Chartered Financial Analyst (CFA) Practice Exam Level 2

What does the F value in an F-Test represent?

1. The mean of squared residuals divided by the total variance

2. The mean square regression divided by the mean square error

3. The ratio of the variance explained by the model to the variance unexplained

4. The comparison of multiple regression coefficients

The correct answer is: The mean square regression divided by the mean square error

The F value in an F-Test represents the statistical ratio used to determine the overall significance of a regression model. It is calculated as the mean square regression divided by the mean square error. In the context of regression analysis, the mean square regression quantifies how well the independent variables explain the variability in the dependent variable, while the mean square error indicates the average of the squared differences between the observed and predicted values, reflecting the unexplained variability. By comparing these two measures, the F value assesses whether the group of independent variables in the model provides a better fit to the data than a model that only includes the mean of the dependent variable. In essence, a higher F value suggests that more of the total variability is explained by the model, indicating its strength. Other interpretations are less accurate in the context of the F-Test. For example, the mean of squared residuals divided by total variance does not capture the relative explanatory power needed for the F-Test. The ratio of the variance explained to the unexplained variance is conceptually similar but not how the F value is formalized in statistical tests. Finally, the comparison of multiple regression coefficients does not relate to the purpose of the F-Test, which is focused on the overall performance of the regression model rather