What happens as the scatter of data values about the regression plane increases? A) Standard error of estimate increases. B) R²decreases. C) (1 -R²) decreases. D) Residual sum of squares decreases. E) (1 -R²), residual sum of squares and standard error of estimate all increase, andR²decreases.

Question

Quizplus · Accepted Answer

As the scatter of data values about the regression plane increases, the fit of the regression model to the data worsens. This results in an increase in the residual sum of squares and the standard error of estimate, indicating that the predictions are less accurate. Additionally, the coefficient of determination (denoted here as R², likely intending to represent R^2) decreases, showing that a smaller proportion of the variance in the dependent variable is explained by the model. Therefore, both (1 - R^2) and the residual sum of squares increase, while R^2 decreases.

What Happens as the Scatter of Data Values About the Regression