### Abstract

The use of the least-squares techniques for parameter estimation is critically evaluated by analyzing linear and non-linear models for situations in which the absolute or relative errors had a constant variance. Special emphasis is given to the estimation of the Monod-model parameters using biodegradation batch-test data. The error structure determines the optimum least-squares technique to be used for parameter estimation. The traditional absolute least-squares criterion, which minimizes the sum of the absolute residuals, should be used only when the absolute error has variance homogeneity. On the other hand, the non-traditional relative least-squares criterion, which minimizes the sum of the relative residuals, is the proper choice for cases in which the relative error has an approximately constant variance, a common characteristic for many analytical assays. The superiority of the relative residuals criterion is accentuated when the magnitude of the dependent variable varies widely.

Original language | English (US) |
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Pages (from-to) | 789-796 |

Number of pages | 8 |

Journal | Water Research |

Volume | 26 |

Issue number | 6 |

DOIs | |

State | Published - Jun 1992 |

Externally published | Yes |

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### Keywords

- Monod kinetics
- batch biodegradation
- least squares
- parameter estimation

### ASJC Scopus subject areas

- Ecological Modeling
- Water Science and Technology
- Waste Management and Disposal
- Pollution

### Cite this

*Water Research*,

*26*(6), 789-796. https://doi.org/10.1016/0043-1354(92)90010-2