Chartered Financial Analyst (CFA) Practice Exam Level 2

What does a significant F-statistic indicate in regression analysis?

1. The model is poorly fitted

2. The model explains a significant amount of variance

3. The independent variables are insignificant

4. The model has overfitting issues

The correct answer is: The model explains a significant amount of variance

A significant F-statistic in regression analysis indicates that the model explains a significant amount of variance in the dependent variable relative to the variance explained by the residual error. Essentially, it tests the null hypothesis that all the regression coefficients are equal to zero, which means that the independent variables collectively have no explanatory power on the dependent variable. A significant F-statistic leads to the rejection of this null hypothesis, suggesting that at least one of the independent variables is significantly related to the dependent variable. This result implies that the model as a whole is statistically significant and that the independent variables included are useful in predicting or explaining the variability in the dependent variable. Therefore, it confirms the relevance of the variables in the context of the regression model. In contrast, the other options do not accurately reflect what a significant F-statistic conveys within the framework of regression analysis. For instance, a model being poorly fitted is not determined solely by the F-statistic but by various diagnostic tests. The significance of independent variables is directly tied to the F-statistic, but it does not imply they are insignificant. Overfitting is a concern that may occur in regression analysis but does not itself correlate with a significant F-statistic.