複数の 線形回帰 (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 線形方程式 that describes how the dependent variable changes as the independent variables change. The general MLR方程式の形は：
Y = β0 + β1X1 + β2X2 + … + βnXn + ε
ここで：
- Y は従属変数です。
- 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 は独立変数です。
- ε は誤差項であり、モデルによって説明されない変動を考慮します。
MLRは、さまざまな分野で広く使用されています。 economics, biology, engineering, and 社会科学 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.