source("http://www.uvm.edu/~rsingle/stat221/data/scripts-221.R")

 dat <- bookdata("ch05q02.txt")
 head(dat)
 
 y.x1x2 <- lm(SBP~QUET+AGE, data=dat)
 anova(y.x1x2) 
  
 y.x2x1 <- lm(SBP~AGE+QUET, data=dat)
 anova(y.x2x1) 


 x.new.df <- data.frame(QUET=3.0, AGE=45)
 x.new.df
 
 predict(y.x1x2, x.new.df, interval="confidence", se.fit=T) 
   131.6077 - qt(1-.025,29)*sqrt(2.474176^2)  #[1] 126.5481   
   131.6077 + qt(1-.025,29)*sqrt(2.474176^2)  #[1] 136.6679

 predict(y.x1x2, x.new.df, interval="prediction", se.fit=T) 
   131.6077 - qt(1-.025,29)*sqrt(79.5 + 2.474176^2)  #[1] 112.6828 
   131.6077 + qt(1-.025,29)*sqrt(79.5 + 2.474176^2)  #[1] 150.5326 

 
       predict(y.x1x2, x.new.df, se.fit=T) 
 ci <- predict(y.x1x2, x.new.df, interval="confidence", se.fit=T) 
 pi <- predict(y.x1x2, x.new.df, interval="prediction", se.fit=T) 
 
 ci$se.fit #NOTE: se.fit has the same value for "confidence" & "prediction"
 pi$se.fit
 
 
 predict(y.x1x2, x.new.df, interval="confidence", se.fit=T) 
 predict(y.x2x1, x.new.df, interval="confidence", se.fit=T) #R is 'smart' about the variable order