A question about linear regression

[chnggary]

Hi David,

For question 58 as attached , there is no sample size n provided, i.e. we can't see the degree of freedom provided. In that case, how can we figure out the t critical values at 95% confidence level. And so we just can't say which X variable j or Intercept are statistically significant. Pls advise.
Sorry for asking u answersing such a stupid question. Many thanks in advance.

 

[T.Flockert]

i think this is a bad question.

It's not quite clear what is meant.

Technically answer d) is right, due to the fact that we only know there are at least (4-1)=3 d.f..

but if we assume n>=7 a) is right or b) for 3<n<7.

In my view of the GARP-questions a) is right.... maybe somone with more experience can comment on that.

 

[David Harper CFA FRM]

Hi chnggary,

The question is looking for answer (a): significant intercept and Variable 2.;
i.e., it's okay to assume the regression contains a modicum of data such that ABS(t-stat = - 2.53) is significant.
Generally, with sufficient sample and 95%/99% we can eyeball t-stat >> 2.0 as significant (i.e., two tailed where null is param = 0).

Technically, I agree with T.Flockert that it's a bit of a lame question for not giving you access to d.f.; it should have something like "daily returns over a one year-horizon" (so you could figure n ~ = 250) or just state sample size outright. I do agree that you need the sample/d.f. to do precise test (but it's only an issue for the X Variable 2, right? The others can be eyeballed without n/d.f.) - David

 

[chnggary]

Dear David,

Thank you for your precise explanation!