CT3 IAI May 2006 Q14(d)

[Chandrima]

Can anyone explain which test they are applying in finding out the 95% confidence interval for this sum? I used test statistic (beta cap - beta)/Se(beta) follows t(n-2) and my 95% C.I. is coming as (0.4319, 1.5317). But in solution, they used some t(n-2),alpha/2 which I'm not being able to understand! Will appreciate if anybody helps me understanding their solution.

 

[Aditya mohan mathur]

Mostly there's a calculation error in the solution.
I'm also getting the same confidence interval as you.

The formula they've applied is
Beta(hat) -+ t(n-2,Alfa/2) * (s/√Sxx)
Which is the general formula for beta's confidence interval.
If we use this, the answer is matching your answer.

 

[Chandrima]

Ok. Thank you. But why they are writing t's degree of freedom like this? I mean, what is the significance of (alpha/2) ?

 

[Aditya mohan mathur]

Confidence interval is always two sided.
That's why Alfa/2

 

[Chandrima]

No I mean, why alpha?? Like, we can write 2.5% if we do two-tailed test at 95% level of significance. But in regression problems, is there any theory which tells level of significance is equivalent to the parameter "alpha"? (sorry if I sound dumb, but I only know that alpha is the intercept parameter of the line of regression).

 

[Aditya mohan mathur]

Both are different alfa's.
In regression, Alfa is the intercept parameter while in hypothesis it is the level of significance

 

[Chandrima]

Both are different alfa's.
In regression, Alfa is the intercept parameter while in hypothesis it is the level of significance

Oh! Thank you!