Least Squares Method - Explained
What is the Least Squares Method?
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Table of ContentsWhat is the Least Squares Method?How is the Least Squares Method Used?Example of the Least Squares MethodThe Line of Best Fit EquationAcademic Research on the Least Squares Method
What is the Least Squares Method?
The least squares method is a procedure of finding the best fit for a data set. This method uses statistics and mathematical regression analysis to find the line of best fit when a data set is given. Using the least squares regression analysis, the distinct behaviors of dependent variables in a data set are predicted or identified. There is a form of relationship that exists between data points and a known independent variable and unknown dependent variable. The least squares method reflects the relationships and behaviors.
How is the Least Squares Method Used?
The least squares method was first used in 1805,when it was published by Legendre. This method contains procedures that find out the best fit curve or line of best fit in any given data set. To identify the best fit, there is an equation used which entails reducing the residuals of the data points. The idea behind the placement of the line of best fit among given data points is identified through the last squares method. For instance, the ordinary application of the least squares method reduce the sum of the square of error present in an equation. When the regression analysis is used, the equation for the line of best fit is formed through the placement of dependent variables and independent variables. Here are the major points you should know about the least squares method;
- The least squares method is a mathematical model of finding the line of best fit for a set of data points.
- The sum of residuals of points is minimized from the curve to find the line of best fit.
- This line of best fit seeks to highlight the relationship that exists between a known independent variable and an unknown dependent variable in a set of data points.
- The behaviors of variables in the data set are also predicted and explained.
Example of the Least Squares Method
Here is an illustration that will help you understand how the least squares method is applied in real life situations. Company XYZ is a company in the fiber industry and Analyst A wants to find out the relationship between the company's stock return and that of the industry index. Using the least squares method, Analyst A can test the reliance of company XYZ 's stock returns in the index returns. To do this, the analysts plots all given returns on a chart or graph. The index returns will be the independent variable while the company's stock return will be designated as dependent variable.
The Line of Best Fit Equation
History has it that the least squares method was developed by Carl Friedrich Gauss in 1795. This method allows for the identification of the line of best fit to a set of data points that contain both dependent and independent variables. There are software models that were developed to help determine the line of best fit, the models also explain the interaction between data points. Oftentimes, determining the line of best fit is important in regression analysis as it helps to identify the dependence on non-dependence of variables.
Academic Research on the Least Squares Method