The multiple coefficient of determination for a multiple regression model with two explanatory variables X₁ and X₂: A)measures the variation around the predicted regression equation. B)measures the proportion of variation in Y that is explained by X₁ and X₂. C)measures the proportion of variation in Y that is explained by X₁ holding X₂ constant. D)has the same sign as b₁.

Question

Quizplus · Accepted Answer

The multiple coefficient of determination, denoted by R-squared, measures the proportion of variation in the dependent variable (Y) that is explained by the combined effects of the two explanatory variables (X₁ and X₂) in the multiple regression model. Therefore, choice B is the correct answer. Choices A and C are partially correct but do not capture the complete meaning of R-squared. Choice D is incorrect as the sign of R-squared is not related to the sign of any regression coefficient.

The Multiple Coefficient of Determination for a Multiple Regression Model