Neter, Kutner, Nachtsheim, and Wasserman (1996) relate the speed, y, with which a particular insurance innovation is adopted to the size of the insurance firm, x, and the type of firm. The dependent variable y is measured by the number of months elapsed between the time the first firm adopted the innovation and the time the firm being considered adopted the innovation. The size of the firm, x, is measured by the total assets of the firm, and the type of firm—a qualitative independent variable—is either a mutual company or a stock company. The data in Table 14.11 are observed.
a. Discuss why the data plot in Figure 14.18 indicates that the model might appropriately describe the observed data.
y = β0 + β1x + β2DS = ε
Here D S equals 1 if the firm is a stock company and 0 if the firm is a mutual company.
b. The model of part a implies that the mean adoption time of an insurance innovation by mutual companies having an asset size x equals
β0 + β1x + β2(0) = β0 + β1x
and that the mean adoption time by stock companies having an asset size x equals
β0 + β1x + β2(1) = β0 + β1x + β2
The difference between these two means equals the model parameter β2. In your own words, interpret the practical meaning of β2.
c. Figure presents the Excel output of a regression analysis of the insurance innovation data using the model of part a. (1) Using the output, test H0: β2 = 0 versus Ha: β2 ≠ 0 by setting α = .05 and .01. (2) Interpret the practical meaning of the result of this test. (3) Also, use the computer output to find, report, and interpret a 95 percent confidence interval for β2.