(a) Find the design matrix for the orthogonal polynomial model Y = T,,{+e corresponding to the model...
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(a) Find the design matrix for the orthogonal polynomial model Y = T,",{+e corresponding to the model Yij = f30 + f31 x i + f32x~ + f33x~ + eij, i = 1,2,3,4, j = 1, ... , N, where Xi = a + (i - l)t.
Hint: First consider the case N = l.
(b) For the model Yij = /.L + Qi + eij, i = 1,2,3,4, j = 1, ... ,N and for k = 1,2,3, find the contrast 2: AikQi such that the test of Ho : 2: AikQi = °
is the same as the test of Ho : '"'{k = 0, i.e., find the polynomial contrasts.
Exercise 6.12 X3 = 5, X4 = 8.
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