What does the coefficient of determination measure in regression analysis?

The coefficient of determination, commonly denoted as R-squared, quantifies the proportion of variance in the dependent variable that can be explained by the independent variables in a regression model. When the R-squared value is calculated, it provides insights into how well the model fits the data. A higher R-squared value indicates that a larger percentage of the variability in the dependent variable is captured by the model, meaning the model does a better job of explaining the data.

For example, if an R-squared value is 0.80, this would suggest that 80% of the variation in the dependent variable can be accounted for by the independent variables, leaving only 20% of the variation unexplained. This explanation of the variability is crucial for understanding model performance and effectiveness in predictive analytics.

The other options do not accurately describe the primary purpose of the coefficient of determination. While A refers to the nature of relationships between variables, it does not specifically convey the concept of explained variation. C speaks to the reliability of predictive modeling, which is more about the overall performance of the model rather than the specific measure of explained variance. D mentions the strength of correlation, which is related but does not capture the full extent of how well the independent variables explain the