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12.4 Memo Problem: Insurance Costs

To: Analysis Staff
From: Top Modeler
Date: May 28, 2008
Re: Operating Costs for Insurance Company

Our clients’ management team would like us to compare a straight-forward linear model with the multiplicative model that we came up with for our original submission. They want to know if there is anything to be gained from their basing their management decisions on the more complicated multiplicative model. Or is a linear model almost as good? As we all know, simpler is better. But if there is indeed something to be gained from using the more complicated multiplicative model then we should point out exactly what it is. Otherwise, we should recommend that they use the simpler linear model.

Actually, this request should enable us to sharpen our analysis considerably. For example, we can now compare the R2 and S e that we calculated for our multiplicative model to the R2 and S e generated by the linear model (we don’t have to calculate these latter ourselves, however, since they are valid for linear models). Also, we can compare the fitted vs. observed graphs and the residual vs. fits graphs of the two models to see if we can detect a difference in goodness of fit or accuracy.

Attachment: Data file C12 Insurance.xls [.rda]

Here’s how you might go about dealing with this assignment:

  1. Run a linear regression model, along with the two diagnostic graphs (fits, residuals).
  2. Compute the cost predicted by the linear model with 100 home and 2000 auto policies .
  3. Do a marginal cost analysis for the linear model (if one more home policy is sold, then the cost will increase by what dollar amount, holding the number of auto policies at 2000; do a similar thing for auto policies).
  4. Run your multiplicative model, generate your two diagnostic graphs and calculate your own R2 and S e.
  5. Compute the cost predicted by the multiplicative model at the 100 and 2000 levels.
  6. Do a parameter cost analysis for the multiplicative model (if the number of home policies increases by 1%, then the cost will increase by what %, holding the number of auto polices at the current level; do this for levels of 100 home and 2000 auto policies, then do the similar thing to analyze how costs change if the number of auto policies changes).
  7. Do a nice summary presentation and analysis for your two models, including side-by-side graphs and maybe a table or two showing R2, S e, the costs predicted by the two models at the 100 and 2000 levels, and your marginal and parameter change analysis - lay it all out for the client.
  8. Make a summary statement as to which model you recommend for our client and why.

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