What is true about the coefficient of determination, R²?

The coefficient of determination, R², accurately measures the proportion of variability in the dependent variable that can be explained by the independent variables in a regression model. Specifically, R² is calculated by taking the ratio of the variance of the predicted values to the variance of the actual values. A higher R² value indicates that a larger proportion of the variance is accounted for by the model, which implies that the predictors are effectively capturing the relationship in the data.

This concept is crucial for evaluating how well a model fits the data, as it quantifies the effectiveness of the independent variables in explaining changes in the dependent variable. The closer the R² value is to 1, the better the model explains the variability, while values closer to 0 indicate that the model does not explain much of the variability.

In contrast to this correct option, R² does not indicate strength in non-linear relationships, as it is primarily used in linear regression contexts. It can take a value of zero, particularly in cases where the independent variables fail to explain any variability in the dependent variable. Lastly, R² does not measure total variance of the dependent variable; it specifically measures explained variance relative to total variance. Therefore, the understanding of R² as a measure of explained variance