最小二乗法（OLS）は、基本的な統計手法であり、 回帰分析 to estimate the parameters of a 線形関係 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 線形モデル.
単回帰分析では、 線形回帰, 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
ただし：
- Y は従属変数です、
- X は独立変数です、
- β0 はy切片です、
- β1 直線の傾きはβ1であり、
- ε 誤差項を表します。
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は、経済学、社会科学などさまざまな分野で広く使用されています、 機械学習, 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.