QUADREG Call :: SAS/IML(R) 13.1 User's Guide

QUADREG Call

RUN QUADREG (xopt, yopt, type, parms, x, y) ;

The QUADREG module fits a quadratic response surface to data. It is primarily used for demonstration purposes. The inputs to the QUADREG subroutine are as follows:

xopt: is a returned value that contains $m \times 1$ critical factor values.
yopt: is a returned value that contains the critical response value.
type: is a returned character string that contains the solution type (maximum or minimum).
parms: is a returned value that contains the parameter estimates for the quadratic model.
$x$: is an $n \times m$ data matrix, where $m$ is the number of factor variables and $n$ is the number of data points.
$y$: is an $n \times 1$ response vector.

The QUADREG module fits a regression model with a complete quadratic set of regressions across several factors. The estimated model parameters are divided into a vector of linear coefficients and a matrix of quadratic coefficients to obtain critical factor values that optimize the response. It further determines the type of the optima (maximum, minimum, or saddle point) by computing the eigenvalues of the estimated parameters.

x = { -1 -1,   -1  0,   -1  1,   0 -1,
       0  0,    0  1,    1 -1,   1  0,   1  1 };
y = { 71.7, 75.2, 76.3, 79.2, 81.5, 80.2, 80.1, 79.1, 75.8 };
run quadreg( xopt, yopt, nature, parms, x, y );
print parms[rowname={c b1 b2 a11 a12 a22} label="Parameter Estimates"],
    xopt[rowname={x1 x2} label="Critical Factor Values"],
    nature[label=""] "Response" yopt [label=""];

Figure 25.1: Parameter Estimates and Optima

Parameter Estimates
C	81.222222
B1	1.9666667
B2	0.2166667
A11	-3.933333
A12	-2.225
A22	-1.383333

Critical Factor Values
X1	0.2949376
X2	-0.158881

Maximum

Response

81.495032