# R example:  Regression with qualitative (categorical) predictors  


# We use the Insurance innovation data in Table 8.2 of the book  

# type = 0 indicates a mutual company  
# type = 1 indicates a stock company   

# Save the data file into a directory and 
# use the full path name:

insur.inn.data <- read.table(file = "z:/My Documents/teaching/stat_705/insuranceinnovationdata.txt", 
header=FALSE, col.names = c('time', 'size', 'type'))

# attaching the data frame:

attach(insur.inn.data)

# Fitting the regression model through ordinary least squares:  

insur.inn.reg <- lm(time ~ size + type) 

summary(insur.inn.reg)

anova(insur.inn.reg)

# getting a 95% confidence interval for the true beta_1 (an indirect way):

alpha <- 0.05
b1 <- summary(insur.inn.reg)$coef[2,1]
s.b1 <- summary(insur.inn.reg)$coef[2,2]
error.df <- summary(insur.inn.reg)$df[2]
lower <- b1 - qt(1-alpha/2, df=error.df)*s.b1
upper <- b1 + qt(1-alpha/2, df=error.df)*s.b1
print(paste(100*(1-alpha), "percent CI for beta_1:", lower, upper))

# getting a 95% confidence interval for the true beta_2 (an indirect way):

alpha <- 0.05
b2 <- summary(insur.inn.reg)$coef[3,1]
s.b2 <- summary(insur.inn.reg)$coef[3,2]
error.df <- summary(insur.inn.reg)$df[2]
lower <- b2 - qt(1-alpha/2, df=error.df)*s.b2
upper <- b2 + qt(1-alpha/2, df=error.df)*s.b2
print(paste(100*(1-alpha), "percent CI for beta_2:", lower, upper))

############################################################# 

# Example of predictor with 4 categories  

# shirt size example  

# Save the data file into a directory and 
# use the full path name:

shirt.data <- read.table(file = "z:/My Documents/teaching/stat_705/shirtdata.txt", 
header=FALSE, col.names = c('amount', 'size'))

# attaching the data frame:

attach(shirt.data)

x1 <- ifelse(size=="medium", 1, 0)
x2 <- ifelse(size=="large", 1, 0)
x3 <- ifelse(size=="xlarge", 1, 0)

# Looking at the data set:  

print(cbind(shirt.data, x1,x2,x3))

# Fitting the regression model through ordinary least squares:  

shirt.reg <- lm(amount ~ x1 + x2 + x3)

summary(shirt.reg)

anova(shirt.reg)

# Interpreting estimated regression coefficients:                       

# We estimate that shoppers with "medium" shirt size spend $13.80 LESS  
# on AVERAGE than shoppers with "small" shirt size.                     

# We estimate that shoppers with "large" shirt size spend $18.50 LESS   
# on AVERAGE than shoppers with "small" shirt size.