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. One concern is the effect the increasing ticket prices have on the number of individuals who go to the theaters to view movies.
a. Construct a scatter plot depicting the relationship between the total number of admissions and the U.S. ticket price.
b. Determine the order of the polynomial that is suggested by the scatter plot produced in part a. Obtain the estimated regression equation of the polynomial selected.
c. Examine the p -value associated with the F -test for the polynomial you have selected in part a. Relate these results to those of the t -tests for the individual parameters and the adjusted coefficient of determination. To what is this attributed?
d. Conduct t -tests to remove higher order components until no components can be removed.