When performing linear regression with one variable, one can compute Fisher's test with value $F$, and derive Student's test $T=\sqrt{F}$.
When there is more than one variable, the relationship $T=\sqrt{F}$ no longer holds. Is there a relationship between $F$ and the different Student tests $T_i$ (one for each variable)? Perhaps a system of equations?
EDIT :
I am referring to the F test in Excel's linear regression report:
Note : crossposted here with no answer.