BREADWRAPPER DATA: MYERS, TABLE 3.1, LACK-OF-FIT 1 15:28 Monday, October 27, 2003 OBS Y X1 X2 X3 LOF 1 6.6 225.0 46.0 0.50 22504600.50 2 6.9 285.0 46.0 0.50 28504600.50 3 7.9 225.0 64.0 0.50 22506400.50 4 6.1 285.0 64.0 0.50 28506400.50 5 9.2 225.0 46.0 1.70 22504601.70 6 6.8 285.0 46.0 1.70 28504601.70 7 10.4 225.0 64.0 1.70 22506401.70 8 7.3 285.0 64.0 1.70 28506401.70 9 9.8 204.5 55.0 1.10 20455501.10 10 5.0 305.5 55.0 1.10 30555501.10 11 6.9 255.0 39.9 1.10 25503991.10 12 6.3 255.0 70.1 1.10 25507011.10 13 4.0 255.0 55.0 0.09 25505500.09 14 8.6 255.0 55.0 2.11 25505502.11 15 10.1 255.0 55.0 1.10 25505501.10 16 9.9 255.0 55.0 1.10 25505501.10 17 12.2 255.0 55.0 1.10 25505501.10 18 9.7 255.0 55.0 1.10 25505501.10 19 9.7 255.0 55.0 1.10 25505501.10 20 9.6 255.0 55.0 1.10 25505501.10 BREADWRAPPER DATA: MYERS, TABLE 3.1, LACK-OF-FIT 2 COMPLETE SECOND ORDER RESPONSE SURFACE 15:28 Monday, October 27, 2003 General Linear Models Procedure Number of observations in data set = 20 BREADWRAPPER DATA: MYERS, TABLE 3.1, LACK-OF-FIT 3 COMPLETE SECOND ORDER RESPONSE SURFACE 15:28 Monday, October 27, 2003 General Linear Models Procedure Dependent Variable: Y Sum of Mean Source DF Squares Square F Value Pr > F Model 9 70.30222586 7.81135843 6.58 0.0034 Error 10 11.86777414 1.18677741 Corrected Total 19 82.17000000 R-Square C.V. Root MSE Y Mean 0.855570 13.36679 1.0893931 8.1500000 Source DF Type I SS Mean Square F Value Pr > F X1 1 16.63881631 16.63881631 14.02 0.0038 X2 1 0.10447963 0.10447963 0.09 0.7728 X3 1 14.22502256 14.22502256 11.99 0.0061 X1*X1 1 4.62457488 4.62457488 3.90 0.0766 X2*X2 1 12.55041557 12.55041557 10.58 0.0087 X3*X3 1 18.99891692 18.99891692 16.01 0.0025 X1*X2 1 0.98000000 0.98000000 0.83 0.3849 X1*X3 1 2.00000000 2.00000000 1.69 0.2234 X2*X3 1 0.18000000 0.18000000 0.15 0.7051 Source DF Type III SS Mean Square F Value Pr > F X1 1 8.75789291 8.75789291 7.38 0.0217 X2 1 12.14304413 12.14304413 10.23 0.0095 X3 1 4.98043464 4.98043464 4.20 0.0677 X1*X1 1 8.31093864 8.31093864 7.00 0.0245 X2*X2 1 15.64802512 15.64802512 13.19 0.0046 X3*X3 1 18.99891692 18.99891692 16.01 0.0025 X1*X2 1 0.98000000 0.98000000 0.83 0.3849 X1*X3 1 2.00000000 2.00000000 1.69 0.2234 X2*X3 1 0.18000000 0.18000000 0.15 0.7051 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT -104.8567555 -3.24 0.0088 32.32600635 X1 0.4947545 2.72 0.0217 0.18212710 X2 1.7302740 3.20 0.0095 0.54092336 X3 14.2620309 2.05 0.0677 6.96197381 X1*X1 -0.0008425 -2.65 0.0245 0.00031837 X2*X2 -0.0129141 -3.63 0.0046 0.00355646 X3*X3 -3.1846081 -4.00 0.0025 0.79593246 X1*X2 -0.0012963 -0.91 0.3849 0.00142651 X1*X3 -0.0277778 -1.30 0.2234 0.02139770 X2*X3 0.0277778 0.39 0.7051 0.07132567 BREADWRAPPER DATA: MYERS, TABLE 3.1, LACK-OF-FIT 4 PURE ERROR CALCULATION 15:28 Monday, October 27, 2003 General Linear Models Procedure Class Level Information Class Levels Values LOF 15 20455501.1 22504600.5 22504601.7 22506400.5 22506401.7 25503991.1 25505501.1 25507011.1 28504600.5 28504601.7 28506400.5 28506401.7 30555501.1 25505500.09 25505502.11 Number of observations in data set = 20 BREADWRAPPER DATA: MYERS, TABLE 3.1, LACK-OF-FIT 5 PURE ERROR CALCULATION 15:28 Monday, October 27, 2003 General Linear Models Procedure Dependent Variable: Y Sum of Mean Source DF Squares Square F Value Pr > F Model 14 77.21000000 5.51500000 5.56 0.0344 Error 5 4.96000000 0.99200000 Corrected Total 19 82.17000000 R-Square C.V. Root MSE Y Mean 0.939637 12.22076 0.9959920 8.1500000 Source DF Type I SS Mean Square F Value Pr > F LOF 14 77.21000000 5.51500000 5.56 0.0344 Source DF Type III SS Mean Square F Value Pr > F LOF 14 77.21000000 5.51500000 5.56 0.0344 BREADWRAPPER DATA: MYERS, TABLE 3.1, LACK-OF-FIT 6 USE OF PROC GLM FOR LOF TEST: FF-TEST FOR LOF IS LOF TEST 15:28 Monday, October 27, 2003 General Linear Models Procedure Class Level Information Class Levels Values LOF 15 20455501.1 22504600.5 22504601.7 22506400.5 22506401.7 25503991.1 25505501.1 25507011.1 28504600.5 28504601.7 28506400.5 28506401.7 30555501.1 25505500.09 25505502.11 Number of observations in data set = 20 BREADWRAPPER DATA: MYERS, TABLE 3.1, LACK-OF-FIT 7 USE OF PROC GLM FOR LOF TEST: FF-TEST FOR LOF IS LOF TEST 15:28 Monday, October 27, 2003 General Linear Models Procedure Dependent Variable: Y Sum of Mean Source DF Squares Square F Value Pr > F Model 14 77.21000000 5.51500000 5.56 0.0344 Error 5 4.96000000 0.99200000 Corrected Total 19 82.17000000 R-Square C.V. Root MSE Y Mean 0.939637 12.22076 0.9959920 8.1500000 Source DF Type I SS Mean Square F Value Pr > F X1 1 16.63881631 16.63881631 16.77 0.0094 X2 1 0.10447963 0.10447963 0.11 0.7587 X3 1 14.22502256 14.22502256 14.34 0.0128 X1*X1 1 4.62457488 4.62457488 4.66 0.0833 X2*X2 1 12.55041557 12.55041557 12.65 0.0163 X3*X3 1 18.99891692 18.99891692 19.15 0.0072 X1*X2 1 0.98000000 0.98000000 0.99 0.3659 X1*X3 1 2.00000000 2.00000000 2.02 0.2149 X2*X3 1 0.18000000 0.18000000 0.18 0.6878 LOF 5 6.90777414 1.38155483 1.39 0.3626 Source DF Type III SS Mean Square F Value Pr > F X1 0 0.00000000 . . . X2 0 0.00000000 . . . X3 0 0.00000000 . . . X1*X1 0 0.00000000 . . . X2*X2 0 0.00000000 . . . X3*X3 0 0.00000000 . . . X1*X2 0 0.00000000 . . . X1*X3 0 0.00000000 . . . X2*X3 0 0.00000000 . . . LOF 5 6.90777414 1.38155483 1.39 0.3626 BREADWRAPPER DATA: MYERS, TABLE 3.1, LACK-OF-FIT 8 USE OF PROS RSREG FOR SECOND ORDER RESPONSE SUEFACE AND LOF TEST 15:28 Monday, October 27, 2003 Coding Coefficients for the Independent Variables Factor Subtracted off Divided by X1 255.000000 50.500000 X2 55.000000 15.100000 X3 1.100000 1.010000 BREADWRAPPER DATA: MYERS, TABLE 3.1, LACK-OF-FIT 9 USE OF PROS RSREG FOR SECOND ORDER RESPONSE SUEFACE AND LOF TEST 15:28 Monday, October 27, 2003 Response Surface for Variable Y Response Mean 8.150000 Root MSE 1.089393 R-Square 0.8556 Coef. of Variation 13.3668 Degrees of Type I Sum Regression Freedom of Squares R-Square F-Ratio Prob > F Linear 3 30.968318 0.3769 8.698 0.0039 Quadratic 3 36.173907 0.4402 10.160 0.0022 Crossproduct 3 3.160000 0.0385 0.888 0.4804 Total Regress 9 70.302226 0.8556 6.582 0.0034 Degrees of Sum of Residual Freedom Squares Mean Square F-Ratio Prob > F Lack of Fit 5 6.907774 1.381555 1.393 0.3626 Pure Error 5 4.960000 0.992000 Total Error 10 11.867774 1.186777 Degrees of Parameter Standard T for H0: Parameter Freedom Estimate Error Parameter=0 Prob > |T| INTERCEPT 1 -104.856756 32.326006 -3.244 0.0088 X1 1 0.494754 0.182127 2.717 0.0217 X2 1 1.730274 0.540923 3.199 0.0095 X3 1 14.262031 6.961974 2.049 0.0677 X1*X1 1 -0.000843 0.000318 -2.646 0.0245 X2*X1 1 -0.001296 0.001427 -0.909 0.3849 X2*X2 1 -0.012914 0.003556 -3.631 0.0046 X3*X1 1 -0.027778 0.021398 -1.298 0.2234 X3*X2 1 0.027778 0.071326 0.389 0.7051 X3*X3 1 -3.184608 0.795932 -4.001 0.0025 Parameter Estimate from Coded Parameter Data INTERCEPT 10.164481 X1 -1.857339 X2 0.146894 X3 1.717341 X1*X1 -2.148619 BREADWRAPPER DATA: MYERS, TABLE 3.1, LACK-OF-FIT 10 USE OF PROS RSREG FOR SECOND ORDER RESPONSE SUEFACE AND LOF TEST 15:28 Monday, October 27, 2003 Parameter Estimate from Coded Parameter Data X2*X1 -0.988491 X2*X2 -2.944533 X3*X1 -1.416806 X3*X2 0.423639 X3*X3 -3.248619 Degrees of Sum of Factor Freedom Squares Mean Square F-Ratio Prob > F X1 4 27.929755 6.982439 5.884 0.0106 X2 4 16.912505 4.228126 3.563 0.0470 X3 4 35.403939 8.850985 7.458 0.0047 BREADWRAPPER DATA: MYERS, TABLE 3.1, LACK-OF-FIT 11 USE OF PROS RSREG FOR SECOND ORDER RESPONSE SUEFACE AND LOF TEST 15:28 Monday, October 27, 2003 Canonical Analysis of Response Surface (based on coded data) Critical Value Factor Coded Uncoded X1 -0.601632 224.617600 X2 0.155108 57.342128 X3 0.405626 1.509682 Predicted value at stationary point 11.082889 Eigenvectors Eigenvalues X1 X2 X3 -1.588955 0.837134 -0.368401 -0.404336 -3.155857 0.305414 0.928038 -0.213231 -3.596959 0.453794 0.055013 0.889407 Stationary point is a maximum.