
       "\\item 5.7\n",
       "\\item 5.2\n",
       "\\item 5.5\n",
       "\\item 5.3\n",
       "\\item 5.3\n",
       "\\item 6.05\n",
       "\\item 5.2\n",
       "\\item 5.2\n",
       "\\item 5.5\n",
       "\\item 5.4\n",
       "\\item 5.2\n",
       "\\item 5.7\n",
       "\\item 6\n",
       "\\item 5.8\n",
       "\\item 5.54\n",
       "\\item 5.6\n",
       "\\item 5.4\n",
       "\\item 5.3\n",
       "\\item 5.8\n",
       "\\item 5.2\n",
       "\\item 5.3\n",
       "\\item 6.35\n",
       "\\item 5.8\n",
       "\\item 5.6\n",
       "\\item 5.2\n",
       "\\item 5.2\n",
       "\\item 6.2\n",
       "\\item 5.7\n",
       "\\item 5.2\n",
       "\\item 5.1\n",
       "\\item 5.6\n",
       "\\item 5.6\n",
       "\\item 5.9\n",
       "\\item 5\n",
       "\\item 5.2\n",
       "\\item 5.1\n",
       "\\item 5.85\n",
       "\\item 5.3\n",
       "\\item 5.3\n",
       "\\item 5.4\n",
       "\\item 5.1\n",
       "\\item 6.6\n",
       "\\item 6.2\n",
       "\\item 5.3\n",
       "\\item 5.2\n",
       "\\item 5.8\n",
       "\\item 6\n",
       "\\item 5.4\n",
       "\\item 6.35\n",
       "\\item 5.4\n",
       "\\item 6.1\n",
       "\\item 5.1\n",
       "\\item 5.5\n",
       "\\item 5.944444444\n",
       "\\item 5.9\n",
       "\\item 5.45\n",
       "\\item 5.566666667\n",
       "\\item 5.4\n",
       "\\item 5.4\n",
       "\\item 5.35\n",
       "\\item 5.9\n",
       "\\item 5.6\n",
       "\\item 5.533333333\n",
       "\\item 5.3\n",
       "\\item 5.75\n",
       "\\item 6.25\n",
       "\\item 5.2\n",
       "\\item 5.7\n",
       "\\item 5.3\n",
       "\\item 5.5\n",
       "\\item 5.5\n",
       "\\item 6.75\n",
       "\\item 5.3\n",
       "\\item 5.4\n",
       "\\item 5.5\n",
       "\\item 5.5\n",
       "\\item 6.05\n",
       "\\item 6.085714286\n",
       "\\item 5.6\n",
       "\\item 5.7\n",
       "\\item 6.05\n",
       "\\item 5.2\n",
       "\\item 5.2\n",
       "\\item 5.2\n",
       "\\item 5.3\n",
       "\\item 5.6\n",
       "\\item 6.2\n",
       "\\item 5.45\n",
       "\\item 5.2\n",
       "\\item 5\n",
       "\\item 5.7\n",
       "\\item 5.666666667\n",
       "\\item 5.3\n",
       "\\item 5.5\n",
       "\\item 6.091666667\n",
       "\\item 5.566666667\n",
       "\\item 5.2\n",
       "\\item 5.1\n",
       "\\item 6.133333333\n",
       "\\item 5.7\n",
       "\\item 5.2\n",
       "\\item 5.4\n",
       "\\item 4.6\n",
       "\\item 5.7\n",
       "\\item 5.35\n",
       "\\item 5.6\n",
       "\\item 6.05\n",
       "\\item 5.6\n",
       "\\item 5.9\n",
       "\\item 5.2\n",
       "\\item 5.2\n",
       "\\item 6.2\n",
       "\\item 5.4\n",
       "\\item 5.1\n",
       "\\item 5.5\n",
       "\\item 5.35\n",
       "\\item 5.1\n",
       "\\item 5.5\n",
       "\\item 5.1\n",
       "\\item 6.1\n",
       "\\item 5.4\n",
       "\\item 5.75\n",
       "\\item 5.133333333\n",
       "\\item 5.5\n",
       "\\item 5.2\n",
       "\\item 5.3\n",
       "\\item 5.2\n",
       "\\item 5.85\n",
       "\\item 5.6\n",
       "\\item 5.5\n",
       "\\item 5.4\n",
       "\\item 5.8\n",
       "\\item 5.1\n",
       "\\item 5.333333333\n",
       "\\item 6.3\n",
       "\\item 5.9\n",
       "\\item 5.9\n",
       "\\item 5.45\n",
       "\\item 6.4\n",
       "\\item 5.55\n",
       "\\item 5.3\n",
       "\\item 5.2\n",
       "\\item 5.575\n",
       "\\item 5.7\n",
       "\\item 5.4\n",
       "\\item 5.566666667\n",
       "\\item 5.25\n",
       "\\item 5.5\n",
       "\\item 5.1\n",
       "\\item 5.666666667\n",
       "\\item 5.1\n",
       "\\item 5.3\n",
       "\\item 5\n",
       "\\item 5.1\n",
       "\\item 5.6\n",
       "\\item 6.425\n",
       "\\item 4.9\n",
       "\\item 5.4\n",
       "\\item 5.65\n",
       "\\item 6.4\n",
       "\\item 6.5\n",
       "\\item 5\n",
       "\\item 5.2\n",
       "\\item 5.7\n",
       "\\item 5.1\n",
       "\\item 5.375\n",
       "\\item 5.2\n",
       "\\item 5.1\n",
       "\\item 5.4\n",
       "\\item 5.1\n",
       "\\item 5.25\n",
       "\\item 5.1\n",
       "\\item 5.45\n",
       "\\item 4.9\n",
       "\\item 5.2\n",
       "\\item 5.666666667\n",
       "\\item 5.5\n",
       "\\item 5.2\n",
       "\\item 5.45\n",
       "\\item 5.7\n",
       "\\item 5.2\n",
       "\\item 6.8\n",
       "\\item 5.325\n",
       "\\item 5.4\n",
       "\\item 5\n",
       "\\item 5.3\n",
       "\\item 5.333333333\n",
       "\\item 5.2\n",
       "\\item 5.2\n",
       "\\item 5.3\n",
       "\\item 5.3\n",
       "\\item 5.1\n",
       "\\item 5.65\n",
       "\\item 4.9\n",
       "\\item 5.1\n",
       "\\item 5.6\n",
       "\\item 5\n",
       "\\item 5.4\n",
       "\\item 5.433333333\n",
       "\\item 5.3\n",
       "\\item 5.033333333\n",
       "\\item 4.8\n",
       "\\item 5.75\n",
       "\\item 4.95\n",
       "\\item 4.7\n",
       "\\item 6.4\n",
       "\\item 4.7\n",
       "\\item 5.171428571\n",
       "\\item 4.9\n",
       "\\item 4.8\n",
       "\\item 4.8\n",
       "\\item 4.9\n",
       "\\item 5.45\n",
       "\\item 5.2\n",
       "\\item 4.9\n",
       "\\item 4.8\n",
       "\\item 4.966666667\n",
       "\\item 4.8\n",
       "\\item 5.85\n",
       "\\item 5.45\n",
       "\\item 5.4\n",
       "\\item 5.5\n",
       "\\item 5.7\n",
       "\\item 4.9\n",
       "\\item 5.866666667\n",
       "\\item 4.9\n",
       "\\item 5.433333333\n",
       "\\item 5.55\n",
       "\\item 5.6\n",
       "\\item 5.3\n",
       "\\item 5.1\n",
       "\\item 5.730769231\n",
       "\\item 5.45\n",
       "\\item 4.8\n",
       "\\item 4.8\n",
       "\\item 5.557142857\n",
       "\\item 5.15\n",
       "\\item 6.2\n",
       "\\item 5.1\n",
       "\\item 5.233333333\n",
       "\\item 4.9\n",
       "\\item 5.1\n",
       "\\item 5.3\n",
       "\\item 4.9\n",
       "\\item 5\n",
       "\\item 5.15\n",
       "\\item 5.4\n",
       "\\item 4.8\n",
       "\\item 5.616666667\n",
       "\\item 5.2\n",
       "\\item 5.3\n",
       "\\item 5.2\n",
       "\\item 5.2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 6.65\n",
       "2. 5.8\n",
       "3. 5.8\n",
       "4. 6.8\n",
       "5. 5.5\n",
       "6. 6\n",
       "7. 6\n",
       "8. 5.55\n",
       "9. 7.2\n",
       "10. 5.4\n",
       "11. 5.2\n",
       "12. 5.2\n",
       "13. 7\n",
       "14. 5.4\n",
       "15. 5.3\n",
       "16. 5.8\n",
       "17. 5.9\n",
       "18. 5.5\n",
       "19. 5.9\n",
       "20. 5.5\n",
       "21. 5.8\n",
       "22. 5.9\n",
       "23. 5.6\n",
       "24. 5.45\n",
       "25. 5.8\n",
       "26. 5.5\n",
       "27. 5.2\n",
       "28. 5.2\n",
       "29. 6.4\n",
       "30. 6\n",
       "31. 5.9\n",
       "32. 5.4\n",
       "33. 5.8\n",
       "34. 6.233333333\n",
       "35. 5.9\n",
       "36. 5.55\n",
       "37. 6.233333333\n",
       "38. 5.1\n",
       "39. 5.2\n",
       "40. 5.6\n",
       "41. 5.3\n",
       "42. 5.9\n",
       "43. 5.2\n",
       "44. 5.6\n",
       "45. 5.85\n",
       "46. 5.5\n",
       "47. 5.7\n",
       "48. 5.2\n",
       "49. 5.5\n",
       "50. 5.3\n",
       "51. 5.3\n",
       "52. 6.05\n",
       "53. 5.2\n",
       "54. 5.2\n",
       "55. 5.5\n",
       "56. 5.4\n",
       "57. 5.2\n",
       "58. 5.7\n",
       "59. 6\n",
       "60. 5.8\n",
       "61. 5.54\n",
       "62. 5.6\n",
       "63. 5.4\n",
       "64. 5.3\n",
       "65. 5.8\n",
       "66. 5.2\n",
       "67. 5.3\n",
       "68. 6.35\n",
       "69. 5.8\n",
       "70. 5.6\n",
       "71. 5.2\n",
       "72. 5.2\n",
       "73. 6.2\n",
       "74. 5.7\n",
       "75. 5.2\n",
       "76. 5.1\n",
       "77. 5.6\n",
       "78. 5.6\n",
       "79. 5.9\n",
       "80. 5\n",
       "81. 5.2\n",
       "82. 5.1\n",
       "83. 5.85\n",
       "84. 5.3\n",
       "85. 5.3\n",
       "86. 5.4\n",
       "87. 5.1\n",
       "88. 6.6\n",
       "89. 6.2\n",
       "90. 5.3\n",
       "91. 5.2\n",
       "92. 5.8\n",
       "93. 6\n",
       "94. 5.4\n",
       "95. 6.35\n",
       "96. 5.4\n",
       "97. 6.1\n",
       "98. 5.1\n",
       "99. 5.5\n",
       "100. 5.944444444\n",
       "101. 5.9\n",
       "102. 5.45\n",
       "103. 5.566666667\n",
       "104. 5.4\n",
       "105. 5.4\n",
       "106. 5.35\n",
       "107. 5.9\n",
       "108. 5.6\n",
       "109. 5.533333333\n",
       "110. 5.3\n",
       "111. 5.75\n",
       "112. 6.25\n",
       "113. 5.2\n",
       "114. 5.7\n",
       "115. 5.3\n",
       "116. 5.5\n",
       "117. 5.5\n",
       "118. 6.75\n",
       "119. 5.3\n",
       "120. 5.4\n",
       "121. 5.5\n",
       "122. 5.5\n",
       "123. 6.05\n",
       "124. 6.085714286\n",
       "125. 5.6\n",
       "126. 5.7\n",
       "127. 6.05\n",
       "128. 5.2\n",
       "129. 5.2\n",
       "130. 5.2\n",
       "131. 5.3\n",
       "132. 5.6\n",
       "133. 6.2\n",
       "134. 5.45\n",
       "135. 5.2\n",
       "136. 5\n",
       "137. 5.7\n",
       "138. 5.666666667\n",
       "139. 5.3\n",
       "140. 5.5\n",
       "141. 6.091666667\n",
       "142. 5.566666667\n",
       "143. 5.2\n",
       "144. 5.1\n",
       "145. 6.133333333\n",
       "146. 5.7\n",
       "147. 5.2\n",
       "148. 5.4\n",
       "149. 4.6\n",
       "150. 5.7\n",
       "151. 5.35\n",
       "152. 5.6\n",
       "153. 6.05\n",
       "154. 5.6\n",
       "155. 5.9\n",
       "156. 5.2\n",
       "157. 5.2\n",
       "158. 6.2\n",
       "159. 5.4\n",
       "160. 5.1\n",
       "161. 5.5\n",
       "162. 5.35\n",
       "163. 5.1\n",
       "164. 5.5\n",
       "165. 5.1\n",
       "166. 6.1\n",
       "167. 5.4\n",
       "168. 5.75\n",
       "169. 5.133333333\n",
       "170. 5.5\n",
       "171. 5.2\n",
       "172. 5.3\n",
       "173. 5.2\n",
       "174. 5.85\n",
       "175. 5.6\n",
       "176. 5.5\n",
       "177. 5.4\n",
       "178. 5.8\n",
       "179. 5.1\n",
       "180. 5.333333333\n",
       "181. 6.3\n",
       "182. 5.9\n",
       "183. 5.9\n",
       "184. 5.45\n",
       "185. 6.4\n",
       "186. 5.55\n",
       "187. 5.3\n",
       "188. 5.2\n",
       "189. 5.575\n",
       "190. 5.7\n",
       "191. 5.4\n",
       "192. 5.566666667\n",
       "193. 5.25\n",
       "194. 5.5\n",
       "195. 5.1\n",
       "196. 5.666666667\n",
       "197. 5.1\n",
       "198. 5.3\n",
       "199. 5\n",
       "200. 5.1\n",
       "201. 5.6\n",
       "202. 6.425\n",
       "203. 4.9\n",
       "204. 5.4\n",
       "205. 5.65\n",
       "206. 6.4\n",
       "207. 6.5\n",
       "208. 5\n",
       "209. 5.2\n",
       "210. 5.7\n",
       "211. 5.1\n",
       "212. 5.375\n",
       "213. 5.2\n",
       "214. 5.1\n",
       "215. 5.4\n",
       "216. 5.1\n",
       "217. 5.25\n",
       "218. 5.1\n",
       "219. 5.45\n",
       "220. 4.9\n",
       "221. 5.2\n",
       "222. 5.666666667\n",
       "223. 5.5\n",
       "224. 5.2\n",
       "225. 5.45\n",
       "226. 5.7\n",
       "227. 5.2\n",
       "228. 6.8\n",
       "229. 5.325\n",
       "230. 5.4\n",
       "231. 5\n",
       "232. 5.3\n",
       "233. 5.333333333\n",
       "234. 5.2\n",
       "235. 5.2\n",
       "236. 5.3\n",
       "237. 5.3\n",
       "238. 5.1\n",
       "239. 5.65\n",
       "240. 4.9\n",
       "241. 5.1\n",
       "242. 5.6\n",
       "243. 5\n",
       "244. 5.4\n",
       "245. 5.433333333\n",
       "246. 5.3\n",
       "247. 5.033333333\n",
       "248. 4.8\n",
       "249. 5.75\n",
       "250. 4.95\n",
       "251. 4.7\n",
       "252. 6.4\n",
       "253. 4.7\n",
       "254. 5.171428571\n",
       "255. 4.9\n",
       "256. 4.8\n",
       "257. 4.8\n",
       "258. 4.9\n",
       "259. 5.45\n",
       "260. 5.2\n",
       "261. 4.9\n",
       "262. 4.8\n",
       "263. 4.966666667\n",
       "264. 4.8\n",
       "265. 5.85\n",
       "266. 5.45\n",
       "267. 5.4\n",
       "268. 5.5\n",
       "269. 5.7\n",
       "270. 4.9\n",
       "271. 5.866666667\n",
       "272. 4.9\n",
       "273. 5.433333333\n",
       "274. 5.55\n",
       "275. 5.6\n",
       "276. 5.3\n",
       "277. 5.1\n",
       "278. 5.730769231\n",
       "279. 5.45\n",
       "280. 4.8\n",
       "281. 4.8\n",
       "282. 5.557142857\n",
       "283. 5.15\n",
       "284. 6.2\n",
       "285. 5.1\n",
       "286. 5.233333333\n",
       "287. 4.9\n",
       "288. 5.1\n",
       "289. 5.3\n",
       "290. 4.9\n",
       "291. 5\n",
       "292. 5.15\n",
       "293. 5.4\n",
       "294. 4.8\n",
       "295. 5.616666667\n",
       "296. 5.2\n",
       "297. 5.3\n",
       "298. 5.2\n",
       "299. 5.2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  [1] 6.650000 5.800000 5.800000 6.800000 5.500000 6.000000 6.000000 5.550000\n",
       "  [9] 7.200000 5.400000 5.200000 5.200000 7.000000 5.400000 5.300000 5.800000\n",
       " [17] 5.900000 5.500000 5.900000 5.500000 5.800000 5.900000 5.600000 5.450000\n",
       " [25] 5.800000 5.500000 5.200000 5.200000 6.400000 6.000000 5.900000 5.400000\n",
       " [33] 5.800000 6.233333 5.900000 5.550000 6.233333 5.100000 5.200000 5.600000\n",
       " [41] 5.300000 5.900000 5.200000 5.600000 5.850000 5.500000 5.700000 5.200000\n",
       " [49] 5.500000 5.300000 5.300000 6.050000 5.200000 5.200000 5.500000 5.400000\n",
       " [57] 5.200000 5.700000 6.000000 5.800000 5.540000 5.600000 5.400000 5.300000\n",
       " [65] 5.800000 5.200000 5.300000 6.350000 5.800000 5.600000 5.200000 5.200000\n",
       " [73] 6.200000 5.700000 5.200000 5.100000 5.600000 5.600000 5.900000 5.000000\n",
       " [81] 5.200000 5.100000 5.850000 5.300000 5.300000 5.400000 5.100000 6.600000\n",
       " [89] 6.200000 5.300000 5.200000 5.800000 6.000000 5.400000 6.350000 5.400000\n",
       " [97] 6.100000 5.100000 5.500000 5.944444 5.900000 5.450000 5.566667 5.400000\n",
       "[105] 5.400000 5.350000 5.900000 5.600000 5.533333 5.300000 5.750000 6.250000\n",
       "[113] 5.200000 5.700000 5.300000 5.500000 5.500000 6.750000 5.300000 5.400000\n",
       "[121] 5.500000 5.500000 6.050000 6.085714 5.600000 5.700000 6.050000 5.200000\n",
       "[129] 5.200000 5.200000 5.300000 5.600000 6.200000 5.450000 5.200000 5.000000\n",
       "[137] 5.700000 5.666667 5.300000 5.500000 6.091667 5.566667 5.200000 5.100000\n",
       "[145] 6.133333 5.700000 5.200000 5.400000 4.600000 5.700000 5.350000 5.600000\n",
       "[153] 6.050000 5.600000 5.900000 5.200000 5.200000 6.200000 5.400000 5.100000\n",
       "[161] 5.500000 5.350000 5.100000 5.500000 5.100000 6.100000 5.400000 5.750000\n",
       "[169] 5.133333 5.500000 5.200000 5.300000 5.200000 5.850000 5.600000 5.500000\n",
       "[177] 5.400000 5.800000 5.100000 5.333333 6.300000 5.900000 5.900000 5.450000\n",
       "[185] 6.400000 5.550000 5.300000 5.200000 5.575000 5.700000 5.400000 5.566667\n",
       "[193] 5.250000 5.500000 5.100000 5.666667 5.100000 5.300000 5.000000 5.100000\n",
       "[201] 5.600000 6.425000 4.900000 5.400000 5.650000 6.400000 6.500000 5.000000\n",
       "[209] 5.200000 5.700000 5.100000 5.375000 5.200000 5.100000 5.400000 5.100000\n",
       "[217] 5.250000 5.100000 5.450000 4.900000 5.200000 5.666667 5.500000 5.200000\n",
       "[225] 5.450000 5.700000 5.200000 6.800000 5.325000 5.400000 5.000000 5.300000\n",
       "[233] 5.333333 5.200000 5.200000 5.300000 5.300000 5.100000 5.650000 4.900000\n",
       "[241] 5.100000 5.600000 5.000000 5.400000 5.433333 5.300000 5.033333 4.800000\n",
       "[249] 5.750000 4.950000 4.700000 6.400000 4.700000 5.171429 4.900000 4.800000\n",
       "[257] 4.800000 4.900000 5.450000 5.200000 4.900000 4.800000 4.966667 4.800000\n",
       "[265] 5.850000 5.450000 5.400000 5.500000 5.700000 4.900000 5.866667 4.900000\n",
       "[273] 5.433333 5.550000 5.600000 5.300000 5.100000 5.730769 5.450000 4.800000\n",
       "[281] 4.800000 5.557143 5.150000 6.200000 5.100000 5.233333 4.900000 5.100000\n",
       "[289] 5.300000 4.900000 5.000000 5.150000 5.400000 4.800000 5.616667 5.200000\n",
       "[297] 5.300000 5.200000 5.200000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mag1 <- df$mag.vec1[f1]\n",
    "mag1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "f2 <- df$mag.vec2 >3.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>5.45</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>6.1</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.933333333</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>6.7</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>6</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>6</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>6.4</li>\n",
       "\t<li>6.5</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.75</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>6.45</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.875</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>6.6</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>6.6</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.85</li>\n",
       "\t<li>5.633333333</li>\n",
       "\t<li>6.2</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>6</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>6.8</li>\n",
       "\t<li>6.05</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.15</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.25</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.9</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.666666667</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>6.4</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>6.1</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.55</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>6.4</li>\n",
       "\t<li>6.1</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>6.15</li>\n",
       "\t<li>6.1</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>6.4</li>\n",
       "\t<li>5.35</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.75</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>6</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.05</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>6</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.55</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>6.575</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.25</li>\n",
       "\t<li>5.966666667</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>6.25</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.95</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>5.65</li>\n",
       "\t<li>6.090909091</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.533333333</li>\n",
       "\t<li>5.533333333</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>6.042857143</li>\n",
       "\t<li>5.64</li>\n",
       "\t<li>5.8</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.45</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.65</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.35</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.433333333</li>\n",
       "\t<li>5.133333333</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>6.4</li>\n",
       "\t<li>5.82</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.55</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>5.64</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.66</li>\n",
       "\t<li>4.85</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5</li>\n",
       "\t<li>6</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.4</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>4.7</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>5.7</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5.333333333</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.275</li>\n",
       "\t<li>4.85</li>\n",
       "\t<li>4.7</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>5.433333333</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>6.525</li>\n",
       "\t<li>6</li>\n",
       "\t<li>4.85</li>\n",
       "\t<li>5.25</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.1</li>\n",
       "\t<li>5.05</li>\n",
       "\t<li>5.3</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.65</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.666666667</li>\n",
       "\t<li>5.4125</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.32</li>\n",
       "\t<li>5.2</li>\n",
       "\t<li>5.6</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>5.525</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5.5</li>\n",
       "\t<li>4.9</li>\n",
       "\t<li>5</li>\n",
       "\t<li>5</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 5.45\n",
       "\\item 5.8\n",
       "\\item 5.5\n",
       "\\item 6.1\n",
       "\\item 5.8\n",
       "\\item 5.9\n",
       "\\item 5.6\n",
       "\\item 5.4\n",
       "\\item 5.933333333\n",
       "\\item 5.6\n",
       "\\item 6.7\n",
       "\\item 5.9\n",
       "\\item 5.5\n",
       "\\item 5.5\n",
       "\\item 6\n",
       "\\item 5.6\n",
       "\\item 6\n",
       "\\item 5.3\n",
       "\\item 5.2\n",
       "\\item 6.4\n",
       "\\item 6.5\n",
       "\\item 5.3\n",
       "\\item 5.75\n",
       "\\item 5.5\n",
       "\\item 6.45\n",
       "\\item 5.8\n",
       "\\item 5.8\n",
       "\\item 5.7\n",
       "\\item 5.875\n",
       "\\item 5.8\n",
       "\\item 6.6\n",
       "\\item 5.5\n",
       "\\item 5.5\n",
       "\\item 5.4\n",
       "\\item 5.8\n",
       "\\item 5.5\n",
       "\\item 5.2\n",
       "\\item 5.6\n",
       "\\item 5.4\n",
       "\\item 5.6\n",
       "\\item 6.6\n",
       "\\item 5.9\n",
       "\\item 5.9\n",
       "\\item 5.85\n",
       "\\item 5.633333333\n",
       "\\item 6.2\n",
       "\\item 5.1\n",
       "\\item 5.4\n",
       "\\item 5.1\n",
       "\\item 5.7\n",
       "\\item 6\n",
       "\\item 5.2\n",
       "\\item 6.8\n",
       "\\item 6.05\n",
       "\\item 5.1\n",
       "\\item 5.15\n",
       "\\item 5.2\n",
       "\\item 5.4\n",
       "\\item 5.8\n",
       "\\item 5.4\n",
       "\\item 5.3\n",
       "\\item 5.6\n",
       "\\item 5.6\n",
       "\\item 5.25\n",
       "\\item 5.5\n",
       "\\item 5.3\n",
       "\\item 5.7\n",
       "\\item 5.9\n",
       "\\item 5.7\n",
       "\\item 5.3\n",
       "\\item 5.1\n",
       "\\item 5.666666667\n",
       "\\item 5.3\n",
       "\\item 5.1\n",
       "\\item 6.4\n",
       "\\item 5.5\n",
       "\\item 5.5\n",
       "\\item 5.3\n",
       "\\item 5.5\n",
       "\\item 5.3\n",
       "\\item 6.1\n",
       "\\item 5.5\n",
       "\\item 5.5\n",
       "\\item 5.2\n",
       "\\item 5.55\n",
       "\\item 5.7\n",
       "\\item 5\n",
       "\\item 5.8\n",
       "\\item 5.4\n",
       "\\item 5.6\n",
       "\\item 6.4\n",
       "\\item 6.1\n",
       "\\item 5.7\n",
       "\\item 5.4\n",
       "\\item 5.3\n",
       "\\item 5.4\n",
       "\\item 6.15\n",
       "\\item 6.1\n",
       "\\item 5.5\n",
       "\\item 5.5\n",
       "\\item 5.1\n",
       "\\item 5.1\n",
       "\\item 5.5\n",
       "\\item 6.4\n",
       "\\item 5.35\n",
       "\\item 5.2\n",
       "\\item 5.7\n",
       "\\item 5.3\n",
       "\\item 5.75\n",
       "\\item 5.5\n",
       "\\item 6\n",
       "\\item 5.6\n",
       "\\item 5.3\n",
       "\\item 5.6\n",
       "\\item 5.1\n",
       "\\item 5\n",
       "\\item 5.4\n",
       "\\item 5.05\n",
       "\\item 5.2\n",
       "\\item 5.2\n",
       "\\item 5.8\n",
       "\\item 5.2\n",
       "\\item 5.5\n",
       "\\item 5.1\n",
       "\\item 5\n",
       "\\item 5.4\n",
       "\\item 6\n",
       "\\item 5.2\n",
       "\\item 5.2\n",
       "\\item 5.8\n",
       "\\item 5.8\n",
       "\\item 5\n",
       "\\item 5.8\n",
       "\\item 5\n",
       "\\item 5.3\n",
       "\\item 5.55\n",
       "\\item 5.3\n",
       "\\item 5.5\n",
       "\\item 5.5\n",
       "\\item 5.2\n",
       "\\item 5.2\n",
       "\\item 6.575\n",
       "\\item 5\n",
       "\\item 5.2\n",
       "\\item 5.4\n",
       "\\item 5.25\n",
       "\\item 5.966666667\n",
       "\\item 5.3\n",
       "\\item 5.3\n",
       "\\item 5.3\n",
       "\\item 5.2\n",
       "\\item 6.25\n",
       "\\item 5.3\n",
       "\\item 5.2\n",
       "\\item 5.1\n",
       "\\item 5.95\n",
       "\\item 5.3\n",
       "\\item 4.9\n",
       "\\item 5.65\n",
       "\\item 6.090909091\n",
       "\\item 5.2\n",
       "\\item 5.533333333\n",
       "\\item 5.533333333\n",
       "\\item 5.4\n",
       "\\item 5.2\n",
       "\\item 5\n",
       "\\item 5.4\n",
       "\\item 6.042857143\n",
       "\\item 5.64\n",
       "\\item 5.8\n",
       "\\item 5.2\n",
       "\\item 5.6\n",
       "\\item 5.5\n",
       "\\item 5.3\n",
       "\\item 5.45\n",
       "\\item 5.1\n",
       "\\item 5.2\n",
       "\\item 5.65\n",
       "\\item 5.4\n",
       "\\item 5.1\n",
       "\\item 5.35\n",
       "\\item 5.2\n",
       "\\item 5.6\n",
       "\\item 5\n",
       "\\item 5.4\n",
       "\\item 5.4\n",
       "\\item 5.433333333\n",
       "\\item 5.133333333\n",
       "\\item 5.3\n",
       "\\item 5.4\n",
       "\\item 5.6\n",
       "\\item 6.4\n",
       "\\item 5.82\n",
       "\\item 5.1\n",
       "\\item 5.5\n",
       "\\item 5.5\n",
       "\\item 5\n",
       "\\item 5.2\n",
       "\\item 5.1\n",
       "\\item 5.1\n",
       "\\item 5.4\n",
       "\\item 5.3\n",
       "\\item 5.1\n",
       "\\item 5.6\n",
       "\\item 5.1\n",
       "\\item 5.3\n",
       "\\item 5.5\n",
       "\\item 5.1\n",
       "\\item 5.1\n",
       "\\item 5.55\n",
       "\\item 4.9\n",
       "\\item 5.64\n",
       "\\item 5.2\n",
       "\\item 5.4\n",
       "\\item 5.3\n",
       "\\item 5.2\n",
       "\\item 5.66\n",
       "\\item 4.85\n",
       "\\item 5.2\n",
       "\\item 5.3\n",
       "\\item 5\n",
       "\\item 6\n",
       "\\item 5.2\n",
       "\\item 5.7\n",
       "\\item 5.4\n",
       "\\item 5.2\n",
       "\\item 4.9\n",
       "\\item 4.7\n",
       "\\item 5.2\n",
       "\\item 5.1\n",
       "\\item 4.9\n",
       "\\item 4.9\n",
       "\\item 5.7\n",
       "\\item 5.3\n",
       "\\item 5.333333333\n",
       "\\item 5\n",
       "\\item 5.275\n",
       "\\item 4.85\n",
       "\\item 4.7\n",
       "\\item 5.1\n",
       "\\item 5.2\n",
       "\\item 5.5\n",
       "\\item 5.433333333\n",
       "\\item 5.2\n",
       "\\item 6.525\n",
       "\\item 6\n",
       "\\item 4.85\n",
       "\\item 5.25\n",
       "\\item 5.2\n",
       "\\item 5.2\n",
       "\\item 5.1\n",
       "\\item 5.05\n",
       "\\item 5.3\n",
       "\\item 5\n",
       "\\item 5.2\n",
       "\\item 5\n",
       "\\item 5.2\n",
       "\\item 5.65\n",
       "\\item 5.2\n",
       "\\item 5.666666667\n",
       "\\item 5.4125\n",
       "\\item 5\n",
       "\\item 5.32\n",
       "\\item 5.2\n",
       "\\item 5.6\n",
       "\\item 4.9\n",
       "\\item 5.525\n",
       "\\item 5\n",
       "\\item 5.5\n",
       "\\item 4.9\n",
       "\\item 5\n",
       "\\item 5\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 5.45\n",
       "2. 5.8\n",
       "3. 5.5\n",
       "4. 6.1\n",
       "5. 5.8\n",
       "6. 5.9\n",
       "7. 5.6\n",
       "8. 5.4\n",
       "9. 5.933333333\n",
       "10. 5.6\n",
       "11. 6.7\n",
       "12. 5.9\n",
       "13. 5.5\n",
       "14. 5.5\n",
       "15. 6\n",
       "16. 5.6\n",
       "17. 6\n",
       "18. 5.3\n",
       "19. 5.2\n",
       "20. 6.4\n",
       "21. 6.5\n",
       "22. 5.3\n",
       "23. 5.75\n",
       "24. 5.5\n",
       "25. 6.45\n",
       "26. 5.8\n",
       "27. 5.8\n",
       "28. 5.7\n",
       "29. 5.875\n",
       "30. 5.8\n",
       "31. 6.6\n",
       "32. 5.5\n",
       "33. 5.5\n",
       "34. 5.4\n",
       "35. 5.8\n",
       "36. 5.5\n",
       "37. 5.2\n",
       "38. 5.6\n",
       "39. 5.4\n",
       "40. 5.6\n",
       "41. 6.6\n",
       "42. 5.9\n",
       "43. 5.9\n",
       "44. 5.85\n",
       "45. 5.633333333\n",
       "46. 6.2\n",
       "47. 5.1\n",
       "48. 5.4\n",
       "49. 5.1\n",
       "50. 5.7\n",
       "51. 6\n",
       "52. 5.2\n",
       "53. 6.8\n",
       "54. 6.05\n",
       "55. 5.1\n",
       "56. 5.15\n",
       "57. 5.2\n",
       "58. 5.4\n",
       "59. 5.8\n",
       "60. 5.4\n",
       "61. 5.3\n",
       "62. 5.6\n",
       "63. 5.6\n",
       "64. 5.25\n",
       "65. 5.5\n",
       "66. 5.3\n",
       "67. 5.7\n",
       "68. 5.9\n",
       "69. 5.7\n",
       "70. 5.3\n",
       "71. 5.1\n",
       "72. 5.666666667\n",
       "73. 5.3\n",
       "74. 5.1\n",
       "75. 6.4\n",
       "76. 5.5\n",
       "77. 5.5\n",
       "78. 5.3\n",
       "79. 5.5\n",
       "80. 5.3\n",
       "81. 6.1\n",
       "82. 5.5\n",
       "83. 5.5\n",
       "84. 5.2\n",
       "85. 5.55\n",
       "86. 5.7\n",
       "87. 5\n",
       "88. 5.8\n",
       "89. 5.4\n",
       "90. 5.6\n",
       "91. 6.4\n",
       "92. 6.1\n",
       "93. 5.7\n",
       "94. 5.4\n",
       "95. 5.3\n",
       "96. 5.4\n",
       "97. 6.15\n",
       "98. 6.1\n",
       "99. 5.5\n",
       "100. 5.5\n",
       "101. 5.1\n",
       "102. 5.1\n",
       "103. 5.5\n",
       "104. 6.4\n",
       "105. 5.35\n",
       "106. 5.2\n",
       "107. 5.7\n",
       "108. 5.3\n",
       "109. 5.75\n",
       "110. 5.5\n",
       "111. 6\n",
       "112. 5.6\n",
       "113. 5.3\n",
       "114. 5.6\n",
       "115. 5.1\n",
       "116. 5\n",
       "117. 5.4\n",
       "118. 5.05\n",
       "119. 5.2\n",
       "120. 5.2\n",
       "121. 5.8\n",
       "122. 5.2\n",
       "123. 5.5\n",
       "124. 5.1\n",
       "125. 5\n",
       "126. 5.4\n",
       "127. 6\n",
       "128. 5.2\n",
       "129. 5.2\n",
       "130. 5.8\n",
       "131. 5.8\n",
       "132. 5\n",
       "133. 5.8\n",
       "134. 5\n",
       "135. 5.3\n",
       "136. 5.55\n",
       "137. 5.3\n",
       "138. 5.5\n",
       "139. 5.5\n",
       "140. 5.2\n",
       "141. 5.2\n",
       "142. 6.575\n",
       "143. 5\n",
       "144. 5.2\n",
       "145. 5.4\n",
       "146. 5.25\n",
       "147. 5.966666667\n",
       "148. 5.3\n",
       "149. 5.3\n",
       "150. 5.3\n",
       "151. 5.2\n",
       "152. 6.25\n",
       "153. 5.3\n",
       "154. 5.2\n",
       "155. 5.1\n",
       "156. 5.95\n",
       "157. 5.3\n",
       "158. 4.9\n",
       "159. 5.65\n",
       "160. 6.090909091\n",
       "161. 5.2\n",
       "162. 5.533333333\n",
       "163. 5.533333333\n",
       "164. 5.4\n",
       "165. 5.2\n",
       "166. 5\n",
       "167. 5.4\n",
       "168. 6.042857143\n",
       "169. 5.64\n",
       "170. 5.8\n",
       "171. 5.2\n",
       "172. 5.6\n",
       "173. 5.5\n",
       "174. 5.3\n",
       "175. 5.45\n",
       "176. 5.1\n",
       "177. 5.2\n",
       "178. 5.65\n",
       "179. 5.4\n",
       "180. 5.1\n",
       "181. 5.35\n",
       "182. 5.2\n",
       "183. 5.6\n",
       "184. 5\n",
       "185. 5.4\n",
       "186. 5.4\n",
       "187. 5.433333333\n",
       "188. 5.133333333\n",
       "189. 5.3\n",
       "190. 5.4\n",
       "191. 5.6\n",
       "192. 6.4\n",
       "193. 5.82\n",
       "194. 5.1\n",
       "195. 5.5\n",
       "196. 5.5\n",
       "197. 5\n",
       "198. 5.2\n",
       "199. 5.1\n",
       "200. 5.1\n",
       "201. 5.4\n",
       "202. 5.3\n",
       "203. 5.1\n",
       "204. 5.6\n",
       "205. 5.1\n",
       "206. 5.3\n",
       "207. 5.5\n",
       "208. 5.1\n",
       "209. 5.1\n",
       "210. 5.55\n",
       "211. 4.9\n",
       "212. 5.64\n",
       "213. 5.2\n",
       "214. 5.4\n",
       "215. 5.3\n",
       "216. 5.2\n",
       "217. 5.66\n",
       "218. 4.85\n",
       "219. 5.2\n",
       "220. 5.3\n",
       "221. 5\n",
       "222. 6\n",
       "223. 5.2\n",
       "224. 5.7\n",
       "225. 5.4\n",
       "226. 5.2\n",
       "227. 4.9\n",
       "228. 4.7\n",
       "229. 5.2\n",
       "230. 5.1\n",
       "231. 4.9\n",
       "232. 4.9\n",
       "233. 5.7\n",
       "234. 5.3\n",
       "235. 5.333333333\n",
       "236. 5\n",
       "237. 5.275\n",
       "238. 4.85\n",
       "239. 4.7\n",
       "240. 5.1\n",
       "241. 5.2\n",
       "242. 5.5\n",
       "243. 5.433333333\n",
       "244. 5.2\n",
       "245. 6.525\n",
       "246. 6\n",
       "247. 4.85\n",
       "248. 5.25\n",
       "249. 5.2\n",
       "250. 5.2\n",
       "251. 5.1\n",
       "252. 5.05\n",
       "253. 5.3\n",
       "254. 5\n",
       "255. 5.2\n",
       "256. 5\n",
       "257. 5.2\n",
       "258. 5.65\n",
       "259. 5.2\n",
       "260. 5.666666667\n",
       "261. 5.4125\n",
       "262. 5\n",
       "263. 5.32\n",
       "264. 5.2\n",
       "265. 5.6\n",
       "266. 4.9\n",
       "267. 5.525\n",
       "268. 5\n",
       "269. 5.5\n",
       "270. 4.9\n",
       "271. 5\n",
       "272. 5\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  [1] 5.450000 5.800000 5.500000 6.100000 5.800000 5.900000 5.600000 5.400000\n",
       "  [9] 5.933333 5.600000 6.700000 5.900000 5.500000 5.500000 6.000000 5.600000\n",
       " [17] 6.000000 5.300000 5.200000 6.400000 6.500000 5.300000 5.750000 5.500000\n",
       " [25] 6.450000 5.800000 5.800000 5.700000 5.875000 5.800000 6.600000 5.500000\n",
       " [33] 5.500000 5.400000 5.800000 5.500000 5.200000 5.600000 5.400000 5.600000\n",
       " [41] 6.600000 5.900000 5.900000 5.850000 5.633333 6.200000 5.100000 5.400000\n",
       " [49] 5.100000 5.700000 6.000000 5.200000 6.800000 6.050000 5.100000 5.150000\n",
       " [57] 5.200000 5.400000 5.800000 5.400000 5.300000 5.600000 5.600000 5.250000\n",
       " [65] 5.500000 5.300000 5.700000 5.900000 5.700000 5.300000 5.100000 5.666667\n",
       " [73] 5.300000 5.100000 6.400000 5.500000 5.500000 5.300000 5.500000 5.300000\n",
       " [81] 6.100000 5.500000 5.500000 5.200000 5.550000 5.700000 5.000000 5.800000\n",
       " [89] 5.400000 5.600000 6.400000 6.100000 5.700000 5.400000 5.300000 5.400000\n",
       " [97] 6.150000 6.100000 5.500000 5.500000 5.100000 5.100000 5.500000 6.400000\n",
       "[105] 5.350000 5.200000 5.700000 5.300000 5.750000 5.500000 6.000000 5.600000\n",
       "[113] 5.300000 5.600000 5.100000 5.000000 5.400000 5.050000 5.200000 5.200000\n",
       "[121] 5.800000 5.200000 5.500000 5.100000 5.000000 5.400000 6.000000 5.200000\n",
       "[129] 5.200000 5.800000 5.800000 5.000000 5.800000 5.000000 5.300000 5.550000\n",
       "[137] 5.300000 5.500000 5.500000 5.200000 5.200000 6.575000 5.000000 5.200000\n",
       "[145] 5.400000 5.250000 5.966667 5.300000 5.300000 5.300000 5.200000 6.250000\n",
       "[153] 5.300000 5.200000 5.100000 5.950000 5.300000 4.900000 5.650000 6.090909\n",
       "[161] 5.200000 5.533333 5.533333 5.400000 5.200000 5.000000 5.400000 6.042857\n",
       "[169] 5.640000 5.800000 5.200000 5.600000 5.500000 5.300000 5.450000 5.100000\n",
       "[177] 5.200000 5.650000 5.400000 5.100000 5.350000 5.200000 5.600000 5.000000\n",
       "[185] 5.400000 5.400000 5.433333 5.133333 5.300000 5.400000 5.600000 6.400000\n",
       "[193] 5.820000 5.100000 5.500000 5.500000 5.000000 5.200000 5.100000 5.100000\n",
       "[201] 5.400000 5.300000 5.100000 5.600000 5.100000 5.300000 5.500000 5.100000\n",
       "[209] 5.100000 5.550000 4.900000 5.640000 5.200000 5.400000 5.300000 5.200000\n",
       "[217] 5.660000 4.850000 5.200000 5.300000 5.000000 6.000000 5.200000 5.700000\n",
       "[225] 5.400000 5.200000 4.900000 4.700000 5.200000 5.100000 4.900000 4.900000\n",
       "[233] 5.700000 5.300000 5.333333 5.000000 5.275000 4.850000 4.700000 5.100000\n",
       "[241] 5.200000 5.500000 5.433333 5.200000 6.525000 6.000000 4.850000 5.250000\n",
       "[249] 5.200000 5.200000 5.100000 5.050000 5.300000 5.000000 5.200000 5.000000\n",
       "[257] 5.200000 5.650000 5.200000 5.666667 5.412500 5.000000 5.320000 5.200000\n",
       "[265] 5.600000 4.900000 5.525000 5.000000 5.500000 4.900000 5.000000 5.000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mag2 <- df$mag.vec2[f2]\n",
    "mag2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let us now look at distributions of this variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "\tdensity.default(x = mag1)\n",
       "\n",
       "Data: mag1 (299 obs.);\tBandwidth 'bw' = 0.1074\n",
       "\n",
       "       x               y            \n",
       " Min.   :4.278   Min.   :0.0001409  \n",
       " 1st Qu.:5.089   1st Qu.:0.0222232  \n",
       " Median :5.900   Median :0.1470975  \n",
       " Mean   :5.900   Mean   :0.3079241  \n",
       " 3rd Qu.:6.711   3rd Qu.:0.5164522  \n",
       " Max.   :7.522   Max.   :1.0924363  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "density(mag1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IKjF2AdQRIRveDoBVhHkERELzh6AdYR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\nAQQJEECQAAH/AQryAKlZaUP2AAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"density.default(x = mag1)\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(density(mag1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "\tdensity.default(x = mag2)\n",
       "\n",
       "Data: mag2 (272 obs.);\tBandwidth 'bw' = 0.09905\n",
       "\n",
       "       x               y            \n",
       " Min.   :4.403   Min.   :0.0001719  \n",
       " 1st Qu.:5.076   1st Qu.:0.0521279  \n",
       " Median :5.750   Median :0.1618912  \n",
       " Mean   :5.750   Mean   :0.3707885  \n",
       " 3rd Qu.:6.424   3rd Qu.:0.6629319  \n",
       " Max.   :7.097   Max.   :1.1720900  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "density(mag2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fL097Z31m5TeikRDT2J9STJirDXkQ7N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\nEAlAAEQCEACRAAT4H9Ho+k7tRQ+/AAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"density.default(x = mag2)\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(density(mag2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in xy.coords(x, y, xlabel, ylabel, log): 'x' and 'y' lengths differ\n",
     "output_type": "error",
     "traceback": [
      "Error in xy.coords(x, y, xlabel, ylabel, log): 'x' and 'y' lengths differ\nTraceback:\n",
      "1. plot(mag1, mag2)",
      "2. plot.default(mag1, mag2)",
      "3. xy.coords(x, y, xlabel, ylabel, log)",
      "4. stop(\"'x' and 'y' lengths differ\")"
     ]
    }
   ],
   "source": [
    "plot(mag1,mag2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using method of moments estimate parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(MASS)\n",
    "\n",
    "MM_Estimator <- function( data.sample, distribution){\n",
    "  \n",
    "  if (distribution == \"Point Mass\"){\n",
    "    #######  Point Mass #######\n",
    "    param <- 1\n",
    "    #data.sample <- 10\n",
    "    m1 <- data.sample/1\n",
    "    print(paste(\"Distribution - Point Mass(a) ; Moment1 (m1) = \", m1, \"; Parameter1 (a) = \", m1 ))\n",
    "  }\n",
    "  \n",
    "  else if (distribution == \"Bernoulli\"){\n",
    "    ####### Bernoulli #######\n",
    "    param <- 1\n",
    "    #data.sample <- bern.data\n",
    "    m1 <- 1/length(data.sample) * sum(data.sample)\n",
    "    print(paste(\"Distribution - Bernoulli Distribution(p) ; Moment1 (m1) = \", m1, \"; Estimated Parameter1 (p) = \", m1 ))\n",
    "  }\n",
    "  \n",
    "  else if (distribution == \"Binomial\"){\n",
    "    ####### Binomial #######\n",
    "    param <- 2\n",
    "    #data.sample <- binom.data\n",
    "    m1 <- 1/length(data.sample) * sum(data.sample)\n",
    "    m2 <- 1/length(data.sample) * sum(data.sample^2)\n",
    "    # We have np = m1 and np(1-p) = m2-m1^2\n",
    "    p = 1 - ((m2 - (m1^2))/m1)\n",
    "    n = m1/p\n",
    "    print(paste(\"Distribution - Binomial Distribution(n,p) ; Moment1 (m1) = \", m1, \"; Moment2 (m2) = \", m2,\"; Estimated Parameter1 (n) = \", n\n",
    "                , \"; Estimated Parameter2 (p) = \", p))\n",
    "  }\n",
    "  \n",
    "  else if (distribution == \"Geometric\"){\n",
    "    ####### Geometric #######\n",
    "    param <- 1\n",
    "    #data.sample <- geom.data\n",
    "    m1 <- 1/length(data.sample) * sum(data.sample)\n",
    "    #we have p = 1/mean\n",
    "    p = 1/m1\n",
    "    print(paste(\"Distribution - Geometric Distribution (p) ; Moment1 (m1) = \", m1, \"; Estimated Parameter1 (p) = \", p ))\n",
    "  }\n",
    "  \n",
    "  else if (distribution == \"Poisson\"){\n",
    "    ####### Poisson #######\n",
    "    param <- 1\n",
    "    #data.sample <- pois.data\n",
    "    m1 <- 1/length(data.sample) * sum(data.sample)#we have p = 1/mean\n",
    "    lambda = m1\n",
    "    print(paste(\"Distribution - Poisson Distribution (lambda) ; Moment1 (m1) = \", m1, \"; Estimated Parameter1 (lambda) = \", lambda ))\n",
    "  }\n",
    "  \n",
    "  else if (distribution == \"Uniform\"){\n",
    "    ####### Uniform #######\n",
    "    param <- 2\n",
    "    #data.sample <- unif.data\n",
    "    m1 <- 1/length(data.sample) * sum(data.sample)\n",
    "    m2 <- 1/length(data.sample) * sum(data.sample^2)\n",
    "    a <- m1 - sqrt(3* (m2 - m1^2))\n",
    "    b <- m1 + sqrt(3* (m2 - m1^2))\n",
    "    print(paste(\"Distribution - Uniform Distribution(a,b) ; Moment1 (m1) = \", m1, \"; Moment2 (m2) = \", m2,\"; Estimated Parameter1 (a) = \", a\n",
    "                , \"; Estimated Parameter2 (b) = \", b))\n",
    "  }\n",
    "  \n",
    "  else if (distribution == \"Normal\"){\n",
    "    ####### Normal #######\n",
    "    param <- 2\n",
    "    #data.sample <- norm.data\n",
    "    m1 <- 1/length(data.sample) * sum(data.sample)\n",
    "    m2 <- 1/length(data.sample) * sum(data.sample^2)\n",
    "    mu <- m1\n",
    "    sig <- sqrt(m2 - m1^2)\n",
    "    print(paste(\"Distribution - Normal Distribution(mu,sigma) ; Moment1 (m1) = \", m1, \"; Moment2 (m2) = \", m2,\"; Estimated Parameter1 (mu) = \", mu\n",
    "                , \"; Estimated Parameter2 (sigma) = \", sig))\n",
    "  }\n",
    "  \n",
    "  else if (distribution == \"Exponential\"){\n",
    "    ####### Exponential #######\n",
    "    param <- 1\n",
    "    #data.sample <- expo.data\n",
    "    m1 <- 1/length(data.sample) * sum(data.sample)\n",
    "    #we have p = 1/mean\n",
    "    beta <- m1\n",
    "    print(paste(\"Distribution - Exponential Distribution (beta) ; Moment1 (m1) = \", m1, \"; Estimated Parameter1 (beta) = \", beta ))\n",
    "  }\n",
    "  \n",
    "  else if (distribution == \"Gamma\"){\n",
    "    ####### Gamma #######\n",
    "    param <- 2\n",
    "    #data.sample <- gamma.data\n",
    "    m1 <- 1/length(data.sample) * sum(data.sample)\n",
    "    m2 <- 1/length(data.sample) * sum(data.sample^2)\n",
    "    beta <- (m2 - m1^2)/m1\n",
    "    alpha <- m1/ beta\n",
    "    print(paste(\"Distribution - Gamma Distribution(alpha, beta) ; Moment1 (m1) = \", m1, \"; Moment2 (m2) = \", m2,\n",
    "                \"; Estimated Parameter1 (alpha) = \", alpha\n",
    "                , \"; Estimated Parameter2 (beta) = \", beta))\n",
    "  }\n",
    "  \n",
    "  else if (distribution == \"Beta\"){\n",
    "    ####### Beta #######\n",
    "    param <- 2\n",
    "    #data.sample <- beta.data\n",
    "    m1 <- 1/length(data.sample) * sum(data.sample)\n",
    "    m2 <- 1/length(data.sample) * sum(data.sample^2)\n",
    "    alpha <- (m1^2 - (m1*m2))/(m2 - m1^2)\n",
    "    beta <- (alpha/ m1) - alpha\n",
    "    print(paste(\"Distribution - Beta Distribution(alpha, beta) ; Moment1 (m1) = \", m1, \"; Moment2 (m2) = \", m2,\n",
    "                \"; Estimated Parameter1 (alpha) = \", alpha\n",
    "                , \"; Estimated Parameter2 (beta) = \", beta))\n",
    "  }\n",
    "  \n",
    "  else if (distribution == \"Student T\"){\n",
    "    ####### Student T #######\n",
    "    param <- 1\n",
    "    #data.sample <- studt.data\n",
    "    m1 <- 1/length(data.sample) * sum(data.sample)\n",
    "    m2 <- 1/length(data.sample) * sum(data.sample^2)\n",
    "    #we have p = 1/mean\n",
    "    v <- 2*(m2 - m1^2)/(m2- m1^2 - 1)\n",
    "    print(paste(\"Distribution - Student T (v) ; Moment1 (m1) = \", m1,\"; Moment2 (m2) = \", m2, \"; Estimated Parameter1 (v) = \", v, \"(NOTE : This\n",
    "                v value is from Second moment of Student T test, however, 2nd moment wont exist based on \n",
    "                assumptions of Methods of moments as Student T test has only 1 parameter\" ))\n",
    "  }\n",
    "  \n",
    "  else if (distribution == \"Chi-Square\"){\n",
    "    ####### Chi - Square #######\n",
    "    param <-1\n",
    "    #data.sample <- chi.sqaure.data\n",
    "    m1 <- 1/length(data.sample) * sum(data.sample)\n",
    "    p <- m1\n",
    "    print(paste(\"Distribution - Chi-sqaure (p) ; Moment1 (m1) = \", m1, \"; Estimated Parameter1 (p) = \", p ))\n",
    "  }\n",
    "  \n",
    "  else if (distribution == \"Multinomial\"){\n",
    "    ####### Multinomial #######\n",
    " #   data.sample <- multi.nom.data\n",
    "    m1 <- rowSums(data.sample)/ncol(data.sample)\n",
    "    m2 <- data.sample %*% t(data.sample)/ncol(data.sample)\n",
    "    #calculation just p1 to find n\n",
    "    p1 <- 1 + m1[1] - (m2[1,1]/m1[1])\n",
    "    n <- m1[1]/p1\n",
    "    p <- m1/n\n",
    "    cat(\"Distribution - Multinominal Distribution(n, prob) ; \",  \"Estimated Parameter1 (n) = \", n, \"; Estimated Parameter2 (prob) = \", p)\n",
    "  }\n",
    "  \n",
    "  else if (distribution == \"Multivariate Normal\"){\n",
    "    ####### Multivariate Normal #######\n",
    "    #data.sample <- mv.norm.data\n",
    "    m1 <- rowSums(data.sample)/ncol(data.sample)\n",
    "    m2 <- data.sample %*% t(data.sample)/ncol(data.sample)\n",
    "    sd <- sqrt(m2 - m1 %*% t(m1))\n",
    "    cat(\"Distribution - Multivariate Normal Distribution(mu, sigma) ; \",  \"Estimated Parameter1 (mu) = \", m1, \"; Estimated Parameter2 (sigma) = \", sd)\n",
    "  }\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Distribution - Normal Distribution(mu,sigma) ; Moment1 (m1) =  5.49026031010702 ; Moment2 (m2) =  30.3241559285143 ; Estimated Parameter1 (mu) =  5.49026031010702 ; Estimated Parameter2 (sigma) =  0.425673179537832\"\n"
     ]
    }
   ],
   "source": [
    "MM_Estimator(mag1,  \"Normal\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Distribution - Exponential Distribution (beta) ; Moment1 (m1) =  5.49026031010702 ; Estimated Parameter1 (beta) =  5.49026031010702\"\n"
     ]
    }
   ],
   "source": [
    "MM_Estimator(mag1,  \"Exponential\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Distribution - Gamma Distribution(alpha, beta) ; Moment1 (m1) =  5.49026031010702 ; Moment2 (m2) =  30.3241559285143 ; Estimated Parameter1 (alpha) =  166.354019003935 ; Estimated Parameter2 (beta) =  0.0330034726120873\"\n"
     ]
    }
   ],
   "source": [
    "MM_Estimator(mag1,  \"Gamma\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Distribution - Normal Distribution(mu,sigma) ; Moment1 (m1) =  5.46293357683456 ; Moment2 (m2) =  29.9947287970342 ; Estimated Parameter1 (mu) =  5.46293357683456 ; Estimated Parameter2 (sigma) =  0.388697224234748\"\n"
     ]
    }
   ],
   "source": [
    "MM_Estimator(mag2,  \"Normal\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Distribution - Exponential Distribution (beta) ; Moment1 (m1) =  5.46293357683456 ; Estimated Parameter1 (beta) =  5.46293357683456\"\n"
     ]
    }
   ],
   "source": [
    "MM_Estimator(mag2,  \"Exponential\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Distribution - Gamma Distribution(alpha, beta) ; Moment1 (m1) =  5.46293357683456 ; Moment2 (m2) =  29.9947287970342 ; Estimated Parameter1 (alpha) =  197.528134193966 ; Estimated Parameter2 (beta) =  0.0276564834631108\"\n"
     ]
    }
   ],
   "source": [
    "MM_Estimator(mag2,  \"Gamma\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimation using MLE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function for MLE for distributions - gamma, beta, poisson, normal, exponential, and uniform distributions\n",
    "\n",
    "library(matlib)\n",
    "\n",
    "# MLE function\n",
    "mle_func <- function(x, func_name) {\n",
    "  if (func_name == \"Gamma\") {\n",
    "    #cat(\"GAMMA DISTRIBUTION \\n\")\n",
    "    mean.val <- mean(x)\n",
    "    s <- log(mean.val) - ((sum(log(x)))/length(x))\n",
    "    alpha.val <- (3 - s + sqrt( ((s-3)^2) + (24 * s) ))/(12 * s)\n",
    "    beta.val <- mean.val/alpha.val\n",
    "    #cat(\"The population estimate for gamma distribution is : alpha = \", alpha.val, \", beta = \", beta.val, \"\\n\")\n",
    "    #cat(\"\\n\")\n",
    "    return(c(alpha.val,beta.val))\n",
    "  }\n",
    "  else if (func_name == \"Beta\") {\n",
    "    #cat(\"BETA DISTRIBUTION \\n\")\n",
    "    iter = 100\n",
    "    # Initial values for alpha and beta are from the MOM estimator\n",
    "    x.mean <- mean(x)\n",
    "    x.var <- (sum(x * x))/length(x)\n",
    "    alpha.val <- ((x.mean ^ 2) - (x.mean * x.var))/(x.var - (x.mean ^ 2))\n",
    "    beta.val <- (alpha.val * (1 - x.mean))/(x.mean)\n",
    "    # Numerical approximation\n",
    "    final.val <- c(alpha.val, beta.val)\n",
    "    for (i in 1:100) {\n",
    "      g1 <- digamma(alpha.val) - digamma(alpha.val + beta.val) - (sum(log(x))/length(x))\n",
    "      g2 <- digamma(beta.val) - digamma(alpha.val + beta.val) - (sum(log(1-x))/length(x))\n",
    "      g.val <- c(g1, g2)\n",
    "      # Matrix G terms\n",
    "      term.11 <- trigamma(alpha.val) - trigamma(alpha.val + beta.val)\n",
    "      term.12 <- -trigamma(alpha.val + beta.val)\n",
    "      term.22 <- trigamma(beta.val) - trigamma(alpha.val + beta.val)\n",
    "      G <- matrix(c(term.11, term.12, term.12, term.22), nrow = 2, ncol = 2, byrow = TRUE)\n",
    "      G.inv <- inv(G)\n",
    "      # Final values\n",
    "      final.val <- final.val - t(G.inv %*% g.val)\n",
    "      alpha.val <- final.val[1]\n",
    "      beta.val <- final.val[2]\n",
    "    }\n",
    "    #cat(\"The population estimate for beta distribution is :  alpha  = \", alpha.val, \", beta = \", beta.val, \"\\n\")\n",
    "    #cat(\"\\n\")\n",
    "    return(c(c(alpha.val,beta.val)))\n",
    "  }\n",
    "  else if (func_name == \"Poisson\") {\n",
    "    lambda.val <- mean(x)\n",
    "    #cat(\"POISSON DISTRIBUTION \\n\")\n",
    "    #cat(\"The population estimate for poisson distribution is :  lambda = \", lambda.val, \"\\n\")\n",
    "    #cat(\"\\n\")\n",
    "    return(lambda.val)\n",
    "  }\n",
    "  else if (func_name == \"Normal\") {\n",
    "    mu.val <- mean(x)\n",
    "    sigma.val <- sum(((x - mean(x))^2))/length(x)\n",
    "    #cat(\"NORMAL DISTRIBUTION \\n\")\n",
    "    #cat(\"The population estimate for normal distribution are :  mu = \", mu.val, \", sigma = \", sigma.val, \"\\n\")\n",
    "    #cat(\"\\n\")\n",
    "    return(c(mu.val,sigma.val))\n",
    "  }\n",
    "  else if (func_name == \"Exponential\") {\n",
    "    beta.val <- mean(x)\n",
    "    #cat(\"EXPONENTIAL DISTRIBUTION \\n\")\n",
    "    #cat(\"The population estimate for exponential distribution is :  beta = \", beta.val, \"\\n\")\n",
    "    #cat(\"\\n\")\n",
    "    return(beta.val)\n",
    "  }\n",
    "  else if (func_name == \"Uniform\") {\n",
    "    a <- min(x)\n",
    "    b <- max(x)\n",
    "    #cat(\"UNIFORM DISTRIBUTION \\n\")\n",
    "    #cat(\"The population estimate for uniform distribution are : a = \", a, \", b = \", b, \"\\n\")\n",
    "    #cat(\"\\n\")\n",
    "    return(c(a,b))\n",
    "  }\n",
    "  else {\n",
    "    cat(\"Please enter a valid distribution!\")\n",
    "  }\n",
    "}\n",
    "\n",
    "# Goodness of fitness test\n",
    "gof <- function(x, nboot = 1000, func_name) {\n",
    "  # Call the corresponding function\n",
    "  thetahat<-mle_func(x, func_name)\n",
    "  n<-length(x)\n",
    "  #conditioning on distname\n",
    "  if (func_name == \"Gamma\") {\n",
    "    qhat<-qgamma(c(1:n)/(n+1),shape = thetahat[1], scale = thetahat[2])\n",
    "  }\n",
    "  else if (func_name == \"Beta\") {\n",
    "    qhat<-qbeta(c(1:n)/(n+1),shape1 = thetahat[1], shape2 = thetahat[2])\n",
    "  }\n",
    "  else if (func_name == \"Poisson\") {\n",
    "    qhat<-qpois(c(1:n)/(n+1), lambda = thetahat)\n",
    "  }\n",
    "  else if (func_name == \"Normal\") {\n",
    "    qhat<-qnorm(c(1:n)/(n+1), mean =  thetahat[1], sd = thetahat[2])\n",
    "  }\n",
    "  else if (func_name == \"Exponential\") {\n",
    "    qhat<-qexp(c(1:n)/(n+1), rate = thetahat)\n",
    "  }\n",
    "  else if (func_name == \"Uniform\") {\n",
    "    qhat<-qunif(c(1:n)/(n+1),min = thetahat[1], max = thetahat[2])\n",
    "  }\n",
    "  D0<-ks.test(x,qhat)$statistic\n",
    "  Dvec<-NULL\n",
    "  for(i in 1:nboot) {\n",
    "    if (func_name == \"Gamma\") {\n",
    "      xstar<-rgamma(n, shape = thetahat[1], scale = thetahat[2])\n",
    "      thetahatstart<-mle_func(xstar, func_name = func_name)\n",
    "      qhatstar<-qgamma(c(1:n)/(n+1),shape = thetahatstart[1], scale = thetahatstart[2])\n",
    "    }\n",
    "    else if (func_name == \"Beta\") {\n",
    "      xstar<-rbeta(n, shape1 = thetahat[1], shape2 = thetahat[2])\n",
    "      thetahatstart<-mle_func(xstar, func_name = func_name)\n",
    "      qhatstar<-qbeta(c(1:n)/(n+1),shape1 = thetahatstart[1], shape2 = thetahatstart[2])\n",
    "    }\n",
    "    else if (func_name == \"Poisson\") {\n",
    "      xstar<-rpois(n, lambda = thetahat)\n",
    "      thetahatstart<-mle_func(xstar, func_name = func_name)\n",
    "      qhatstar<-qpois(c(1:n)/(n+1), lambda = thetahatstart)\n",
    "    }\n",
    "    else if (func_name == \"Normal\") {\n",
    "      xstar<-rnorm(n, mean = thetahat[1], sd = thetahat[2])\n",
    "      thetahatstart<-mle_func(xstar, func_name = func_name)\n",
    "      qhatstar<-qnorm(c(1:n)/(n+1),mean = thetahatstart[1], sd = thetahatstart[2])\n",
    "    }\n",
    "    else if (func_name == \"Exponential\") {\n",
    "      xstar<-rexp(n, rate = thetahat)\n",
    "      thetahatstart<-mle_func(xstar, func_name = func_name)\n",
    "      qhatstar<-qexp(c(1:n)/(n+1),rate = thetahatstart)\n",
    "    }\n",
    "    else if (func_name == \"Uniform\") {\n",
    "      xstar<-runif(n, min = thetahat[1], max = thetahat[2])\n",
    "      thetahatstart<-mle_func(xstar, func_name = func_name)\n",
    "      qhatstar<-qunif(c(1:n)/(n+1),min = thetahatstart[1], max = thetahatstart[2])\n",
    "    }\n",
    "    D_star <- ks.test(xstar,qhatstar)$statistic\n",
    "    Dvec<-c(Dvec,D_star)\n",
    "  }\n",
    "  P<-sum(Dvec>D0)/nboot\n",
    "  cat(\"The p-value is : \", P)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>5.49026031010702</li>\n",
       "\t<li>0.181197655777849</li>\n",
       "</ol>\n"
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      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 5.49026031010702\n",
       "\\item 0.181197655777849\n",
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       "1. 5.49026031010702\n",
       "2. 0.181197655777849\n",
       "\n",
       "\n"
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      "text/plain": [
       "[1] 5.4902603 0.1811977"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mle_func(mag1,  \"Normal\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>172.902930417023</li>\n",
       "\t<li>0.0317534254443525</li>\n",
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      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 172.902930417023\n",
       "\\item 0.0317534254443525\n",
       "\\end{enumerate*}\n"
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       "1. 172.902930417023\n",
       "2. 0.0317534254443525\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 172.90293042   0.03175343"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mle_func(mag1,  \"Gamma\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "5.49026031010702"
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       "5.49026031010702"
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       "5.49026031010702"
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      "text/plain": [
       "[1] 5.49026"
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    }
   ],
   "source": [
    "mle_func(mag1,  \"Exponential\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>5.46293357683456</li>\n",
       "\t<li>0.151085532127803</li>\n",
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       "\\begin{enumerate*}\n",
       "\\item 5.46293357683456\n",
       "\\item 0.151085532127803\n",
       "\\end{enumerate*}\n"
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      "text/markdown": [
       "1. 5.46293357683456\n",
       "2. 0.151085532127803\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 5.4629336 0.1510855"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mle_func(mag2,  \"Normal\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>205.064642616862</li>\n",
       "\t<li>0.0266400560677902</li>\n",
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      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 205.064642616862\n",
       "\\item 0.0266400560677902\n",
       "\\end{enumerate*}\n"
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      "text/markdown": [
       "1. 205.064642616862\n",
       "2. 0.0266400560677902\n",
       "\n",
       "\n"
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      "text/plain": [
       "[1] 205.06464262   0.02664006"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "mle_func(mag2,  \"Gamma\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "5.46293357683456"
      ],
      "text/latex": [
       "5.46293357683456"
      ],
      "text/markdown": [
       "5.46293357683456"
      ],
      "text/plain": [
       "[1] 5.462934"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mle_func(mag2,  \"Exponential\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we do goodness of fit to check for the parameters estimated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitting model to the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "832"
      ],
      "text/latex": [
       "832"
      ],
      "text/markdown": [
       "832"
      ],
      "text/plain": [
       "[1] 832"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nrow(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "mag1_1 <- df[1:830,2]\n",
    "mag1_2 <- df[2:831,2]\n",
    "mag1_3 <- df[3:832,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "mag2_1 <- df[1:830,3]\n",
    "mag2_2 <- df[2:831,3]\n",
    "mag2_3 <- df[3:832,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8qhG/U8+6JrzcGAkBZf/3hb3L2NFNKR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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(mag1_2,mag2_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nAUKCACFBgJAgQEgQICQI+B//RqZnsM9jQgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(mag1_3,mag2_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "I1 <- as.logical((mag1_3 > 3.05) * (mag2_3>3.05))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/7fLvqGuC/8P4KxQ2q+znLdpZchhugr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\nQEgQQEgQQEgQQEgQQEgQ4H/5GtI+vqQxjwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(mag1_3[I1],mag2_3[I1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we try to predict the earthquake based on the last 2 observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "y <- (mag1_3 > 3.05) * (mag2_3>3.05) *1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.149397590361446"
      ],
      "text/latex": [
       "0.149397590361446"
      ],
      "text/markdown": [
       "0.149397590361446"
      ],
      "text/plain": [
       "[1] 0.1493976"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(y)/length(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_new <- as.data.frame(cbind(mag1_1,mag1_2,mag2_1,mag2_2, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>mag1_1</th><th scope=col>mag1_2</th><th scope=col>mag2_1</th><th scope=col>mag2_2</th><th scope=col>y</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>3   </td><td>3.00</td><td>3.00</td><td>5.45</td><td>0   </td></tr>\n",
       "\t<tr><td>3   </td><td>3.00</td><td>5.45</td><td>3.00</td><td>0   </td></tr>\n",
       "\t<tr><td>3   </td><td>3.00</td><td>3.00</td><td>3.00</td><td>0   </td></tr>\n",
       "\t<tr><td>3   </td><td>3.00</td><td>3.00</td><td>3.00</td><td>0   </td></tr>\n",
       "\t<tr><td>3   </td><td>3.00</td><td>3.00</td><td>3.00</td><td>0   </td></tr>\n",
       "\t<tr><td>3   </td><td>6.65</td><td>3.00</td><td>3.00</td><td>0   </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       " mag1\\_1 & mag1\\_2 & mag2\\_1 & mag2\\_2 & y\\\\\n",
       "\\hline\n",
       "\t 3    & 3.00 & 3.00 & 5.45 & 0   \\\\\n",
       "\t 3    & 3.00 & 5.45 & 3.00 & 0   \\\\\n",
       "\t 3    & 3.00 & 3.00 & 3.00 & 0   \\\\\n",
       "\t 3    & 3.00 & 3.00 & 3.00 & 0   \\\\\n",
       "\t 3    & 3.00 & 3.00 & 3.00 & 0   \\\\\n",
       "\t 3    & 6.65 & 3.00 & 3.00 & 0   \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "mag1_1 | mag1_2 | mag2_1 | mag2_2 | y | \n",
       "|---|---|---|---|---|---|\n",
       "| 3    | 3.00 | 3.00 | 5.45 | 0    | \n",
       "| 3    | 3.00 | 5.45 | 3.00 | 0    | \n",
       "| 3    | 3.00 | 3.00 | 3.00 | 0    | \n",
       "| 3    | 3.00 | 3.00 | 3.00 | 0    | \n",
       "| 3    | 3.00 | 3.00 | 3.00 | 0    | \n",
       "| 3    | 6.65 | 3.00 | 3.00 | 0    | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  mag1_1 mag1_2 mag2_1 mag2_2 y\n",
       "1 3      3.00   3.00   5.45   0\n",
       "2 3      3.00   5.45   3.00   0\n",
       "3 3      3.00   3.00   3.00   0\n",
       "4 3      3.00   3.00   3.00   0\n",
       "5 3      3.00   3.00   3.00   0\n",
       "6 3      6.65   3.00   3.00   0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(df_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### feature engineering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let us create variable called change which shows rate change from obervation 1 to observation2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_new['change_1'] <- (df_new['mag1_2'] - df_new['mag1_1'] )/df_new['mag1_1']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_new['change_2'] <- (df_new['mag2_2'] - df_new['mag2_1'] )/df_new['mag2_1']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>mag1_1</th><th scope=col>mag1_2</th><th scope=col>mag2_1</th><th scope=col>mag2_2</th><th scope=col>y</th><th scope=col>change_1</th><th scope=col>change_2</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>3         </td><td>3.00      </td><td>3.00      </td><td>5.45      </td><td>0         </td><td>0.000000  </td><td> 0.8166667</td></tr>\n",
       "\t<tr><td>3         </td><td>3.00      </td><td>5.45      </td><td>3.00      </td><td>0         </td><td>0.000000  </td><td>-0.4495413</td></tr>\n",
       "\t<tr><td>3         </td><td>3.00      </td><td>3.00      </td><td>3.00      </td><td>0         </td><td>0.000000  </td><td> 0.0000000</td></tr>\n",
       "\t<tr><td>3         </td><td>3.00      </td><td>3.00      </td><td>3.00      </td><td>0         </td><td>0.000000  </td><td> 0.0000000</td></tr>\n",
       "\t<tr><td>3         </td><td>3.00      </td><td>3.00      </td><td>3.00      </td><td>0         </td><td>0.000000  </td><td> 0.0000000</td></tr>\n",
       "\t<tr><td>3         </td><td>6.65      </td><td>3.00      </td><td>3.00      </td><td>0         </td><td>1.216667  </td><td> 0.0000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllll}\n",
       " mag1\\_1 & mag1\\_2 & mag2\\_1 & mag2\\_2 & y & change\\_1 & change\\_2\\\\\n",
       "\\hline\n",
       "\t 3          & 3.00       & 3.00       & 5.45       & 0          & 0.000000   &  0.8166667\\\\\n",
       "\t 3          & 3.00       & 5.45       & 3.00       & 0          & 0.000000   & -0.4495413\\\\\n",
       "\t 3          & 3.00       & 3.00       & 3.00       & 0          & 0.000000   &  0.0000000\\\\\n",
       "\t 3          & 3.00       & 3.00       & 3.00       & 0          & 0.000000   &  0.0000000\\\\\n",
       "\t 3          & 3.00       & 3.00       & 3.00       & 0          & 0.000000   &  0.0000000\\\\\n",
       "\t 3          & 6.65       & 3.00       & 3.00       & 0          & 1.216667   &  0.0000000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "mag1_1 | mag1_2 | mag2_1 | mag2_2 | y | change_1 | change_2 | \n",
       "|---|---|---|---|---|---|\n",
       "| 3          | 3.00       | 3.00       | 5.45       | 0          | 0.000000   |  0.8166667 | \n",
       "| 3          | 3.00       | 5.45       | 3.00       | 0          | 0.000000   | -0.4495413 | \n",
       "| 3          | 3.00       | 3.00       | 3.00       | 0          | 0.000000   |  0.0000000 | \n",
       "| 3          | 3.00       | 3.00       | 3.00       | 0          | 0.000000   |  0.0000000 | \n",
       "| 3          | 3.00       | 3.00       | 3.00       | 0          | 0.000000   |  0.0000000 | \n",
       "| 3          | 6.65       | 3.00       | 3.00       | 0          | 1.216667   |  0.0000000 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  mag1_1 mag1_2 mag2_1 mag2_2 y change_1 change_2  \n",
       "1 3      3.00   3.00   5.45   0 0.000000  0.8166667\n",
       "2 3      3.00   5.45   3.00   0 0.000000 -0.4495413\n",
       "3 3      3.00   3.00   3.00   0 0.000000  0.0000000\n",
       "4 3      3.00   3.00   3.00   0 0.000000  0.0000000\n",
       "5 3      3.00   3.00   3.00   0 0.000000  0.0000000\n",
       "6 3      6.65   3.00   3.00   0 1.216667  0.0000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(df_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ ., data = df_new)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.37412 -0.17517 -0.11976 -0.09006  0.90994 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error t value Pr(>|t|)  \n",
       "(Intercept) -0.154438   0.077477  -1.993   0.0466 *\n",
       "mag1_1      -0.018307   0.032788  -0.558   0.5768  \n",
       "mag1_2       0.069562   0.038826   1.792   0.0736 .\n",
       "mag2_1       0.036799   0.033569   1.096   0.2733  \n",
       "mag2_2      -0.006554   0.041933  -0.156   0.8758  \n",
       "change_1    -0.165672   0.133792  -1.238   0.2160  \n",
       "change_2     0.037072   0.141648   0.262   0.7936  \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.3536 on 823 degrees of freedom\n",
       "Multiple R-squared:  0.02464,\tAdjusted R-squared:  0.01753 \n",
       "F-statistic: 3.465 on 6 and 823 DF,  p-value: 0.002182\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(lm(y~., df_new))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "lm_predict <- predict(lm(y~., df_new))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AFCggAhQYCQIEBIECAkCBASBAgJAoQE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\nCBASBPwPDhk5uXCJwesAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(lm_predict,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(pROC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+ObJz/jN78oN3rrOkb+/IWef75D2rd/JR61Tkh+DNf9jaR2Hudj/O4TF61Zq/fx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\nhAQIICRAACEBAggJEPAfTahV2fTI4isAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g <- roc(y ~ lm_predict, data = df_new)\n",
    "plot(g) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FOERpTnmQ0LhnR6kCQ2j3uxrS7YrU+f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\nCSGCAAkhggAJIYL+P6B0ZOiNIovCAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "corrplot(cor(df_new))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(corrplot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ mag1_2, data = df_new)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.2280 -0.1799 -0.1268 -0.1268  0.8732 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)  \n",
       "(Intercept)  0.05082    0.04122   1.233   0.2180  \n",
       "mag1_2       0.02531    0.01010   2.506   0.0124 *\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.3556 on 828 degrees of freedom\n",
       "Multiple R-squared:  0.00753,\tAdjusted R-squared:  0.006332 \n",
       "F-statistic: 6.282 on 1 and 828 DF,  p-value: 0.01238\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(lm(y~mag1_2, df_new))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "lm_predict <- predict(lm(y~mag1_2, df_new))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qo1/ICcP+az6SuTH397W6dnc8vHtQ7r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\nSBAgJAgQEgT8A6I19cELXwTUAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(lm_predict,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YKOosYO2TA4yIiONBFSEOgodqIhnfft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\nAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g <- roc(y ~ lm_predict, data = df_new)\n",
    "plot(g) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "830"
      ],
      "text/latex": [
       "830"
      ],
      "text/markdown": [
       "830"
      ],
      "text/plain": [
       "[1] 830"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nrow(df_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "  0   1 \n",
       "706 124 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table(df_new$y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "lets sample 150's from data - balancing the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_1 <- df_new[df_new['y'] == 1,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_0 <- df_new[df_new['y'] == 0,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_0_sample <- df_0[sample(nrow(df_0),size = 150),]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_bal <- rbind(df_1,df_0_sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>mag1_1</th><th scope=col>mag1_2</th><th scope=col>mag2_1</th><th scope=col>mag2_2</th><th scope=col>y</th><th scope=col>change_1</th><th scope=col>change_2</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>9</th><td>3.0        </td><td>3.0        </td><td>3.0        </td><td>3.0        </td><td>1          </td><td> 0.00000000</td><td> 0.0000000 </td></tr>\n",
       "\t<tr><th scope=row>41</th><td>3.0        </td><td>7.2        </td><td>3.0        </td><td>3.0        </td><td>1          </td><td> 1.40000000</td><td> 0.0000000 </td></tr>\n",
       "\t<tr><th scope=row>43</th><td>5.4        </td><td>5.2        </td><td>5.4        </td><td>3.0        </td><td>1          </td><td>-0.03703704</td><td>-0.4444444 </td></tr>\n",
       "\t<tr><th scope=row>107</th><td>5.9        </td><td>5.6        </td><td>3.0        </td><td>3.0        </td><td>1          </td><td>-0.05084746</td><td> 0.0000000 </td></tr>\n",
       "\t<tr><th scope=row>128</th><td>5.2        </td><td>3.0        </td><td>3.0        </td><td>6.4        </td><td>1          </td><td>-0.42307692</td><td> 1.1333333 </td></tr>\n",
       "\t<tr><th scope=row>164</th><td>3.0        </td><td>3.0        </td><td>3.0        </td><td>3.0        </td><td>1          </td><td> 0.00000000</td><td> 0.0000000 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllll}\n",
       "  & mag1\\_1 & mag1\\_2 & mag2\\_1 & mag2\\_2 & y & change\\_1 & change\\_2\\\\\n",
       "\\hline\n",
       "\t9 & 3.0         & 3.0         & 3.0         & 3.0         & 1           &  0.00000000 &  0.0000000 \\\\\n",
       "\t41 & 3.0         & 7.2         & 3.0         & 3.0         & 1           &  1.40000000 &  0.0000000 \\\\\n",
       "\t43 & 5.4         & 5.2         & 5.4         & 3.0         & 1           & -0.03703704 & -0.4444444 \\\\\n",
       "\t107 & 5.9         & 5.6         & 3.0         & 3.0         & 1           & -0.05084746 &  0.0000000 \\\\\n",
       "\t128 & 5.2         & 3.0         & 3.0         & 6.4         & 1           & -0.42307692 &  1.1333333 \\\\\n",
       "\t164 & 3.0         & 3.0         & 3.0         & 3.0         & 1           &  0.00000000 &  0.0000000 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | mag1_1 | mag1_2 | mag2_1 | mag2_2 | y | change_1 | change_2 | \n",
       "|---|---|---|---|---|---|\n",
       "| 9 | 3.0         | 3.0         | 3.0         | 3.0         | 1           |  0.00000000 |  0.0000000  | \n",
       "| 41 | 3.0         | 7.2         | 3.0         | 3.0         | 1           |  1.40000000 |  0.0000000  | \n",
       "| 43 | 5.4         | 5.2         | 5.4         | 3.0         | 1           | -0.03703704 | -0.4444444  | \n",
       "| 107 | 5.9         | 5.6         | 3.0         | 3.0         | 1           | -0.05084746 |  0.0000000  | \n",
       "| 128 | 5.2         | 3.0         | 3.0         | 6.4         | 1           | -0.42307692 |  1.1333333  | \n",
       "| 164 | 3.0         | 3.0         | 3.0         | 3.0         | 1           |  0.00000000 |  0.0000000  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "    mag1_1 mag1_2 mag2_1 mag2_2 y change_1    change_2  \n",
       "9   3.0    3.0    3.0    3.0    1  0.00000000  0.0000000\n",
       "41  3.0    7.2    3.0    3.0    1  1.40000000  0.0000000\n",
       "43  5.4    5.2    5.4    3.0    1 -0.03703704 -0.4444444\n",
       "107 5.9    5.6    3.0    3.0    1 -0.05084746  0.0000000\n",
       "128 5.2    3.0    3.0    6.4    1 -0.42307692  1.1333333\n",
       "164 3.0    3.0    3.0    3.0    1  0.00000000  0.0000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(df_bal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ ., data = df_bal)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.6912 -0.4236 -0.2923  0.4915  0.7077 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)  \n",
       "(Intercept) -0.23108    0.18929  -1.221   0.2233  \n",
       "mag1_1      -0.04772    0.07982  -0.598   0.5504  \n",
       "mag1_2       0.17426    0.09141   1.906   0.0577 .\n",
       "mag2_1       0.13912    0.07960   1.748   0.0817 .\n",
       "mag2_2      -0.09119    0.09729  -0.937   0.3495  \n",
       "change_1    -0.33953    0.32240  -1.053   0.2932  \n",
       "change_2     0.34137    0.33296   1.025   0.3062  \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.4849 on 267 degrees of freedom\n",
       "Multiple R-squared:  0.07524,\tAdjusted R-squared:  0.05446 \n",
       "F-statistic: 3.621 on 6 and 267 DF,  p-value: 0.001804\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(lm(y~., df_bal))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "lm_predict <- predict(lm(y~., df_bal))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gQICQKEBAFCggAhQYCQIEBIECAkCBAS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\nJAgQEgQICQKEBAFCggAhQYCQIEBIEPA/RsqWSX2GRTwAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y1 <- df_bal$y\n",
    "plot(lm_predict,y1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EiHdjWp2t+1HEd6jY7yJRjSOvycj2F1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\niZmHmwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g <- roc(y ~ lm_predict, data = df_bal)\n",
    "plot(g) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us try neural networks "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(nnet)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All the above models did not consider training and testing data seperately. Let us not split our data into test and train.\n",
    "We train the model on train and test the model on the test data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 90% of the sample size\n",
    "smp_size <- floor(0.9 * nrow(df_new))\n",
    "\n",
    "## set the seed to make your partition reproducible\n",
    "set.seed(123)\n",
    "train_ind <- sample(seq_len(nrow(df_new)), size = smp_size)\n",
    "\n",
    "train <- df_new[train_ind, ]\n",
    "test <- df_new[-train_ind, ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 90% of the sample size\n",
    "smp_size <- floor(0.9 * nrow(df_bal))\n",
    "\n",
    "## set the seed to make your partition reproducible\n",
    "set.seed(123)\n",
    "train_ind <- sample(seq_len(nrow(df_bal)), size = smp_size)\n",
    "\n",
    "train_bal <- df_bal[train_ind, ]\n",
    "test_bal <- df_bal[-train_ind, ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# weights:  241\n",
      "initial  value 183.557609 \n",
      "final  value 116.000000 \n",
      "converged\n"
     ]
    }
   ],
   "source": [
    "nn_all_30 <- nnet(y~., train ,size = 30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# weights:  801\n",
      "initial  value 109.038957 \n",
      "iter  10 value 93.958847\n",
      "iter  20 value 93.217290\n",
      "iter  30 value 92.589350\n",
      "iter  40 value 91.655437\n",
      "iter  50 value 90.182238\n",
      "iter  60 value 88.263043\n",
      "iter  70 value 85.921538\n",
      "iter  80 value 82.944668\n",
      "iter  90 value 80.236074\n",
      "iter 100 value 77.085357\n",
      "final  value 77.085357 \n",
      "stopped after 100 iterations\n"
     ]
    }
   ],
   "source": [
    "nn_all_100 <- nnet(y~., train ,size = 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_nn_all_30 <- predict(nn_all_30,test, type = 'raw')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in roc.default(response, m[[predictors]], ...):\n",
      "\"Deprecated use a matrix as predictor. Unexpected results may be produced, please pass a numeric vector.\""
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g <- roc(y ~ pred_nn_all_30, data = test)\n",
    "plot(g) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_nn_all_100 <- predict(nn_all_100,test, type = 'raw')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in roc.default(response, m[[predictors]], ...):\n",
      "\"Deprecated use a matrix as predictor. Unexpected results may be produced, please pass a numeric vector.\""
     ]
    },
    {
     "data": {
      "image/png": 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e1OdYZER7K4rt2pypDoSBjXtTvVGBId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\nlB8AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g <- roc(y ~ pred_nn_all_100, data = test)\n",
    "plot(g) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# weights:  121\n",
      "initial  value 106.542629 \n",
      "iter  10 value 57.201629\n",
      "iter  20 value 53.173035\n",
      "iter  30 value 51.682638\n",
      "iter  40 value 50.579717\n",
      "iter  50 value 47.901183\n",
      "iter  60 value 45.852693\n",
      "iter  70 value 44.103669\n",
      "iter  80 value 42.213674\n",
      "iter  90 value 41.517267\n",
      "iter 100 value 41.037512\n",
      "final  value 41.037512 \n",
      "stopped after 100 iterations\n"
     ]
    }
   ],
   "source": [
    "nn_bal_15 <- nnet(y~., train_bal ,size = 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# weights:  241\n",
      "initial  value 64.590689 \n",
      "iter  10 value 54.065950\n",
      "iter  20 value 51.578091\n",
      "iter  30 value 49.231539\n",
      "iter  40 value 47.082622\n",
      "iter  50 value 44.697261\n",
      "iter  60 value 40.997991\n",
      "iter  70 value 38.317114\n",
      "iter  80 value 37.347483\n",
      "iter  90 value 36.806980\n",
      "iter 100 value 36.089197\n",
      "final  value 36.089197 \n",
      "stopped after 100 iterations\n"
     ]
    }
   ],
   "source": [
    "nn_bal_30 <- nnet(y~., train_bal ,size = 30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_nn_bal_15 <- predict(nn_bal_15,test_bal, type = 'raw')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in roc.default(response, m[[predictors]], ...):\n",
      "\"Deprecated use a matrix as predictor. Unexpected results may be produced, please pass a numeric vector.\""
     ]
    },
    {
     "data": {
      "image/png": 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3l7euhImegpQt317Ab22ul6sruUjrQJ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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g <- roc(y ~ pred_nn_bal_15, data = test_bal)\n",
    "plot(g) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}