In regression analysis, what is another name for the r² value?

The r² value, commonly known as the coefficient of determination, quantifies the proportion of the variance in the dependent variable that can be explained by the independent variable(s) in a regression model. This metric ranges from 0 to 1, where a value closer to 1 indicates a strong relationship between the variables, meaning that a significant proportion of the variability in the outcome can be accounted for by the predictor(s).

Understanding this concept is crucial in regression analysis because it provides insight into the effectiveness of the model. A higher r² suggests that the model fits the data well, indicating that it can reliably predict outcomes based on new data from the same population.

Other options, while relevant in their own contexts, do not correctly describe the r² value. For example, while "variance explained" refers to the same underlying concept that r² represents, it is not the formal term used in regression analysis. Similarly, "standard error" and "impact factor" refer to different concepts entirely and are not interchangeable with the coefficient of determination. Recognizing the correct terminology is essential for clear communication in statistics and risk management.