Consider the following to answer the question(s) below:
National birth rates (births per 1,000) may be influenced by the average national life expectancy in years and the national literacy rate (% of population that can read and write). Data for 49 countries were obtained and the regression results follow.
-If an additional explanatory variable was added to the model, what would happen to R2?
A) It would stay the same or increase.
B) It would always decrease.
C) It can decrease.
D) It can become negative.
E) If the coefficient of the additional variable is negative, R2 dramatically decreases.

Question

Consider the following to answer the question(s) below:
National birth rates (births per 1,000) may be influenced by the average national life expectancy in years and the national literacy rate (% of population that can read and write). Data for 49 countries were obtained and the regression results follow. 
-If an additional explanatory variable was added to the model, what would happen to R2?
A) It would stay the same or increase. 
B) It would always decrease. 
C) It can decrease. 
D) It can become negative. 
E) If the coefficient of the additional variable is negative, R2 dramatically decreases.

Quizplus · Accepted Answer

Adding an additional explanatory variable to a model can either increase the R^2 value or leave it unchanged, as R^2 measures the proportion of the variance in the dependent variable that is predictable from the independent variables. Adding more variables can improve the model's fit (increase R^2) or have no effect if the new variable has no explanatory power, but it cannot decrease R^2 because R^2 is based on the sum of squared residuals, which can only stay the same or decrease (improve) with additional variables.

Consider the Following to Answer the Question(s) Below