Insurance companies make a leaving trying to correctly assess the probability of particular events, and also the probability of certain individuals incurring in given types of accidents. Imagine for a second that we have access (legally of course) to data on individuals that have insured their cars in New York State. The insurance company (Let's call is Patakazo Inc.) gives us a set of demographic and socio-economic variables, among them the probability that each of those drivers will incur in an accident in the next year.

a) If the average probability of an accident of those insured with Patakazo is 7%, and the average value of the cars insured by the same company is $23,000, what is the average premium paid by New Yorkers insured with Patakazo if we assume the insurance company makes zero economic profits.

provide an econometric model that tries to explain using a set of variables the accident probabilities provided by the insurance company? Suggest a methodology to estimate the model.

c)Spell out which variables do you think belong in your econometric model and what do you think would be the sign of their coefficients if we were to use regression analysis to estimate the model. What would the interpretation be of those coefficients?

d)If I told you that a regression that tries to explain the variation in accident probabilities just with indicators of the individuals' gender (male equal to 1, female equal to zero) delivers a Residual Sum of Squares of about 88% of the Total Sum of Squares, could you tell me a rough estimate of the R-squared and explain its meaning?

e)If to the conjectured regression introduced in d) I add a measure of whether the person wears a seal-belt when driving, would you expect the coefficient on gender to increase or decrease? (assume the coefficient on gender in the simple regression was positive) Why? How is this related to the concept of Omitted Variable Bias?