base_algos/R/Logistic regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(ggplot2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binary Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>oxygen</th><th scope=col>survive</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>10</td><td>0 </td></tr>\n",
       "\t<tr><td> 5</td><td>0 </td></tr>\n",
       "\t<tr><td>75</td><td>1 </td></tr>\n",
       "\t<tr><td>14</td><td>0 </td></tr>\n",
       "\t<tr><td> 8</td><td>0 </td></tr>\n",
       "\t<tr><td>50</td><td>1 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " oxygen & survive\\\\\n",
       "\\hline\n",
       "\t 10 & 0 \\\\\n",
       "\t  5 & 0 \\\\\n",
       "\t 75 & 1 \\\\\n",
       "\t 14 & 0 \\\\\n",
       "\t  8 & 0 \\\\\n",
       "\t 50 & 1 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "oxygen | survive | \n",
       "|---|---|---|---|---|---|\n",
       "| 10 | 0  | \n",
       "|  5 | 0  | \n",
       "| 75 | 1  | \n",
       "| 14 | 0  | \n",
       "|  8 | 0  | \n",
       "| 50 | 1  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  oxygen survive\n",
       "1 10     0      \n",
       "2  5     0      \n",
       "3 75     1      \n",
       "4 14     0      \n",
       "5  8     0      \n",
       "6 50     1      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Loading data\n",
    "log_reg_bin <- read.csv(\"../../datasets/log_reg_bin.csv\")\n",
    "head(log_reg_bin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Making output variable as factors <categorial>\n",
    "log_reg_bin$survive <- as.factor(log_reg_bin$survive)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Making train and test data\n",
    "set.seed(42)\n",
    "ind <- sample(x = nrow(log_reg_bin), size = floor(0.75 * nrow(log_reg_bin)))\n",
    "\n",
    "log_bin_train <- log_reg_bin[ind,]\n",
    "log_bin_test <- log_reg_bin[-ind,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“glm.fit: fitted probabilities numerically 0 or 1 occurred”"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:  glm(formula = survive ~ oxygen, family = binomial(link = \"logit\"), \n",
       "    data = log_bin_train)\n",
       "\n",
       "Coefficients:\n",
       "(Intercept)       oxygen  \n",
       "    -92.173        2.303  \n",
       "\n",
       "Degrees of Freedom: 10 Total (i.e. Null);  9 Residual\n",
       "Null Deviance:\t    15.16 \n",
       "Residual Deviance: 3.97e-10 \tAIC: 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Building logistic regression model\n",
    "log_bin_model <- glm(formula = survive~oxygen,\n",
    "                     data = log_bin_train,\n",
    "                     family = binomial(link = \"logit\"))\n",
    "log_bin_model\n",
    "# From the model we can state that for a unit change in \"oxygen\", log odds change by 230.3%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“glm.fit: fitted probabilities numerically 0 or 1 occurred”"
     ]
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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1paamFhofvpjeN4cXExj8cjXxekI5FI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\nAIO8Kg2zMkKpAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualizing the model\n",
    "xval = log_bin_train$oxygen\n",
    "yval = predict(log_bin_model,data.frame(oxygen = log_bin_train$oxygen),type = \"response\")\n",
    "options(repr.plot.width=4, repr.plot.height=3)\n",
    "ggplot() +\n",
    "  stat_smooth(method = \"glm\", method.args = list(family = \"binomial\"), \n",
    "              aes(xval, yval, col =\"Probability model\")) +\n",
    "          geom_point(aes(log_bin_train$oxygen, \n",
    "                         ifelse(as.numeric(log_bin_train$survive) == 2, 1,0), \n",
    "                         col = \"Original data\")) +\n",
    "          scale_colour_manual(\"\", \n",
    "                              breaks = c(\"Probability model\", \"Original data\"), \n",
    "                              values = c(\"red\", \"green\")) +  \n",
    "          ylab(\"p(oxygen)\") + xlab(\"oxygen\") + ggtitle(\"Binomial Logistic Regression\") +\n",
    "          theme_bw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>pred_prob</th><th scope=col>pred_surv</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>2.220446e-16</td><td>0           </td></tr>\n",
       "\t<tr><td>9.532594e-03</td><td>0           </td></tr>\n",
       "\t<tr><td>9.999990e-01</td><td>1           </td></tr>\n",
       "\t<tr><td>1.000000e+00</td><td>1           </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " pred\\_prob & pred\\_surv\\\\\n",
       "\\hline\n",
       "\t 2.220446e-16 & 0           \\\\\n",
       "\t 9.532594e-03 & 0           \\\\\n",
       "\t 9.999990e-01 & 1           \\\\\n",
       "\t 1.000000e+00 & 1           \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "pred_prob | pred_surv | \n",
       "|---|---|---|---|\n",
       "| 2.220446e-16 | 0            | \n",
       "| 9.532594e-03 | 0            | \n",
       "| 9.999990e-01 | 1            | \n",
       "| 1.000000e+00 | 1            | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  pred_prob    pred_surv\n",
       "1 2.220446e-16 0        \n",
       "2 9.532594e-03 0        \n",
       "3 9.999990e-01 1        \n",
       "4 1.000000e+00 1        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Predicting if a person survive based on our built model and test data\n",
    "\n",
    "# Determining prob. for each oxygen value\n",
    "log_pred <- data.frame(predict(log_bin_model, data.frame(oxygen = log_bin_test$oxygen), type = \"response\"))\n",
    "colnames(log_pred) <- \"pred_prob\"\n",
    "\n",
    "# Assigning threshold probability - based on domain knowledge\n",
    "thr_prob <- 0.5\n",
    "\n",
    "# Categorizing survival based on predicted probabilities\n",
    "log_pred$pred_surv <- ifelse(log_pred$pred_prob <=0.5, 0, 1)\n",
    "log_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Oxygen</th><th scope=col>Actual Survival</th><th scope=col>Predicted Survival</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>10</td><td>0 </td><td>0 </td></tr>\n",
       "\t<tr><td>38</td><td>0 </td><td>0 </td></tr>\n",
       "\t<tr><td>46</td><td>0 </td><td>1 </td></tr>\n",
       "\t<tr><td>66</td><td>1 </td><td>1 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " Oxygen & Actual Survival & Predicted Survival\\\\\n",
       "\\hline\n",
       "\t 10 & 0  & 0 \\\\\n",
       "\t 38 & 0  & 0 \\\\\n",
       "\t 46 & 0  & 1 \\\\\n",
       "\t 66 & 1  & 1 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Oxygen | Actual Survival | Predicted Survival | \n",
       "|---|---|---|---|\n",
       "| 10 | 0  | 0  | \n",
       "| 38 | 0  | 0  | \n",
       "| 46 | 0  | 1  | \n",
       "| 66 | 1  | 1  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  Oxygen Actual Survival Predicted Survival\n",
       "1 10     0               0                 \n",
       "2 38     0               0                 \n",
       "3 46     0               1                 \n",
       "4 66     1               1                 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Comparing actual and predicted values\n",
    "cmp_df <- data.frame(log_bin_test$oxygen, log_bin_test$survive, log_pred$pred_surv)\n",
    "names(cmp_df) <- c(\"Oxygen\", \"Actual Survival\", \"Predicted Survival\")\n",
    "cmp_df\n",
    "actual <- cmp_df$`Actual Survival`\n",
    "predicted <- cmp_df$`Predicted Survival`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>0</th><th scope=col>1</th><th scope=col>Sum</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>0</th><td>2</td><td>1</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>1</th><td>0</td><td>1</td><td>1</td></tr>\n",
       "\t<tr><th scope=row>Sum</th><td>2</td><td>2</td><td>4</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & 0 & 1 & Sum\\\\\n",
       "\\hline\n",
       "\t0 & 2 & 1 & 3\\\\\n",
       "\t1 & 0 & 1 & 1\\\\\n",
       "\tSum & 2 & 2 & 4\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | 0 | 1 | Sum | \n",
       "|---|---|---|\n",
       "| 0 | 2 | 1 | 3 | \n",
       "| 1 | 0 | 1 | 1 | \n",
       "| Sum | 2 | 2 | 4 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "      predicted\n",
       "actual 0 1 Sum\n",
       "   0   2 1 3  \n",
       "   1   0 1 1  \n",
       "   Sum 2 2 4  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "75"
      ],
      "text/latex": [
       "75"
      ],
      "text/markdown": [
       "75"
      ],
      "text/plain": [
       "[1] 75"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Finding accuracy of the model\n",
    "log_acc <- addmargins(table(actual, predicted)); log_acc\n",
    "# Adding starting 2 Values of parent diagonal {2 + 1}, dividing by total value {4} \n",
    "((log_acc[1] + log_acc[5])/log_acc[9]) * 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multinomial Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>budget</th><th scope=col>cars</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 100000</td><td>Toyota </td></tr>\n",
       "\t<tr><td> 250000</td><td>Toyota </td></tr>\n",
       "\t<tr><td> 500000</td><td>Toyota </td></tr>\n",
       "\t<tr><td> 750000</td><td>Toyota </td></tr>\n",
       "\t<tr><td>1000000</td><td>Toyota </td></tr>\n",
       "\t<tr><td>2000000</td><td>Ferrari</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " budget & cars\\\\\n",
       "\\hline\n",
       "\t  100000 & Toyota \\\\\n",
       "\t  250000 & Toyota \\\\\n",
       "\t  500000 & Toyota \\\\\n",
       "\t  750000 & Toyota \\\\\n",
       "\t 1000000 & Toyota \\\\\n",
       "\t 2000000 & Ferrari\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "budget | cars | \n",
       "|---|---|---|---|---|---|\n",
       "|  100000 | Toyota  | \n",
       "|  250000 | Toyota  | \n",
       "|  500000 | Toyota  | \n",
       "|  750000 | Toyota  | \n",
       "| 1000000 | Toyota  | \n",
       "| 2000000 | Ferrari | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  budget  cars   \n",
       "1  100000 Toyota \n",
       "2  250000 Toyota \n",
       "3  500000 Toyota \n",
       "4  750000 Toyota \n",
       "5 1000000 Toyota \n",
       "6 2000000 Ferrari"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'Bugatti'</li>\n",
       "\t<li>'Ferrari'</li>\n",
       "\t<li>'Toyota'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'Bugatti'\n",
       "\\item 'Ferrari'\n",
       "\\item 'Toyota'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'Bugatti'\n",
       "2. 'Ferrari'\n",
       "3. 'Toyota'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"Bugatti\" \"Ferrari\" \"Toyota\" "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "log_reg_mul <- read.csv(\"../../datasets/log_reg_mul.csv\")\n",
    "head(log_reg_mul)\n",
    "levels(log_reg_mul$cars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>budget</th><th scope=col>cars</th><th scope=col>ref</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 100000</td><td>Toyota </td><td>Toyota </td></tr>\n",
       "\t<tr><td> 250000</td><td>Toyota </td><td>Toyota </td></tr>\n",
       "\t<tr><td> 500000</td><td>Toyota </td><td>Toyota </td></tr>\n",
       "\t<tr><td> 750000</td><td>Toyota </td><td>Toyota </td></tr>\n",
       "\t<tr><td>1000000</td><td>Toyota </td><td>Toyota </td></tr>\n",
       "\t<tr><td>2000000</td><td>Ferrari</td><td>Ferrari</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " budget & cars & ref\\\\\n",
       "\\hline\n",
       "\t  100000 & Toyota  & Toyota \\\\\n",
       "\t  250000 & Toyota  & Toyota \\\\\n",
       "\t  500000 & Toyota  & Toyota \\\\\n",
       "\t  750000 & Toyota  & Toyota \\\\\n",
       "\t 1000000 & Toyota  & Toyota \\\\\n",
       "\t 2000000 & Ferrari & Ferrari\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "budget | cars | ref | \n",
       "|---|---|---|---|---|---|\n",
       "|  100000 | Toyota  | Toyota  | \n",
       "|  250000 | Toyota  | Toyota  | \n",
       "|  500000 | Toyota  | Toyota  | \n",
       "|  750000 | Toyota  | Toyota  | \n",
       "| 1000000 | Toyota  | Toyota  | \n",
       "| 2000000 | Ferrari | Ferrari | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  budget  cars    ref    \n",
       "1  100000 Toyota  Toyota \n",
       "2  250000 Toyota  Toyota \n",
       "3  500000 Toyota  Toyota \n",
       "4  750000 Toyota  Toyota \n",
       "5 1000000 Toyota  Toyota \n",
       "6 2000000 Ferrari Ferrari"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# setting reference category -> \"Ferrari\"\n",
    "log_reg_mul$ref <- relevel(log_reg_mul$cars, ref = \"Ferrari\")\n",
    "head(log_reg_mul)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Making train and test data\n",
    "set.seed(41)\n",
    "ind <- sample(x = nrow(log_reg_mul), size = floor(0.70 * nrow(log_reg_mul)))\n",
    "\n",
    "log_mul_train <- log_reg_mul[ind,-2]      # excluding \"cars\" column\n",
    "log_mul_test <- log_reg_mul[-ind,-2]      # excluding \"cars\" column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# weights:  9 (4 variable)\n",
      "initial  value 10.986123 \n",
      "iter  10 value 0.473473\n",
      "iter  20 value 0.042648\n",
      "iter  30 value 0.018414\n",
      "iter  40 value 0.010653\n",
      "iter  50 value 0.008845\n",
      "iter  60 value 0.008080\n",
      "iter  70 value 0.007073\n",
      "iter  70 value 0.007073\n",
      "final  value 0.007073 \n",
      "converged\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Call:\n",
       "multinom(formula = ref ~ ., data = log_mul_train)\n",
       "\n",
       "Coefficients:\n",
       "        (Intercept)        budget\n",
       "Bugatti   -25.66995  3.595444e-06\n",
       "Toyota     20.08826 -1.361525e-05\n",
       "\n",
       "Residual Deviance: 0.01414667 \n",
       "AIC: 8.014147 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# building logistic multinomial model\n",
    "library(nnet)\n",
    "log_mul_model <- multinom(ref~., data = log_mul_train)\n",
    "log_mul_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Ferrari</th><th scope=col>Bugatti</th><th scope=col>Toyota</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>7.363455e-09 </td><td>7.497389e-20 </td><td> 1.000000e+00</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>1.707230e-06 </td><td>7.323405e-17 </td><td> 9.999983e-01</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>9.999998e-01 </td><td>1.168638e-07 </td><td> 5.741764e-08</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>4.568020e-07 </td><td>9.999995e-01 </td><td> 1.438915e-64</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>8.292626e-21 </td><td>1.000000e+00 </td><td>2.411861e-130</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & Ferrari & Bugatti & Toyota\\\\\n",
       "\\hline\n",
       "\t1 & 7.363455e-09  & 7.497389e-20  &  1.000000e+00\\\\\n",
       "\t3 & 1.707230e-06  & 7.323405e-17  &  9.999983e-01\\\\\n",
       "\t7 & 9.999998e-01  & 1.168638e-07  &  5.741764e-08\\\\\n",
       "\t12 & 4.568020e-07  & 9.999995e-01  &  1.438915e-64\\\\\n",
       "\t15 & 8.292626e-21  & 1.000000e+00  & 2.411861e-130\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Ferrari | Bugatti | Toyota | \n",
       "|---|---|---|---|---|\n",
       "| 1 | 7.363455e-09  | 7.497389e-20  |  1.000000e+00 | \n",
       "| 3 | 1.707230e-06  | 7.323405e-17  |  9.999983e-01 | \n",
       "| 7 | 9.999998e-01  | 1.168638e-07  |  5.741764e-08 | \n",
       "| 12 | 4.568020e-07  | 9.999995e-01  |  1.438915e-64 | \n",
       "| 15 | 8.292626e-21  | 1.000000e+00  | 2.411861e-130 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   Ferrari      Bugatti      Toyota       \n",
       "1  7.363455e-09 7.497389e-20  1.000000e+00\n",
       "3  1.707230e-06 7.323405e-17  9.999983e-01\n",
       "7  9.999998e-01 1.168638e-07  5.741764e-08\n",
       "12 4.568020e-07 9.999995e-01  1.438915e-64\n",
       "15 8.292626e-21 1.000000e+00 2.411861e-130"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# predicting probabilities using model and test data\n",
    "log_mul_pred <- predict(log_mul_model, log_mul_test, type = \"prob\"); log_mul_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>1</dt>\n",
       "\t\t<dd>1</dd>\n",
       "\t<dt>3</dt>\n",
       "\t\t<dd>1</dd>\n",
       "\t<dt>7</dt>\n",
       "\t\t<dd>1</dd>\n",
       "\t<dt>12</dt>\n",
       "\t\t<dd>1</dd>\n",
       "\t<dt>15</dt>\n",
       "\t\t<dd>1</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[1] 1\n",
       "\\item[3] 1\n",
       "\\item[7] 1\n",
       "\\item[12] 1\n",
       "\\item[15] 1\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "1\n",
       ":   13\n",
       ":   17\n",
       ":   112\n",
       ":   115\n",
       ":   1\n",
       "\n"
      ],
      "text/plain": [
       " 1  3  7 12 15 \n",
       " 1  1  1  1  1 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# verifying if all 3 probabilities in a row sum to 1\n",
    "apply(log_mul_pred, 1, sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>Toyota</li>\n",
       "\t<li>Toyota</li>\n",
       "\t<li>Ferrari</li>\n",
       "\t<li>Bugatti</li>\n",
       "\t<li>Bugatti</li>\n",
       "</ol>\n",
       "\n",
       "<details>\n",
       "\t<summary style=display:list-item;cursor:pointer>\n",
       "\t\t<strong>Levels</strong>:\n",
       "\t</summary>\n",
       "\t<ol class=list-inline>\n",
       "\t\t<li>'Ferrari'</li>\n",
       "\t\t<li>'Bugatti'</li>\n",
       "\t\t<li>'Toyota'</li>\n",
       "\t</ol>\n",
       "</details>"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item Toyota\n",
       "\\item Toyota\n",
       "\\item Ferrari\n",
       "\\item Bugatti\n",
       "\\item Bugatti\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\emph{Levels}: \\begin{enumerate*}\n",
       "\\item 'Ferrari'\n",
       "\\item 'Bugatti'\n",
       "\\item 'Toyota'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. Toyota\n",
       "2. Toyota\n",
       "3. Ferrari\n",
       "4. Bugatti\n",
       "5. Bugatti\n",
       "\n",
       "\n",
       "\n",
       "**Levels**: 1. 'Ferrari'\n",
       "2. 'Bugatti'\n",
       "3. 'Toyota'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] Toyota  Toyota  Ferrari Bugatti Bugatti\n",
       "Levels: Ferrari Bugatti Toyota"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# classifying categories based on the probability\n",
    "log_mul_class <- predict(log_mul_model, log_mul_test, type = \"class\"); log_mul_class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Actual</th><th scope=col>Predicted</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>Toyota </td><td>Toyota </td></tr>\n",
       "\t<tr><td>Toyota </td><td>Toyota </td></tr>\n",
       "\t<tr><td>Ferrari</td><td>Ferrari</td></tr>\n",
       "\t<tr><td>Bugatti</td><td>Bugatti</td></tr>\n",
       "\t<tr><td>Bugatti</td><td>Bugatti</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " Actual & Predicted\\\\\n",
       "\\hline\n",
       "\t Toyota  & Toyota \\\\\n",
       "\t Toyota  & Toyota \\\\\n",
       "\t Ferrari & Ferrari\\\\\n",
       "\t Bugatti & Bugatti\\\\\n",
       "\t Bugatti & Bugatti\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Actual | Predicted | \n",
       "|---|---|---|---|---|\n",
       "| Toyota  | Toyota  | \n",
       "| Toyota  | Toyota  | \n",
       "| Ferrari | Ferrari | \n",
       "| Bugatti | Bugatti | \n",
       "| Bugatti | Bugatti | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  Actual  Predicted\n",
       "1 Toyota  Toyota   \n",
       "2 Toyota  Toyota   \n",
       "3 Ferrari Ferrari  \n",
       "4 Bugatti Bugatti  \n",
       "5 Bugatti Bugatti  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Comparing predicted output with actual value\n",
    "cmp_df <- data.frame(log_mul_test$ref, log_mul_class)\n",
    "colnames(cmp_df) <- c(\"Actual\",\"Predicted\"); cmp_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Ferrari</th><th scope=col>Bugatti</th><th scope=col>Toyota</th><th scope=col>Sum</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Ferrari</th><td>1</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><th scope=row>Bugatti</th><td>0</td><td>2</td><td>0</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>Toyota</th><td>0</td><td>0</td><td>2</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>Sum</th><td>1</td><td>2</td><td>2</td><td>5</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llll}\n",
       "  & Ferrari & Bugatti & Toyota & Sum\\\\\n",
       "\\hline\n",
       "\tFerrari & 1 & 0 & 0 & 1\\\\\n",
       "\tBugatti & 0 & 2 & 0 & 2\\\\\n",
       "\tToyota & 0 & 0 & 2 & 2\\\\\n",
       "\tSum & 1 & 2 & 2 & 5\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Ferrari | Bugatti | Toyota | Sum | \n",
       "|---|---|---|---|\n",
       "| Ferrari | 1 | 0 | 0 | 1 | \n",
       "| Bugatti | 0 | 2 | 0 | 2 | \n",
       "| Toyota | 0 | 0 | 2 | 2 | \n",
       "| Sum | 1 | 2 | 2 | 5 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "         Predicted\n",
       "Actual    Ferrari Bugatti Toyota Sum\n",
       "  Ferrari 1       0       0      1  \n",
       "  Bugatti 0       2       0      2  \n",
       "  Toyota  0       0       2      2  \n",
       "  Sum     1       2       2      5  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "100"
      ],
      "text/latex": [
       "100"
      ],
      "text/markdown": [
       "100"
      ],
      "text/plain": [
       "[1] 100"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Finding accuracy of the model\n",
    "log_mul_acc <- addmargins(table(cmp_df)); log_mul_acc\n",
    "\n",
    "((log_mul_acc[1] + log_mul_acc[6] + log_mul_acc[11])/log_mul_acc[16]) * 100\n",
    "# 100% accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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