When testing whether there is a linear relation between the response variable and the explanatory variables, we

Question:

When testing whether there is a linear relation between the response variable and the explanatory variables, we use an F-test. If the P-value indicates that we reject the null hypothesis, H0: β1 = β 2 =...= βk = 0, what conclusion should we come to? Is it possible that one of the bi is zero if we reject the null hypothesis?