9.11 Consider a RCBD with subsampling. Specifically, suppose 3 treatments, b = 4 blocks, and n = 2 observations per experimental unit. (i) Give a linear model for data from such an experiment. (ii) Outline the ANOVA table, giving sources of variation, d.f., E(MS). (iii) Write SAS statements to carry out the ANOVA in (ii). Now suppose we have supplementary information in the form of a covariate x for each experimental unit. (iv) Give a linear model for analyzing data from such an experiment. (v) Outline the corresponding ANOVA table, giving sources of variation and d.f. (vi) Give a SAS statement for carrying out the ANOVA in (v). Using the following data set

(where the two numbers in parentheses represent the duplicate observations and the number underneath represents the covariate ) perform the two ANOVAS as explained in (iii) and (vi).

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Treatment 1 2 3 Block 1 (5,7) (10,9) (15, 18) 2 4 5 Block 2 (10, 11) (14, 13) (20, 22) 4 5 3 Block 3 (12, 15) 7 (18, 20) 3 (24,27) 5 Block 4 (20, 18) (21,24) (35, 33) 6 2 8