Recall that Certified Public Accountants (CPAs) were surveyed on their firms' likelihood of reporting sustainability policies (measured as a probability between 0 and 1). The CPAs were divided into four groups depending on firm size (large or small) and firm type (public or private): large/public, large/private, small/public, and small/private. One goal of the analysis is to determine whether the mean likelihood of reporting sustainability policies differs depending on firm size and firm type.
a. Consider a single qualitative variable representing the four size/type categories. Create the appropriate dummy variables for representing this qualitative variable as an independent variable in a regression model for predicting likelihood of reporting sustainability policies (y).
b. Give the equation of the model, part a, and interpret each of the model parameters.
c. The global P-test for the model resulted in p-value < .001. Give a practical interpretation of this result.
d. Now consider treating firm size and firm type as two different qualitative independent variables in a model for likelihood of reporting sustainability policies (y). Create the appropriate dummy variables for representing these qualitative variables in the model.
e. Refer to part d. Write a model for E(y) as a function of firm size and firm type, but do not include interaction. (This model is called the main effects model.)
f. Refer to the model, part e. For each combination of firm size and firm type (e.g., large/public), write E(y) as a function of the model parameters.
g. Use the results, part f, to show that for the main effects model, the difference between the mean likelihoods for large and small firms does not depend on firm type.
h. Write a model for E(y) as a function of firm size, firm type, and size × type interaction.
i. Refer to the model, part h. For each combination of firm size and firm type (e.g., large/public), write E(y) as a function of the model parameters.
j. Use the results, part i, to show that for the interaction model, the difference between the mean likelihoods for large and small firms does depend on firm type.
For Information: Refer to the Business and Society (March 2011) study on how firm size and firm type impact corporate sustainability behaviors. Exercise 9.7.