# R example for Weighted Least Squares  
# We use the blood pressure data in Table 11.1 of the book  

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

bloodpressure.data <- 
read.table(file = "z:/My Documents/teaching/stat_704/bloodpressuredata.txt", 
header=FALSE, col.names = c('age', 'dbp'))

# attaching the data frame:

attach(bloodpressure.data)

# Regressing the response, dbp, against the predictor, age 

bp.reg <- lm(dbp ~ age) 

# The plots show some definite nonconstant error variance  

plot(age, dbp); abline(bp.reg)

plot(age, resid(bp.reg)); abline(h=0)

# Plot of absolute residuals against age shows that   
# absolute residuals may increase linearly with age.

abs.res <- abs(resid(bp.reg)) 

plot(age, abs.res)  


# Regressing the absolute residuals against the predictor, age  
 
bp.reg2 <- lm(abs.res ~ age)

# Defining the weights using the fitted values from this second regression:  

weight.vec <- 1/((fitted(bp.reg2))^2);


# Using the weights option in lm to get the WLS estimates:  
 
bp.wls.reg <- lm(dbp ~ age, weights = weight.vec)

summary(bp.wls.reg)

# A residual plot for the WLS regression:

plot(age, resid(bp.wls.reg)); abline(h=0)