a. Run a regression of LNPAID on AGE. Is AGE a statistically significant variable? To respond to this question, use a formal test of hypothesis. State your null and alternative hypotheses, decision-making criterion, and decision-making rule. Also comment on the goodness of fit of this variable.

b. Consider using class as a single explanatory variable. Use the one factor to estimate the model and respond to the following questions.

b(i). What is the point estimate of claims in class C7, drivers aged 5069 , driving to work or school, fewer than 30 miles per week with annual mileage of less than 7500, in natural logarithmic units?

b(ii). Determine the corresponding \(95 \%\) confidence interval of expected claims, in natural logarithmic units.

b(iii). Convert the 95\% confidence interval of expected claims that you determined in part b(ii) to dollars.

c. Run a regression of LNPAID on AGE, GENDER, and the categorical variables STATE CODE and CLASS.

c(i). Is GENDER a statistically significant variable? To respond to this question, use a formal test of hypothesis. State your null and alternative hypotheses, decision-making criterion, and decisionmaking rule.

c(ii). Is CLASS a statistically significant variable? To respond to this question, use a formal test of hypothesis. State your null and alternative hypotheses, decision-making criterion, and decisionmaking rule.

c(iii). Use the model to provide a point estimate of claims in dollars (not \(\log\) dollars) for a male age 60 in state 2 in class \(\mathrm{C} 7\).

c(iv). Write down the coefficient associated with class \(\mathrm{C} 7\) and interpret this coefficient.