1 EXAMPLE 25. ANALYSIS OF COVARIANCE: ORANGES DATA 1 12:23 Saturday, January 26, 2002 The GLM Procedure Class Level Information Class Levels Values STORE 6 1 2 3 4 5 6 DAYS 6 1 2 3 4 5 6 Number of observations 36 1 EXAMPLE 25. ANALYSIS OF COVARIANCE: ORANGES DATA 2 12:23 Saturday, January 26, 2002 The GLM Procedure Dependent Variable: Q1 Sum of Source DF Squares Mean Square F Value Model 12 1225.367548 102.113962 5.75 Error 23 408.308242 17.752532 Corrected Total 35 1633.675790 Source Pr > F Model 0.0002 Error Corrected Total R-Square Coeff Var Root MSE Q1 Mean 0.750068 41.23842 4.213375 10.21711 Source DF Type I SS Mean Square F Value STORE 5 313.4198071 62.6839614 3.53 DAYS 5 250.3972723 50.0794545 2.82 P1 1 622.0082168 622.0082168 35.04 P2 1 39.5422519 39.5422519 2.23 Source Pr > F STORE 0.0163 DAYS 0.0396 P1 <.0001 P2 0.1492 Source DF Type III SS Mean Square F Value STORE 5 223.8326734 44.7665347 2.52 DAYS 5 433.0968700 86.6193740 4.88 P1 1 538.1688512 538.1688512 30.32 P2 1 39.5422519 39.5422519 2.23 Source Pr > F STORE 0.0583 DAYS 0.0035 P1 <.0001 P2 0.1492 1 EXAMPLE 25. ANALYSIS OF COVARIANCE: ORANGES DATA 3 12:23 Saturday, January 26, 2002 The GLM Procedure Dependent Variable: Q1 Standard Parameter Estimate Error t Value Pr > |t| Intercept 51.69987930 B 9.79103443 5.28 <.0001 STORE 1 -7.64532641 B 2.69194414 -2.84 0.0093 STORE 2 -5.60226472 B 2.46416942 -2.27 0.0327 STORE 3 -7.36284806 B 2.46416942 -2.99 0.0066 STORE 4 -4.36498239 B 2.48754952 -1.75 0.0926 STORE 5 -5.02052157 B 2.43612208 -2.06 0.0508 STORE 6 0.00000000 B . . . DAYS 1 -5.83036664 B 2.51932754 -2.31 0.0299 DAYS 2 -4.89997548 B 2.44708866 -2.00 0.0572 DAYS 3 2.26978922 B 2.54028189 0.89 0.3808 DAYS 4 -2.65249315 B 2.44667751 -1.08 0.2895 DAYS 5 4.04702055 B 2.55655852 1.58 0.1271 DAYS 6 0.00000000 B . . . P1 -0.83036470 0.15081334 -5.51 <.0001 P2 0.14884706 0.09973319 1.49 0.1492 NOTE: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable. 1 EXAMPLE 25. ANALYSIS OF COVARIANCE: ORANGES DATA 4 12:23 Saturday, January 26, 2002 The GLM Procedure Least Squares Means Standard DAYS Q1 LSMEAN Error Pr > |t| 1 5.5644154 1.7680833 0.0045 2 6.4948065 1.7289585 0.0010 3 13.6645712 1.7515046 <.0001 4 8.7422889 1.7339197 <.0001 5 15.4418026 1.7858085 <.0001 6 11.3947820 1.7667260 <.0001 1 EXAMPLE 25. ANALYSIS OF COVARIANCE: ORANGES DATA 5 12:23 Saturday, January 26, 2002 The GLM Procedure Class Level Information Class Levels Values DAYS 6 1 2 3 4 5 6 Number of observations 36 1 EXAMPLE 25. ANALYSIS OF COVARIANCE: ORANGES DATA 6 12:23 Saturday, January 26, 2002 The GLM Procedure Dependent Variable: Q1 Sum of Source DF Squares Mean Square F Value Model 7 1001.534875 143.076411 6.34 Error 28 632.140915 22.576461 Corrected Total 35 1633.675790 Source Pr > F Model 0.0002 Error Corrected Total R-Square Coeff Var Root MSE Q1 Mean 0.613056 46.50502 4.751469 10.21711 Source DF Type I SS Mean Square F Value DAYS 5 250.3972723 50.0794545 2.22 P1 1 696.7332860 696.7332860 30.86 P2 1 54.4043164 54.4043164 2.41 Source Pr > F DAYS 0.0805 P1 <.0001 P2 0.1318 Source DF Type III SS Mean Square F Value DAYS 5 422.2165894 84.4433179 3.74 P1 1 691.2448912 691.2448912 30.62 P2 1 54.4043164 54.4043164 2.41 Source Pr > F DAYS 0.0102 P1 <.0001 P2 0.1318 1 EXAMPLE 25. ANALYSIS OF COVARIANCE: ORANGES DATA 7 12:23 Saturday, January 26, 2002 The GLM Procedure Dependent Variable: Q1 Standard Parameter Estimate Error t Value Pr > |t| Intercept 42.48130557 B 8.68108395 4.89 <.0001 DAYS 1 -5.84339403 B 2.83830488 -2.06 0.0489 DAYS 2 -4.94232186 B 2.75781810 -1.79 0.0839 DAYS 3 2.07108475 B 2.83956405 0.73 0.4718 DAYS 4 -2.76650487 B 2.75314779 -1.00 0.3236 DAYS 5 3.70498538 B 2.83099062 1.31 0.2013 DAYS 6 0.00000000 B . . . P1 -0.76073579 0.13748199 -5.53 <.0001 P2 0.16472695 0.10611479 1.55 0.1318 NOTE: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable. 1 EXAMPLE 25. ANALYSIS OF COVARIANCE: ORANGES DATA 8 12:23 Saturday, January 26, 2002 The GLM Procedure Least Squares Means Standard DAYS Q1 LSMEAN Error Pr > |t| 1 5.6697422 1.9905507 0.0081 2 6.5708144 1.9459940 0.0022 3 13.5842210 1.9687616 <.0001 4 8.7466313 1.9549135 0.0001 5 15.2181216 1.9870757 <.0001 6 11.5131362 1.9802278 <.0001 1 EXAMPLE 25. ANALYSIS OF COVARIANCE: ORANGES DATA 9 12:23 Saturday, January 26, 2002 The GLM Procedure Class Level Information Class Levels Values DAYS 6 1 2 3 4 5 6 Number of observations 36 1 EXAMPLE 25. ANALYSIS OF COVARIANCE: ORANGES DATA 10 12:23 Saturday, January 26, 2002 The GLM Procedure Dependent Variable: Q1 Sum of Source DF Squares Mean Square F Value Model 11 1111.522562 101.047506 4.64 Error 24 522.153228 21.756384 Corrected Total 35 1633.675790 Source Pr > F Model 0.0008 Error Corrected Total R-Square Coeff Var Root MSE Q1 Mean 0.680381 45.65257 4.664374 10.21711 Source DF Type I SS Mean Square F Value DAYS 5 250.3972723 50.0794545 2.30 P1 1 696.7332860 696.7332860 32.02 P1*DAYS 5 164.3920040 32.8784008 1.51 Source Pr > F DAYS 0.0765 P1 <.0001 P1*DAYS 0.2236 Source DF Type III SS Mean Square F Value DAYS 5 201.1717701 40.2343540 1.85 P1 1 554.7860985 554.7860985 25.50 P1*DAYS 5 164.3920040 32.8784008 1.51 Source Pr > F DAYS 0.1412 P1 <.0001 P1*DAYS 0.2236 1 EXAMPLE 25. ANALYSIS OF COVARIANCE: ORANGES DATA 11 12:23 Saturday, January 26, 2002 The GLM Procedure Dependent Variable: Q1 Standard Parameter Estimate Error t Value Pr > |t| Intercept 73.27263578 B 13.48373708 5.43 <.0001 DAYS 1 -54.59714671 B 19.73545845 -2.77 0.0107 DAYS 2 -34.78570099 B 20.25105926 -1.72 0.0987 DAYS 3 -27.94295765 B 29.42842946 -0.95 0.3518 DAYS 4 -24.12342640 B 21.39334761 -1.13 0.2706 DAYS 5 4.62631110 B 30.62842608 0.15 0.8812 DAYS 6 0.00000000 B . . . P1 -1.22521164 B 0.26520396 -4.62 0.0001 P1*DAYS 1 1.00474758 B 0.39410534 2.55 0.0176 P1*DAYS 2 0.60164207 B 0.39876566 1.51 0.1444 P1*DAYS 3 0.61415851 B 0.57034268 1.08 0.2923 P1*DAYS 4 0.42959726 B 0.41510986 1.03 0.3110 P1*DAYS 5 0.02936476 B 0.57034268 0.05 0.9594 P1*DAYS 6 0.00000000 B . . . NOTE: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable. 1 EXAMPLE 25. ANALYSIS OF COVARIANCE: ORANGES DATA 12 12:23 Saturday, January 26, 2002 The GLM Procedure Least Squares Means Standard DAYS Q1 LSMEAN Error Pr > |t| 1 7.3828299 2.0114043 0.0012 2 6.5463159 1.9225330 0.0023 3 14.0301792 1.9174009 <.0001 4 8.3960731 1.9095049 0.0002 5 16.6450125 2.4685628 <.0001 6 10.5145730 1.9187590 <.0001