Dear John,

As much as I know, it´s not possible. But I am just an user of stats, not a specialist. I strongly recommend that you follow a stats' professor on youtube: Brandon Foltz.

He taught me the best classes in stats ever.

Good look.

Prof. Hess

Take a look:

https://www.youtube.com/watch?v=ZkjP5RJLQF4

Thank you very much Prof Hess. I will follow the link immediately.

Yes especially in cases of multicollinearity. Gujarati (2003) indicate that

"In cases of high collinearity, it is possible to find that one or more of the coefficients are individually statistically insignificant on the basis of the t test. Yet the R2 in such situations may be so high, say, in excess of 0.9, that on the basis of the F test one can convincingly reject the hypothesis that β2 = β3 = · · · = βk = 0. Indeed, this is one of the signals of multicollinearity—insignificant t values but a high overall R2 (and a significant F value)!"

Thank you for sharing that perspective Richard W Wamalwa.