The coefficient of multiple determination r²_Y_.12 A) measures the proportion of variation in Y that is explained by X₁ and X₂. B) measures the proportion of variation in Y that is explained by X₁ holding X₂ constant. C) will have the same sign as b₁. D) measures the variation around the predicted regression equation.

Question

Quizplus · Accepted Answer

The coefficient of multiple determination, denoted by r^2, measures the proportion of variation in the dependent variable (Y) that is explained by the independent variables (X₁ and X₂) included in the regression model. Therefore, choice A is correct as it accurately describes the meaning of r^2. On the other hand, choice B is not entirely accurate as r^2 measures the variation explained by all independent variables, not just one while holding the other constant. Choice C is incorrect as there is no direct relationship between the sign of b₁ and r^2. Finally, choice D is also incorrect as it refers to the residual variation that is not explained by the regression equation, rather than the proportion of variation explained by the independent variables.

The Coefficient of Multiple Determination R2Y.12

The Coefficient of Multiple Determination R²_Y_.12