00293 �99c9cd0aba879c895882ead40e05ef

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Experimental Design Models with Random Components

Observation	Observed Value	Predicted Value	Residual
10	30.60000000	30.85000000	-0.25000000
11	30.91000000	30.85000000	0.06000000
12	30.70000000	30.85000000	-0.15000000
13	30.74000000	30.77000000	-0.03000000
14	30.89000000	30.77000000	0.12000000
15	30.69000000	30.77000000	-0.08000000
16	30.76000000	30.77000000	-0.01000000
17	30.84000000	30.78500000	0.05500000
18	30.85000000	30.78500000	0.06500000
19	30.71000000	30.78500000	-0.07500000
20	30.74000000	30.78500000	-0.04500000
21	30.78000000	30.68000000	0.10000000
22	30.53000000	30.68000000	-0.15000000
23	30.71000000	30.68000000	0.03000000
24	30.70000000	30.68000000	0.02000000
25	30.93000000	30.94500000	-0.01500000

Figurę 6. (continued).

model. The large variability associated with site 1 can also be seen in this residual plot. In Figurę 7b, the residuals are plotted against day and the large variability at day 6 is evident. Figurę 7c illustrates the residuals against site with the large variability at site 1 evident.

Figurę 8 reanalyzes the data after eliminating all responses at site 1. There are 112 remaining measurements. The ANOVA estimates of the components in Figurę 8 are ąuite different from the results for the fuli data. The maximum likelihood estimates for the reduced data are shown in Figurę 9. Notę that the negative ANOVA estimate for interaction component is estimated to be 0 by the maximum likelihood method. The restricted maximum likelihood estimates are shown in Figurę 10. Again, the interaction component is estimated to be 0. The ANOVA estimates are recomputed for the reduced model without the interaction term in Figurę 11. Notice that the results match the restricted maximum likelihood estimates in Figurę 10.