STAT 516 HW 2B

COMPUTER CALCULATIONS:

1.  Look at the data in Table 8.31 on page 464-465 of the textbook.  These data are also 
given in the R code labeled "Liver data set" on the course web page.

Using R to help with the analysis, answer the following questions about the data set:

(a)  Fit the regression model with the survival time, TIME, as the dependent variable, and 
CLOT, PROG, ENZ, and LIV as the independent variables.  Perform a residual analysis, providing
any relevant plots that you use to check model assumptions. Comment on any possible model violations.

(b) Fit the regression model with the (natural) log survival time, LOGTIME, as the dependent variable,
 and CLOT, PROG, ENZ, and LIV as the independent variables.  Perform a residual analysis, providing
any relevant plots that you use to check model assumptions.  Are any model violations alleviated? 

(c) Using the model you fit in (b), calculate a 90% prediction interval for the (natural) LOG survival time
 for a patient with clotting potential CLOT=5.5, recovery prognosis PROG=57, protein measure ENZ=62, 
and white blood cell count LIV=2.63.  Then convert this interval to a 90% prediction interval for the 
survival time itself, for such a patient.

(c) Find the R^2 value for the regression equation from part (b).  
Interpret its value in the context of this problem.

(d) Consider the MLR model described in (b).  Are there severe outliers 
in the model? If so, which observations are outliers?  

(e) Consider the MLR model described in (b).  Are there high-leverage 
points in the model? If so, which observations are high-leverage points?   

(f) Consider the MLR model described in (b).  Based on the DFFITS 
criterion, are there influence points in the model? If so, which 
observations are influence points?   

(g) Consider the model you fit in (b).  Is there evidence of 
multicollinearity?  Explain your answer with numerical evidence.

(h) Use R to help with an automatic variable selection with LOGTIME 
as the dependent variable and CLOT, PROG, ENZ, and LIV as the 
POTENTIAL independent variables.  Of all possible models, which appears 
to be "best"?  Explain your choice(s) clearly, using evidence from R
and the various variable-selection criteria we discussed in class.



CONCEPT QUESTIONS:

Answer Concept Questions 5, 9, 12 on page 423.