* ch08eg2.sas, second-order model with 2 regressors, * using data from table 8.1, page 300; options ls=78; ; data; input y x1 x2; x11=x1**2; x22=x2**2; x12=x1*x2; lines; 150 0.6 10 86 1.0 10 49 1.4 10 288 0.6 20 157 1.0 20 131 1.0 20 184 1.0 20 109 1.4 20 279 0.6 30 235 1.0 30 224 1.4 30 ; * proc glm provides more info for F-tests than does proc reg; proc glm; model y = x1 x2 x12 x11 x22; title 'Second-order polynomial regression, page 300.'; ; * The Response Surface REGression procedure is set up to fit a * second-order regression model. Proc RSReg is illustrated here, * requesting an optional LOF test which requires the user first * to sort the data set by the regressors; proc sort; by x1 x2; proc rsreg; model y = x1 x2 / lackfit; Second-order polynomial regression, page 300. 1 The GLM Procedure Number of observations 11 Second-order polynomial regression, page 300. 2 The GLM Procedure Dependent Variable: y Sum of Source DF Squares Mean Square F Value Pr > F Model 5 55365.56140 11073.11228 10.57 0.0109 Error 5 5240.43860 1048.08772 Corrected Total 10 60606.00000 R-Square Coeff Var Root MSE y Mean 0.913533 18.82220 32.37418 172.0000 Source DF Type I SS Mean Square F Value Pr > F x1 1 18704.16667 18704.16667 17.85 0.0083 x2 1 34201.50000 34201.50000 32.63 0.0023 x12 1 529.00000 529.00000 0.50 0.5092 x11 1 1645.96667 1645.96667 1.57 0.2656 x22 1 284.92807 284.92807 0.27 0.6244 Source DF Type III SS Mean Square F Value Pr > F x1 1 4220.416729 4220.416729 4.03 0.1011 x2 1 988.380358 988.380358 0.94 0.3761 x12 1 529.000000 529.000000 0.50 0.5092 x11 1 1901.194737 1901.194737 1.81 0.2359 x22 1 284.928070 284.928070 0.27 0.6244 Standard Parameter Estimate Error t Value Pr > |t| Intercept 337.7214912 149.9616345 2.25 0.0741 x1 -539.5175439 268.8603253 -2.01 0.1011 x2 8.9171053 9.1824941 0.97 0.3761 x12 2.8750000 4.0467729 0.71 0.5092 x11 171.2171053 127.1254973 1.35 0.2359 x22 -0.1060526 0.2034008 -0.52 0.6244 Second-order polynomial regression, page 300. 3 The RSREG Procedure Coding Coefficients for the Independent Variables Factor Subtracted off Divided by x1 1.000000 0.400000 x2 20.000000 10.000000 Response Surface for Variable y Response Mean 172.000000 Root MSE 32.374183 R-Square 0.9135 Coefficient of Variation 18.8222 Type I Sum Regression DF of Squares R-Square F Value Pr > F Linear 2 52906 0.8729 25.24 0.0024 Quadratic 2 1930.894737 0.0319 0.92 0.4565 Crossproduct 1 529.000000 0.0087 0.50 0.5092 Total Model 5 55366 0.9135 10.57 0.0109 Sum of Residual DF Squares Mean Square F Value Pr > F Lack of Fit 3 3835.771930 1278.590643 1.82 0.3738 Pure Error 2 1404.666667 702.333333 Total Error 5 5240.438596 1048.087719 Parameter Estimate Standard from Coded Parameter DF Estimate Error t Value Pr > |t| Data Intercept 1 337.721491 149.961634 2.25 0.0741 162.842105 x1 1 -539.517544 268.860325 -2.01 0.1011 -55.833333 x2 1 8.917105 9.182494 0.97 0.3761 75.500000 x1*x1 1 171.217105 127.125497 1.35 0.2359 27.394737 x2*x1 1 2.875000 4.046773 0.71 0.5092 11.500000 x2*x2 1 -0.106053 0.203401 -0.52 0.6244 -10.605263 Sum of Factor DF Squares Mean Square F Value Pr > F x1 3 21134 7044.787135 6.72 0.0332 x2 3 35015 11672 11.14 0.0119 Second-order polynomial regression, page 300. 4 The RSREG Procedure Canonical Analysis of Response Surface Based on Coded Data Critical Value Factor Coded Uncoded x1 0.244139 1.097656 x2 3.691921 56.919214 Predicted value at stationary point: 295.396597 Eigenvectors Eigenvalues x1 x2 28.245744 0.989225 0.146407 -11.456271 -0.146407 0.989225 Stationary point is a saddle point.