i. The multiple standard error of estimate measures the variation about the regression plane when two independent variables are considered. ii. 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. iii. The coefficient of multiple determination reports the strength of the association between the dependent variable and the set of independent variables. 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

The multiple standard error of estimate indeed measures the variation of the actual data points from the estimated values of the dependent variable in a multiple regression context, making statement (i) correct. The coefficient of multiple determination, often denoted as $R^2$, actually measures the proportion of the variance in the dependent variable that is predictable from the independent variables, making statement (iii) correct as it correctly describes the role of $R^2$ in indicating the strength of the association between the dependent variable and the set of independent variables. Statement (ii) is incorrect because the multiple coefficient of determination reports the proportion of the variation in Y that is explained by the variation in the set of independent variables, not the unexplained portion.

I the Multiple Standard Error of Estimate Measures the Variation