7.4. In an ordinal r x c table, we could assign ordered scores and use a linear trend model, E(Y | X = «,)= a + ßty. With the least squares estimator b of jö, show that the Pearson statistic for testing independence partitions into X2(I)=X2(L) + X2(I|L), where X2(I | L) = b2/Var(b). Here X2(L) has df = re - r - c for testing the fit of the linear model, and X2(I | L) has df = 1 for testing HQ: independence, given that the linear model holds (Yates 1948). The test based on X2(I | L)

is an alternative to tests in Section 7.3. Section 5 presented this model, but using ML to estimate parameters.