Modeling monthly collision claims. A mid-Atlantic state automobile insurance company is interested in developing a regression model to help predict the monthly collision claims of its policyholders. A company analyst has proposed modeling monthly collision claims 1y2 as a function of the percentage of claims by drivers under age 30 1x12 and the average daily temperature during the month 1x22. She believes that as the percentage of claims by drivers under age 30 increases, claims will rise because younger drivers are usually involved in more serious accidents than older CLAIMS Data for Exercise 12.172 (first and last 5 months) Month Monthly Collision Claims, y ($) Percentage of Monthly Claimants Under the Age of 30, x1 Average Daily Temperature During the Month, x2 (°F) 1 116,250 31.5 2 217,180 60.8 33.0 3 43,436 45.1 45.0 4 159,265 56.4 53.9 5 130,308 53.3 63.9 f f f f 44 136,528 53.1 76.6 45 193,608 59.8 68.6 46 38,722 45.6 62.4 47 212,309 63.9 50.0 48 118,796 52.3 42.3 drivers. She also believes that claims will rise as the average daily temperature decreases because lower temperatures are associated with icy, hazardous driving conditions. In order to develop a preliminary model, data were collected for a mid-Atlantic state over a 3-year period. The data are saved in the file. (The first and last five observations are listed in the table at the bottom of the page.)

a. Use a statistical software package to fit the complete second-order model E1y2 = b0 + b1x1 + b2x2 + b3x1x2 + b4x1 2 + b5x2 2

b. Test the hypothesis H0: b4 = b5 = 0 using a = .05. Interpret the results in practical terms.

c. Do the results support the analysts’ beliefs? Explain. (You may need to conduct further tests of hypotheses to answer this question.)