The coefficient of multiple determination r²_Y_.12 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) will have the same sign as b₁.

Question

Quizplus · Accepted Answer

The coefficient of multiple determination (r-squared) measures the proportion of variation in the dependent variable (Y) that is explained by the independent variables (X₁ and X₂) in the multiple regression equation. Therefore, choice B is the correct answer. Choice A is incorrect because r-squared does not measure variation around the predicted regression line, but rather the proportion of variation in Y that is explained by the regression equation. Choice C is incorrect because it refers to adjusting for only one independent variable, which is not the case in multiple regression. Choice D is incorrect because the sign of the regression coefficient (b) does not necessarily determine the sign of r-squared.

The Coefficient of Multiple Determination R2Y.12

The Coefficient of Multiple Determination R²_Y_.12