Modeling industry performance. The performance of an industry is often measured by the level of excess (or unutilized) capacity within the industry. Researchers examined the relationship between excess capacity y and several market variables in 273 U.S. manufacturing industries (Quarterly Journal of Business and Economics, Summer 1986). Two qualitative independent variables considered in the study were Market concentration (low, moderate, and high) and Industry type (producer or consumer).
(a) Write the main effects model for E(y) as a function of the two qualitative variables.
(b) Interpret the β coefficients in the main effects model.
(c) Write the model for E(y) that includes interaction between market concentration and industry type.
(d) Interpret the β coefficients in the interaction model.
(e) How would you test the hypothesis that the difference between the mean excess capacity levels of producer and consumer industry types is the same across all three market concentrations?