The Coefficient of Determination (R²) for a Regression Equation with One

Multiple Choice

The coefficient of determination (r²) for a regression equation with one independent variable (X₁) is 0.63. A second independent variable (X₂) is added to the equation, and the coefficient of determination changes to 0.64. Which of the following would we conclude?

A) Together, X₁ and X₂ explain only about 40% of the variability in the dependent variable.
B) X₂ contributes little over and above the effect of X₁ to our ability to understand variability in the dependent variable.
C) Adding X₂ increases our ability to understand variability in the dependent variable by a considerable margin.
D) X₂ intervenes between X₁ and the dependent variable.