Moindres carrés ordinaires (OLS) est une méthode statistique fondamentale utilisée en analyse de régression to estimate the parameters of a relation linéaire between one or more independent variables and a dependent variable. The primary objective of OLS is to minimize the sum of the squared differences between the observed values and the values predicted by the modèle linéaire.
En régression simple régression linéaire, OLS seeks to find the best-fitting straight line through a scatter plot of data points. This line is defined by the equation:
Y = β0 + β1X + ε
où :
- Y est la variable dépendante,
- X est la variable indépendante,
- β0 est l'ordonnée à l'origine,
- β1 est la pente de la ligne, et
- ε représente le terme d'erreur.
To determine the coefficients (β0 and β1), OLS calculates the values that minimize the residual sum of squares (RSS), which is the total squared difference between the actual data points and the predictions made by the model. This method assumes that the errors are normally distributed, have constant variance, and are independent of each other.
L'OLS est largement utilisé dans divers domaines, notamment en économie, en sciences sociales et en apprentissage automatique, for tasks such as predicting outcomes and understanding relationships between variables. However, it has limitations, such as sensitivity to outliers and the assumption of linearity. When these assumptions do not hold, alternative methods like robust regression or polynomial regression may be more appropriate.