/*
** Lesson 5.4: Ridge Regression and Principal Components
*/
use gpe2;
output file = gpe\output5.4 reset;
load data[17,7] = gpe\longley.txt;
data = data[2:17,.];           
year = data[.,1];
pgnp = data[.,2];
gnp = data[.,3];
af = data[.,5];               
em = data[.,7];
call reset;
_names = {"em","year","pgnp","gnp","af"};
call estimate(em,year~pgnp~gnp~af);

/* explanatory variables including constant */
x = year~pgnp~gnp~af~ones(rows(year),1);
/* ridge regression */
r=0.3;
a = invpd(eye(cols(x))+r*invpd(x'x));
br = a*__b;
vbr = a*__vb*a';
print "Ridge Regression Model:";
print " Coefficient    Std Error";;
print br~sqrt(diag(vbr));

/* Principal Components */ 
@ compute char. roots and vectors of X'X @	
{r,v}=eigrs2(x'x); 
v = selif(v',r.>0.1)';
bpc = v*v'__b;
vbpc = v*v'__vb*v*v';
print; 
print "Principal Components Model:";
print " Coefficient    Std Error";;
print bpc~sqrt(diag(vbpc));
end;