/* product.sas  */
title  "Test H0: beta1 * beta2 = 0 on the SAT data";


data PennState;
     infile '/home/brunner0/441s20/openSAT.data.txt' firstobs=2;  
     input id verbal math gpa;             /* Skipping the header */

proc reg plots=none;
     title2 'Proc reg to get starting values';     	 
     model gpa = verbal math;

proc nlmixed ;
   title2 "Testing H0: beta1 beta2 = 0";
   parms beta0 = 0.60807  beta1 = 0.00231  beta2 = 0.00099736  sigmasq = 0.30069;
   L = beta0 + beta1*verbal + beta2*math;
   model gpa ~ normal(L,sigmasq);
   contrast 'Product' beta1*beta2;
run;