Linear regression is a form of statistical analysis that attempts to identify a relationship between an independent variable and one or more dependent variables.
Generally linear regression is aimed at causal relationships, where a change in the independent variable causes a predictable change in the dependent variable.
Linear regression forms the basis of much of the statistical analysis that is performed in finance.
Linear Regression Example
One of the simplest examples of causal linear relationships is that between the price of a good and the quantity of that good that is produced.
If 1 unit of good A is produced when the price is $1, 2 units when the price is $2 and 3 units when the price is $3, then the price of good A and and the units of good A produced have a 1:1 linear relationship.
This linear regression could also be represented by a straight line on a graph showing the independent variable (price) and dependent variable (quantity).
Linear Regression in Finance
Much of the complex analysis that takes place in the financial world is based on linear regression.
Charting the causal relationship between 2 or more elements can help investors to create a comprehensive understanding of how the market changes and reacts to both events and cyclical forces.
Moreover, investors can use linear regression to identify unknown relationships between financial elements that can give them an edge in interpreting the market and forecasting price changes.
Fundamentally linear regression is based on the idea that one change causes another change to happen. Of course, the world of finance is full of such relationships, but rarely, if ever, are they so simple as to be described in a one-to-one linear relationship.
That is why linear regression involves many advanced statistical techniques for attempting to extract and isolate causal relationships, so that investors can attempt to find some sense of clarity in the incredibly complex interplay of market factors.
There are, however, a number of major problems with the use of linear regression in financial analysis.
First there is the problem of correlation without causation. This means that while there is a statistical relationship between two variables, one does not cause the other. Similarly, it can occur that the relationship is actually caused in reverse or by a 3rd unknown factor.
Many investors can be lulled into a false sense of security that linear regression provides without realizing that there is more to explaining and forecasting the market than identifying relationships using linear regression.
The second major issue with linear regression in finance is that it is ultimately limited to past relationships.
While it is reasonable to assume that a strong linear relationship between two or more factors will continue into the future, there is no reason that they must do so. Furthermore, the weaker or the more complex the relationship, the less predictive value the products of linear regression have.
A linear relationship will have a degree of variance, which is the band within which the relationship can fluctuate. Therefore, even if you can predict a relationship on average over time, you cannot predict when that relationship will be at its average and when it will be at one of the upper or lower limits of its variance.
Linear Regression and Trading
Many day traders will use linear regression analysis in an attempt to create explanatory and forecasting charts of factors that are relevant to what they are trading.
These linear regression tools can be invaluable for providing a fundamental understanding of what is happening in the market, but day traders should be cautious when attempting to use linear regression to directly forecast price action.
Beyond direct use, all day traders should be comfortable with the basic principles of linear regression, as much of the top analysis available for day traders to use will be based on linear regression and assume a comfort with basic statistical analysis.
Linear regression is a key part of the statistical analysis used in finance. While it can be extremely useful for creating explanatory models of past market performance, it is more limited when used in the attempt to directly forecast upcoming price changes.
All day traders would be well served by spending some time to familiarize themselves with the basics of linear regression, if only so they can take advantage of much of the free and paid market analysis that will be based on it.