Chapter 12, Problem 12.172ACA

Modeling monthly collision claims. A medium-sized 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 (y) in the Middle Atlantic states as a function of the percentage of claims by drivers under age 30 (x₁) and the average daily temperature during the month (x₁). 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 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 the state of New Jersey over a 3-year period. The data are saved in the file. (The first and last five observations are listed in the table below.)

a.    Use a statistical software package to fit the complete second-order model

$E\left(y\right)={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_1{x}_2+{\beta }_4{x}_{{}_1}^2+{\beta }_5{x}_2^2$

1. b. Test the hypothesis H₀: β₄ = β₅ = 0 using α = .05. Interpret the results in practical terms.
2. c. Do the results support the analysts’ beliefs? Explain. (You may need to conduct further tests of hypotheses to answer this question.)