Victor Le
#load data
library(readr)
online = read_csv('data.csv')#factorize categorical
online$OperatingSystems = factor(online$OperatingSystems)
online$Browser = factor(online$Browser)
online$Region = factor(online$Region)
online$TrafficType = factor(online$TrafficType)
online$VisitorType = factor(online$VisitorType)
online$Weekend = factor(online$Weekend)
online$Month = factor(online$Month)
online$Revenue = factor(online$Revenue)
#split 70-30
#want even amounts of YES/NO for Revenue
revenue_yes = which(online$Revenue == 'TRUE')
revenue_no = which(online$Revenue == 'FALSE')
set.seed(630)
# set.seed(1)
train_id = c(sample(revenue_yes, size = trunc(0.7 * length(revenue_yes))),
sample(revenue_no, size = trunc(0.7 * length(revenue_no))))
training = online[train_id, ]
testing = online[-train_id, ]
summary(training)## Administrative Administrative_Duration Informational
## Min. : 0.000 Min. : 0.00 Min. : 0.0000
## 1st Qu.: 0.000 1st Qu.: 0.00 1st Qu.: 0.0000
## Median : 1.000 Median : 7.00 Median : 0.0000
## Mean : 2.305 Mean : 79.39 Mean : 0.5071
## 3rd Qu.: 4.000 3rd Qu.: 91.83 3rd Qu.: 0.0000
## Max. :27.000 Max. :3398.75 Max. :16.0000
##
## Informational_Duration ProductRelated ProductRelated_Duration
## Min. : 0.00 Min. : 0.00 Min. : 0.0
## 1st Qu.: 0.00 1st Qu.: 7.00 1st Qu.: 182.2
## Median : 0.00 Median : 18.00 Median : 598.8
## Mean : 34.03 Mean : 31.91 Mean : 1194.3
## 3rd Qu.: 0.00 3rd Qu.: 38.00 3rd Qu.: 1458.3
## Max. :2549.38 Max. :686.00 Max. :63973.5
##
## BounceRates ExitRates PageValues SpecialDay
## Min. :0.000000 Min. :0.00000 Min. : 0.000 Min. :0.00000
## 1st Qu.:0.000000 1st Qu.:0.01429 1st Qu.: 0.000 1st Qu.:0.00000
## Median :0.003161 Median :0.02514 Median : 0.000 Median :0.00000
## Mean :0.022368 Mean :0.04339 Mean : 5.921 Mean :0.06155
## 3rd Qu.:0.016798 3rd Qu.:0.05000 3rd Qu.: 0.000 3rd Qu.:0.00000
## Max. :0.200000 Max. :0.20000 Max. :361.764 Max. :1.00000
##
## Month OperatingSystems Browser Region TrafficType
## May :2360 2 :4633 2 :5585 1 :3384 2 :2729
## Nov :2072 3 :1815 1 :1702 3 :1658 1 :1747
## Mar :1367 1 :1763 4 : 527 2 : 807 3 :1454
## Dec :1207 4 : 341 5 : 324 4 : 801 4 : 736
## Oct : 386 8 : 56 6 : 121 6 : 578 13 : 526
## Aug : 317 6 : 14 10 : 118 7 : 545 10 : 310
## (Other): 921 (Other): 8 (Other): 253 (Other): 857 (Other):1128
## VisitorType Weekend Revenue
## New_Visitor :1164 FALSE:6621 FALSE:7295
## Other : 60 TRUE :2009 TRUE :1335
## Returning_Visitor:7406
##
##
##
## #Check side-by-side boxplots for numerical variables
library(ggplot2)
library(dplyr)
library(tidyr)
# Standardize the numerical data in the training set and testing set using the mean and std of the training data set
num_col = c('Administrative','Administrative_Duration', 'Informational','Informational_Duration','ProductRelated','ProductRelated_Duration', 'BounceRates','ExitRates','PageValues','SpecialDay')
training.norm = training
testing.norm = testing
for(i in num_col){
mean_col = mean(pull(training,i))
std_col = sd(pull(training,i))
training.norm[i] = scale(training[i], center = mean_col, scale = std_col)
testing.norm[i] = scale(testing[i], center = mean_col, scale = std_col)
}We want to start with some simple models and contextualize the results that get. Let’s start with Naive Bayes, a tried and true first-starter.
# load the necessary packages for naive bayes
# install.packages('e1071')
library(e1071)## Warning: package 'e1071' was built under R version 3.6.3# Apply a Naive-Bayes to the model
NB_model = naiveBayes(Revenue~., data = training.norm)
# print(NB_model)
# predictions
pred_train = predict(NB_model, newdata = training.norm)
mean(pred_train != training.norm$Revenue)## [1] 0.1887601pred_test = predict(NB_model, newdata = testing.norm)
mean(pred_test != testing.norm$Revenue)## [1] 0.1837838table(pred_test, testing.norm$Revenue)##
## pred_test FALSE TRUE
## FALSE 2611 164
## TRUE 516 409Another simple, flexible model that we can use for predicting.
# Apply Logistic Regression to model
logreg_model = glm(Revenue~., data = training.norm, family = binomial)
# summary(logreg_model)
# make predictions on the training set
pred_train_probs = predict(logreg_model, training.norm)## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading# To get actually get predictions of the model, we need to convert back to probabilities
pred_train = binomial()$linkinv(pred_train_probs)
pred_train_log = rep('FALSE', nrow(training.norm))
pred_train_log[pred_train > 0.5] = 'TRUE'
mean(pred_train_log != training.norm$Revenue)## [1] 0.1165701# testing error (training data didn't contain TrafficType 17, so model couldn't train on it, so have to exclude it)
pred_test_probs = predict(logreg_model, testing.norm[testing.norm$TrafficType != 17,] )## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleadingpred_test = binomial()$linkinv(pred_test_probs)
pred_test_log = rep('FALSE', nrow(testing.norm[testing.norm$TrafficType != 17,]))
pred_test_log[pred_test > 0.5] = 'TRUE'
mean(pred_test_log != testing.norm[testing.norm$TrafficType != 17,]$Revenue)## [1] 0.1132739Turns out the testing error was reasonable given the training error. Let’s see if we can improve upon the logistic regression model by only fitting on significant predictors.
# Using only significant predictors from a glm
logreg_model.red = glm(Revenue~ProductRelated_Duration + ExitRates + PageValues + Month + Browser+ TrafficType + VisitorType, data = training.norm, family = binomial)
# summary(logreg_model.red)
# training error
pred_train_probs = predict(logreg_model.red, training.norm)
pred_train = binomial()$linkinv(pred_train_probs)
pred_train_log = rep('FALSE', nrow(training.norm))
pred_train_log[pred_train > 0.5] = 'TRUE'
mean(pred_train_log != training.norm$Revenue)## [1] 0.1158749Ok, so the training error was only marginally better. Let’s see testing error.
# testing error (training data didn't contain TrafficType 17, so model couldn't train on it, so have to exclude it)
pred_test_probs = predict(logreg_model.red, testing.norm[testing.norm$TrafficType != 17,] )
pred_test = binomial()$linkinv(pred_test_probs)
pred_test_log = rep('FALSE', nrow(testing.norm[testing.norm$TrafficType != 17,]))
pred_test_log[pred_test > 0.5] = 'TRUE'
mean(pred_test_log != testing.norm[testing.norm$TrafficType != 17,]$Revenue)## [1] 0.1140849Unfortunately, even with a reduced model, the testing and training errors remain similar.
Let’s see how a simple KNN would do.
# K-nearest neighbors
library(class)
pred_train = knn(training.norm[num_col], training.norm[num_col], training$Revenue, k = 50)
table(pred_train, training$Revenue)##
## pred_train FALSE TRUE
## FALSE 7101 749
## TRUE 194 586mean(pred_train != training$Revenue)## [1] 0.10927pred_test = knn(training.norm[num_col], testing.norm[num_col], training$Revenue, k = 50)
table(pred_test, testing$Revenue)##
## pred_test FALSE TRUE
## FALSE 3047 322
## TRUE 80 251mean(pred_test != testing$Revenue)## [1] 0.1086486With KNN, we do have to do some cross-validation. The following section simply validates our previous choice of k = 50.
k_vec = c(1,5,11,51,101,201,401)
errors_train = c()
errors_test = c()
for(j in 1:length(k_vec)){
pred_train = knn(training.norm[num_col], training.norm[num_col], training$Revenue, k = k_vec[j])
pred_test = knn(training.norm[num_col], testing.norm[num_col], training$Revenue, k = k_vec[j])
errors_test[j] = mean(pred_test!= testing$Revenue)
errors_train[j] = mean(pred_train != training$Revenue)
}
errors = data.frame(errors_train, errors_test, k_vec)
ggplot(errors, aes(x=k_vec)) + geom_line(aes(y = errors_train), col = 'red') + geom_point(aes(y=errors_train), col = 'red') + geom_line(aes(y=errors_test), col = 'blue') + geom_point(aes(y=errors_test),col='blue')
# Apply SVM to model
library(e1071)
# with SVM, we can simply use tune to determine the best hyperparameters
# tune.out = tune(svm, Revenue~., data = training.norm, ranges = list(cost = c(0.1, 1, 10, 100), kernel = c('linear','radial')))
# summary(tune.out)From the output, it seems like the best hyperparameters were C=10, and the radial kernel.
# final model
svm_model = svm(Revenue~., data = training.norm, cost = 10, kernel = 'radial')
# summary(svm_model)
pred_train = predict(svm_model, newdata = training.norm)
mean(pred_train != training.norm$Revenue)## [1] 0.09362688pred_test = predict(svm_model, newdata = testing.norm)
mean(pred_test != testing.norm$Revenue)## [1] 0.1027027# Confusion matrix
table(pred_test, testing.norm$Revenue)##
## pred_test FALSE TRUE
## FALSE 3030 283
## TRUE 97 290That’s a good set of models! Let’s organize our results and see where we stand now.
library(knitr)## Warning: package 'knitr' was built under R version 3.6.3model_errors.1 = c(0.1887601, 0.1837838)
model_errors.2 = c(0.1165701, 0.1132739)
model_errors.3 = c(0.1093859, 0.1091892)
model_errors.4 = c(0.09362688, 0.1027027)
model_errors = rbind(model_errors.1, model_errors.2, model_errors.3, model_errors.4)
colnames(model_errors) = c('Training Error', 'Testing Error')
rownames(model_errors) = c('Naive Bayes', 'Logistic Regression','KNN','SVM')
knitr::kable(model_errors)| Training Error | Testing Error | |
|---|---|---|
| Naive Bayes | 0.1887601 | 0.1837838 |
| Logistic Regression | 0.1165701 | 0.1132739 |
| KNN | 0.1093859 | 0.1091892 |
| SVM | 0.0936269 | 0.1027027 |