What is the purpose of the method of least squares?

The method of least squares specifically targets finding the best-fit line for a set of data points by minimizing the residuals, which are the differences between observed values and the values predicted by the model. In practical applications, this method is crucial in regression analysis, where the goal is to identify the linear relationship between independent and dependent variables. By minimizing the sum of the squares of these residuals, the method ensures that the fitted line is as close as possible to all data points on average.

This technique is widely used in various fields such as statistics, finance, and the sciences, providing a reliable way to analyze trends and make predictions. By focusing on minimizing these residuals, we can derive a linear equation that represents the overall trend in the data, which is the essence of the least squares approach.