When two regression models applied on the same data set have the same response variable but a different number of explanatory variables, the model that would evidently provide the better fit is the one with a ________.
A) lower standard error of the estimate and a higher coefficient of determination
B) higher standard error of the estimate and a higher coefficient of determination
C) higher coefficient of determination and a lower adjusted coefficient of determination
D) lower standard error of the estimate and a higher adjusted coefficient of determination

Question

Quizplus · Accepted Answer

A model with a lower standard error of the estimate indicates less dispersion of observed values from the regression line, suggesting a better fit. A higher adjusted coefficient of determination (adjusted R^2) also indicates a better fit, especially important when comparing models with different numbers of explanatory variables, as it adjusts for the number of variables in the model.

When Two Regression Models Applied on the Same Data Set