What is tested by the F test for a multiple regression relationship?

The F test evaluates the overall significance of the regression model in a multiple regression analysis. It assesses whether at least one of the independent variables in the model significantly contributes to explaining the variability in the dependent variable. Essentially, it tests the null hypothesis that all regression coefficients (except the intercept) are equal to zero, indicating that the model has no explanatory power.

When the F test yields a significant result, it suggests that the independent variables together provide a better fit to the data than a model with no predictors. This is crucial in understanding whether the regression equation as a whole is useful for making predictions or understanding relationships within the data.

The other options focus on specific aspects of regression analysis, such as individual predictors or the goodness of fit, which are addressed using different statistical tests and metrics rather than the F test itself.