TABLE 14-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y).To provide its customers with information on that matter,a large real estate firm used the following 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X₁)and the amount of insulation in inches (X₂).Given below is EXCEL output of the regression model. Also SSR (X₁ ∣ X₂)= 8343.3572 and SSR (X₂ ∣ X₁)= 4199.2672
-True or False: When an explanatory variable is dropped from a multiple regression model,the adjusted r² can increase.

Question

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y).To provide its customers with information on that matter,a large real estate firm used the following 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X₁)and the amount of insulation in inches (X₂).Given below is EXCEL output of the regression model.

Also SSR (X₁ ∣ X₂)= 8343.3572 and SSR (X₂ ∣ X₁)= 4199.2672
-True or False: When an explanatory variable is dropped from a multiple regression model,the adjusted r² can increase.

Quizplus · Accepted Answer

When an explanatory variable is dropped from a multiple regression model, the adjusted R-squared may increase because it adjusts for the number of variables in the model. However, this does not always indicate better model fit or better predictive ability. It is important to consider other measures of model fit and predictive ability when deciding which variables to include in the final model.

TABLE 14-6 One of the Most Common Questions of Prospective House Buyers