### Abstract:

There are many phenomena in the world that, upon close observation, are
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.