In a multiple regression model, the adjusted
A)cannot be negative.
B)can sometimes be negative.
C)has to fall between 0 and
D)a and c

Question

In a multiple regression model, the adjusted 
A)cannot be negative. 
B)can sometimes be negative. 
C)has to fall between 0 and 
D)a and c

Quizplus · Accepted Answer

The adjusted R-squared value is a measure of how well the regression model fits the data, accounting for the number of variables included in the model. It can range from 0 to 1, where a value of 1 indicates that the model perfectly explains the variation in the dependent variable and a value of 0 indicates that the model does not explain any of the variation.

Since the adjusted R-squared is calculated based on the R-squared and the number of variables in the model, it can be negative if the model is particularly bad, i.e., if the R-squared is close to 0 and the number of variables is high. Therefore, option A is incorrect.

Option B is also incorrect because the adjusted R-squared may or may not be negative depending on the specific model.

Option C is partially correct: since the adjusted R-squared is a proportion, it must fall between 0 and 1. However, the upper bound is not necessarily 1, as it depends on the number of variables in the model. Therefore, option C is incorrect.

Thus, the best choice is D, which correctly states that the adjusted R-squared cannot be negative and must fall between 0 and some upper bound determined by the number of variables in the model. The adjusted R-squared has to fall between 0 and 1 (option C), but it can sometimes be negative (option B) if the model is overfitting the data. However, it cannot be negative if the model is not overfitting and all the predictor variables are contributing to the model (option A). Therefore, both options A and C are correct.

In a Multiple Regression Model, the Adjusted