rm(list=ls())
accident_data <- matrix(c(1601, 510, 162527, 412368),
nrow = 2,
byrow = FALSE,
dimnames = list(Seat_Belt = c("None", "Seat Belt"),
Injury = c("Fatal", "Nonfatal")))
print(accident_data)
## Injury
## Seat_Belt Fatal Nonfatal
## None 1601 162527
## Seat Belt 510 412368
# Calculate proportions
prop_fatal_none <- accident_data[1,1] / sum(accident_data[1,])
prop_fatal_belt <- accident_data[2,1] / sum(accident_data[2,])
prop_fatal_belt
## [1] 0.001235232
prop_fatal_none
## [1] 0.009754582
#Difference in proportions
diff_prop <- prop_fatal_none - prop_fatal_belt
diff_prop
## [1] 0.00851935
#Relative Risk (RR)
relative_risk <- prop_fatal_none / prop_fatal_belt
relative_risk
## [1] 7.896965
#Odds Ratio (OR)
odds_none <- accident_data[1,1] / accident_data[1,2]
odds_belt <- accident_data[2,1] / accident_data[2,2]
odds_ratio <- odds_none / odds_belt
odds_ratio
## [1] 7.964905
par(mfrow = c(2, 2), mar = c(5, 4, 4, 2) + 0.1)
barplot(t(accident_data),
main = "Accident Outcomes by Seat Belt Use\n(Counts)",
xlab = "Seat Belt Use",
ylab = "Number of Accidents",
col = c("red", "blue"))
prop_data <- prop.table(accident_data, margin = 1)
barplot(t(prop_data),
main = "Accident Outcomes by Seat Belt Use\n(Proportions)",
xlab = "Seat Belt Use",
ylab = "Proportion",
col = c("red", "blue"),
ylim = c(0, 1))
fatality_rates <- c(prop_fatal_none, prop_fatal_belt)
barplot(fatality_rates * 100,
names.arg = c("No Belt", "Seat Belt"),
main = "Fatality Rates by Seat Belt Use",
xlab = "Seat Belt Use",
ylab = "Fatality Rate (%)",
col = c("red", "blue"),
ylim = c(0, 2))
risk_measures <- c(Difference = diff_prop * 100,
Relative_Risk = relative_risk,
Odds_Ratio = odds_ratio)
barplot(risk_measures,
main = "Risk Measures for No Seat Belt vs Seat Belt",
ylab = "Value",
col = "blue",
las = 2)
abline(h = 1, col = "red", lty = 2, lwd = 2)
text(1:3, risk_measures + 0.5, labels = round(risk_measures, 2))
#Problem 3
rm(list=)
Data=read.csv("C:/Users/Sabuj Ganguly/OneDrive/Documents/PhD 1st sem/STAT 5034 Inference/TSkull_19.csv")
training_set <- Data[Data$Holdout == 0, ]
validation_set <- Data[Data$Holdout == 1, ]
#Pairwise scatter plots for training set
variables <- c("Length", "Breadth", "Height", "Fheight", "Fbreadth")
#pairwise scatterplot matrix
pairs(training_set[, variables],
col = ifelse(training_set$Type == 1, "red", "blue"),
pch = 16,
main = "Pairwise Scatter Plots by Type\n(Red: Type 1, Blue: Type 2)")
# ranking
type1 <- training_set[training_set$Type == 1, variables]
type2 <- training_set[training_set$Type == 2, variables]
mean_diffs <- abs(colMeans(type1) - colMeans(type2))
overlap_metric <- mean_diffs / (apply(type1, 2, sd) + apply(type2, 2, sd))
ranking <- order(overlap_metric, decreasing = TRUE)
cat("1.", variables[ranking[1]], "- Shows good separation between types\n")
## 1. Length - Shows good separation between types
cat("2.", variables[ranking[2]], "- Moderate separation\n")
## 2. Fheight - Moderate separation
cat("3.", variables[ranking[3]], "- Some separation visible\n")
## 3. Fbreadth - Some separation visible
cat("4.", variables[ranking[4]], "- Limited separation\n")
## 4. Height - Limited separation
cat("5.", variables[ranking[5]], "- Poor separation\n\n")
## 5. Breadth - Poor separation
for(var in variables) {
mean_type1 <- mean(training_set[training_set$Type == 1, var])
mean_type2 <- mean(training_set[training_set$Type == 2, var])
mean_diff <- mean_type2 - mean_type1
cat(var, ":\n")
cat(" Type 1 mean:", round(mean_type1, 3), "\n")
cat(" Type 2 mean:", round(mean_type2, 3), "\n")
cat(" Mean difference:", round(mean_diff, 3), "\n")
cat(" Effect size (unstandardized):", round(mean_diff, 3), "\n\n")
}
## Length :
## Type 1 mean: 175.538
## Type 2 mean: 187.136
## Mean difference: 11.598
## Effect size (unstandardized): 11.598
##
## Breadth :
## Type 1 mean: 139.154
## Type 2 mean: 138.773
## Mean difference: -0.381
## Effect size (unstandardized): -0.381
##
## Height :
## Type 1 mean: 133.077
## Type 2 mean: 135.545
## Mean difference: 2.469
## Effect size (unstandardized): 2.469
##
## Fheight :
## Type 1 mean: 70.385
## Type 2 mean: 76.818
## Mean difference: 6.434
## Effect size (unstandardized): 6.434
##
## Fbreadth :
## Type 1 mean: 130.269
## Type 2 mean: 137.5
## Mean difference: 7.231
## Effect size (unstandardized): 7.231
#install.packages("rpart")
#install.packages("rpart.plot")
#install.packages("caret")
library(rpart)
## Warning: package 'rpart' was built under R version 4.5.1
library(rpart.plot)
## Warning: package 'rpart.plot' was built under R version 4.5.1
library(caret)
## Warning: package 'caret' was built under R version 4.5.1
## Loading required package: ggplot2
## Loading required package: lattice
set.seed(123)
formula <- as.formula("Type ~ Length + Breadth + Height + Fheight + Fbreadth")
#fitting trees with tuning parameters
tune_grid <- expand.grid(
minsplit = c(2, 5, 10), # Minimum observations to split
minbucket = c(1, 3, 5), #Minimum observations in terminal node
cp = c(0.001, 0.01, 0.1, 0.5)
)
tree_results <- list()
train_performance <- data.frame()
validation_performance <- data.frame()
#Fitting trees
for(i in 1:nrow(tune_grid)) {
cat("Fitting tree", i, "of", nrow(tune_grid), "\n")
# Fit tree with current parameters
tree <- rpart(formula,
data = training_set,
method = "class",
control = rpart.control(
minsplit = tune_grid$minsplit[i],
minbucket = tune_grid$minbucket[i],
cp = tune_grid$cp[i],
xval = 10 #10 fold cross val
))
tree_name <- paste0("tree_", i)
tree_results[[tree_name]] <- tree
#Training performance
train_pred <- predict(tree, training_set, type = "class")
train_accuracy <- mean(train_pred == training_set$Type)
#Validation performance
val_pred <- predict(tree, validation_set, type = "class")
val_accuracy <- mean(val_pred == validation_set$Type)
train_performance <- rbind(train_performance,
data.frame(Tree = tree_name,
Minsplit = tune_grid$minsplit[i],
Minbucket = tune_grid$minbucket[i],
CP = tune_grid$cp[i],
Accuracy = train_accuracy,
Nodes = nrow(tree$frame)))
validation_performance <- rbind(validation_performance,
data.frame(Tree = tree_name,
Minsplit = tune_grid$minsplit[i],
Minbucket = tune_grid$minbucket[i],
CP = tune_grid$cp[i],
Accuracy = val_accuracy,
Nodes = nrow(tree$frame)))
}
## Fitting tree 1 of 36
## Fitting tree 2 of 36
## Fitting tree 3 of 36
## Fitting tree 4 of 36
## Fitting tree 5 of 36
## Fitting tree 6 of 36
## Fitting tree 7 of 36
## Fitting tree 8 of 36
## Fitting tree 9 of 36
## Fitting tree 10 of 36
## Fitting tree 11 of 36
## Fitting tree 12 of 36
## Fitting tree 13 of 36
## Fitting tree 14 of 36
## Fitting tree 15 of 36
## Fitting tree 16 of 36
## Fitting tree 17 of 36
## Fitting tree 18 of 36
## Fitting tree 19 of 36
## Fitting tree 20 of 36
## Fitting tree 21 of 36
## Fitting tree 22 of 36
## Fitting tree 23 of 36
## Fitting tree 24 of 36
## Fitting tree 25 of 36
## Fitting tree 26 of 36
## Fitting tree 27 of 36
## Fitting tree 28 of 36
## Fitting tree 29 of 36
## Fitting tree 30 of 36
## Fitting tree 31 of 36
## Fitting tree 32 of 36
## Fitting tree 33 of 36
## Fitting tree 34 of 36
## Fitting tree 35 of 36
## Fitting tree 36 of 36
#performance metrics combined
performance <- merge(train_performance, validation_performance,
by = c("Tree", "Minsplit", "Minbucket", "CP", "Nodes"),
suffixes = c("_Train", "_Validation"))
#overfitting gap
performance$Overfitting_Gap <- performance$Accuracy_Train - performance$Accuracy_Validation
#sorting by validation accuracy
performance <- performance[order(performance$Accuracy_Validation, decreasing = TRUE), ]
print(performance)
## Tree Minsplit Minbucket CP Nodes Accuracy_Train Accuracy_Validation
## 1 tree_1 2 1 0.001 7 1.0000000 0.625
## 2 tree_10 2 1 0.010 7 1.0000000 0.625
## 3 tree_11 5 1 0.010 7 1.0000000 0.625
## 4 tree_12 10 1 0.010 7 1.0000000 0.625
## 12 tree_2 5 1 0.001 7 1.0000000 0.625
## 23 tree_3 10 1 0.001 7 1.0000000 0.625
## 5 tree_13 2 3 0.010 3 0.9166667 0.500
## 6 tree_14 5 3 0.010 3 0.9166667 0.500
## 7 tree_15 10 3 0.010 3 0.9166667 0.500
## 8 tree_16 2 5 0.010 3 0.9166667 0.500
## 9 tree_17 5 5 0.010 3 0.9166667 0.500
## 10 tree_18 10 5 0.010 3 0.9166667 0.500
## 11 tree_19 2 1 0.100 3 0.9166667 0.500
## 13 tree_20 5 1 0.100 3 0.9166667 0.500
## 14 tree_21 10 1 0.100 3 0.9166667 0.500
## 15 tree_22 2 3 0.100 3 0.9166667 0.500
## 16 tree_23 5 3 0.100 3 0.9166667 0.500
## 17 tree_24 10 3 0.100 3 0.9166667 0.500
## 18 tree_25 2 5 0.100 3 0.9166667 0.500
## 19 tree_26 5 5 0.100 3 0.9166667 0.500
## 20 tree_27 10 5 0.100 3 0.9166667 0.500
## 21 tree_28 2 1 0.500 3 0.9166667 0.500
## 22 tree_29 5 1 0.500 3 0.9166667 0.500
## 24 tree_30 10 1 0.500 3 0.9166667 0.500
## 25 tree_31 2 3 0.500 3 0.9166667 0.500
## 26 tree_32 5 3 0.500 3 0.9166667 0.500
## 27 tree_33 10 3 0.500 3 0.9166667 0.500
## 28 tree_34 2 5 0.500 3 0.9166667 0.500
## 29 tree_35 5 5 0.500 3 0.9166667 0.500
## 30 tree_36 10 5 0.500 3 0.9166667 0.500
## 31 tree_4 2 3 0.001 3 0.9166667 0.500
## 32 tree_5 5 3 0.001 3 0.9166667 0.500
## 33 tree_6 10 3 0.001 3 0.9166667 0.500
## 34 tree_7 2 5 0.001 3 0.9166667 0.500
## 35 tree_8 5 5 0.001 3 0.9166667 0.500
## 36 tree_9 10 5 0.001 3 0.9166667 0.500
## Overfitting_Gap
## 1 0.3750000
## 2 0.3750000
## 3 0.3750000
## 4 0.3750000
## 12 0.3750000
## 23 0.3750000
## 5 0.4166667
## 6 0.4166667
## 7 0.4166667
## 8 0.4166667
## 9 0.4166667
## 10 0.4166667
## 11 0.4166667
## 13 0.4166667
## 14 0.4166667
## 15 0.4166667
## 16 0.4166667
## 17 0.4166667
## 18 0.4166667
## 19 0.4166667
## 20 0.4166667
## 21 0.4166667
## 22 0.4166667
## 24 0.4166667
## 25 0.4166667
## 26 0.4166667
## 27 0.4166667
## 28 0.4166667
## 29 0.4166667
## 30 0.4166667
## 31 0.4166667
## 32 0.4166667
## 33 0.4166667
## 34 0.4166667
## 35 0.4166667
## 36 0.4166667
#best validation tree
best_val_idx <- which.max(performance$Accuracy_Validation)
best_val_tree <- performance[best_val_idx, ]
best_tree <- tree_results[[best_val_tree$Tree]]
#simplest tree
simplest_idx <- which.min(performance$Nodes)
simplest_tree <- performance[simplest_idx, ]
simple_tree_obj <- tree_results[[simplest_tree$Tree]]
#complex tree
complex_idx <- which.max(performance$Nodes)
complex_tree <- performance[complex_idx, ]
complex_tree_obj <- tree_results[[complex_tree$Tree]]
print(best_val_tree)
## Tree Minsplit Minbucket CP Nodes Accuracy_Train Accuracy_Validation
## 1 tree_1 2 1 0.001 7 1 0.625
## Overfitting_Gap
## 1 0.375
print(simplest_tree)
## Tree Minsplit Minbucket CP Nodes Accuracy_Train Accuracy_Validation
## 5 tree_13 2 3 0.01 3 0.9166667 0.5
## Overfitting_Gap
## 5 0.4166667
print(complex_tree)
## Tree Minsplit Minbucket CP Nodes Accuracy_Train Accuracy_Validation
## 1 tree_1 2 1 0.001 7 1 0.625
## Overfitting_Gap
## 1 0.375
#plotting the trees
plot_tree <- function(tree, title) {
plot(tree, uniform = TRUE, main = title, margin = 0.1)
text(tree, use.n = TRUE, all = TRUE, cex = 0.8)
}
#key trees
cat("1. Best Validation Tree (Tree", best_val_tree$Tree, "):\n")
## 1. Best Validation Tree (Tree tree_1 ):
print(best_tree)
## n= 24
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 24 11 1 (0.54166667 0.45833333)
## 2) Length< 180.75 13 1 1 (0.92307692 0.07692308)
## 4) Breadth< 151.75 12 0 1 (1.00000000 0.00000000) *
## 5) Breadth>=151.75 1 0 2 (0.00000000 1.00000000) *
## 3) Length>=180.75 11 1 2 (0.09090909 0.90909091)
## 6) Breadth>=148.25 1 0 1 (1.00000000 0.00000000) *
## 7) Breadth< 148.25 10 0 2 (0.00000000 1.00000000) *
plot_tree(best_tree, paste("Best Validation Tree - Accuracy:",
round(best_val_tree$Accuracy_Validation, 3)))
cat("\n2. Simplest Tree (Tree", simplest_tree$Tree, "):\n")
##
## 2. Simplest Tree (Tree tree_13 ):
print(simple_tree_obj)
## n= 24
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 24 11 1 (0.54166667 0.45833333)
## 2) Length< 180.75 13 1 1 (0.92307692 0.07692308) *
## 3) Length>=180.75 11 1 2 (0.09090909 0.90909091) *
plot_tree(simple_tree_obj, paste("Simplest Tree -", simplest_tree$Nodes, "nodes"))
cat("\n3. Most Complex Tree (Tree", complex_tree$Tree, "):\n")
##
## 3. Most Complex Tree (Tree tree_1 ):
print(complex_tree_obj)
## n= 24
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 24 11 1 (0.54166667 0.45833333)
## 2) Length< 180.75 13 1 1 (0.92307692 0.07692308)
## 4) Breadth< 151.75 12 0 1 (1.00000000 0.00000000) *
## 5) Breadth>=151.75 1 0 2 (0.00000000 1.00000000) *
## 3) Length>=180.75 11 1 2 (0.09090909 0.90909091)
## 6) Breadth>=148.25 1 0 1 (1.00000000 0.00000000) *
## 7) Breadth< 148.25 10 0 2 (0.00000000 1.00000000) *
plot_tree(complex_tree_obj, paste("Most Complex Tree -", complex_tree$Nodes, "nodes"))
#overfitting
overfit_threshold <- 0.2
overfit_trees <- performance[performance$Overfitting_Gap > overfit_threshold, ]
cat("TREES WITH SIGNIFICANT OVERFITTING (Gap >", overfit_threshold, "):\n")
## TREES WITH SIGNIFICANT OVERFITTING (Gap > 0.2 ):
if(nrow(overfit_trees) > 0) {
print(overfit_trees[, c("Tree", "Nodes", "Accuracy_Train", "Accuracy_Validation", "Overfitting_Gap")])
} else {
cat("No significant overfitting detected\n")
}
## Tree Nodes Accuracy_Train Accuracy_Validation Overfitting_Gap
## 1 tree_1 7 1.0000000 0.625 0.3750000
## 2 tree_10 7 1.0000000 0.625 0.3750000
## 3 tree_11 7 1.0000000 0.625 0.3750000
## 4 tree_12 7 1.0000000 0.625 0.3750000
## 12 tree_2 7 1.0000000 0.625 0.3750000
## 23 tree_3 7 1.0000000 0.625 0.3750000
## 5 tree_13 3 0.9166667 0.500 0.4166667
## 6 tree_14 3 0.9166667 0.500 0.4166667
## 7 tree_15 3 0.9166667 0.500 0.4166667
## 8 tree_16 3 0.9166667 0.500 0.4166667
## 9 tree_17 3 0.9166667 0.500 0.4166667
## 10 tree_18 3 0.9166667 0.500 0.4166667
## 11 tree_19 3 0.9166667 0.500 0.4166667
## 13 tree_20 3 0.9166667 0.500 0.4166667
## 14 tree_21 3 0.9166667 0.500 0.4166667
## 15 tree_22 3 0.9166667 0.500 0.4166667
## 16 tree_23 3 0.9166667 0.500 0.4166667
## 17 tree_24 3 0.9166667 0.500 0.4166667
## 18 tree_25 3 0.9166667 0.500 0.4166667
## 19 tree_26 3 0.9166667 0.500 0.4166667
## 20 tree_27 3 0.9166667 0.500 0.4166667
## 21 tree_28 3 0.9166667 0.500 0.4166667
## 22 tree_29 3 0.9166667 0.500 0.4166667
## 24 tree_30 3 0.9166667 0.500 0.4166667
## 25 tree_31 3 0.9166667 0.500 0.4166667
## 26 tree_32 3 0.9166667 0.500 0.4166667
## 27 tree_33 3 0.9166667 0.500 0.4166667
## 28 tree_34 3 0.9166667 0.500 0.4166667
## 29 tree_35 3 0.9166667 0.500 0.4166667
## 30 tree_36 3 0.9166667 0.500 0.4166667
## 31 tree_4 3 0.9166667 0.500 0.4166667
## 32 tree_5 3 0.9166667 0.500 0.4166667
## 33 tree_6 3 0.9166667 0.500 0.4166667
## 34 tree_7 3 0.9166667 0.500 0.4166667
## 35 tree_8 3 0.9166667 0.500 0.4166667
## 36 tree_9 3 0.9166667 0.500 0.4166667
#underfit trees
underfit_threshold <- 0.6
underfit_trees <- performance[performance$Accuracy_Train < underfit_threshold, ]
cat("\nTREES WITH POTENTIAL UNDERFITTING (Train Accuracy <", underfit_threshold, "):\n")
##
## TREES WITH POTENTIAL UNDERFITTING (Train Accuracy < 0.6 ):
if(nrow(underfit_trees) > 0) {
print(underfit_trees[, c("Tree", "Nodes", "Accuracy_Train", "Accuracy_Validation")])
} else {
cat("No significant underfitting detected\n")
}
## No significant underfitting detected
cat("Effect of Complexity Parameter (cp):\n")
## Effect of Complexity Parameter (cp):
cp_effect <- aggregate(cbind(Accuracy_Train, Accuracy_Validation, Nodes, Overfitting_Gap) ~ CP,
data = performance, mean)
print(round(cp_effect, 3))
## CP Accuracy_Train Accuracy_Validation Nodes Overfitting_Gap
## 1 0.001 0.944 0.542 4.333 0.403
## 2 0.010 0.944 0.542 4.333 0.403
## 3 0.100 0.917 0.500 3.000 0.417
## 4 0.500 0.917 0.500 3.000 0.417
cat("\nEffect of Minsplit:\n")
##
## Effect of Minsplit:
minsplit_effect <- aggregate(cbind(Accuracy_Train, Accuracy_Validation, Nodes) ~ Minsplit,
data = performance, mean)
print(round(minsplit_effect, 3))
## Minsplit Accuracy_Train Accuracy_Validation Nodes
## 1 2 0.931 0.521 3.667
## 2 5 0.931 0.521 3.667
## 3 10 0.931 0.521 3.667
#analysis of best tree on validation set
# Predictions on validation set
val_pred <- predict(best_tree, validation_set, type = "class")
val_prob <- predict(best_tree, validation_set, type = "prob")
# Confusion matrix
conf_matrix <- table(Predicted = val_pred, Actual = validation_set$Type)
cat("Confusion Matrix (Validation Set):\n")
## Confusion Matrix (Validation Set):
print(conf_matrix)
## Actual
## Predicted 1 2
## 1 4 3
## 2 0 1
# Performance metrics
accuracy <- sum(diag(conf_matrix)) / sum(conf_matrix)
if(ncol(conf_matrix) == 2) {
sensitivity <- conf_matrix[2,2] / sum(conf_matrix[,2]) # True positive rate
specificity <- conf_matrix[1,1] / sum(conf_matrix[,1]) # True negative rate
precision <- conf_matrix[2,2] / sum(conf_matrix[2,]) # Positive predictive value
cat("\nPerformance Metrics:\n")
cat("Accuracy:", round(accuracy, 3), "\n")
cat("Sensitivity:", round(sensitivity, 3), "\n")
cat("Specificity:", round(specificity, 3), "\n")
cat("Precision:", round(precision, 3), "\n")
}
##
## Performance Metrics:
## Accuracy: 0.625
## Sensitivity: 0.25
## Specificity: 1
## Precision: 1
# Variable importance
imp <- best_tree$variable.importance
if(!is.null(imp)) {
imp_sorted <- sort(imp, decreasing = TRUE)
print(round(imp_sorted, 3))
barplot(imp_sorted, main = "Variable Importance in Best Tree",
ylab = "Importance", las = 2, cex.names = 0.8)
}
## Length Fbreadth Fheight Height Breadth
## 8.252 4.501 4.501 4.501 4.415
results_summary <- list(
Best_Tree = best_val_tree,
Best_Tree_Object = best_tree,
Performance_Summary = performance,
Validation_Confusion_Matrix = conf_matrix,
Variable_Importance = imp_sorted
)
results_summary
## $Best_Tree
## Tree Minsplit Minbucket CP Nodes Accuracy_Train Accuracy_Validation
## 1 tree_1 2 1 0.001 7 1 0.625
## Overfitting_Gap
## 1 0.375
##
## $Best_Tree_Object
## n= 24
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 24 11 1 (0.54166667 0.45833333)
## 2) Length< 180.75 13 1 1 (0.92307692 0.07692308)
## 4) Breadth< 151.75 12 0 1 (1.00000000 0.00000000) *
## 5) Breadth>=151.75 1 0 2 (0.00000000 1.00000000) *
## 3) Length>=180.75 11 1 2 (0.09090909 0.90909091)
## 6) Breadth>=148.25 1 0 1 (1.00000000 0.00000000) *
## 7) Breadth< 148.25 10 0 2 (0.00000000 1.00000000) *
##
## $Performance_Summary
## Tree Minsplit Minbucket CP Nodes Accuracy_Train Accuracy_Validation
## 1 tree_1 2 1 0.001 7 1.0000000 0.625
## 2 tree_10 2 1 0.010 7 1.0000000 0.625
## 3 tree_11 5 1 0.010 7 1.0000000 0.625
## 4 tree_12 10 1 0.010 7 1.0000000 0.625
## 12 tree_2 5 1 0.001 7 1.0000000 0.625
## 23 tree_3 10 1 0.001 7 1.0000000 0.625
## 5 tree_13 2 3 0.010 3 0.9166667 0.500
## 6 tree_14 5 3 0.010 3 0.9166667 0.500
## 7 tree_15 10 3 0.010 3 0.9166667 0.500
## 8 tree_16 2 5 0.010 3 0.9166667 0.500
## 9 tree_17 5 5 0.010 3 0.9166667 0.500
## 10 tree_18 10 5 0.010 3 0.9166667 0.500
## 11 tree_19 2 1 0.100 3 0.9166667 0.500
## 13 tree_20 5 1 0.100 3 0.9166667 0.500
## 14 tree_21 10 1 0.100 3 0.9166667 0.500
## 15 tree_22 2 3 0.100 3 0.9166667 0.500
## 16 tree_23 5 3 0.100 3 0.9166667 0.500
## 17 tree_24 10 3 0.100 3 0.9166667 0.500
## 18 tree_25 2 5 0.100 3 0.9166667 0.500
## 19 tree_26 5 5 0.100 3 0.9166667 0.500
## 20 tree_27 10 5 0.100 3 0.9166667 0.500
## 21 tree_28 2 1 0.500 3 0.9166667 0.500
## 22 tree_29 5 1 0.500 3 0.9166667 0.500
## 24 tree_30 10 1 0.500 3 0.9166667 0.500
## 25 tree_31 2 3 0.500 3 0.9166667 0.500
## 26 tree_32 5 3 0.500 3 0.9166667 0.500
## 27 tree_33 10 3 0.500 3 0.9166667 0.500
## 28 tree_34 2 5 0.500 3 0.9166667 0.500
## 29 tree_35 5 5 0.500 3 0.9166667 0.500
## 30 tree_36 10 5 0.500 3 0.9166667 0.500
## 31 tree_4 2 3 0.001 3 0.9166667 0.500
## 32 tree_5 5 3 0.001 3 0.9166667 0.500
## 33 tree_6 10 3 0.001 3 0.9166667 0.500
## 34 tree_7 2 5 0.001 3 0.9166667 0.500
## 35 tree_8 5 5 0.001 3 0.9166667 0.500
## 36 tree_9 10 5 0.001 3 0.9166667 0.500
## Overfitting_Gap
## 1 0.3750000
## 2 0.3750000
## 3 0.3750000
## 4 0.3750000
## 12 0.3750000
## 23 0.3750000
## 5 0.4166667
## 6 0.4166667
## 7 0.4166667
## 8 0.4166667
## 9 0.4166667
## 10 0.4166667
## 11 0.4166667
## 13 0.4166667
## 14 0.4166667
## 15 0.4166667
## 16 0.4166667
## 17 0.4166667
## 18 0.4166667
## 19 0.4166667
## 20 0.4166667
## 21 0.4166667
## 22 0.4166667
## 24 0.4166667
## 25 0.4166667
## 26 0.4166667
## 27 0.4166667
## 28 0.4166667
## 29 0.4166667
## 30 0.4166667
## 31 0.4166667
## 32 0.4166667
## 33 0.4166667
## 34 0.4166667
## 35 0.4166667
## 36 0.4166667
##
## $Validation_Confusion_Matrix
## Actual
## Predicted 1 2
## 1 4 3
## 2 0 1
##
## $Variable_Importance
## Length Fbreadth Fheight Height Breadth
## 8.252331 4.501271 4.501271 4.501271 4.414548