Least Squares Method: What It Means, How to Use It, With Examples

What Is the Least Squares Method?

The least squares method is a form of mathematical regression analysis used to determine the line of best fit for a set of data, providing a visual demonstration of the relationship between the data points. Each point of data represents the relationship between a known independent variable and an unknown dependent variable. This method is commonly used by statisticians and traders who want to identify trading opportunities and trends.

Understanding the Least Squares Method

The least squares method is a form of regression analysis that provides the overall rationale for the placement of the line of best fit among the data points being studied. It begins with a set of data points using two variables, which are plotted on a graph along the x- and y-axis. Traders and analysts can use this as a tool to pinpoint bullish and bearish trends in the market along with potential trading opportunities.

The most common application of this method is sometimes referred to as linear or ordinary. It aims to create a straight line that minimizes the sum of squares of the errors generated by the results of the associated equations, such as the squared residuals resulting from differences in the observed value and the value anticipated based on that model.

For instance, an analyst may use the least squares method to generate a line of best fit that explains the potential relationship between independent and dependent variables. The line of best fit determined from the least squares method has an equation that highlights the relationship between the data points.

If the data shows a lean relationship between two variables, it results in a least-squares regression line. This minimizes the vertical distance from the data points to the regression line. The term least squares is used because it is the smallest sum of squares of errors, which is also called the variance. A non-linear least-squares problem, on the other hand, has no closed solution and is generally solved by iteration.

Advantages and Disadvantages of the Least Squares Method

The best way to find the line of best fit is by using the least squares method. But traders and analysts may come across some issues, as this isn't always a fool-proof way to do so. Some of the pros and cons of using this method are listed below.

Advantages

One of the main benefits of using this method is that it is easy to apply and understand. That's because it only uses two variables (one that is shown along the x-axis and the other on the y-axis) while highlighting the best relationship between them.

Investors and analysts can use the least square method by analyzing past performance and making predictions about future trends in the economy and stock markets. As such, it can be used as a decision-making tool.

Disadvantages

The primary disadvantage of the least square method lies in the data used. It can only highlight the relationship between two variables. As such, it doesn't take any others into account. And if there are any outliers, the results become skewed.

Example of the Least Squares Method

Here's a hypothetical example to show how the least square method works. Let's assume that an analyst wishes to test the relationship between a company’s stock returns, and the returns of the index for which the stock is a component. In this example, the analyst seeks to test the dependence of the stock returns on the index returns.

To achieve this, all of the returns are plotted on a chart. The index returns are then designated as the independent variable, and the stock returns are the dependent variable. The line of best fit provides the analyst a line showing the relationship between dependent and independent variables.

The Bottom Line

Traders and analysts have a number of tools available to help make predictions about the future performance of the markets and economy. The least squares method is a form of regression analysis that is used by many technical analysts to identify trading opportunities and market trends. It uses two variables that are plotted on a graph to show how they're related.