options nodate nonumber ps=54 ls=80;

/* This analyzes data from Homework #3 in matrix form */


proc iml;

n=50;

x={
       1    2395  307.82    31.6,
       1     432  385.32   82.99,
       1     520  261.84   85.26,
       1     687  698.04   54.32,
       1     930   203.8   59.62,
       1    1028 1771.63   61.52,
       1     224 1423.15    68.4,
       1     590  219.13   66.91,
       1    1037  519.56   55.69,
       1    2237  237.17   59.94,
       1    1838  756.84   38.21,
       1     413 2569.56   63.04,
       1     951   555.1   86.21,
       1     700  193.58   85.45,
       1     767  372.93   50.48,
       1    1643  193.47   45.56,
       1    1145  357.28   57.77,
       1     607  199.78   55.22,
       1    1851  305.97   68.95,
       1    1440  356.84   70.51,
       1    1005  498.69   50.37,
       1    1506  260.86   31.58,
       1    2125  453.26   51.31,
       1    1900   512.6    62.4,
       1    1129   248.8   57.92,
       1     895  278.91   47.11,
       1    1052  267.93    90.3,
       1    1121  364.78   45.94,
       1     814   202.5   70.04,
       1    2592  428.47   21.15,
       1     446 2663.36   98.22,
       1    1649  436.19   55.41,
       1     483  876.19   35.19,
       1     258 1748.91    88.2,
       1     895  514.13   61.96,
       1    2182  620.54   63.35,
       1    1238  508.04   55.99,
       1    1671   217.5   33.88,
       1     859  536.52   81.42,
       1     817  225.65   66.32,
       1     500  266.19    53.4,
       1    1521 3149.13   23.04,
       1    1407  432.39   42.15,
       1    2693  183.15   48.01,
       1    2521  304.67    36.1,
       1     372  703.36   66.35,
       1    1671  659.78   47.01,
       1     495  218.91    70.7,
       1    1670  312.39   49.16,
       1     590 1475.32   45.52
};

y={
  167.57,
   208.6,
   99.44,
  142.84,
  151.41,
  275.67,
   70.61,
  188.73,
  138.51,
  152.85,
  174.72,
  163.37,
  141.69,
  253.85,
   154.4,
  154.74,
  182.28,
  186.83,
  263.37,
  175.61,
   121.3,
  161.36,
  216.47,
  225.27,
  165.13,
  176.27,
  130.11,
  170.67,
   170.4,
  174.32,
   85.38,
  209.13,
  166.16,
   75.76,
  146.93,
  265.27,
  178.55,
  209.57,
  211.09,
  148.08,
  232.15,
  132.86,
  173.49,
  174.48,
  254.96,
  134.18,
  186.88,
  116.01,
  173.56,
    97.4
} ;
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-4;

dfr=3;

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;