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You decide to predict gasoline prices in different cities and towns in the U.S. 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 businesses 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.

Question: If variables that measure the number of new businesses starts in the last year and population density of the city are removed form the multiple regression model, which of the following is true?

A. The coefficient of multiple determination will definitely increase.
B. The adjusted r2 will definitely increase
C. The adjusted r2 can never increase
D. The coefficient of multiple determination can never increase

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The solution discusses If variables that measure the number of new businesses starts in the last year and population density of the city are removed form the multiple regression model, which of the following is true?

A. The coefficient of multiple determination will definitely increase.
B. The adjusted r2 will definitely increase
C. The adjusted r2 can never increase
D. The coefficient of multiple determination can never increase

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