BRIEF ANSWERS TO PRACTICE PROBLEMS:

SAS code given below!


Practice Problem 
-------------------

(a) See page 536 for the form of the logistic regression model.

(b) See SAS code for model fitting.  
Note beta_0_hat = -4.048 and beta_1_hat = 0.057.

(c) Hosmer-Lemeshow test has a P-value of 0.5403, so we conclude the logistic 
model is appropriate.

(d) The Wald test about beta_1 has a P-value of 0.0149, so at alpha = .05, we 
conclude ventricle size has a significant effect on the probability 
of abnormal brain wave behavior.

(e) The estimated odds ratio is 1.059, so we estimate that the odds of having 
an abnormal brain wave reading increases by 105.9% (by a factor of 1.059) when
the ventricle size increases by one unit.

(f) Since the estimate of beta_1 is positive, a person with a smaller venticle 
size is estimated to have a lesser probability of abnormal brain wave behavior 
than a person with a larger ventricle size.

(g) Run the SAS code below to see the plot (it is a monotone increasing curve).


/* ************ SAS code *************************** */


data brain;                                                                                                                           
input VENT    EEG;                                                                                                                      
cards;                                                                                                                                  
 53      0                                                                                                                              
 37      0                                                                                                                              
 63      0                                                                                                                              
 25      0                                                                                                                              
 60      0                                                                                                                              
 58      0                                                                                                                              
 56      0                                                                                                                              
 59      0                                                                                                                              
 50      0                                                                                                                              
 58      1                                                                                                                              
 70      0                                                                                                                              
 68      1                                                                                                                              
 50      0                                                                                                                              
 59      0                                                                                                                              
 51      0                                                                                                                              
 76      0                                                                                                                              
 74      1                                                                                                                              
 62      1                                                                                                                              
 41      0                                                                                                                              
 65      0                                                                                                                              
 50      0                                                                                                                              
 94      1                                                                                                                              
 73      1                                                                                                                              
 72      0                                                                                                                              
 45      1                                                                                                                              
 56      0                                                                                                                              
 56      0                                                                                                                              
 75      0                                                                                                                              
 76      0                                                                                                                              
 78      1                                                                                                                              
 50      0                                                                                                                              
 68      0                                                                                                                              
 47      0                                                                                                                              
 66      0                                                                                                                              
 42      1                                                                                                                              
 76      1                                                                                                                              
 57      0                                                                                                                              
 65      0                                                                                                                              
 51      0                                                                                                                              
 83      1                                                                                                                              
 51      0                                                                                                                              
 80      1                                                                                                                              
 70      0                                                                                                                              
 68      1                                                                                                                              
 49      0                                                                                                                              
 56      1                                                                                                                              
 58      1                                                                                                                              
 58      1                                                                                                                              
 64      1                                                                                                                              
 60      1                                                                                                                              
 57      0                                                                                                                              
 54      0                                                                                                                              
 58      0                                                                                                                              
 63      1                                                                                                                              
 61      0                                                                                                                              
 70      0                                                                                                                              
 40      0                                                                                                                              
 51      1                                                                                                                              
 58      1                                                                                                                              
 70      1                                                                                                                              
 57      1                                                                                                                              
 84      0                                                                                                                              
 58      0                                                                                                                              
 51      1                                                                                                                              
 57      0                                                                                                                              
 85      1                                                                                                                              
 50      0                                                                                                                              
 48      0                                                                                                                              
 67      1                                                                                                                              
 62      0                                                                                                                              
 65      0
;
run;

PROC LOGISTIC DESCENDING DATA=brain;
MODEL EEG = VENT / LACKFIT;
OUTPUT OUT=NEW P=PRED L=LOWER U=UPPER;
RUN;


PROC SORT DATA=NEW; 
BY VENT;
symbol1 i = join v=circle l=32  c = black;
symbol2 i = join v=star l=32  c = black;
symbol3 i = join v=star l=32  c = black;
PROC GPLOT DATA=NEW;
PLOT PRED*VENT LOWER*VENT UPPER*VENT / OVERLAY;
RUN;