From p. 277 of R Cookbook:

Let's say I have a R model lm(formula = y ~ u + v + w) and the Summary() shows:

Multiple R-Squared: 0.4981, Adjust R-Squared: 0.4402 F-statistic:
8.603 on 3 and 26 DF, p-value: 0.0003915

Using Adjusted r-Squared I can say that my model explains 44.02% of the variance of y with the remaining 55.98 unexplained.

Question: Does the associated F-statistic (with the p-value being < .05) tell me:

1. the model, in general, is significant (not taking into account other values from Summary)
2. the model is significant in explaining the 44.02% variance (adjusted r-squared)