Homework assignment 1

Problems 1-6: Text problems 5.1, 5.7*, 5.9, 6.5, 6.6, 6.13*,  (problems with a * will definitely not be graded)

Problem 7: Show that the two expressions for F0 at the top of page 117 are equal.

Problem 8: For the Canadian prestige data, for the model containing education, income, and women, test the H0 that slopes of income and women are both 0.


Hint on problem 6.13 with SAS - Define new versions of the education variable in the DATA step:

 data canadianprestige ;
 infile 'c:\temp\prestige.txt' firstobs = 2 ;
 length occupation $ 25 ;
 input occupation $ education income women prestige census type $ ;
 ed10 = education + 10*rannor(0) ; 
 * the rannor() function generates random normal variates with mean 0 
     and variance 1.  By multiplying by 10 we get a random 
     variable with variance of 10^2 = 100 ;
 * ... etc for more variables with measurement error ;
 title 'Canadian Prestige data';
 run ;

then perform several multiple regressions like the following ...

 proc reg data = canadianprestige ;
  model prestige = income  ;
  model prestige = education income  ;
  model prestige = ed10 income  ;
  * ... other regressions here ;
 run ;

Hint on problem 6.13 with R - Define new education variables as components of the CanPres1 object:

CanPres1 <- read.table("c:/temp/prestige.txt",header=T)
names(CanPres1)

CanPres1$ed10 <- CanPres1$education + 10*rnorm(dim(CanPres1)[1]) 
 # ... define several more variables like this

then perform several multiple regressions like the following ...

CanPres1.lm0 <- lm(CanPres1$prestige ~ CanPres1$income)
CanPres1.lmed0 <- lm(CanPres1$prestige ~ CanPres1$income +CanPres1$education)
CanPres1.lmed10 <- lm(CanPres1$prestige ~ CanPres1$income +CanPres1$ed10)
 # ... other regressions here ;