When Will the Coefficient of Determination Decrease When a Second

Multiple Choice

When will the coefficient of determination decrease when a second independent variable is added alongside the initial independent variable in a regression analysis?

A) when X₂ predicts less variation in Y than does X₁
B) when X₁ predicts less variation in Y than does X₂
C) when the partial slopes are drastically different from one another
D) It will not decrease; the coefficient of determination with two variables represents variation explained by X₂ after X₁ has been accounted for, which cannot be less than the initial r² value.