Show your work for any parts where you are asked to compute BY HAND.

I want to see the R-code used for each part. DO NOT show all of 
the output, just the relevant pieces to answer the questions. 
Cut and paste *relevant* R commands and *relevant* output into a 
word processor such as MS Word. 

DO NOT INCLUDE OUTPUT THAT YOU DO NOT REFER TO OR USE IN THE PROBLEM, 
otherwise points will be deducted.

1. 
The last 3 paragraphs on p.185 describe a confidence interval for a linear
function of the regression coefficients using data for the main example for 
chapter 9 (height and age as predictors of weight, in that order). The data 
can be accessed using the following command: 
  dat <- otherdata("KKNR_table8-1.txt")

Using this data, 
a) Compute the estimated regression coefficients using matrix commands in R. 
   Identify each coefficient with a greek letter (since R will use whatever name 
   was assigned to the variables by default). 
   NOTE: %*% is used by R to represent matrix multiplication, not * which is for
   scalar multiplication.
b) Compute the residuals using matrix commands in R. Show only the first 3 residuals. 

2. 
Using the same data,
a) Reproduce the Variance Covariance (VCV) matrix at the top of p.186 using R.
b) Verify that the standard errors of the regression coefficients from the
   summary(model) command in R match appropriate values in the VCV matrix. Show 
   only the coefficient information from the summary() command, not all of it.
c) Reproduce the 95% CI for L = Beta_1 + Beta_2 on p.185 *AND* state an interpretation 
   of what this interval represents in the context of this data. *ALSO*, circle the 
   values used for your interval in the output from parts (a) & (b). 
d) Compute a 90% CI for L = 2*Beta_1 - Beta_2 *AND* state an interpretation of 
   what this interval represents in the context of this data. 
   NOTE: you might want to look at the answer to chapter 9 #15 before doing this 
   problem (answers are in the back of the book).

3. 
Using the same data, consider an individual that is 50 inches tall and 10 years old.
a) For this individual, identify the estimated variance of a fitted value 
   ( s^2{Y.hat|X} ) and the estimated variance of the regression model ( s^2{Y|X} ) from 
   the predict() function in R. Label each value.
b) Compute BY HAND a 95% CI for the true mean weight of an individual of this height & age.
   (Verify your CI using R).
c) Compute BY HAND a 95% Prediction Interval for the true mean weight of an individual of 
   this height & age. (Verify your CI using R).