How much does advertising impact market penetration? To assess the impact of advertising in the tobacco industry, a study looked at the
amount of money spent on advertising a particular brand of cigarettes and brand preference among adolescents and adults. The data are shown below: (Source: Center for Disease Control Website).
Brand Advertising ($ millions) % Adolescents % Adults
Marlboro 75 60 23.5
Camel 43 13.3 6.7
Newport 35 12.7 4.8
Kool 21 1.2 3.9
Winston 17 1.2 3.9
Benson & Hedges 4 1 3
Salem 3 0.3 2.5

a) Explore the possibility of a linear relation between advertising and brand preference for adults and for adolescent separately. Do there seem to be strong linear relationships, base 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 = axB? what preference would the model predict for advertising of $60 million? What are the advantages and disadvantages of a nonlinear model for this relationship?