Which statistical procedure uses the F-statistic to test the overall fit of a linear model?

Which statistical procedure uses the F-statistic to test the overall fit of a linear model?

• A. Analysis of Covariance
• B. Bar chart
• C. Analysis of Variance
• D. Anderson-Rubin method

Answer: (C)

The key idea is that the F-statistic measures whether a linear model as a whole provides a better fit to the data than a model with no predictors. In ANOVA, variance is partitioned into what the model explains and what remains as error. The F statistic compares the mean square explained by the model to the mean square error; a larger value indicates the predictors collectively account for more variance than would be expected by chance, signaling a significant overall fit. This is why the procedure that uses the F-statistic to test the overall fit of a linear model is the Analysis of Variance. It’s the standard framework for testing whether the group means differ (in its classical form) or, in regression form, whether the predictors together significantly improve the model. The other options are not about assessing the overall model fit in this sense: a bar chart is descriptive, the Anderson-Rubin method is for IV regressions, and ANCOVA is a related but more specific test involving covariates.

The key idea is that the F-statistic measures whether a linear model as a whole provides a better fit to the data than a model with no predictors. In ANOVA, variance is partitioned into what the model explains and what remains as error. The F statistic compares the mean square explained by the model to the mean square error; a larger value indicates the predictors collectively account for more variance than would be expected by chance, signaling a significant overall fit.

This is why the procedure that uses the F-statistic to test the overall fit of a linear model is the Analysis of Variance. It’s the standard framework for testing whether the group means differ (in its classical form) or, in regression form, whether the predictors together significantly improve the model. The other options are not about assessing the overall model fit in this sense: a bar chart is descriptive, the Anderson-Rubin method is for IV regressions, and ANCOVA is a related but more specific test involving covariates.