TABLE 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, the number of firms that manufacture automobile parts in and around the city, the number of new business starts in the last year, population density of the city, percentage of local taxes on gasoline, and the number of people using public transportation. 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 Table 13-9, if variables that measure the number of new business starts in the last year and population density of the city were removed from the multiple regression model, which of the following would be true?
A) The adjusted r² will definitely increase.
B) The adjusted r² 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 variables from a regression model can lead to a decrease in the coefficient of multiple determination (R²), but it cannot increase it. Adjusted R², however, can increase if the removed variables do not contribute significantly to the model.

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