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We propose a goodness-of-fit test statistic for linear regression with heterogeneous variance, which is asymptotically chi-square if the given model is correct. The test statistic is computed as a quadratic form of observed minus predicted responses. We apply the method to a linear regression for an ordinal categorical response, the wheezing status of a child (no wheeze, wheeze with cold, wheeze apart from cold) as a function of maternal smoking and city of residence.

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