The F statistic in a multiple regression is significant if at least one of the predictors has a significant t statistic at a given α.

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The F statistic determines whether at least one of the predictors in the model is contributing significantly to the variation in the dependent variable. If the F statistic is significant, it means that the overall model is contributing significantly to the variation in the dependent variable, and at least one predictor is significant. The significant t statistic for any of the predictors indicates that the particular predictor is contributing significantly to the variation in the dependent variable, but it is not necessary for every predictor to have a significant t statistic for the F statistic to be significant.

The F Statistic in a Multiple Regression Is Significant If