Ordinary Least Squares Method
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In statistics, the ordinary least squares (OLS) method is a fundamental regression analysis technique. This approach estimates linear relationships between two variables by minimizing the sum of squared residuals to determine the optimal fitted line. The core principle involves finding the best linear fit through minimizing the squared distances between data points and the regression line. The mathematical implementation typically involves solving normal equations: β = (XᵀX)⁻¹Xᵀy, where X represents the predictor matrix and y is the response vector. In Python, this can be implemented using numpy's linear algebra module with numpy.linalg.lstsq(), while MATLAB users can employ the backslash operator (\) for matrix division. This method finds applications across numerous domains including economics, social sciences, and natural sciences for predictive modeling and relationship analysis.
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