SpyAli

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 )