The National Association of Theatre Owners is the largest exhibition trade organization in the world, representing more than 26,000 movie screens in all 50 states and in more than 20 countries worldwide. Its membership includes the largest cinema chains and hundreds of independent theater owners. It publishes statistics concerning the movie sector of the economy. The file titled Flicks contains data on total U.S. box office grosses ($billion), total number of admissions (billion), average U.S. ticket price ($), and number of movie screens.
a. Construct a regression equation in which total U.S. box office grosses are predicted using the other variables.
b. Produce the appropriate residual plots to determine if the linear function is the appropriate regression function for this data set.
c. Square each of the independent variables and add them to the model on which the regression equation in part a was built. Produce the new regression equation.
d. Use a residual plot to determine if the quadratic model in part c alleviates the problem identified in part b.
e. Construct a probability plot to determine if the error terms are normally distributed for the updated model.