15.26       What is a qualitative independent variable?

15.27       How do we use dummy variables to model the effects of a qualitative independent variable?

15.28       What does the parameter multiplied by a dummy variable express?

 

METHODS AND APPLICATIONS

15.29       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 15.10

 

Plot of the Insurance

on the next page are observed.

DS InsInnov

a    Discuss why the data plot in the page margin indicates that the model

 

y = b0 + b1x + b2DS + e

might appropriately describe the observed data. Here DS 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

 

b0 + b1x + b2(0) = b0 + b1x

Innovation Data

 

 

 

 

 

and that the mean adoption time by stock companies having an asset size x equals

b0 + b1x + b2(1) = b0 + b1x + b2

The difference between these two means equals the model parameter b2. In your own words, interpret the practical meaning of b2.

c    Figure 15.18 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: b2 = 0 versus Ha: b2 * 0 by set- ting a = .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 b2.

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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