/sci/ - Science & Math

[Anonymous No.8981779]

Hi guys! Stuck on an econometrics/stats question

Assume the following model is estimated

[math]y_t = b_1 + b_2 x_{2t} + b_3 x_{3t} + b_4 x_{4t} + b_5 x_{5t} + e_t[/math]

(a) What is the null hypotheses of “the” regression -statistic? Why is this null hypothesis always of interest? What exactly would constitute the alternative hypothesis in this case? (b) Which would you expect to be bigger – the unrestricted residual sum of squares or the restricted residual sum of squares and why?


Little stuck on this question, first I wanted to understand what exactly I'm looking at- looks like a static time series analysis, interestingly I've never seen b1 denoted as the intercept rather b0.

-the other obvious characteristics is t1 is absorbed by e, not by beta's (percepts a correlation?) - i wonder if this effects the null hypothesis of the model? - what exactly does this mean about the model itself? why are we ignore t1, why is b1 the intercept? (is it just simple convention?)

[Anonymous No.8981795]

>>8981779
Don't create threads for this kind of shit. Put it in the stupid questions thread, you dirty fucking social scientist.

That being said, I can help you.

You are looking at just an archetypal regression with multiple x's. If it were a time-series model, then it would have t-1, t-2, etc.

The b1 or b0 is just a notation difference. Doesn't mean anything different, so your intuition that it's the intercept is still right.

(a) "The" regression statistic could either mean the F-statistic (but probably not, since it is asking for the null hypotheses, plural) or the t-statistics. The null hypothesis of the F-test is that all betas are equal to 0. The null hypothesis of the t-test is that any individual beta (the one being tested) is 0.

The null hypothesis is of interest because it is where we derive our test statistics from, as well as our assumption(s) going into the model.

The alternative hypothesis is constituted of some form of beta != 0, whether greater, less than, or simply not equal.

(b) This is a fucking dumb question.

The restricted will have larger residual sum of squared errors, since the unrestricted has no restrictions on the fit.


That all being said, you are making this too hard on yourself. This is obviously an easy question, and you were making it difficult.

[Anonymous No.8981797]

>>8981779
But seriously, don't make a thread for this dumb shit.


Cunt.

[Anonymous No.8981807]

>>8981795
>The null hypothesis is of interest because it is where we derive our test statistics from, as well as our assumption(s) going into the model.

Sorry for the BS thread anon. I did econometrics back in '08, and I'm rusty with this. I must of been confusing one of the assumptions for AR(1) model's linearity

Regarding what you said for H0, when do we ever consider in our calculations H0 = 0? Is there a _more_ correct convenction For H1 (ie. less than, greater than or not equal to)