Qualitative Explanatory Variables

Question 1

Measure average effect of a factor

Answer 1

Main Effect:
ME(A) = Y^-(A+) - Y^-(A-)
Average response when A is +, Average response when A is -

Question 2

2 factor interaction

Answer 2

Question 3

For interactions A and B, a positive interaction is?

Answer 3

Question 4

For interactions A and B, no interaction?

Answer 4

Question 5

Interactions of A, B and C

Answer 5

Question 6

Full factorial design

Answer 6

Given m factors, this is an experiment with all 2^m combinations

Question 7

Linear model for factorial experiments

Answer 7

Question 8

Vector form of linear model for factorial experiments

Answer 8

Where r is the max number or repetitions of any Y

Question 9

For a factorial design

Answer 9

NI, where N=r2^m

Question 10

For factorial design

Answer 10

Question 11

For factorial models, all regression params are?

Answer 11

Estimated independently and there is no need to make adjustments for other terms in the model. Fitting sub models doesn’t change parameter estimates

Question 12

ME(x_i) =

Answer 12

2β_i

Question 13

Single replicate design?

Answer 13

r=1
Only one observation for each treatment/combination of treatments.
Can’t conduct hypothesis testing as no estimate for σ^2
(As residual is (r-1)2^m)