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.
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.
Ok. Thank you. But why they are writing t's degree of freedom like this? I mean, what is the significance of (alpha/2) ?
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).
Both are different alfa's. In regression, Alfa is the intercept parameter while in hypothesis it is the level of significance
