Advanced Auto offers baseline automobile coverage across several states of the Midwestern United States. The company generally offers a single policy option in all regions where it operates, but allows local managers to adjust the deductible for the policy they sell. Note that the deductible for a given policy represents the amount the policyholder must pay out of pocket before the insurance company begins paying a claim. For example, if a policy-holder files a claim for $1,500 and holds a policy with a $400 deductible, the policyholder must pay $400 and the insurance company pays $1,100. Advanced Auto is interested in learning how the choice of deductible for the policy it offers in a region affects the rate of claims filed by policyholders. To accomplish this task, the company collected data from 500 separate markets that it serves at a given point in time. Table A.4 provides summary statistics for the variables Advanced Auto collected.

The variables in Table A.4 are as follows. Claims per 100 is the number of claims per 100 policyholders that were filed the previous year in that market. Deductible is the deductible chosen by the local manager for the policy offered in that market. % Local Pop. 2565 is the percentage of the local population aged 25 to 65 years old. % Local Pop. Married is the percentage of the local population that is married. Local Traffic Index is a rating between 1 and 10 of the level of traffic on the roads in the local market, where 10 is a very high level of traffic and 1 is a very low level of traffic. Local Wealth Index is a rating between 1 and 10 of the wealth level of residents in the local market, where 10 is a very high level of wealth and 1 is a very low level of wealth.

To learn the effect of the policys deductible on the claim rate, analysts at Advanced Auto assumed the following data-generating process for the claim rate in market i:

Claimsi = + 1Deducti + 2Age25_26i + 3Marriedi + 4Traffici + 5Wealthi + Ui

The analysts then regressed the claim rate on the deductible and the other variables in the assumed determining function. The results of this regression are in Table A.5.

1. Describe the results in Table A.4.

   1. Is variation in Deductible important? If so, why?

2. Explain the results for Deductible in Table A.5.

   1. What does the point estimate mean?

   2. What does p-value mean?

   3. What do the upper and lower bounds for the 95% confidence interval mean?

3. What purpose does including variables besides Deductible in the regression serve?

4. Are the variables besides Deductible that are in the regression all controls, or do any play the role of a proxy variable? What is the difference?

5. Predict the effect of raising the policy deductible by $200 on claim rates.

6. Detail the line of reasoning necessary to make your prediction in Question 5.

7. Identify at least one argument why your estimates may not be suitable for making the active prediction you made in Question 5. Be sure to highlight where your line of reasoning breaks down if this opposing argument is correct.

I MIN MAX 34.61 1000 VARIABLE Claims per 100 Deductible % Local Pop. 25-65 % Local Pop. Married Local Traffic Index Local Wealth Index MEAN 10.864 496.4 60.342 62.99 5.638 5.522 STD. DEV. 9.408 282.961 8.925 10.509 2.866 2.949 Intercept STANDARD ERROR 1.7911 0.0007 0.0170 0.0145 COEFFICIENTS 29.1421 -0.0323 0.0028 -0.0352 0.0340 -0.0710 Deductible % Between 25-65 % Married Traffic Index Wealth Index STAT 16.2704 -44.0612 0.1631 -2.4286 0.5927 -1.3112 P-VALUE 0.0000 0.0000 0.8705 0.0155 0.5537 0.1904 LOWER 95% 25.6229 -0.0337 -0.0307 -0.0636 -0.0788 -0.1774 UPPER 95% 32.6612 -0.0309 0.0362 -0.0067 0.1468 0.0354 0.0574 0.0541 I MIN MAX 34.61 1000 VARIABLE Claims per 100 Deductible % Local Pop. 25-65 % Local Pop. Married Local Traffic Index Local Wealth Index MEAN 10.864 496.4 60.342 62.99 5.638 5.522 STD. DEV. 9.408 282.961 8.925 10.509 2.866 2.949 Intercept STANDARD ERROR 1.7911 0.0007 0.0170 0.0145 COEFFICIENTS 29.1421 -0.0323 0.0028 -0.0352 0.0340 -0.0710 Deductible % Between 25-65 % Married Traffic Index Wealth Index STAT 16.2704 -44.0612 0.1631 -2.4286 0.5927 -1.3112 P-VALUE 0.0000 0.0000 0.8705 0.0155 0.5537 0.1904 LOWER 95% 25.6229 -0.0337 -0.0307 -0.0636 -0.0788 -0.1774 UPPER 95% 32.6612 -0.0309 0.0362 -0.0067 0.1468 0.0354 0.0574 0.0541