I'm doing practice problems and i'm having a bit of difficulty with this one. I'm not used to deal with quadratic forms in regression. I tried my possible to answer it but i'm not sure it's right?
For:
a) I tested the Nul hypotheses that B2 = 0 and Ha that it's not equal to 0. From the first table, i'm given that P value for XSQ is 0.174, which is higher than 0.05 so i can't reject H0 and the quadratic term is not significant.
T* distribution = -0.008247/0.004986 = -1.654
For B1, i do the same thing and i get that the p value in the table is 0.090 which is higher than 0.05, thus H0 can't be reject and the term isn't significant?
T* distribution = 0.6341/0.2844 = 2.23
b) Here i test H0: B1 = B0 = 0 and Ha: at least one of them isn't equal to 0. But from the second table we get that the p-value is 0.042, which is lower than 0.05 so we reject H0.?
Am i right so far?
EDIT: I'm blocked for c, i don't know how to find intervals for both at the same time. I think i have to use t distribution with (n-p-1) but here n = 6, p = 2?
Thank you very much for your time!
Yes, your understanding is correct on both of them. Here you can just treat XSQ as another independent variable, i.e. your X as X1 and XSQ as X2.
Also, the reason that p-value for X is great than your threshold/cut-off point 0.05 is the existence of XSQ. If you drop XSQ from your equation, X should become significant, i.e. its p-value should fall below 0.05.
One may think of dropping X instead of XSQ. My guess is that this might make XSQ appear to be significant. However, in practice we usually try the main effects (X in your case) before going to their higher orders, unless there is some evidence from business knowledge/intuition, theory, or empirical experience. The rationale behind is that it is easier to interpret the results, and usually (not always) more predictive than the higher orders.