Mínimos Quadrados Ordinários (OLS) é um método estatístico fundamental usado em análise de regressão to estimate the parameters of a relação linear 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 linear.
Na regressão linear simples, regressão linear, 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
onde:
- Y é a variável dependente,
- X é a variável independente,
- β0 é o intercepto y,
- β1 é a inclinação da linha, e
- ε ε representa o termo de erro.
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.
OLS é amplamente utilizado em várias áreas, incluindo economia, ciências sociais, e aprendizado de máquina, 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.