Which of the following is not true regarding the coefficient of determination for a linear regression with a single independent variable?

The coefficient of determination, commonly denoted as ( R^2 ), serves as a crucial metric in evaluating the performance of linear regression models. Its primary role is to summarize how well the independent variable explains the variability of the dependent variable. Understanding why the statement about predicting future activity is not true provides insight into ( R^2 ) and its limitations.

While ( R^2 ) does indicate how well the current model fits the data it was trained on, it does not directly inform the prediction of future values. This is because ( R^2 ) is computed based on the sample data, and a high ( R^2 ) could be misleading when it comes to forecasting unseen data. Factors such as changes in trends, seasonality, or external influences that were not accounted for in the model can significantly impact future predictions.

In contrast, the other statements are accurate representations of how the coefficient of determination functions. It is indeed bounded between 0 and 1, ensuring it can never exceed 1.0, reflects the strength of the relationship between the independent and dependent variables as it is derived from the correlation coefficient, and successfully encapsulates the goodness-of-fit for a regression model, indicating how much variation in the dependent variable is