## Analysis of a Blocked Response Surface Design

``` /****************************************************************/
/*          S A S   S A M P L E   L I B R A R Y                 */
/*                                                              */
/*    NAME: RSREGRDG                                            */
/*   TITLE: Analysis of a Blocked Response Surface Design       */
/* PRODUCT: STAT                                                */
/*  SYSTEM: ALL                                                 */
/*    KEYS: response surface methods,                           */
/*   PROCS: RSREG                                               */
/*    DATA: Example in Myers (1976), pp. 189-193.               */
/*                                                              */
/* SUPPORT: RDT          UPDATE: January 2010                   */
/*     REF: Myers, Raymond H. (1976), "Response Surface Metho-  */
/*              dology", Blacksburg, Virginia: Virginia Poly-   */
/*              technic Institute and State University.         */
/*    MISC:                                                     */
/*                                                              */
/****************************************************************/

/*
/  The data is a central composite design in two factor variables
/  X1 and X2 and response variable Y.  The design has been situa-
/  ted into two blocks orthogonal to the linear and quadratic
/  terms of the model.
/---------------------------------------------------------------*/
data A;
input Block X1 X2 Y;
datalines;
-1   -1.0    0.000   61.8
-1    0.5    0.866   86.0
-1    0.5   -0.866   86.3
-1    0.0    0.000   97.1
-1    0.0    0.000   95.9
1   -0.5    0.866   72.9
1   -0.5   -0.866   61.3
1    1.0    0.000   92.3
1    0.0    0.000   91.5
1    0.0    0.000   89.7
;

/*
/  Sort by the independent variables so that we can examine
/  lack-of-fit.
/---------------------------------------------------------------*/
proc sort;
by block x1 x2;
run;

/*
/  Analyze by declaring BLOCK to be a covariate rather than a
/  factor variable: the ridge of maximum response will be
/  computed for an "average" block (see the documentation for
/  RSREG on the treatment of covariates in the ridge analysis.)
/---------------------------------------------------------------*/
proc rsreg;
model y = block x1 x2 / covar = 1 lackfit;
ridge max;
run;

```