Modèles statistiques classiques
Introduction
![images/eq81.png images/eq81.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq81.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq11.png images/eq11.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq11.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq82.png images/eq82.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq82.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
Modèles |
Variable de réponse |
Variable explicative |
Régression linéaire simple |
1 variable continue |
1 variable continue |
ANCOVA |
1 ou plusieurs variables qualitatives et continues |
|
Régression linéaire multiple |
||
ANOVA |
1 ou plusieurs variables qualitatives ou facteurs |
|
MANOVA |
Plusieurs variables continues |
|
Analyse discriminante |
1 variable catégorielle spécifiquement dichotomique |
1 ou plusieurs variables qualitatives et continues |
Régression logistique |
Analyse de la variance (ANOVA)
Dans le précédent chapitre, on a abordé plusieurs tests, dont notamment le test de comparaison de moyennes d’un - cas de comparaison par rapport à une référence, c’est pour ça que l’on parle de test de conformité - ou deux échantillons de données. L’ensemble de ces tests est souvent dénommé T-Test à cause de la loi T de Student que suit la distribution sous-jacente de l’échantillon.
![images/eq68.png images/eq68.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq68.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq69.png images/eq69.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq69.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq68.png images/eq68.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq68.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq83.png images/eq83.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq83.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq69.png images/eq69.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq69.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq83.png images/eq83.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq83.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq84.png images/eq84.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq84.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq82.png images/eq82.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq82.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
Modèles de régression linéaire
![images/eq146.png images/eq146.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq146.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq146.png images/eq146.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq146.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/08EP54.png images/08EP54.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/08EP54.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq147.png images/eq147.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq147.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq148.png images/eq148.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq148.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/08EP55.png images/08EP55.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/08EP55.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq149.png images/eq149.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq149.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/08EP56.png images/08EP56.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/08EP56.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq150.png images/eq150.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq150.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq149.png images/eq149.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq149.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq151.png images/eq151.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq151.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq150.png images/eq150.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq150.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
Dans cette section, la régression linéaire sera abordée sous plusieurs aspects à travers des applications R.
1. Régression linéaire simple
a. Formalisation et estimation
![images/eq152.png images/eq152.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq152.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/08EP57.png images/08EP57.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/08EP57.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
Donc, la relation entre Y et X pourra se formuler comme suit :
![images/08EP58.png images/08EP58.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/08EP58.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq153.png images/eq153.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq153.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq154.png images/eq154.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq154.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq155.png images/eq155.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq155.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq154.png images/eq154.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq154.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq155.png images/eq155.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq155.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
Selon cette méthode, trouver ces paramètres revient à minimiser la somme des carrés des résidus ou Sum of Square Error (SSE) :
![images/08EP59.png images/08EP59.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/08EP59.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq156.png images/eq156.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq156.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq157.png images/eq157.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq157.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq154.png images/eq154.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq154.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/eq155.png images/eq155.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/eq155.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
![images/08EP60.png images/08EP60.png](https://www.eni-training.com/download/04a3b5ba-59e1-49ce-971d-6c2e56abe541/images/08EP60.png?id=AAEAAAD%2f%2f%2f%2f%2fAQAAAAAAAAAMAgAAAE1FbmkuRWRpdGlvbnMuTWVkaWFwbHVzLCBWZXJzaW9uPTEuMC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49bnVsbAUBAAAAJ0VuaS5FZGl0aW9ucy5NZWRpYXBsdXMuQ29tbW9uLldhdGVybWFyawIAAAAHcGlzVGV4dAlwaWR0ZURhdGUBAA0CAAAABgMAAAAwdGVzdCB2Ml84IC0gZmZhNjQzOWQtZDZjYi00NzYxLWJhYTMtZWZkZDNiZDcwMWM25rSq0F7p2IgL)
Ces estimateurs sont sans biais compte tenu du théorème GAUSS - MARKOV. Ainsi, sans trop...