Question: Consider a twostage procedure in which one tests for linearity of the effect of a predictor X on a property of the response C(Y |X)

Consider a two–stage procedure in which one tests for linearity of the effect of a predictor X on a property of the response C(Y |X) against a quadratic alternative. If the two–tailed test of linearity is significant at the α level, a two d.f. test of association between X and Y is done. If the test for linearity is not significant, the square term is dropped and a linear model is fitted. The test of association between X and Y is then (apparently) a one d.f. test.

a. Write a formal expression for the test statistic for association.

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