What does an r-squared value indicate in a regression model?

The r-squared value, also known as the coefficient of determination, provides a quantitative measure of how well the regression model fits the actual data points. It represents the proportion of variance in the dependent variable that can be predicted from the independent variables. A higher r-squared value indicates a better fit, meaning that a larger proportion of the variance in the dependent variable is captured by the model. For instance, an r-squared of 0.85 suggests that 85% of the variation in the outcome can be explained by the model, while the remaining 15% is due to other factors not accounted for in the model.

This statistical measure is particularly critical in evaluating the performance of regression models, allowing analysts to compare different models and assess their predictive capability. In contrast, other options focus on aspects not directly related to the goodness of fit: the standard error of predictions is a measure of how far the predicted values deviate from the actual values; outliers may influence the regression outcome but are not what the r-squared quantifies; and causative links imply a direct relationship between variables, which r-squared does not establish as it simply measures correlation and fit.