What does the coefficient of determination (r2) represent in a regression context?

The coefficient of determination, denoted as r², quantifies the proportion of the variance for a dependent variable that is explained by one or more independent variables in a regression model. It provides insight into how well the independent variables account for the variability in the dependent variable, ranging from 0 to 1. An r² value of 0 indicates that the model does not explain any variance, while a value of 1 signifies that it explains all the variance. This makes r² a crucial metric for assessing the effectiveness of the model in capturing the relationship between variables.

Understanding this concept is fundamental for financial analysts and decision-makers when using regression analysis to inform capital and operating budgeting decisions. A higher r² suggests a better fit, enhancing the reliability of predictions made based on the model. In the context of budgeting, this means that understanding how certain factors influence financial outcomes can lead to more accurate forecasts and better resource allocation.

Other aspects, such as statistical significance, cost escalation, or time-series analysis, do not directly pertain to this specific measure of variance explanation within the regression framework, thereby clarifying why r² is singularly significant in evaluating the effectiveness of regression models.