# Generalized Linear Models and Their Applications to Actuarial Modeling

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 dc.contributor.author Smith, James dc.date.accessioned 2020-09-01T17:42:14Z dc.date.available 2020-09-01T17:42:14Z dc.date.issued 2004 dc.identifier.citation Smiths, J. (2004). Generalized Linear Models and Their Applications to Actuarial Modeling. Mathematics Exchange, 2(2), 40-42. en_US dc.identifier.uri http://cardinalscholar.bsu.edu/handle/123456789/202298 dc.description Article published in Mathematics Exchange 2(2), 2004. en_US dc.description.abstract There are many phenomena in the world that, upon close observation, are en_US clearly related. For example, when profits decline, unemployment rises. When weather conditions worsen, drivers have more accidents. The goal of an actuary is to model such relationships. Perhaps the most well-known and accepted method for modeling relationships is linear regression. The simplest version of this method is known as the standard linear model. It relates two variables X and Y by Y = α + βX. The variable X is taken as the independent variable, and Y is a variable assumed to depend on X. Here, α and β are constants whose values depend on the relationship between X and Y . While such a model may be useful for predicting the outcome of Y , given a value for X, the prediction will not be exact. Instead, each observation will satisfy the equation y = α + βx + ε , where α + βx = yˆ represents the fitted (predicted) value, iiiii and εi is the error term that measures the difference between the fitted value andtheactualoutcome. Inotherwordsε =y −yˆ fori=1,2,...,N,where N is the number of observations. dc.title Generalized Linear Models and Their Applications to Actuarial Modeling en_US dc.type Article en_US
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