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Abstract

For linear models with heterogeneous error structure, four variance function models are examined for predicting the error structure in two loblolly pine data sets and one white oak data set. An index of fit and a simulation study were used to determine which models were best. The size of coefficients for linear and higher order terms varied drastically across different data sets, thus it is not desirable to recommend a general model containing both linear and higher order terms. The unspecified exponent model σ2vi = σ2(Di2 Hi)k 1 is recommended for all data sets considered. The k1 values ranged from 1.8 to 2.1. We recommend k1 = 2.0 for simplicity.

Keywords

linear regression

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Apr 26th, 1:30 PM

ESTIMATING VARIANCE FUNCTIONS FOR WEIGHTED LINEAR REGRESSION

For linear models with heterogeneous error structure, four variance function models are examined for predicting the error structure in two loblolly pine data sets and one white oak data set. An index of fit and a simulation study were used to determine which models were best. The size of coefficients for linear and higher order terms varied drastically across different data sets, thus it is not desirable to recommend a general model containing both linear and higher order terms. The unspecified exponent model σ2vi = σ2(Di2 Hi)k 1 is recommended for all data sets considered. The k1 values ranged from 1.8 to 2.1. We recommend k1 = 2.0 for simplicity.