Least Squares Method (LSM) is a statistical procedure used to determine the optimal fit for a set of data points by minimizing the sum of the offsets or residuals of points from the plotted curve. It is the most commonly used method for the analysis of linear equations, and is employed in many branches of science, from physics and engineering calculations to surveys and questionnaires.

LSM is based on the concept of minimizing the sum of the squares of the errors, which determines the most optimal fit for linear regression models. The aim of this method is to obtain the best-fitting model by minimizing the sum of the squares of the errors, which are the differences between the values predicted by the model and the observed values. The sum of the squares of the errors is also referred to as the residual sum of squares.

In order to use the LSM, the user first needs to provide a set of data points, the coordinates of which define the underlying mapping between the independent and dependent variables. Using the coordinates, the user can then fit the best-fit line to the data points by minimizing the sum of the errors (or residuals as they are referred to in LSM).

The best-fit line obtained using LSM is usually referred to as the Least Squares Regression Line, or the Line of Best Fit. This line will show the model’s ability to predict the behavior of the dependent variable and can be used to make objective decisions about the relationship between the independent variable and dependent variable. It is also useful in predicting future behavior from the same pattern of past data.

The least squares method is widely used in many fields of research, including mathematics, economics, psychology, statistics, engineering, and many others. It is an important tool in the estimation of complicated relationships that cannot be directly estimated. In addition, it provides a solid theoretical basis for the application of rigorous statistical methods to the analysis of data.