 # Least Squares Method

Updated on September 30, 2022 , 2028 views

## What is the Least Squares Method?

The least-squares method is a mathematical regression analysis form which is used to show the line of best fit for a set of data. This provides a visual demonstration of the relationship between data points. The derivation of least squares method is attributed to Carl Friedrich Gauss in 1795. This data point represents a relationship between a known independent variable and an unknown dependent variable. In other words, the least-squares method provides the overall rationale for the line placement of best fit among data points that are being studied. The most common application of this method aims to create a straight line that minimises the sum of the squares of the errors generated by results of equations that are associated. These equations could be squared residuals which are results from differences in observed value and anticipated value based on that model.

Regression analysis method starts with a set of data points that are to be plotted on an X and Y-axis graph. An analyst will use the least-squares method example to generate a line best fit to explain the relationship between the independent and dependent variables. Under this analysis, dependent variables are illustrated on the vertical y-axis why independent variables are shown horizontal X-Axis. This formed equation for the best fit line which is determined from the least-squares method.

However, this kind of equation does not exist with a non-linear least squares problem. The non-linear least-squares problem has no closed solution and is usually solved by iteration.

## Line of Best Fit

The line of best fit is usually determined from the method of least squares formula which tells the relationship between data points. Line of best-fit equations can be determined through computer software models that includes a summary of outputs for analysis. Here the coefficients and summary output explain the dependence of the variable being tested.

## Least Squares Regression Line

In data, if you see a leaner relationship between two variables, the line that best fits this linear relationship is known as a least-squares regression line. This line minimises the vertical distance from the data points to the regression line.