Analysing and modelling relationships between variables are getting more and more important. In this work, we introduce generalized linear models, and develop them from linear regression models. We discuss theoretical assumptions for these models, and give an in-depth explanation of exponential families of distributions and the associated canonical link functions. We classify the most standard types of explanatory variables, and provide several examples for easier understanding. We explain the procedure for comparing nested models with deviance.
We apply the theory described above to constructing models for lapsed, paid up, and
surrendered life insurance policies. For a clearer picture, different forms of life insurance and
their relationships with lapsed, paid up and surrendered policies are presented. We analyse the
influences of individual explanatory variables on the response variable, and determine which
explanatory observations are essential and which are not. With this, an insurance company
may gain insight into complex relationships in its portfolio and better readiness for risk
factors in the future.
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