The SAS System 1 Obs variety pesticide yield 1 1 1 49 2 1 1 39 3 1 2 50 4 1 2 55 5 1 3 43 6 1 3 38 7 1 4 43 8 1 4 58 9 2 1 55 10 2 1 41 11 2 2 67 12 2 2 58 13 2 3 53 14 2 3 42 15 2 4 85 16 2 4 73 17 3 1 66 18 3 1 68 19 3 2 85 20 3 2 92 21 3 3 69 22 3 3 62 23 3 4 85 24 3 4 89 2 Obs variety pesticide _TYPE_ _FREQ_ yield std 1 1 1 0 2 44.0 7.0711 2 1 2 0 2 52.5 3.5355 3 1 3 0 2 40.5 3.5355 4 1 4 0 2 50.5 10.6066 5 2 1 0 2 48.0 9.8995 6 2 2 0 2 62.5 6.3640 7 2 3 0 2 47.5 7.7782 8 2 4 0 2 79.0 8.4853 9 3 1 0 2 67.0 1.4142 10 3 2 0 2 88.5 4.9497 11 3 3 0 2 65.5 4.9497 12 3 4 0 2 87.0 2.8284 Plot B: Interaction Plot 3 The ANOVA Procedure Class Level Information Class Levels Values pesticide 4 1 2 3 4 variety 3 1 2 3 Number of Observations Read 24 Number of Observations Used 24 Plot B: Interaction Plot 4 The ANOVA Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Model 5 5661.041667 1132.208333 20.97 Error 18 971.916667 53.995370 Corrected Total 23 6632.958333 Source Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE yield Mean 0.853472 12.03793 7.348154 61.04167 Source DF Anova SS Mean Square F Value pesticide 3 1992.458333 664.152778 12.30 variety 2 3668.583333 1834.291667 33.97 Source Pr > F pesticide 0.0001 variety <.0001 Plot B: Interaction Plot 5 The ANOVA Procedure Class Level Information Class Levels Values pesticide 4 1 2 3 4 variety 3 1 2 3 Number of Observations Read 24 Number of Observations Used 24 Plot B: Interaction Plot 6 The ANOVA Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Model 11 6115.458333 555.950758 12.89 Error 12 517.500000 43.125000 Corrected Total 23 6632.958333 Source Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE yield Mean 0.921981 10.75816 6.566963 61.04167 Source DF Anova SS Mean Square F Value pesticide 3 1992.458333 664.152778 15.40 variety 2 3668.583333 1834.291667 42.53 pesticide*variety 6 454.416667 75.736111 1.76 Source Pr > F pesticide 0.0002 variety <.0001 pesticide*variety 0.1913 Plot B: Interaction Plot 7 The GLM Procedure Class Level Information Class Levels Values pesticide 4 1 2 3 4 variety 3 1 2 3 Number of Observations Read 24 Number of Observations Used 24 Plot B: Interaction Plot 8 The GLM Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Model 5 5661.041667 1132.208333 20.97 Error 18 971.916667 53.995370 Corrected Total 23 6632.958333 Source Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE yield Mean 0.853472 12.03793 7.348154 61.04167 Source DF Type I SS Mean Square F Value pesticide 3 1992.458333 664.152778 12.30 variety 2 3668.583333 1834.291667 33.97 Source Pr > F pesticide 0.0001 variety <.0001 Source DF Type III SS Mean Square F Value pesticide 3 1992.458333 664.152778 12.30 variety 2 3668.583333 1834.291667 33.97 Source Pr > F pesticide 0.0001 variety <.0001 9 The GLM Procedure Class Level Information Class Levels Values pesticide 4 1 2 3 4 variety 3 1 2 3 Number of Observations Read 24 Number of Observations Used 24 10 The GLM Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Model 11 6115.458333 555.950758 12.89 Error 12 517.500000 43.125000 Corrected Total 23 6632.958333 Source Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE yield Mean 0.921981 10.75816 6.566963 61.04167 Source DF Type I SS Mean Square F Value pesticide 3 1992.458333 664.152778 15.40 variety 2 3668.583333 1834.291667 42.53 pesticide*variety 6 454.416667 75.736111 1.76 Source Pr > F pesticide 0.0002 variety <.0001 pesticide*variety 0.1913 Source DF Type III SS Mean Square F Value pesticide 3 1992.458333 664.152778 15.40 variety 2 3668.583333 1834.291667 42.53 pesticide*variety 6 454.416667 75.736111 1.76 Source Pr > F pesticide 0.0002 variety <.0001 pesticide*variety 0.1913 Plot F: Residual Plots by Variety for Model with Interaction 11 d d d d d u u u u u i i i i i i m m m m m n n n n n n m m m m m t t t t t t y y y y y e e e e e e _ _ _ _ _ r r r r r r v v p p p a a a a a a y a a e e e c c c c c c i r r s s s t t t t t t O e i i t t t _ _ _ _ _ _ b l _ _ _ _ _ 1 1 1 2 2 2 s d 1 2 1 2 3 1 2 3 1 2 3 1 49 1 0 1 0 0 1 0 0 0 0 0 2 39 1 0 1 0 0 1 0 0 0 0 0 3 50 1 0 0 1 0 0 1 0 0 0 0 4 55 1 0 0 1 0 0 1 0 0 0 0 5 43 1 0 0 0 1 0 0 1 0 0 0 6 38 1 0 0 0 1 0 0 1 0 0 0 7 43 1 0 0 0 0 0 0 0 0 0 0 8 58 1 0 0 0 0 0 0 0 0 0 0 9 55 0 1 1 0 0 0 0 0 1 0 0 10 41 0 1 1 0 0 0 0 0 1 0 0 11 67 0 1 0 1 0 0 0 0 0 1 0 12 58 0 1 0 1 0 0 0 0 0 1 0 13 53 0 1 0 0 1 0 0 0 0 0 1 14 42 0 1 0 0 1 0 0 0 0 0 1 15 85 0 1 0 0 0 0 0 0 0 0 0 16 73 0 1 0 0 0 0 0 0 0 0 0 17 66 0 0 1 0 0 0 0 0 0 0 0 18 68 0 0 1 0 0 0 0 0 0 0 0 19 85 0 0 0 1 0 0 0 0 0 0 0 20 92 0 0 0 1 0 0 0 0 0 0 0 21 69 0 0 0 0 1 0 0 0 0 0 0 22 62 0 0 0 0 1 0 0 0 0 0 0 23 85 0 0 0 0 0 0 0 0 0 0 0 24 89 0 0 0 0 0 0 0 0 0 0 0 Plot F: Residual Plots by Variety for Model with Interaction 12 The REG Procedure Model: MODEL1 Dependent Variable: yield Number of Observations Read 24 Number of Observations Used 24 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 5 5661.04167 1132.20833 20.97 <.0001 Error 18 971.91667 53.99537 Corrected Total 23 6632.95833 Root MSE 7.34815 R-Square 0.8535 Dependent Mean 61.04167 Adj R-Sq 0.8128 Coeff Var 12.03793 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 88.12500 3.67408 23.99 <.0001 dummy_vari_1 1 -30.12500 3.67408 -8.20 <.0001 dummy_vari_2 1 -17.75000 3.67408 -4.83 0.0001 dummy_pest_1 1 -19.16667 4.24246 -4.52 0.0003 dummy_pest_2 1 -4.33333 4.24246 -1.02 0.3206 dummy_pest_3 1 -21.00000 4.24246 -4.95 0.0001 Plot F: Residual Plots by Variety for Model with Interaction 13 The REG Procedure Model: MODEL1 Dependent Variable: yield Output Statistics Dependent Predicted Std Error Std Error Student Obs Variable Value Mean Predict Residual Residual Residual 1 49.0000 38.8333 3.6741 10.1667 6.364 1.598 2 39.0000 38.8333 3.6741 0.1667 6.364 0.0262 3 50.0000 53.6667 3.6741 -3.6667 6.364 -0.576 4 55.0000 53.6667 3.6741 1.3333 6.364 0.210 5 43.0000 37.0000 3.6741 6.0000 6.364 0.943 6 38.0000 37.0000 3.6741 1.0000 6.364 0.157 7 43.0000 58.0000 3.6741 -15.0000 6.364 -2.357 8 58.0000 58.0000 3.6741 -3.55E-15 6.364 -56E-17 9 55.0000 51.2083 3.6741 3.7917 6.364 0.596 10 41.0000 51.2083 3.6741 -10.2083 6.364 -1.604 11 67.0000 66.0417 3.6741 0.9583 6.364 0.151 12 58.0000 66.0417 3.6741 -8.0417 6.364 -1.264 13 53.0000 49.3750 3.6741 3.6250 6.364 0.570 14 42.0000 49.3750 3.6741 -7.3750 6.364 -1.159 15 85.0000 70.3750 3.6741 14.6250 6.364 2.298 16 73.0000 70.3750 3.6741 2.6250 6.364 0.412 17 66.0000 68.9583 3.6741 -2.9583 6.364 -0.465 18 68.0000 68.9583 3.6741 -0.9583 6.364 -0.151 19 85.0000 83.7917 3.6741 1.2083 6.364 0.190 20 92.0000 83.7917 3.6741 8.2083 6.364 1.290 21 69.0000 67.1250 3.6741 1.8750 6.364 0.295 22 62.0000 67.1250 3.6741 -5.1250 6.364 -0.805 23 85.0000 88.1250 3.6741 -3.1250 6.364 -0.491 24 89.0000 88.1250 3.6741 0.8750 6.364 0.137 Output Statistics Cook's Obs -2-1 0 1 2 D 1 | |*** | 0.142 2 | | | 0.000 3 | *| | 0.018 4 | | | 0.002 5 | |* | 0.049 6 | | | 0.001 7 | ****| | 0.309 8 | | | 0.000 9 | |* | 0.020 10 | ***| | 0.143 11 | | | 0.001 12 | **| | 0.089 13 | |* | 0.018 Plot F: Residual Plots by Variety for Model with Interaction 14 The REG Procedure Model: MODEL1 Dependent Variable: yield Output Statistics Cook's Obs -2-1 0 1 2 D 14 | **| | 0.075 15 | |**** | 0.293 16 | | | 0.009 17 | | | 0.012 18 | | | 0.001 19 | | | 0.002 20 | |** | 0.092 21 | | | 0.005 22 | *| | 0.036 23 | | | 0.013 24 | | | 0.001 Sum of Residuals 0 Sum of Squared Residuals 971.91667 Predicted Residual SS (PRESS) 1727.85185 Plot F: Residual Plots by Variety for Model with Interaction 15 The REG Procedure Model: MODEL1 Dependent Variable: yield Number of Observations Read 24 Number of Observations Used 24 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 11 6115.45833 555.95076 12.89 <.0001 Error 12 517.50000 43.12500 Corrected Total 23 6632.95833 Root MSE 6.56696 R-Square 0.9220 Dependent Mean 61.04167 Adj R-Sq 0.8505 Coeff Var 10.75816 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 87.00000 4.64354 18.74 <.0001 dummy_vari_1 1 -36.50000 6.56696 -5.56 0.0001 dummy_vari_2 1 -8.00000 6.56696 -1.22 0.2466 dummy_pest_1 1 -20.00000 6.56696 -3.05 0.0102 dummy_pest_2 1 1.50000 6.56696 0.23 0.8232 dummy_pest_3 1 -21.50000 6.56696 -3.27 0.0067 interact_11 1 13.50000 9.28709 1.45 0.1717 interact_12 1 0.50000 9.28709 0.05 0.9580 interact_13 1 11.50000 9.28709 1.24 0.2393 interact_21 1 -11.00000 9.28709 -1.18 0.2592 interact_22 1 -18.00000 9.28709 -1.94 0.0765 interact_23 1 -10.00000 9.28709 -1.08 0.3028 Plot F: Residual Plots by Variety for Model with Interaction 16 The REG Procedure Model: MODEL1 Dependent Variable: yield Output Statistics Dependent Predicted Std Error Std Error Student Obs Variable Value Mean Predict Residual Residual Residual 1 49.0000 44.0000 4.6435 5.0000 4.644 1.077 2 39.0000 44.0000 4.6435 -5.0000 4.644 -1.077 3 50.0000 52.5000 4.6435 -2.5000 4.644 -0.538 4 55.0000 52.5000 4.6435 2.5000 4.644 0.538 5 43.0000 40.5000 4.6435 2.5000 4.644 0.538 6 38.0000 40.5000 4.6435 -2.5000 4.644 -0.538 7 43.0000 50.5000 4.6435 -7.5000 4.644 -1.615 8 58.0000 50.5000 4.6435 7.5000 4.644 1.615 9 55.0000 48.0000 4.6435 7.0000 4.644 1.507 10 41.0000 48.0000 4.6435 -7.0000 4.644 -1.507 11 67.0000 62.5000 4.6435 4.5000 4.644 0.969 12 58.0000 62.5000 4.6435 -4.5000 4.644 -0.969 13 53.0000 47.5000 4.6435 5.5000 4.644 1.184 14 42.0000 47.5000 4.6435 -5.5000 4.644 -1.184 15 85.0000 79.0000 4.6435 6.0000 4.644 1.292 16 73.0000 79.0000 4.6435 -6.0000 4.644 -1.292 17 66.0000 67.0000 4.6435 -1.0000 4.644 -0.215 18 68.0000 67.0000 4.6435 1.0000 4.644 0.215 19 85.0000 88.5000 4.6435 -3.5000 4.644 -0.754 20 92.0000 88.5000 4.6435 3.5000 4.644 0.754 21 69.0000 65.5000 4.6435 3.5000 4.644 0.754 22 62.0000 65.5000 4.6435 -3.5000 4.644 -0.754 23 85.0000 87.0000 4.6435 -2.0000 4.644 -0.431 24 89.0000 87.0000 4.6435 2.0000 4.644 0.431 Output Statistics Cook's Obs -2-1 0 1 2 D 1 | |** | 0.097 2 | **| | 0.097 3 | *| | 0.024 4 | |* | 0.024 5 | |* | 0.024 6 | *| | 0.024 7 | ***| | 0.217 8 | |*** | 0.217 9 | |*** | 0.189 10 | ***| | 0.189 11 | |* | 0.078 12 | *| | 0.078 13 | |** | 0.117 Plot F: Residual Plots by Variety for Model with Interaction 17 The REG Procedure Model: MODEL1 Dependent Variable: yield Output Statistics Cook's Obs -2-1 0 1 2 D 14 | **| | 0.117 15 | |** | 0.139 16 | **| | 0.139 17 | | | 0.004 18 | | | 0.004 19 | *| | 0.047 20 | |* | 0.047 21 | |* | 0.047 22 | *| | 0.047 23 | | | 0.015 24 | | | 0.015 Sum of Residuals 0 Sum of Squared Residuals 517.50000 Predicted Residual SS (PRESS) 2070.00000