In statistics, what does a coefficient of determination provide?

The coefficient of determination, commonly denoted as R², is a key statistical measure that evaluates how well the model fits the data. Specifically, it provides insight into the strength of the relationship between the independent and dependent variables in a regression model. A higher R² value indicates that a greater proportion of the variance in the dependent variable can be explained by the independent variable(s), signifying that the model has strong predictive capability.

For example, if the coefficient of determination is 0.85, it suggests that 85% of the variance in the dependent variable is predictable from the independent variable. This interpretive power is crucial for assessing model effectiveness, hypothesizing relationships, and making predictions based on the data.

The other options do not accurately represent what the coefficient of determination measures. A measure of central tendency relates to the average or typical value of a dataset, while a measure of variability concerns how spread out the data points are. Lastly, insight into data distribution focuses on how the values are arranged rather than how well a statistical model predicts outcomes. Thus, understanding the coefficient of determination is pivotal for evaluating the predictive success of statistical models.