What method is used to estimate the regression equation that minimizes the sum of squared residuals?

The least squares method is the approach used to estimate the regression equation that minimizes the sum of squared residuals. This technique works by finding the line (or hyperplane in multiple dimensions) that results in the smallest possible sum of the squared differences between the observed values (actual data points) and the predicted values (those calculated by the regression equation).

The principle underlying the least squares method is that by minimizing these squared residuals, you achieve an optimal model fit, which enhances the predictive accuracy and reliability of the regression analysis. This method assumes linear relationships between the independent and dependent variables, making it a foundational technique in statistical modeling and analysis.

Other methods mentioned, such as the maximum likelihood method, are generally used for parameter estimation in statistical models, but they don't specifically focus on minimizing the sum of squared residuals, which is central to the least squares approach. The regression analysis method is a broader term that encompasses various techniques, not just least squares. The generalized method of moments is another estimation technique used in econometrics and statistics but is also distinct from the least squares methodology.