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**Appendix A **

Generalized Linear Regression

Use of the generalized linear regression model is recommended when

there is violation of the assumption that the residuals in the regression equation

are independent and uncorrelated. If it is the case that when one residual is small

or large, others are likely to be small or large, the sum squared of the residuals is

weighted in a way that accounts for these associations. So, for example, in

generalized linear regression, an observation that would be expected to have a

large residual because other observations have large residuals is given a smaller

weight, and a large weight is given to associated small residuals.

We selected this procedure because individual subjects contributed more

than one data point to the final set of responses. We would anticipate that

responses from the same subjects might be associated. Generalized Least Squares

regression helps to fix this violation of the assumption of independence.