### Abstract

Under multi-treatment regression analysis, instead of a sample for each treatment of a linear model, there is a linear regression in the same variables. Then, instead of the action of the treatments on the sample mean values, the action on regression coefficients is studied. When data is unbalanced, the regression matrices differs between regressions. This problem is solved through the use of a block-wise diagonal covariance matrix in the ANOVA procedures. The methodology was then applied to data obtained from experiments of electrodialtic removal of 3 heavy metals from contaminated wood. First, polynomial regressions of the 4th and 3rd were fitted to each metal concentration in the electrolytes through time. Then the unbalanced case of multi-treatment regression analysis was applied aiming to choose the best treatment in jointly removing the 3 metals. Results pointed to the choice of treatment 1 as the most efficient.

Original language | English |
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Title of host publication | Recent Researches in Applied Mathematics, Simulation and Modelling - Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11 |

Pages | 69-74 |

Number of pages | 6 |

Publication status | Published - 29 Nov 2011 |

Event | 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11 - Corfu Island, Greece Duration: 14 Jul 2011 → 16 Jul 2011 |

### Conference

Conference | 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11 |
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Country | Greece |

City | Corfu Island |

Period | 14/07/11 → 16/07/11 |

### Fingerprint

### Keywords

- ANOVA
- F tests
- Multiple comparison
- Multiple regression
- Scheffé
- Unbalanced data

### Cite this

*Recent Researches in Applied Mathematics, Simulation and Modelling - Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11*(pp. 69-74)

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*Recent Researches in Applied Mathematics, Simulation and Modelling - Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11.*pp. 69-74, 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11, Corfu Island, Greece, 14/07/11.

**Multi-treatment regression analysis: the unbalanced case.** / Moreira, Elsa Estevão; Mexia, João Tiago.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Multi-treatment regression analysis: the unbalanced case

AU - Moreira, Elsa Estevão

AU - Mexia, João Tiago

PY - 2011/11/29

Y1 - 2011/11/29

N2 - Under multi-treatment regression analysis, instead of a sample for each treatment of a linear model, there is a linear regression in the same variables. Then, instead of the action of the treatments on the sample mean values, the action on regression coefficients is studied. When data is unbalanced, the regression matrices differs between regressions. This problem is solved through the use of a block-wise diagonal covariance matrix in the ANOVA procedures. The methodology was then applied to data obtained from experiments of electrodialtic removal of 3 heavy metals from contaminated wood. First, polynomial regressions of the 4th and 3rd were fitted to each metal concentration in the electrolytes through time. Then the unbalanced case of multi-treatment regression analysis was applied aiming to choose the best treatment in jointly removing the 3 metals. Results pointed to the choice of treatment 1 as the most efficient.

AB - Under multi-treatment regression analysis, instead of a sample for each treatment of a linear model, there is a linear regression in the same variables. Then, instead of the action of the treatments on the sample mean values, the action on regression coefficients is studied. When data is unbalanced, the regression matrices differs between regressions. This problem is solved through the use of a block-wise diagonal covariance matrix in the ANOVA procedures. The methodology was then applied to data obtained from experiments of electrodialtic removal of 3 heavy metals from contaminated wood. First, polynomial regressions of the 4th and 3rd were fitted to each metal concentration in the electrolytes through time. Then the unbalanced case of multi-treatment regression analysis was applied aiming to choose the best treatment in jointly removing the 3 metals. Results pointed to the choice of treatment 1 as the most efficient.

KW - ANOVA

KW - F tests

KW - Multiple comparison

KW - Multiple regression

KW - Scheffé

KW - Unbalanced data

UR - http://www.scopus.com/inward/record.url?scp=82055200211&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781618040169

SP - 69

EP - 74

BT - Recent Researches in Applied Mathematics, Simulation and Modelling - Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11

ER -