The Center for Disease Control has collected the following data on cigarette advertising and brand preferences among adolescents and adults.

a. Explore the possibility of a linear relation between advertising and brand preference for adults and for adolescents separately. Do there seem to be strong linear relationships, based on a scatter plot and the correlation?
b. Build linear models to represent the relation between advertising and brand preference for these two groups. What preferences would the models predict for advertising of $60 million?
c. Build nonlinear models to represent the relation between advertising and brand preference for these two groups, using the power function y = ax^b. What preferences would the models predict for advertising of $60 million? What are the advantages and disadvantages of a nonlinear model for this relationship?

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Brand Marlboro Camel Newport Kool Winston Benson & Hedges Salem Advertising ($ million) 75 43 35 21 17 43 Brand preference Adolescent Adult (%) (%) 60.0 13.3 12.7 1.2 1.2 1.0 0.3 23.5 6.7 4.8 3.9 3.9 3.0 2.5