SCENARIO 13-9
You decide to predict gasoline prices in different cities and towns in the United States for your term project.Your dependent variable is price of gasoline per gallon and your explanatory variables are per capita income and the number of firms that manufacture automobile parts in and around the city.You collected data of 32 cities and obtained a regression sum of squares SSR= 122.8821.Your computed value of standard error of the estimate is 1.9549.
-Referring to SCENARIO 13-9, if the variable that measures the number of firms that manufacture automobile parts in and around the city is removed from the multiple regression model, which of the following would be true?
A)The adjusted r 2 will definitely increase.
B)The adjusted r 2 cannot increase.
C)The coefficient of multiple determination will not increase.
D)The coefficient of multiple determination will definitely increase.

Question

Quizplus · Accepted Answer

Removing a variable from the model, especially one that does not contribute significantly to explaining the variance in the dependent variable, can lead to a decrease in the coefficient of multiple determination (R^2), as it measures the proportion of the variance in the dependent variable that is predictable from the independent variables. Removing a variable may reduce the explanatory power of the model, thus R^2 is not likely to increase.

SCENARIO 13-9 You Decide to Predict Gasoline Prices in Different Cities and Cities