Los Mínimos Cuadrados Ordinarios (OLS) son un método estadístico fundamental utilizado en análisis de regresión to estimate the parameters of a relación lineal 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 modelo lineal.
En la regresión lineal simple, regresión lineal, 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
donde:
- Y es la variable dependiente,
- X es la variable independiente,
- β0 es la intersección en Y,
- β1 es la pendiente de la línea, y
- ε representa el término de error.
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.
El OLS se usa ampliamente en diversos campos, incluyendo economía, ciencias sociales, y aprendizaje automático, 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.