In a multiple regression, a large value of the test statistic F indicates that most of the variation in y is explained by the regression equation, and that the model is useful; while a small value of F indicates that most of the variation in y is unexplained by the regression equation, and that the model is useless.

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This statement is true. The F-test in multiple regression is used to test the overall significance of the regression model. A large F statistic indicates that the regression model is significant and useful for predicting the outcome variable y, while a small F statistic indicates that the model is not significant and provides little information about y.

In a Multiple Regression, a Large Value of the Test