options nodate nonumber ps=54 ls=80;

/* This analyzyes your data from take-home project 1 in matrix form 
Replace the values in the Y vector with your data   */


proc iml;

n=12;

x={1 0,
   1 0,
   1 10,
   1 10,
   1 20,
   1 20,
   1 30,
   1 30,
   1 40,
   1 40,
   1 50,
   1 50};

y={6, 12, 33, 28, 48, 55, 67, 79, 86, 91, 109, 113};
xpx=x`*x;

xpy=x`*y;

xpxinv=inv(xpx);

b=xpxinv*xpy;

h=x*xpxinv*x`;

yhat=h*y;

i_n=i(n);

e=(i_n-h)*y;

j_n=j(n,n,1/n);

ssto=y`*(i_n-j_n)*y;

sse=y`*(i_n-h)*y;

ssr=y`*(h-j_n)*y;

dfe=n-2;

dfr=1;

mse=sse/dfe;

msr=ssr/dfr;

f=msr/mse;
s2_b=xpxinv*mse;

print y x yhat e;

print b s2_b;

print h;

print ssto ssr sse msr mse f;

run;

stop;