STAT 516 HW 2 

Please write your answers neatly and clearly!

Also, PLEASE make sure your answers to these questions are
written in the same order as the questions are listed in 
the assignment!!

HAND CALCULATIONS:

1. On page 400 (problem 1), data are given for 8 observations.  
On the top of page 401, the SAS output for the multiple regression 
of Y on X1 and X2 is given.  Also given are the actual Y values, 
the predicted Y values, and the residuals for the 8 observations.

Do the following by hand, SHOWING WORK.
(You may use a hand calculator to help with the calculations.)

(a) Use the estimated regression line to verify that the listed 
predicted values for observations 1 and 2 are correct.  Also verify 
that the residuals for observations 1 and 2 are correct.

(b) Add up the squares of the residuals for all 8 observations and 
verify that the result matches the SSE given in the ANOVA table.

COMPUTER CALCULATIONS:

(NOTE:  For any hypothesis tests, you may use alpha = 0.05.)

2.  Look at the data in Table 8.29 on page 409 of the textbook.  
These data are also given in the SAS code "basketballdata.txt" on 
the course web page.

Complete a SAS program and answer the following questions about the data set:

(a)  Estimate the multiple regression model with GOALMADE as the 
dependent variable and WEIGHT, HEIGHT, and DASH100 as the independent 
variables.  State the estimated regression equation.  Carefully interpret 
the partial regression coefficient for HEIGHT.

(b)  Using the P-values listed in SAS, carefully state what the t-tests 
about the regression coefficients tell you about the individual effects 
of WEIGHT, HEIGHT, and DASH100 on GOALMADE.  

(c) Using a TEST statement in SAS, test whether at least one of WEIGHT and 
DASH100 is needed in the model, given that HEIGHT is in the model.
State the hypotheses and give the P-value of the test.

(d) Using the model you fit in (a), calculate a 90% prediction interval 
for the number of goals made for a new person who is six feet tall, 
weighs 155 pounds, and runs a 11.6 second 100-yard dash.

(e) Repeat part (d), except use a model which includes WEIGHT and HEIGHT 
but not DASH100.  What do you conclude from this interval compared to 
the one in (d)?

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

3.  Look at the data in Table 8.31 on page 411 of the textbook.  
These data are also given in the SAS code "liverdata.txt" on the 
course web page.

Complete a SAS program to 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.  Comment on any possible 
model violations.

(b) Fit the regression model with the log survival time, LOGTIME, 
as the dependent variable, and CLOT, PROG, ENZ, and LIV as the 
independent variables.  Perform a residual analysis.  Are any 
model violations alleviated? 
(NOTE: For this residual analysis, in adapting the sample code, change 
the PRED and RES in the code to PRED2 and RES2 so that they won't have 
the same names as the values in the residual analysis in part (a).)

(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) Use SAS 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 SAS 
and the various variable-selection criteria we discussed in class.

CONCEPT QUESTIONS:

4.  Answer Concept Questions 1,3,4,9 on pages 399-400.