for sample 1 No.12 “to prove multicollinearity is not a problem…” the answer by CFAI is low correlation between the two independant variable. which confused me: Notes said in book1 on p200 that even rho is low between the two, it doesn’t necessarily mean multicollinearity is not a problem. However, we can calculate F-statistic ourselves from R squared, which appears to be with pretty high value, of 51.7 (take n-k-1 as 155) or of 67 (or take n-k-1 200). Then high F-statistics and low p-value of independent variable indicate that multicollinearity is not a problem. Can anyone got this one right help me on why not choosing D? Thanks!
Isn’t that backwards? I high F-stat number means that as a whole the independent variables do well in explaining the dependent, but the low/insignificant t-stats show that the independent variables on their own do not explain much.
Sorry, I didn’t quite get it. It’s low p-value, which means high t-statistics for independent varialbe. Actually with p-value<0.01, it explains pretty well. So high F-statistics and low p-value together can be used to indicate low possibility of multicollinearity.
Yea, I misread the post as small t-stats. Since both independently (significant t-stats/small p-values) and together (significant f-stat) are significant, it tells us that these variables explain the dependent variable rather well, you shouldn’t worry about multicollinearity with the information given.
so… why can’t we choose D? (sample 1 Q12)
I don’t have the question or the answers and I don’t know what sample you are talking about.
The issue with using correlation is that if you have more than 2 variables they may all have low correlations but a linear combination of them may be highly correlated. This is not an issue if we have only 2 variables. Therefore if correlation is high we know multicolinearity is a problem however if correlation is close to zero it doesn’t mean MC is not a problem. Was the probmlem a simple linear regression? If so the answer is correct as correlation is sufficient to rule on MC either way.
thanks, Niblita. And Hurricane, thanks a lot, it’s quite helpful.