Chartered Financial Analyst (CFA) Practice Exam Level 2

What does R-squared represent in regression analysis?

1. The proportion of variance explained by the model

2. The total number of predictors in the model

3. The average value of residuals

4. The confidence level of the predictions

The correct answer is: The proportion of variance explained by the model

R-squared, also known as the coefficient of determination, is a key statistic in regression analysis that quantifies how well the independent variables explain the variability of the dependent variable. Specifically, it indicates the proportion of the variance in the dependent variable that can be predicted from the independent variables. A higher R-squared value means that a larger proportion of the variance is accounted for by the model, which suggests that it is effectively capturing the relationship between the variables. For instance, an R-squared of 0.85 implies that 85% of the variance in the dependent variable is explained by the model, while the remaining 15% is attributed to factors not included in the analysis. This aspect makes R-squared extremely useful for assessing the goodness-of-fit of a regression model. In contrast, the other options focus on different concepts in regression analysis: - The total number of predictors refers to the number of independent variables included in the model, which is not directly represented by R-squared. - The average value of residuals pertains to the errors made by the predictions, not to the proportion of variance explained. - The confidence level of the predictions relates to the reliability of the estimates and the degree of certainty in the predictions, which is not captured