As the manager of a focus group company, you are interested in optimizing the number of participants you include in focus groups for your clients. Over the past year, you ran a field experiment, varying the number of participants you provided for each focus group. You collected data on the number of participants (X), focus group costs (C), and revenues (R) from clients in Q01–26.xls.

a. Estimate revenues as a function of focus group size, using both X and X2 in the regression. Write out the equation for revenue as a function of focus group size based on your regression. Are all variables statistically significant?

b. Estimate costs as a function of focus group size, using both X and X2 in the regression. Write out the equation for cost as a function of focus group size based on your regression. Are all variables statistically significant?

c. Note that these results imply the marginal revenue, or marginal benefit, of focus group size is MB(X) = 71.77 – 0.24X and the marginal cost of focus group size is MC(X) = 49.17 + 0.22X. What size of focus group will maximize net benefits?