F test and R2 are both at model level. F test specifies whether independent variables are jointly significant in explaining the dependent variable. R2 measures how well the estimates have explained the actual dependent variable - it is a measure of the strength of the model. R2 & Adjusted R2 are mainly used to assess if the addition of an independent variable has contributed to increased strength of the model. F test is mainly used in conjecture with t test to check and correct for situations where the independent variables are jointly significant (thro F test) but independently insignificant (under t test). Think of the Anova table to remember R2 (need only RSS & TSS) and F test (need square root MSR & square root MSE - ie RSS, TSS, k, n-k-1).