The impact of product differentiation on rate of return on equity. To find out whether firms selling differentiated products (i.e., brand names) experience higher rates of return on their equity capital, J. A. Dalton and S. L. Levin16 obtained the following regression results based on a sample of 48 firms:

where Y = the rate of return on equity
D = 1 for firms with high or moderate product differentiation
X2 = the market share
X3 = the measure of firm size
X4 = the industry growth rate
a. Do firms that product-differentiate earn a higher rate of return? How do you know?
b. Is there a statistical difference in the rate of return on equity capital between firms that do and do not product-differentiate? Show the necessary calculations.
c. Would the answer to (b) change if the authors had used differential slope dummies?
d. Write the equation that allows for both the differential intercept and differential slope dummies.

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f = 1.399 + 1.490D + 0246Xy-9.507Xy-0.016X4i (1.380) (0.056) (4.244) (0017) R2-026 1.079) 4.285) -2.240) (0.941) (0.1433) (0.000) (0.0151) (0.1759) p value