Question

Any comments / direction at all will help:

Exercice 4. An analysis of variance gives the following results. Would you choose the A, B, A B model, or the full model, or any other model? 0 AL l A+ B | 0.001 0.4 cst 0.001 Where Model under Ho d.f. q-pı - po Pr(>F) J(I- 1) I(J- 1) IJ-1 1 - Fan-1J(FA) cst and A & B are: Complete model with interactions. This is the model: One-factor models. These are the models: Additive model. This is the model in which μ¡¡ is represented as a sum with the normal iid noises ξ¡ik.

Answer 1

This is a simple exercise .

Just look at the p values obtained from the hypothesis testing .

We can see that the p value for the hypothesis testing between AB and A+B is 0.001 (<0.005) .This indicates that the null hypothesis is not rejected and hence A+B is significant .

Now see the second case !

We can see that the p value for the hypothesis testing between A+B and B is 0.40(>0.005) .This indicates that the null hypothesis is rejected and hence the alternate hypothesis is valid and hence A+B is significant .

Now to the third case !

We can see that the p value for the hypothesis testing between B and the constant is 0.001 (<0.005) .This indicates that the null hypothesis is not rejected and hence constant is significant .

So in summary we can say that

1. A+B is significant

2. Constant (cst) is significant.

Hence when we design the regression model, we must take into account the factor of A+B and the cst.

Clearly , AB and B are not significant and hence should not be considered.

Hence we arrive at a result that we must go with the (A+B) model.

This is also validated from the logic that the additive model encompasses the collective contribution of both A and B models but negates the noises created by them ( hence siginificant as additive but insignifcant when taken individually)