LogisticRegressionReview2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "library(plyr)\n",
    "library(caTools)\n",
    "library(ggplot2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "songs_data <- read.csv(\"datasets/songs.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>1</th><th scope=col>2</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>year</th><td>2010                              </td><td>2010                              </td></tr>\n",
       "\t<tr><th scope=row>songtitle</th><td>This Is the House That Doubt Built                            </td><td><span style=white-space:pre-wrap>Sticks &amp; Bricks   </span></td></tr>\n",
       "\t<tr><th scope=row>artistname</th><td>A Day to Remember                 </td><td>A Day to Remember                 </td></tr>\n",
       "\t<tr><th scope=row>songID</th><td>SOBGGAB12C5664F054                </td><td>SOPAQHU1315CD47F31                </td></tr>\n",
       "\t<tr><th scope=row>artistID</th><td>AROBSHL1187B9AFB01                </td><td>AROBSHL1187B9AFB01                </td></tr>\n",
       "\t<tr><th scope=row>timesignature</th><td>3                                 </td><td>4                                 </td></tr>\n",
       "\t<tr><th scope=row>timesignature_confidence</th><td>0.853                             </td><td>1.000                             </td></tr>\n",
       "\t<tr><th scope=row>loudness</th><td>-4.262                            </td><td>-4.051                            </td></tr>\n",
       "\t<tr><th scope=row>tempo</th><td> 91.525                           </td><td>140.048                           </td></tr>\n",
       "\t<tr><th scope=row>tempo_confidence</th><td>0.953                             </td><td>0.921                             </td></tr>\n",
       "\t<tr><th scope=row>key</th><td>11                                </td><td>10                                </td></tr>\n",
       "\t<tr><th scope=row>key_confidence</th><td>0.453                             </td><td>0.469                             </td></tr>\n",
       "\t<tr><th scope=row>energy</th><td>0.9666556                         </td><td>0.9847095                         </td></tr>\n",
       "\t<tr><th scope=row>pitch</th><td>0.024                             </td><td>0.025                             </td></tr>\n",
       "\t<tr><th scope=row>timbre_0_min</th><td>0.002                             </td><td>0.000                             </td></tr>\n",
       "\t<tr><th scope=row>timbre_0_max</th><td>57.342                            </td><td>57.414                            </td></tr>\n",
       "\t<tr><th scope=row>timbre_1_min</th><td> -6.496                           </td><td>-37.351                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_1_max</th><td>171.093                           </td><td>171.130                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_2_min</th><td> -81.664                          </td><td>-149.589                          </td></tr>\n",
       "\t<tr><th scope=row>timbre_2_max</th><td> 95.117                           </td><td>180.334                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_3_min</th><td>-285.049                          </td><td>-380.143                          </td></tr>\n",
       "\t<tr><th scope=row>timbre_3_max</th><td>259.426                           </td><td>384.166                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_4_min</th><td>-40.385                           </td><td>-48.662                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_4_max</th><td> 73.630                           </td><td>100.414                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_5_min</th><td>-104.683                          </td><td> -87.267                          </td></tr>\n",
       "\t<tr><th scope=row>timbre_5_max</th><td>183.089                           </td><td> 42.798                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_6_min</th><td>-88.771                           </td><td>-86.895                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_6_max</th><td>73.549                            </td><td>75.455                            </td></tr>\n",
       "\t<tr><th scope=row>timbre_7_min</th><td>-71.127                           </td><td>-65.807                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_7_max</th><td> 82.475                           </td><td>106.918                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_8_min</th><td>-52.025                           </td><td>-61.320                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_8_max</th><td>39.116                            </td><td>35.378                            </td></tr>\n",
       "\t<tr><th scope=row>timbre_9_min</th><td>-35.368                           </td><td>-81.928                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_9_max</th><td>71.642                            </td><td>74.574                            </td></tr>\n",
       "\t<tr><th scope=row>timbre_10_min</th><td>-126.440                          </td><td>-103.808                          </td></tr>\n",
       "\t<tr><th scope=row>timbre_10_max</th><td> 18.658                           </td><td>121.935                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_11_min</th><td>-44.770                           </td><td>-38.892                           </td></tr>\n",
       "\t<tr><th scope=row>timbre_11_max</th><td>25.989                            </td><td>22.513                            </td></tr>\n",
       "\t<tr><th scope=row>Top10</th><td>0                                 </td><td>0                                 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       "  & 1 & 2\\\\\n",
       "\\hline\n",
       "\tyear & 2010                               & 2010                              \\\\\n",
       "\tsongtitle & This Is the House That Doubt Built & Sticks \\& Bricks                 \\\\\n",
       "\tartistname & A Day to Remember                  & A Day to Remember                 \\\\\n",
       "\tsongID & SOBGGAB12C5664F054                 & SOPAQHU1315CD47F31                \\\\\n",
       "\tartistID & AROBSHL1187B9AFB01                 & AROBSHL1187B9AFB01                \\\\\n",
       "\ttimesignature & 3                                  & 4                                 \\\\\n",
       "\ttimesignature\\_confidence & 0.853                              & 1.000                             \\\\\n",
       "\tloudness & -4.262                             & -4.051                            \\\\\n",
       "\ttempo &  91.525                            & 140.048                           \\\\\n",
       "\ttempo\\_confidence & 0.953                              & 0.921                             \\\\\n",
       "\tkey & 11                                 & 10                                \\\\\n",
       "\tkey\\_confidence & 0.453                              & 0.469                             \\\\\n",
       "\tenergy & 0.9666556                          & 0.9847095                         \\\\\n",
       "\tpitch & 0.024                              & 0.025                             \\\\\n",
       "\ttimbre\\_0\\_min & 0.002                              & 0.000                             \\\\\n",
       "\ttimbre\\_0\\_max & 57.342                             & 57.414                            \\\\\n",
       "\ttimbre\\_1\\_min &  -6.496                            & -37.351                           \\\\\n",
       "\ttimbre\\_1\\_max & 171.093                            & 171.130                           \\\\\n",
       "\ttimbre\\_2\\_min &  -81.664                           & -149.589                          \\\\\n",
       "\ttimbre\\_2\\_max &  95.117                            & 180.334                           \\\\\n",
       "\ttimbre\\_3\\_min & -285.049                           & -380.143                          \\\\\n",
       "\ttimbre\\_3\\_max & 259.426                            & 384.166                           \\\\\n",
       "\ttimbre\\_4\\_min & -40.385                            & -48.662                           \\\\\n",
       "\ttimbre\\_4\\_max &  73.630                            & 100.414                           \\\\\n",
       "\ttimbre\\_5\\_min & -104.683                           &  -87.267                          \\\\\n",
       "\ttimbre\\_5\\_max & 183.089                            &  42.798                           \\\\\n",
       "\ttimbre\\_6\\_min & -88.771                            & -86.895                           \\\\\n",
       "\ttimbre\\_6\\_max & 73.549                             & 75.455                            \\\\\n",
       "\ttimbre\\_7\\_min & -71.127                            & -65.807                           \\\\\n",
       "\ttimbre\\_7\\_max &  82.475                            & 106.918                           \\\\\n",
       "\ttimbre\\_8\\_min & -52.025                            & -61.320                           \\\\\n",
       "\ttimbre\\_8\\_max & 39.116                             & 35.378                            \\\\\n",
       "\ttimbre\\_9\\_min & -35.368                            & -81.928                           \\\\\n",
       "\ttimbre\\_9\\_max & 71.642                             & 74.574                            \\\\\n",
       "\ttimbre\\_10\\_min & -126.440                           & -103.808                          \\\\\n",
       "\ttimbre\\_10\\_max &  18.658                            & 121.935                           \\\\\n",
       "\ttimbre\\_11\\_min & -44.770                            & -38.892                           \\\\\n",
       "\ttimbre\\_11\\_max & 25.989                             & 22.513                            \\\\\n",
       "\tTop10 & 0                                  & 0                                 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | 1 | 2 | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| year | 2010                               | 2010                               | \n",
       "| songtitle | This Is the House That Doubt Built | Sticks & Bricks                    | \n",
       "| artistname | A Day to Remember                  | A Day to Remember                  | \n",
       "| songID | SOBGGAB12C5664F054                 | SOPAQHU1315CD47F31                 | \n",
       "| artistID | AROBSHL1187B9AFB01                 | AROBSHL1187B9AFB01                 | \n",
       "| timesignature | 3                                  | 4                                  | \n",
       "| timesignature_confidence | 0.853                              | 1.000                              | \n",
       "| loudness | -4.262                             | -4.051                             | \n",
       "| tempo |  91.525                            | 140.048                            | \n",
       "| tempo_confidence | 0.953                              | 0.921                              | \n",
       "| key | 11                                 | 10                                 | \n",
       "| key_confidence | 0.453                              | 0.469                              | \n",
       "| energy | 0.9666556                          | 0.9847095                          | \n",
       "| pitch | 0.024                              | 0.025                              | \n",
       "| timbre_0_min | 0.002                              | 0.000                              | \n",
       "| timbre_0_max | 57.342                             | 57.414                             | \n",
       "| timbre_1_min |  -6.496                            | -37.351                            | \n",
       "| timbre_1_max | 171.093                            | 171.130                            | \n",
       "| timbre_2_min |  -81.664                           | -149.589                           | \n",
       "| timbre_2_max |  95.117                            | 180.334                            | \n",
       "| timbre_3_min | -285.049                           | -380.143                           | \n",
       "| timbre_3_max | 259.426                            | 384.166                            | \n",
       "| timbre_4_min | -40.385                            | -48.662                            | \n",
       "| timbre_4_max |  73.630                            | 100.414                            | \n",
       "| timbre_5_min | -104.683                           |  -87.267                           | \n",
       "| timbre_5_max | 183.089                            |  42.798                            | \n",
       "| timbre_6_min | -88.771                            | -86.895                            | \n",
       "| timbre_6_max | 73.549                             | 75.455                             | \n",
       "| timbre_7_min | -71.127                            | -65.807                            | \n",
       "| timbre_7_max |  82.475                            | 106.918                            | \n",
       "| timbre_8_min | -52.025                            | -61.320                            | \n",
       "| timbre_8_max | 39.116                             | 35.378                             | \n",
       "| timbre_9_min | -35.368                            | -81.928                            | \n",
       "| timbre_9_max | 71.642                             | 74.574                             | \n",
       "| timbre_10_min | -126.440                           | -103.808                           | \n",
       "| timbre_10_max |  18.658                            | 121.935                            | \n",
       "| timbre_11_min | -44.770                            | -38.892                            | \n",
       "| timbre_11_max | 25.989                             | 22.513                             | \n",
       "| Top10 | 0                                  | 0                                  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "                         1                                  2                 \n",
       "year                     2010                               2010              \n",
       "songtitle                This Is the House That Doubt Built Sticks & Bricks   \n",
       "artistname               A Day to Remember                  A Day to Remember \n",
       "songID                   SOBGGAB12C5664F054                 SOPAQHU1315CD47F31\n",
       "artistID                 AROBSHL1187B9AFB01                 AROBSHL1187B9AFB01\n",
       "timesignature            3                                  4                 \n",
       "timesignature_confidence 0.853                              1.000             \n",
       "loudness                 -4.262                             -4.051            \n",
       "tempo                     91.525                            140.048           \n",
       "tempo_confidence         0.953                              0.921             \n",
       "key                      11                                 10                \n",
       "key_confidence           0.453                              0.469             \n",
       "energy                   0.9666556                          0.9847095         \n",
       "pitch                    0.024                              0.025             \n",
       "timbre_0_min             0.002                              0.000             \n",
       "timbre_0_max             57.342                             57.414            \n",
       "timbre_1_min              -6.496                            -37.351           \n",
       "timbre_1_max             171.093                            171.130           \n",
       "timbre_2_min              -81.664                           -149.589          \n",
       "timbre_2_max              95.117                            180.334           \n",
       "timbre_3_min             -285.049                           -380.143          \n",
       "timbre_3_max             259.426                            384.166           \n",
       "timbre_4_min             -40.385                            -48.662           \n",
       "timbre_4_max              73.630                            100.414           \n",
       "timbre_5_min             -104.683                            -87.267          \n",
       "timbre_5_max             183.089                             42.798           \n",
       "timbre_6_min             -88.771                            -86.895           \n",
       "timbre_6_max             73.549                             75.455            \n",
       "timbre_7_min             -71.127                            -65.807           \n",
       "timbre_7_max              82.475                            106.918           \n",
       "timbre_8_min             -52.025                            -61.320           \n",
       "timbre_8_max             39.116                             35.378            \n",
       "timbre_9_min             -35.368                            -81.928           \n",
       "timbre_9_max             71.642                             74.574            \n",
       "timbre_10_min            -126.440                           -103.808          \n",
       "timbre_10_max             18.658                            121.935           \n",
       "timbre_11_min            -44.770                            -38.892           \n",
       "timbre_11_max            25.989                             22.513            \n",
       "Top10                    0                                  0                 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t(head(songs_data, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t7574 obs. of  39 variables:\n",
      " $ year                    : int  2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 ...\n",
      " $ songtitle               : Factor w/ 7141 levels \"'03 Bonnie & Clyde\",..: 6204 5522 241 3098 47 607 254 4419 2887 6756 ...\n",
      " $ artistname              : Factor w/ 1032 levels \"50 Cent\",\"98 Degrees\",..: 3 3 3 3 3 3 3 3 3 12 ...\n",
      " $ songID                  : Factor w/ 7549 levels \"SOAACNI1315CD4AC42\",..: 595 5439 5252 1716 3431 1020 1831 3964 6904 2473 ...\n",
      " $ artistID                : Factor w/ 1047 levels \"AR00B1I1187FB433EB\",..: 671 671 671 671 671 671 671 671 671 507 ...\n",
      " $ timesignature           : int  3 4 4 4 4 4 4 4 4 4 ...\n",
      " $ timesignature_confidence: num  0.853 1 1 1 0.788 1 0.968 0.861 0.622 0.938 ...\n",
      " $ loudness                : num  -4.26 -4.05 -3.57 -3.81 -4.71 ...\n",
      " $ tempo                   : num  91.5 140 160.5 97.5 140.1 ...\n",
      " $ tempo_confidence        : num  0.953 0.921 0.489 0.794 0.286 0.347 0.273 0.83 0.018 0.929 ...\n",
      " $ key                     : int  11 10 2 1 6 4 10 5 9 11 ...\n",
      " $ key_confidence          : num  0.453 0.469 0.209 0.632 0.483 0.627 0.715 0.423 0.751 0.602 ...\n",
      " $ energy                  : num  0.967 0.985 0.99 0.939 0.988 ...\n",
      " $ pitch                   : num  0.024 0.025 0.026 0.013 0.063 0.038 0.026 0.033 0.027 0.004 ...\n",
      " $ timbre_0_min            : num  0.002 0 0.003 0 0 ...\n",
      " $ timbre_0_max            : num  57.3 57.4 57.4 57.8 56.9 ...\n",
      " $ timbre_1_min            : num  -6.5 -37.4 -17.2 -32.1 -223.9 ...\n",
      " $ timbre_1_max            : num  171 171 171 221 171 ...\n",
      " $ timbre_2_min            : num  -81.7 -149.6 -72.9 -138.6 -147.2 ...\n",
      " $ timbre_2_max            : num  95.1 180.3 157.9 173.4 166 ...\n",
      " $ timbre_3_min            : num  -285 -380.1 -204 -73.5 -128.1 ...\n",
      " $ timbre_3_max            : num  259 384 251 373 389 ...\n",
      " $ timbre_4_min            : num  -40.4 -48.7 -66 -55.6 -43.9 ...\n",
      " $ timbre_4_max            : num  73.6 100.4 152.1 119.2 99.3 ...\n",
      " $ timbre_5_min            : num  -104.7 -87.3 -98.7 -77.5 -96.1 ...\n",
      " $ timbre_5_max            : num  183.1 42.8 141.4 141.2 38.3 ...\n",
      " $ timbre_6_min            : num  -88.8 -86.9 -88.9 -70.8 -110.8 ...\n",
      " $ timbre_6_max            : num  73.5 75.5 66.5 64.5 72.4 ...\n",
      " $ timbre_7_min            : num  -71.1 -65.8 -67.4 -63.7 -55.9 ...\n",
      " $ timbre_7_max            : num  82.5 106.9 80.6 96.7 110.3 ...\n",
      " $ timbre_8_min            : num  -52 -61.3 -59.8 -78.7 -56.5 ...\n",
      " $ timbre_8_max            : num  39.1 35.4 46 41.1 37.6 ...\n",
      " $ timbre_9_min            : num  -35.4 -81.9 -46.3 -49.2 -48.6 ...\n",
      " $ timbre_9_max            : num  71.6 74.6 59.9 95.4 67.6 ...\n",
      " $ timbre_10_min           : num  -126.4 -103.8 -108.3 -102.7 -52.8 ...\n",
      " $ timbre_10_max           : num  18.7 121.9 33.3 46.4 22.9 ...\n",
      " $ timbre_11_min           : num  -44.8 -38.9 -43.7 -59.4 -50.4 ...\n",
      " $ timbre_11_max           : num  26 22.5 25.7 37.1 32.8 ...\n",
      " $ Top10                   : int  0 0 0 0 0 0 0 0 0 1 ...\n"
     ]
    }
   ],
   "source": [
    "str(songs_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 \n",
       " 328  196  186  324  198  258  178  329  380  357  363  282  518  434  479  392 \n",
       "2006 2007 2008 2009 2010 \n",
       " 479  622  415  483  373 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table(songs_data$year)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Top10</th><th scope=col>freq</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0   </td><td>6455</td></tr>\n",
       "\t<tr><td>1   </td><td>1119</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " Top10 & freq\\\\\n",
       "\\hline\n",
       "\t 0    & 6455\\\\\n",
       "\t 1    & 1119\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Top10 | freq | \n",
       "|---|---|\n",
       "| 0    | 6455 | \n",
       "| 1    | 1119 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  Top10 freq\n",
       "1 0     6455\n",
       "2 1     1119"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "count(songs_data, \"Top10\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>7574</li>\n",
       "\t<li>39</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 7574\n",
       "\\item 39\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 7574\n",
       "2. 39\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 7574   39"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(songs_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>7201</li>\n",
       "\t<li>39</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 7201\n",
       "\\item 39\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 7201\n",
       "2. 39\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 7201   39"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>373</li>\n",
       "\t<li>39</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 373\n",
       "\\item 39\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 373\n",
       "2. 39\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 373  39"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#split the data into train and test sets\n",
    "\n",
    "songs_traindata <- subset(songs_data, songs_data$year <= 2009)\n",
    "songs_testdata <- subset(songs_data, songs_data$year > 2009)\n",
    "\n",
    "dim(songs_traindata)\n",
    "dim(songs_testdata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "colsRemove = c(\"year\", \"songtitle\", \"artistname\", \"songID\", \"artistID\")\n",
    "\n",
    "songs_traindata <- songs_traindata[, !names(songs_traindata) %in% colsRemove]\n",
    "songs_testdata <- songs_testdata[, !names(songs_testdata) %in% colsRemove]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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G3qmz8ZSLjblE6Sdabh8HhSr0GBD7zvXXr4iqYatrk9cP++0jfEHVsG0iggdWzX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\n",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "songs_plot <- ggplot(songs_traindata, aes(x = loudness, y = energy)) + \n",
    "                    geom_point(aes(color = factor(Top10), shape = factor(Top10)))\n",
    "\n",
    "songs_plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "songsLog1 <- glm(Top10 ~ . ,\n",
    "                    data = songs_traindata, \n",
    "                     family = binomial)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "glm(formula = Top10 ~ ., family = binomial, data = songs_traindata)\n",
       "\n",
       "Deviance Residuals: \n",
       "    Min       1Q   Median       3Q      Max  \n",
       "-1.9220  -0.5399  -0.3459  -0.1845   3.0770  \n",
       "\n",
       "Coefficients:\n",
       "                           Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)               1.470e+01  1.806e+00   8.138 4.03e-16 ***\n",
       "timesignature             1.264e-01  8.674e-02   1.457 0.145050    \n",
       "timesignature_confidence  7.450e-01  1.953e-01   3.815 0.000136 ***\n",
       "loudness                  2.999e-01  2.917e-02  10.282  < 2e-16 ***\n",
       "tempo                     3.634e-04  1.691e-03   0.215 0.829889    \n",
       "tempo_confidence          4.732e-01  1.422e-01   3.329 0.000873 ***\n",
       "key                       1.588e-02  1.039e-02   1.529 0.126349    \n",
       "key_confidence            3.087e-01  1.412e-01   2.187 0.028760 *  \n",
       "energy                   -1.502e+00  3.099e-01  -4.847 1.25e-06 ***\n",
       "pitch                    -4.491e+01  6.835e+00  -6.570 5.02e-11 ***\n",
       "timbre_0_min              2.316e-02  4.256e-03   5.441 5.29e-08 ***\n",
       "timbre_0_max             -3.310e-01  2.569e-02 -12.882  < 2e-16 ***\n",
       "timbre_1_min              5.881e-03  7.798e-04   7.542 4.64e-14 ***\n",
       "timbre_1_max             -2.449e-04  7.152e-04  -0.342 0.732087    \n",
       "timbre_2_min             -2.127e-03  1.126e-03  -1.889 0.058843 .  \n",
       "timbre_2_max              6.586e-04  9.066e-04   0.726 0.467571    \n",
       "timbre_3_min              6.920e-04  5.985e-04   1.156 0.247583    \n",
       "timbre_3_max             -2.967e-03  5.815e-04  -5.103 3.34e-07 ***\n",
       "timbre_4_min              1.040e-02  1.985e-03   5.237 1.63e-07 ***\n",
       "timbre_4_max              6.110e-03  1.550e-03   3.942 8.10e-05 ***\n",
       "timbre_5_min             -5.598e-03  1.277e-03  -4.385 1.16e-05 ***\n",
       "timbre_5_max              7.736e-05  7.935e-04   0.097 0.922337    \n",
       "timbre_6_min             -1.686e-02  2.264e-03  -7.445 9.66e-14 ***\n",
       "timbre_6_max              3.668e-03  2.190e-03   1.675 0.093875 .  \n",
       "timbre_7_min             -4.549e-03  1.781e-03  -2.554 0.010661 *  \n",
       "timbre_7_max             -3.774e-03  1.832e-03  -2.060 0.039408 *  \n",
       "timbre_8_min              3.911e-03  2.851e-03   1.372 0.170123    \n",
       "timbre_8_max              4.011e-03  3.003e-03   1.336 0.181620    \n",
       "timbre_9_min              1.367e-03  2.998e-03   0.456 0.648356    \n",
       "timbre_9_max              1.603e-03  2.434e-03   0.659 0.510188    \n",
       "timbre_10_min             4.126e-03  1.839e-03   2.244 0.024852 *  \n",
       "timbre_10_max             5.825e-03  1.769e-03   3.292 0.000995 ***\n",
       "timbre_11_min            -2.625e-02  3.693e-03  -7.108 1.18e-12 ***\n",
       "timbre_11_max             1.967e-02  3.385e-03   5.811 6.21e-09 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "(Dispersion parameter for binomial family taken to be 1)\n",
       "\n",
       "    Null deviance: 6017.5  on 7200  degrees of freedom\n",
       "Residual deviance: 4759.2  on 7167  degrees of freedom\n",
       "AIC: 4827.2\n",
       "\n",
       "Number of Fisher Scoring iterations: 6\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(songsLog1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>1</dt>\n",
       "\t\t<dd>0.0328564215706949</dd>\n",
       "\t<dt>2</dt>\n",
       "\t\t<dd>0.0318610976699903</dd>\n",
       "\t<dt>3</dt>\n",
       "\t\t<dd>0.0380681345183232</dd>\n",
       "\t<dt>4</dt>\n",
       "\t\t<dd>0.0660660252609541</dd>\n",
       "\t<dt>5</dt>\n",
       "\t\t<dd>0.00250255183519714</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[1] 0.0328564215706949\n",
       "\\item[2] 0.0318610976699903\n",
       "\\item[3] 0.0380681345183232\n",
       "\\item[4] 0.0660660252609541\n",
       "\\item[5] 0.00250255183519714\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "1\n",
       ":   0.03285642157069492\n",
       ":   0.03186109766999033\n",
       ":   0.03806813451832324\n",
       ":   0.06606602526095415\n",
       ":   0.00250255183519714\n",
       "\n"
      ],
      "text/plain": [
       "          1           2           3           4           5 \n",
       "0.032856422 0.031861098 0.038068135 0.066066025 0.002502552 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "probs <- predict(songsLog1, type = \"response\", newdata = songs_testdata)\n",
    "probs[0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   preds\n",
       "      0   1\n",
       "  0 311   3\n",
       "  1  48  11"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "preds <- ifelse(probs > 0.5, 1, 0)\n",
    "table(songs_testdata$Top10, preds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'Accuracy: 0.863270777479893'"
      ],
      "text/latex": [
       "'Accuracy: 0.863270777479893'"
      ],
      "text/markdown": [
       "'Accuracy: 0.863270777479893'"
      ],
      "text/plain": [
       "[1] \"Accuracy: 0.863270777479893\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "misClassify <- mean(preds != songs_testdata$Top10)\n",
    "paste(\"Accuracy:\", 1 - misClassify)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Top10</th><th scope=col>freq</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0   </td><td>6455</td></tr>\n",
       "\t<tr><td>1   </td><td>1119</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " Top10 & freq\\\\\n",
       "\\hline\n",
       "\t 0    & 6455\\\\\n",
       "\t 1    & 1119\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Top10 | freq | \n",
       "|---|---|\n",
       "| 0    | 6455 | \n",
       "| 1    | 1119 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  Top10 freq\n",
       "1 0     6455\n",
       "2 1     1119"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "count(songs_data, \"Top10\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'Baseline Accuracy: 0.85225772379192'"
      ],
      "text/latex": [
       "'Baseline Accuracy: 0.85225772379192'"
      ],
      "text/markdown": [
       "'Baseline Accuracy: 0.85225772379192'"
      ],
      "text/plain": [
       "[1] \"Baseline Accuracy: 0.85225772379192\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Not Top10 dominates the original database. Therefore the baseline accuracy is:\n",
    "\n",
    "paste(\"Baseline Accuracy:\", (6455)/ (6455 + 1119))"
   ]
  }
 ],
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