##### Chapter 6: Regression Methods -------------------

#### Part 1: Linear Regression -------------------

## Understanding regression ----
## Example: Space Shuttle Launch Data ----
launch <- read.csv("challenger.csv")

# estimate beta manually
b <- cov(launch$temperature, launch$distress_ct) / var(launch$temperature)
b

# estimate alpha manually
a <- mean(launch$distress_ct) - b * mean(launch$temperature)
a

# calculate the correlation of launch data
r <- cov(launch$temperature, launch$distress_ct) /
       (sd(launch$temperature) * sd(launch$distress_ct))
r
cor(launch$temperature, launch$distress_ct)

# computing the slope using correlation
r * (sd(launch$distress_ct) / sd(launch$temperature))

# confirming the regression line using the lm function (not in text)
model <- lm(distress_ct ~ temperature, data = launch)
model
summary(model)

# creating a simple multiple regression function
reg <- function(y, x) {
  x <- as.matrix(x)
  x <- cbind(Intercept = 1, x)
  b <- solve(t(x) %*% x) %*% t(x) %*% y
  colnames(b) <- "estimate"
  print(b)
}

# examine the launch data
str(launch)

# test regression model with simple linear regression
reg(y = launch$distress_ct, x = launch[2])

# use regression model with multiple regression
reg(y = launch$distress_ct, x = launch[2:4])

# confirming the multiple regression result using the lm function (not in text)
# note that launch_id is an id variable and should not be included in the model
model <- lm(distress_ct ~ temperature + pressure + launch_id, data = launch)
model

## Example: Predicting Medical Expenses ----
## Step 2: Exploring and preparing the data ----
insurance <- read.csv("insurance.csv", stringsAsFactors = TRUE)
str(insurance)

# summarize the charges variable
summary(insurance$expenses)

# histogram of insurance charges
hist(insurance$expenses)

# table of region
table(insurance$region)

# exploring relationships among features: correlation matrix
cor(insurance[c("age", "bmi", "children", "expenses")])

# visualing relationships among features: scatterplot matrix
pairs(insurance[c("age", "bmi", "children", "expenses")])

# more informative scatterplot matrix
library(psych)
pairs.panels(insurance[c("age", "bmi", "children", "expenses")])

# set up trainning and test data sets

indx <- sample(1:nrow(insurance), as.integer(0.9*nrow(insurance)))
indx

insurance_train <- insurance[indx,]
insurance_test <- insurance[-indx,]

## Step 3: Training a model on the data ----
ins_model <- lm(expenses ~ age + children + bmi + sex + smoker + region,
                data = insurance_train)
ins_model <- lm(expenses ~ ., data = insurance_train) # this is equivalent to above

# see the estimated beta coefficients
ins_model

## Step 4: Evaluating model performance ----
# see more detail about the estimated beta coefficients
summary(ins_model)

# generate predictions for the testing dataset
ins_pred <- predict(ins_model, insurance_test)

# compare the distribution of predicted values vs. actual values
summary(ins_pred)
summary(insurance_test_vals)

# plot
plot(ins_pred, insurance_test$expenses)

# compare the correlation
cor(ins_pred, insurance_test$expenses)

# function to calculate the mean absolute error
MAE <- function(actual, predicted) {
  mean(abs(actual - predicted))  
}

# mean absolute error between predicted and actual values
MAE(ins_pred, insurance_test_vals)

## Step 5: Improving model performance ----

# add a higher-order "age" term
insurance_train$age2 <- insurance_train$age^2

# add an indicator for BMI >= 30
insurance_train$bmi30 <- ifelse(insurance_train$bmi >= 30, 1, 0)

# create final model
ins_model2 <- lm(expenses ~ age + age2 + children + bmi + sex +
                   bmi30*smoker + region, data = insurance_train)

summary(ins_model2)

#### Part 2: Regression Trees and Model Trees -------------------

## Understanding regression trees and model trees ----
## Example: Calculating SDR ----
# set up the data
tee <- c(1, 1, 1, 2, 2, 3, 4, 5, 5, 6, 6, 7, 7, 7, 7)
at1 <- c(1, 1, 1, 2, 2, 3, 4, 5, 5)
at2 <- c(6, 6, 7, 7, 7, 7)
bt1 <- c(1, 1, 1, 2, 2, 3, 4)
bt2 <- c(5, 5, 6, 6, 7, 7, 7, 7)

# compute the SDR
sdr_a <- sd(tee) - (length(at1) / length(tee) * sd(at1) + length(at2) / length(tee) * sd(at2))
sdr_b <- sd(tee) - (length(bt1) / length(tee) * sd(bt1) + length(bt2) / length(tee) * sd(bt2))

# compare the SDR for each split
sdr_a
sdr_b

## Example: Estimating Wine Quality ----
## Step 2: Exploring and preparing the data ----
wine <- read.csv("whitewines.csv")

# examine the wine data
str(wine)

# the distribution of quality ratings
hist(wine$quality)

# summary statistics of the wine data
summary(wine)

wine_train <- wine[1:3750, ]
wine_test <- wine[3751:4898, ]

## Step 3: Training a model on the data ----
# regression tree using rpart
library(rpart)
m.rpart <- rpart(quality ~ ., data = wine_train)

# get basic information about the tree
m.rpart

# get more detailed information about the tree
summary(m.rpart)

# use the rpart.plot package to create a visualization
library(rpart.plot)

# a basic decision tree diagram
rpart.plot(m.rpart, digits = 3)

# a few adjustments to the diagram
rpart.plot(m.rpart, digits = 4, fallen.leaves = TRUE, type = 3, extra = 101)

## Step 4: Evaluate model performance ----

# generate predictions for the testing dataset
p.rpart <- predict(m.rpart, wine_test)

# compare the distribution of predicted values vs. actual values
summary(p.rpart)
summary(wine_test$quality)

# compare the correlation
cor(p.rpart, wine_test$quality)

# function to calculate the mean absolute error
MAE <- function(actual, predicted) {
  mean(abs(actual - predicted))  
}

# mean absolute error between predicted and actual values
MAE(p.rpart, wine_test$quality)

# mean absolute error between actual values and mean value
mean(wine_train$quality) # result = 5.87
MAE(5.87, wine_test$quality)

## Step 5: Improving model performance ----
# train a M5' Model Tree
library(RWeka)
m.m5p <- M5P(quality ~ ., data = wine_train)

# display the tree
m.m5p

# get a summary of the model's performance
summary(m.m5p)

# generate predictions for the model
p.m5p <- predict(m.m5p, wine_test)

# summary statistics about the predictions
summary(p.m5p)

# correlation between the predicted and true values
cor(p.m5p, wine_test$quality)

# mean absolute error of predicted and true values
# (uses a custom function defined above)
MAE(wine_test$quality, p.m5p)