Society of Actuaries (SOA) PA Practice Exam

What does R^2 represent in a regression model?

1. The overall accuracy of a prediction

2. The number of independent variables in the model

3. The proportion of variance explained by independent variables

4. The significance level of the regression coefficients

The correct answer is: The proportion of variance explained by independent variables

In a regression model, R² (R-squared) represents the proportion of the variance in the dependent variable that can be explained by the independent variables in the model. This measure provides an indication of how well the independent variables account for the variability in the outcome, allowing for a better understanding of the relationship between them. When R² is calculated, it compares the total variance in the dependent variable with the variance that is explained by the regression model. A higher R² value suggests that a larger portion of the variance is explained by the model, indicating that the model has a good fit to the data. Conversely, a lower R² value suggests that the model does not explain much of the variability, which may suggest the need for additional variables or a different modeling approach. The other options focus on different aspects of regression analysis. For instance, the overall accuracy of a prediction can be related to various metrics, such as root mean square error or mean absolute error, rather than just R² alone. The number of independent variables refers to the complexity of the model rather than the explanatory power provided by R². Finally, the significance level of the regression coefficients pertains to the statistical significance of individual predictors in the model and does not convey how much of the dependent