Question

Now consider the following two models: Yi = β0 + β1Xi + ui (M1) Yi = β0 + β1Xi + β2X2 i + ui (M2) 1 and determine whether each of the following statements is true, false or uncertain, and explain why: a) M1 has better out-of-sample fit than M2 b) The R2 will be higher for M1 than for M2 c) M2 and M1 are nested models d) I can test whether M1 and M2 are statistically different by testing for whether β1 = 0 e) The CV will be higher for M1

Answer 1

A) false

M2 will have better goodness of fit test. , Since Rsquare is higher for M2

B)false

R square will be higher , for the model, which will have higher number of explanatory variables.

So M2 has 2 explanatory variables , & M1 has only 1, so Rsquare of M2 should be higher

C)True

Two are nested models, bcoz we can get M1 from M2, if b2 = 0

D) false

Necessary constraint is β2 = 0

E) True

Lower CV imply better goodness of fit

So it will be lower for M2 & higher for M1