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Generalized linear models (GLM)

I think you are off-track because max.loss does not sound like a  
proper Y variable. Because max.loss is an amount that is known, in the  
insurance applications I have seen it would have been modeled within  
an offset term. Many of the examples have used number of ships or  
buildings or the person years of exposure but I do not see that the  
general strategy is limited to only such  considerations.

I would also suggest that you consider links other than Gaussian,  
perhaps negative binomial.

The task for the analyst is then to translate output from the chosen  
model into interpretable meaning on the scale of interest, but I  
assume your course instructor will help with that.