Ordinary Least Squares (OLS) is a fundamental statistical method used in regression analysis to estimate the parameters of a linear relationship 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 linear model.
In simple linear 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
where:
- Y is the dependent variable,
- X is the independent variable,
- β0 is the y-intercept,
- β1 is the slope of the line, and
- ε represents the error term.
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 is widely used in various fields, including economics, social sciences, and machine learning, 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.