What is the least squares criterion?
The least squares criterion is a formula used to measure the accuracy of a straight line by describing the data that was used to generate it. In other words, the formula determines the line of best fit.
This mathematical formula is used to predict the behavior of dependent variables. The approach is also called the least squares regression line.
Understanding the criterion of least squares
The least squares criterion is determined by minimizing the sum of the squares created by a mathematical function. A square is determined by squaring the distance between a data point and the regression line or the average value of the data set.
A least squares analysis begins with a set of data points plotted on a graph. The independent variables are plotted on the horizontal X axis while the dependent variables are plotted on the vertical Y axis. The analyst uses the least squares formula to determine the most precise line that will explain the relationship between an independent variable and a dependent variable.
Common uses of least squares
Advances in computing power in addition to new financial engineering techniques have increased the use of least squares methods and extended its basic principles.
Key points to remember
- The least squares method is used in the fields of finance, economics and investment.
- It is used to estimate the precision of a line in the representation of the data that was used to create it.
- Least squares results can be used to summarize the data and make predictions about linked but unobserved values from the same group or system.
Least squares and related statistical methods have become commonplace in finance, economics and investment, although its beneficiaries are not always aware of their use.
For example, the Robo-advisers now used by many investment platforms use Monte Carlo simulation techniques to manage portfolios, although this is done behind the scenes and out of the sight of the account holders who use them.
Other applications include the chronological analysis of yield distributions, economic forecasting and political strategy, and the modeling of advanced options.
What do the least squares tell you?
Instead of trying to solve an equation exactly, mathematicians use the method of least squares to arrive at a close approximation. This is called a maximum likelihood estimate.
The least squares approach limits the distance between a function and the data points explained by the function. It is used in regression analysis, often in non-linear regression modeling in which a curve is fitted into a data set.
Mathematicians use the least squares method to arrive at an estimate of maximum likelihood.
The least squares approach is a popular method for determining regression equations, and it tells you about the relationship between response and predictor variables.
The modeling methods often used when fitting a function to a curve include the linear method, the polynomial method, the logarithmic method and the Gaussian method.
Linear or ordinary least squares are the simplest and most commonly used linear regression estimator for analyzing observational and experimental data. It finds a straight line of best fit across a given set of data points.