Week 10

Question 1

Alternative form of blocking model

Answer 1

Question 2

Least squares normal equations for alt blocking model in matrix form

Answer 2

Question 3

Orthogonal blocking

Answer 3

Question 4

General approach to arrange 2^m design in k = 2^q blocks of size 2^m-q

Answer 4

1) choose q independent factorial effects (columns) for the defining blocks (typically higher order interactions)

As below,

Then at end:

B1B2 = 1256
B1B3 = 1234
B2B3 = 3456
B1B2B3 = 14678

Question 5

I optimality

Answer 5

Minimises average prediction variance

Used more so when predictions are goal

Question 6

Variance invariance matrix for response vector Y given by

Answer 6

Question 7

Generalise least squares and variance of

Answer 7

GLS