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An exploratory method for dealing with interactions is to assume the model Y = β0 + β1X1 + β2X2 + β3X1X2 + e is true and use a partial residual plot to check the adequacy of the third term (β3X1X2) assuming that Y has a linear association between β1X1 and β2X2. Describe some reasons why this approach might be unsatisfactory.

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