Die Methode der kleinsten Quadrate (OLS) ist eine grundlegende statistische Methode, die in Regressionsanalyse to estimate the parameters of a lineare Beziehung 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 lineares Modell.
Bei der einfachen linearer Regression, 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
wobei:
- Y ist die abhängige Variable,
- X ist die unabhängige Variable,
- β0 ist der y-Achsenabschnitt,
- β1 ist die Steigung der Linie, und
- ε stellt den Fehlerterm dar.
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 wird in verschiedenen Bereichen, einschließlich Wirtschaft, Sozialwissenschaften und maschinellem Lernen, 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.