Adding any independent variable to a regression model will always increase: A)Adjusted R²or $\bar { R } ^ { 2 }$ B)s C)MSE D)R² E)The length of all prediction intervals

Question

Quizplus · Accepted Answer

Adding any independent variable to a regression model will always increase the coefficient of determination, $R^2$, because it explains more variance in the dependent variable, regardless of whether the new variable is actually significant or not. This is because $R^2$ measures the proportion of the variance in the dependent variable that is predictable from the independent variables.

Adding Any Independent Variable to a Regression Model Will Always Rˉ2\bar { R } ^ { 2 }Rˉ2

Adding Any Independent Variable to a Regression Model Will Always $\bar { R } ^ { 2 }$