This expository article details the effects of the choice of underlying models in the statistical analysis of regression. The two models considered are when all the data are jointly normally distributed and when the independent variables are assumed to be constants. The standard results for both these models are conditionally related to each other in a unified manner, and an example is given where new results in one model can be obtained from old results in the other model. Particular emphasis is devoted to demonstrating differences that arise in power function considerations.
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