We propose a valid test to simultaneously test the assumption of independence and googness-fit for a linear regression model. Our approach is based on the difference between two estimators of the marginal distribution $F_Y$ of the response variable $Y$, and thus it is called the MD approach. We setablish the consistency of the MD test. We compare the MD approach to the existing tests through simulation studies. The MD approach has certain advantages over the existing methods and form a nice supplement. We apply the MD approach to a cancer research data.