Question

6. Below is a one-way ANOVA model for comparing three treatments with ni patients receiving treatment i, i 1, 2, 3. Let Yij denote the response of the jth patient receiving the ith treatment, u be the overall mean response, ai the treatment effect and eij the error term. Then, Yg=u a+Eij where, i 1, 2, 3 and j 1,... depends on the subscripts i and j, ni with nl 25, n2 - 30 and n3 20. The response 5if i jis even Yij15 ifii is odd Enter the design matrix X and the response Y into R and calculate a least squares estimator of B using the generalized inverse g, B=(XTX) XT Y (Hint, use rep0)

Answer 1

n <c(25,30,20) Y c) k<0 for (i in 1:3){ for j in 1:n[i]){ k < k+1 + Yk]ifelse(C(i*j)%%2) --0, 5,15) } } > x <matrix (0, nrow sum(n),4) x[,1] <1 x[1:cumsum(n) [1],2] <1 x[(cumsum(n) [1] +1) : cumsum (n) [2] , 3] < 1 > x[(cumsum(n) [2]+1):cumsum(n) [3],4] 1 require(MASS) > beta. hat Cginv(t (x)%*% x))%% t (x )) % % matrix(Y) print (beta. hat) [,1] [1,] 6.3 [2, 3.9 [3,] -1.3 [4, 3.7 > +