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 14.10 on the next page are observed.
TABLE 14.10
The Insurance Innovation Data

a. Discuss why the data plot in the page margin indicates that the model
y = β0 + β1x + β2Ds + ε
might appropriately describe the observed data. Here Ds equals l 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 + βlx + β2(1) = β0 + βlx + β2
The difference between these two means equals the model parameter β2. In your own words, interpret the practical meaning of β2.
c. Figure 14.18 presents the Excel output of a regression analysis of the insurance innovation data using the model of part a. Using the output, test H0: β2 = 0 versus Ha: β2 ‰  0 by setting α = .05 and .01. Interpret the practical meaning of the result of this test. Also, use the computer output to lind, report, and interpret a 95 percent confidence interval for β2.
d. If we add the interaction term xDs to the model of part a, we find that the p-value related to this term is .9821. What does this imply?

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Number of Months Elapsed, Size of Firm (Millions of Dollars), Number of Months Elapsed, Size of Firm (Millions of Dollars), Type of Firm Firm y Mutual 1 28 Mutual12 15 Mutual 13 11 Mutual14 38 Mutual 15 31 Mutual 16 21 Mutual 17 20 Mutual18 13 Mutual 19 30 Mutual 20 Type of Firm Stock Stock Stock Stock Stock Stock Stock Stock Stock Stock Firm y 1 17 2 26 3 21 4 30 151 92 175 164 272 295 31 104 277 210 120 290 238 68 85 224 166 305 124 246 12 19 8 10 16