In multiple regression, if the second predictor variable correlates highly with the predicted variable, than it is quite likely that _________.
A) R 2 = 1.00
B) R 2 r 2
C) R 2 = r 2
D) R 2 r 2

Question

In multiple regression, if the second predictor variable correlates highly with the predicted variable, than it is quite likely that _________.
A) R 2 = 1.00
B) R 2 > r 2
C) R 2 = r 2
D) R 2 r 2

Quizplus · Accepted Answer

In multiple regression, the coefficient of determination (R^2) represents the proportion of the variance in the dependent variable that is predictable from the independent variables. If a second predictor variable correlates highly with the predicted variable, it contributes to explaining additional variance in the predicted variable that is not explained by the first predictor alone. Therefore, the total R^2 (which considers all predictors) is likely to be greater than the r^2 (which might represent the correlation coefficient squared for a single predictor), indicating that R^2 > r^2.

In Multiple Regression, If the Second Predictor Variable Correlates Highly