### Abstract

If for each treatment of a base model we consider a multiple linear regression on the same variables (dependent and independent) a multiple regression design (MRD) is obtained. If the number of observations per regression is equal, the MRD is balanced, otherwise it is unbalanced. The purpose of this work is to show that is possible to extend the study of the full factorial design of fixed effects and the MRD associated to these designs to the unbalanced cases, combining the linear model associated with a commutative Jordan algebra (CJA) and the L-Model theory. The structure of the factorial design used in this work is based on linear spaces on Galois fields as well as on the relationship between a linear model and a CJA.

Original language | English |
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Title of host publication | 2018 International Conference on Mathematics and Statistics, ICoMS 2018 |

Publisher | Association for Computing Machinery |

Pages | 41-45 |

Number of pages | 5 |

ISBN (Electronic) | 9781450365383 |

DOIs | |

Publication status | Published - 15 Jul 2018 |

Event | 2018 International Conference on Mathematics and Statistics, ICoMS 2018 - Porto, Portugal Duration: 15 Jul 2018 → 17 Jul 2018 |

### Conference

Conference | 2018 International Conference on Mathematics and Statistics, ICoMS 2018 |
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Country | Portugal |

City | Porto |

Period | 15/07/18 → 17/07/18 |

### Fingerprint

### Keywords

- Design of experiments
- Linear models
- Multiple linear regression
- Unbalanced designs

### Cite this

*2018 International Conference on Mathematics and Statistics, ICoMS 2018*(pp. 41-45). Association for Computing Machinery. https://doi.org/10.1145/3274250.3274255

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*2018 International Conference on Mathematics and Statistics, ICoMS 2018.*Association for Computing Machinery, pp. 41-45, 2018 International Conference on Mathematics and Statistics, ICoMS 2018, Porto, Portugal, 15/07/18. https://doi.org/10.1145/3274250.3274255

**Multiple regression design for a full factorial base model associated with a commutative Jordan algebra.** / Oliveira, Sandra; Moreira, Elsa; Fonseca, Miguel; Mexia, João T.

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

TY - GEN

T1 - Multiple regression design for a full factorial base model associated with a commutative Jordan algebra

AU - Oliveira, Sandra

AU - Moreira, Elsa

AU - Fonseca, Miguel

AU - Mexia, João T.

PY - 2018/7/15

Y1 - 2018/7/15

N2 - If for each treatment of a base model we consider a multiple linear regression on the same variables (dependent and independent) a multiple regression design (MRD) is obtained. If the number of observations per regression is equal, the MRD is balanced, otherwise it is unbalanced. The purpose of this work is to show that is possible to extend the study of the full factorial design of fixed effects and the MRD associated to these designs to the unbalanced cases, combining the linear model associated with a commutative Jordan algebra (CJA) and the L-Model theory. The structure of the factorial design used in this work is based on linear spaces on Galois fields as well as on the relationship between a linear model and a CJA.

AB - If for each treatment of a base model we consider a multiple linear regression on the same variables (dependent and independent) a multiple regression design (MRD) is obtained. If the number of observations per regression is equal, the MRD is balanced, otherwise it is unbalanced. The purpose of this work is to show that is possible to extend the study of the full factorial design of fixed effects and the MRD associated to these designs to the unbalanced cases, combining the linear model associated with a commutative Jordan algebra (CJA) and the L-Model theory. The structure of the factorial design used in this work is based on linear spaces on Galois fields as well as on the relationship between a linear model and a CJA.

KW - Design of experiments

KW - Linear models

KW - Multiple linear regression

KW - Unbalanced designs

UR - http://www.scopus.com/inward/record.url?scp=85058144356&partnerID=8YFLogxK

U2 - 10.1145/3274250.3274255

DO - 10.1145/3274250.3274255

M3 - Conference contribution

SP - 41

EP - 45

BT - 2018 International Conference on Mathematics and Statistics, ICoMS 2018

PB - Association for Computing Machinery

ER -