Multicollinearity and F-stat

In one of Qbank questions’ correction, the following is stated: "Multicollinearity refers to independent variables that are correlated with each other. Multicollinearity causes standard errors for the regression coefficients to be too high, which, in turn, causes the t-statistics to be too low. However,multicollinearity has no effect on the F-statistic. " I know that one way to detect multicollinearity is to see Low t-stats with HIGH F-stats. but they’re saying that it has no effect on F-stat. It’s all over the Schweser notes that a result of multicollinearity is high F-stat. Am I missing something? Is there a special case? Or is this another bad Qbank question?

F-stat is a combined effect of the explanatory power of ALL variables. If you have multi-collinearity the individual t-stats appear low , so you mistrust the regression , but what has actually happened is that some variables are linear combinations of some others , hence by themselves appear ineffective. Its not wrong to say that if you drop those related variables ( some of them ) your regression explanatory power overall may not improve , but the individual contributions appear more meaningful ( higher t-stats )

I understand that. But in terms of effects of multicollinearity: 1) having low t-stat and high f-stat are an indication of multicollinearity 2) Low t-stats and low f-stat are not an indication of multicollinearity If 1) and 2) are correct, how can the statement “multicollinearity has no effect on the F-statistic” be true?

low f-stat is not due to multi-collinearity by itself , its just a completely wrong choice of the explanation set. If the combination of variables is not enough to explain the outcome , there is no point blaming collinearity for the problem , just do more research ad find which OTHER variables are responsible. Collinearity ,serial correlation and cond. heteroskedasticity are problems that we have to be aware about , but its just good regression that pays the bills

a significant F-stat requires atleast 1 significant T-stat. multi… is where this doesn’t occur, the t-stats are low yet the F-stat is significant