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Nonlinear Regression Modeling
An Illustrative Example of Regression Modeling
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asymptote basic model Bates and Watts Chapter Chirife close-to-linear models conﬁdence intervals conﬁdence regions convergence corresponding toX X1 curve see Figure data points data set error assumption example exhibited close-to-linear expected-value parameter y1 explanatory variable extent of nonlinear far-from-linear ﬁnd ﬁrst ﬁt four-parameter model handbook Hougaard inﬂection point initial estimates least-squares estimates likelihood linear model linear regression models logarithm logistic model maximum method model see Figure nonlinear behavior nonlinear regression models nonnormality normally distributed number of parameters obtained one-parameter parame parameter estimates parameterization properties in estimation rational functions rational functions models Ratkowsky 1983 reasonably close-to-linear Regression Analysis reparameterization replaced by expected-value residual sum residual variance response variable sample scientiﬁc sigmoidal single explanatory variable skewness solution locus statistical properties subroutine sum of squares three-parameter curve three-parameter model tion to-linear two-parameter model variance-covariance matrix Vol Vol Vol water activity worst-behaving parameter X1 and X2 y1 and y2 yield