A.     Which model gives the higher claim frequency for drivers with eight years of schooling?

B.     Which model gives the higher claim frequency for college educated drivers?

C.    Why might a linear model not be proper for these data? How does decreasing marginal utility affects the slopes? If a driver with 9 years of schooling has an expected claim frequency 1 percentage point less than a driver with 8 years of schooling, should the difference from 12 to 13 years of schooling be more or less than 1 percentage point?

D.    How do actuaries treat class dimensions like years of schooling? Do actuaries treat this as a quantitative or qualitative class dimension?

 

i'm guessing part D should be qualitative? would appreciate some intuition on this

[NEAS: Yes; explain why. High school diploma is 8 years of school; college degree is 12 years; a PhD, law degree, or medical degree are about 15 to 18 years; but is the number of years a good estimator of a response variable?

We're comparing fitted GLM's with

(1) the normal distribution with a constant variance (which is the same as using Excel Regression like we have been in previous homework), and

(2) the Poisson distribution. 

 

If you look in the Module 1 section, someone posted a combined PDF with all the module homework, practice problems, and readings.  Exercise 1.4: Line of Best fit, Part A, is similar to this homework.  I took the Poisson loglikelihood = Y Ln(u) - u - ln(y!) where y is the observation and u is the fitted mean and compared it with the classic Excel regression output to answer parts A and B of the homework. 

 

Good luck...

CJLID

I understand the idea behind using YLN(u) -u- ln(Y!), but for some reason I'm confused on how to actually use it.  When you say the observation y and fitted mean u, which values are you referring to in this example?

[NEAS: Y is the observation: 2, 3, or 10. ì is the fitted value at that point: 1.668, 5.000, or 8.333.]

I answered a and b by noting that the slopes between 8-12 and between 12-16 will be weighted differently by the poisson and normal distribution. The poisson weights the less steep slopes greater so it should result in a trend line that is a ccw rotation from the standard regression line. This logic says a) normal and b) poisson.

Is this good enough or do I need to use the poisson log likelihood method?

[NEAS: That is fine; the relation of the variance to the mean gives the solution.]

Looking at the practice problems, excercise 1.5, for the exponential distribution, is f(y) = uexp(-uy) so the log likelikhood would then equal log(u) - uy, not -y/u - log(u), is that wrong?