Múltiplas Regressão Linear (MLR) is a statistical technique used to understand the relationship between two or more independent variables and a dependent variable. This method extends simple linear regression, which models the relationship between a single independent variable and a dependent variable, to accommodate multiple predictors.
In MLR, the dependent variable is assumed to be continuous, while the independent variables can be either continuous or categorical. The goal is to find the best-fitting equação linear that describes how the dependent variable changes as the independent variables change. The general a forma da equação de MLR é:
Y = β0 + β1X1 + β2X2 + … + βnXn + ε
Onde:
- Y é a variável dependente.
- β0 is the intercept of the regression line.
- β1, β2, …, βn are the coefficients representing the relationship strength between each independent variable and the dependent variable.
- X1, X2, …, Xn são as variáveis independentes.
- ε é o termo de erro, que representa a variabilidade não explicada pelo modelo.
O MLR é amplamente utilizado em diversos campos, como economics, biology, engineering, and ciências sociais for prediction and forecasting. However, it requires certain assumptions to be valid, including linearity, independence of errors, homoscedasticity (constant variance of errors), and normality of error terms. Violations of these assumptions can lead to biased estimates and inaccurate conclusions.