If none of the data points for a multiple regression model with two independent variables were on the regression plane, then the coefficient of determination would be:
A)-1.0.
B)1.0.
C)any number between -1 and 1, inclusive.
D)any number greater than or equal to zero but smaller than 1.

Question

Quizplus · Accepted Answer

The coefficient of determination (R-squared) is a measure of how well the regression model fits the data points. It ranges from 0 to 1, where 1 indicates a perfect fit and 0 indicates no relationship between the independent and dependent variables.

If none of the data points for a multiple regression model with two independent variables were on the regression plane, it means that there is no linear relationship between the independent and dependent variables. In this case, the coefficient of determination would still be between 0 and 1, because the model still accounts for some of the variation in the dependent variable.

However, the R-squared value would be smaller than if there were data points on the regression plane, because the model is not capturing as much of the variation in the dependent variable. Therefore, the best choice is D, which indicates that the coefficient of determination would be any number greater than or equal to zero but smaller than 1.

If None of the Data Points for a Multiple Regression