/* Example 9.4.2---*/
proc iml;
y1={ 0.000,  0.000,  0.000, 22.786, 42.130,  0.000, 12.921,
    12.921, 18.435,  26.565, 0.000,  0.000,  0.000,  0.000,
    18.435,  0.000,  0.000, 18.435, 18.435, 36.271,  0.000,
     0.000,  0.000, 12.921, 33.211};
y2={ 0.000, 18.435, 45.000, 53.729, 90.000, 12.921, 18.435,
    42.130, 56.789, 67.214,  0.000, 12.921, 22.786, 46.789,
    67.213,  0.000, 12.921, 42.130, 56.789, 77.079, 12.921,
     0.000, 39.231, 53.729, 67.213};
y3={30.000, 33.211, 60.000, 90.000, 90.000, 26.565, 33.211,
    77.079, 90.000, 90.000,  0.000, 22.786, 77.079, 77.079,
    90.000,  0.000, 22.786, 77.079, 90.000, 90.000, 26.565,
    22.786, 71.565, 90.000, 90.000};
y4={30.000, 33.211, 71.565, 90.000, 90.000, 26.565, 33.211,
    90.000, 90.000, 90.000,  0.000, 30.000, 77.079, 90.000,
    90.000, 12.921, 26.565, 77.079, 90.000, 90.000, 26.565,
    30.000, 90.000, 90.000, 90.000};
y5={30.000, 33.211, 71.565, 90.000, 90.000, 26.565, 33.211,
    90.000, 90.000, 90.000, 12.921, 33.211, 77.079, 90.000,
    90.000, 18.435, 30.000, 77.079, 90.000, 90.000, 26.565,
    30.000, 90.000, 90.000, 90.000};
x1={5.5984, 6.0161, 6.4134, 6.8459, 7.2793, 5.5984, 6.0161,
    6.4135, 6.8459, 7.2793, 5.5984, 6.0161, 6.4135, 6.8459,
    7.2793, 5.5984, 6.0161, 6.4135, 6.8459, 7.2793, 5.5984,
    6.0162, 6.4135, 6.8459, 7.2793};
x2={0.6695, 0.6405, 0.7290, 0.7700, 0.5655, 0.7820, 0.8120,
    0.8215, 0.8690, 0.8395, 0.8615, 0.9045, 1.0280, 1.0445,
    1.0455, 0.6195, 0.5305, 0.5970, 0.6385, 0.6645, 0.5685,
    0.6040, 0.6325, 0.6845, 0.7230};
y=y1||y2||y3||y4||y5;
x=J(25,1,1)||x1||x2;
beta=inv(x`*x)*x`*y;
H=x*inv(x`*x)*x`;
c={0 0 1}; n=25; p=5; q=3; f=n-q;
v=y`*(I(25)-H)*y;
corr=sqrt(inv(diag(v/f)))*v/f*sqrt(inv(diag(v/f)));
W=beta`*c`*inv(c*inv(x`*x)*c`)*c*beta;
u=det(v)/det(v+w);
F0=(f+1-p)/p*(1-u)/u;
Fa=finv(1-0.05, p, f+1-p);
print corr,u F0 Fa;
if F0>Fa then print "F0 > Fa: reject";
         else print "F0 < Fa: accept";
quit;
     CORR
        1  0.363111 -0.124134 -0.333778 -0.322255
 0.363111         1 0.3553223 0.3061168 0.3193277
-0.124134 0.3553223         1 0.9159166 0.8884994
-0.333778 0.3061168 0.9159166         1  0.986194
-0.322255 0.3193277 0.8884994  0.986194         1
              F0             FA
       1.9134753      2.7728532
             F0 < Fa: accept