The coefficient of determination can be described by which statement?

The coefficient of determination, commonly denoted as R², quantifies how well the independent variables in a regression model explain the variability of the dependent variable. It ranges from 0 to 1, where 0 indicates that the independent variables do not explain any of the variability of the dependent variable, and 1 indicates that they explain all the variability.

Because R² reflects the proportion of explained variance, it cannot take on negative values. A negative value would not hold a meaningful interpretation within the context of the analysis, as it would imply that the model is worse than simply using the mean of the dependent variable as a predictor, which isn't feasible within the R² framework.

In contrast, while the coefficient can be zero, indicating no explanatory power, it will never fall below zero. Thus, stating that it cannot be negative is an accurate description of the nature of the coefficient of determination.