STAT 516 HW 2

NOTE:  For all hypothesis tests, you should use alpha=0.05 unless otherwise instructed.

1.  We will analyze the data in Table 7.14 on pg. 366 of the textbook.  The dependent (Y) 
variable is Oxidation and the independent (X) variable is Temperature.

Do the following by hand, SHOWING WORK.  You may use SAS to check your answers if you want.

(a)  Find the correlation coefficient r.  What does this tell you about the 
nature of the relationship between Oxidation and Temperature?  Be specific!

(b) Find the value of r^2, and interpret it in the context of the variables in the problem.

2.  Look at the data in Table 8.29 on page 462 of the textbook.  These data are also 
given in the SAS code labeled "Basket Goals data set" 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.  Carefully interpret the 
partial regression coefficient for HEIGHT.

(b)  Using the t* values and 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.

(d) Find the value of R^2, and interpret it in the context of the variables in the problem.


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

Complete a SAS program and 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? 
(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) 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.

CONCEPT QUESTIONS:

4.  Answer True/False Concept Questions 2,3,13,17,19,20 on pages 365-366.
If the statement is false, either correct it or briefly explain why it is false.

5.  Answer Concept Questions 1,3,4 on pages 450-451.
[Hint for #3:  Use the relationship between F* and R^2 that is given on page 408.  
Also verify in Table A.4A that F_.05(5,24) = 2.62.]