8.15. Kidney function.  Source: Neter Problem 8.15 p. 358

Creatinine clearance (Y) is an important measure of kidney 
function, but is difficult to obtain in a clinical office setting 
because it requires 24-hour urine collection. To determine whether 
this measure can be predicted from some data that are easily 
available, a kidney specialist obtained the data that follow for 
33 male subjects. The predictor variables are serum creatinine 
concentration (X1), age (X2), and weight (X3) 

EXERCISES

8.15. 

a Prepare separate dot plots for each of the three predictor 
variables. Are there any noteworthy features in these plots? 
Comment.

b. Obtain the scatter plot matrix. Also obtain the correlation 
matrix of the X variables. What do the scatter plots suggest about 
the nature of the functional relationship between the response 
variable Y and each predictor variable? Discuss. Are any serious 
multicollinearity problems evident? Explain.

c. Fit the multiple regression function containing the three 
predictor variables as first order terrns. Does it appear that all 
predictor variables should be retained?

8.16. 

Refer to Kidney function Problem 8.15.

a. Using first-order and second-order terms for each of the three 
predictor variables (centered around the mean) in the pool of 
potential X variables (including cross products of the first-order 
terrns), find the three best hierarchical subset regression models 
according to the Ra2 criterion.

b. Is there much difference in Ra2 for the three best subset 
models?

8.20. 

Refer to Kidney function Problems 8.15 and 8.16.

a. Using the same pool of potential X variables as in Problem 
8.16a, find the best subset of variables according to forward 
stepwise regression with F limits of 4.0 and 3.9 to add or delete 
a variable, respectively.

b. How does the best subset according to forward stepwise 
regression compare with the best subset according to the adjusted
r-square* criterion obtained in Problem 8.16a?
-------------------
adjusted r-squared

 = adjusted coefficient of multiple determination 
   
         nÐ1    SSE
 = 1  Ð  --- x  ---- 
         nÐp    SSTO


      Y             X1       X2     X3

 Creatinine   creatinine    Age    Weight
 clearance   concentration 

     132         0.71        38      71
      53         1.48        78      69
     ...

     120         0.82        62     107
      52         1.53        70      75
      73         1.58        63      62
      57         1.37        68      52

Adapted from W. J. Shih and S. Weisberg, 
"Assessing Influence in Multiple Linear 
Regression with Incomplete Data," Technometrics  
28 (1986), pp.231-40.