# Question: Neter Kutner Nachtsheim and Wasserman 1996 relate the speed y

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.

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.

**View Solution:**## Answer to relevant Questions

(1) Discuss the difference between cross- sectional data and time series data. (2) If we record the total number of cars sold in 2012 by each of 10 car salespeople, are the data cross- sectional or time series data? (3) If ...Consider the situation in which a gas company wishes to predict weekly natural gas consumption for its city. In the exercises of Chapter we used the single predictor variable x, average hourly temperature, to predict y, ...A real estate agency collects the data in Table concerning y = sales price of a house (in thousands of dollars) x1 = home size (in hundreds of square feet) x2 = rating (an overall “niceness rating” for the house ...Enterprise Industries produces Fresh, a brand of liquid laundry detergent. In order to manage its inventory more effectively and make revenue projections, the company would like to better predict demand for Fresh. To develop ...Table in the page margin presents quarterly sales of the TRK-50 mountain bike for the previous 16 quarters at a bicycle shop in Switzerland. The time series plot under the sales data shows that the bike sales exhibit an ...Post your question