1. 5.2 Inference for logistic regression
By Wald’s (1943) asymptotic results for ML estimators, parameter estimators in logistic regression models have large-sample normal distributions.
Inference can use Wald, likelihood-ratio and score methods

2. 5.2.1 Types of inference

4. Confidence intervals

12. SAS code /*group data into 8 groups*/ data table4_3a; set table4_3;
W_g=round(W-0.75)+0.75;
if W<23.25 then W_g=22.5;
if W>29.25 then W_g=30.5;
run;
proc sql;
create table table4_3g as
select W_g, count(W_g) as n,
sum(NSa) as y,
mean(W) as width,
sum(Sa) as satell
from table4_3a group by W_g;
quit;
data table4_3g;
set table4_3g;
logcases=log(n);
data table4_3; input C S W Wt NSa=(Sa>0); W1=W ; WW=W1*W1; cards; …

17. /*with quadratic item (W-mean)^2 */
proc genmod data=table4_3 desc;
model NSa=w1 ww/dist=bin link=logit;
run;

21. SAS output/dataset – Table4_3g

22. proc genmod data=table4_3g; model y/n = width / dist = bin link = logit lrci alpha = .01 type3; proc logistic data=table4_3g; model y/n = width / influence stb; output out = predict p = pi_hat lower = LCL upper = UCL; data predict; set predict; rate=y/n; std=sqrt(rate*(1-rate)/n); Lrate=rate-1.96*std; Urate=rate+1.96*std; run; proc print data = predict;

23. symbol1 i=join line=1 color=green value=circle; symbol2 i=join line=1 color=green value=none; symbol3 i=join line=1 color=green value=none; symbol4 i=join line=1 color=blue value=circle; symbol5 i=join line=1 color=blue value=none; symbol6 i=join line=1 color=blue value=none; proc gplot data=predict; plot rate*width Lrate*width Urate*width pi_hat*width LCL*width UCL*width /overlay; Run;

25. /. log linear model with grouped data
/*log linear model with grouped data*/ proc genmod data=table4_3g; model satell = width / dist = poi link = log offset = logcases residuals; run;