i. The multiple coefficient of determination, R², reports the proportion of the variation in Y that is not explained by the variation in the set of independent variables. ii. The coefficient of multiple determination reports the strength of the association between the dependent variable and the set of independent variables. iii. The multiple standard error of estimate for two independent variables measures the variation about a regression plane. A) (i), (ii), and (iii) are all correct statements. B) (i) and (ii) are correct statements but not (iii). C) (i) and (iii) are correct statements but not (ii). D) (ii) and (iii) are correct statements but not (i). E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

- Statement i is incorrect because the multiple coefficient of determination, often denoted as $R^2$, actually reports the proportion of the variation in the dependent variable $Y$ that is explained by the independent variables, not the variation that is not explained.- Statement ii is correct as it accurately describes the purpose of the coefficient of multiple determination, which is to measure the strength of the relationship between the dependent variable and a set of independent variables.- Statement iii is also correct because the multiple standard error of estimate does indeed measure the standard deviation of the observed values from the regression plane (or line, in the case of a single independent variable), indicating the variation of the data points around the predicted values.

I the Multiple Coefficient of Determination, R2, Reports the Proportion

I the Multiple Coefficient of Determination, R², Reports the Proportion