Question

I. (20 points) Consider a completely randomized design involving four treatments: A, B, C. Write a multiple regression equation that can be used to analyze these data, and show how to use regression approach to solving experimental design.

Answer 1

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ANSWER:

EXPLANATION:

As per question given:

The multiple regression equation is y_ij = mu + I + t_ij I = 1, 2, 3, 4 j = 1, 2, 3, --- n_i where y_ij is the yield (or) response from the jth unit receiving the ith treatment, mu is the general mean effect, i is the effect due to The ith treatment and E_ij, a_n i.i.d n(0, Sigma_c^n) Then n = sigma^4_i = 1 n_i is the total number of experimental units Let us assume sigma^4_i = 1 sigma^n_i_j = 1 y_ij G = Grand total of all m obsenatons sigma^n_i_j = 1 y_ij = T_i = Total response from the units receiving ith treatment, Also Assume G = G/M T = T_i/n_i 4 n_i Therefore sigma^4_i = 1 sigma^n_i_j = 1 (y_ij - G)^2 = sigma^4_i sigma^n_i_j = 1 (y_ij - T) * sigma^4_i = 1 n_i (T G)^2 i.e TSS = SSE + SST where TSS = sigma^4_i = 1 sigma^n_i_j = 1 (y_ij - G) is the total sum of squares SST = sigma^T_i = 1 n_i (T - G)^2 is the sum

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