/* EXAMPLE TO DISPLAY LEAST SQUARES ESTIMATION TECHNIQUE */

/* Load in Data */
load path = c:\gauss\classes\econ5340\;
load xydata[52,2] = crime.dat;
data = xydata[2:52,.];

/* Calculate Values for Normal Equations */
nobs = 51;
x = data[.,1];
y = data[.,2];
meanx = meanc(x);
meany = meanc(y);

/* Calculating a and b -- Method #1:  Using Univariate Formulae */
demeanxy = (y - meany) .* (x - meanx);
demeanx = x - meanx;
b2 = sumc(demeanxy)/sumc(demeanx^2);
a2 = meany - b2*meanx;  
print "a = " a2;
print "b = " b2;

/* Calculating a and b -- Method #2:  Using Matrix Formula */
constant = ones(51,1);
xmat = constant~x;
b = inv(xmat' * xmat)*(xmat' * y);
print " ";
print "b vector  = " b; 

/* Predicted Values */
yhat = xmat*b;

/* Graphs */
library pgraph;
graphset;
title("Regression of Prison Population on Violent Crimes");
ylabel("Prisoners/10 thousand people");
xlabel("Violent Crimes/100 thousand people");
_plctrl = -1~0;
xy(x,y~yhat);