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Testing linear regression function adequacy without replication. (English) Zbl 0582.62056
The well known pure error-lack of fit test, which can be used to assess the adequacy of a linear regression model, is generalized to accommodate the case of nonreplication. The asymptotic null distribution of the proposed test statistic is derived.
Also, the proposed test statistic is shown to be asymptotically comparable under general alternatives to the test statistic obtained in the case of replication. Consistency properties associated with pseudo lack of fit and pure error mean squares are given which parallel those obtained in the case of replication. In addition, the test statistic is invariant with respect to location and scale changes made to the regression variables.

MSC:
62J05 Linear regression; mixed models
62F03 Parametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
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