Linear Regression vs. Multiple Regression: An Overview

Regression analysis is a common statistical method used in finance and investing. Linear regression is one of the most common techniques of regression analysis. Multiple regression is a broader class of regressions that encompasses linear and nonlinear regressions with multiple explanatory variables.

Regression as a tool helps pool data together to help people and companies make informed decisions. There are different variables at play in regression, including a dependent variable—the main variable that you're trying to understand—and an independent variable—factors that may have an impact on the dependent variable.

In order to make regression analysis work, you must collect all the relevant data. It can be presented on a graph, with an x-axis and a y-axis.

There are several main reasons people use regression analysis:

  1. To predict future economic conditions, trends, or values
  2. To determine the relationship between two or more variables
  3. To understand how one variable changes when another changes

There are many different kinds of regression analysis. For the purpose of this article, we will look at two: linear regression and multiple regression.

Linear Regression

It is also called a simple linear regression. It establishes the relationship between two variables using a straight line. Linear regression attempts to draw a line that comes closest to the data by finding the slope and intercept that define the line and minimize regression errors.

If two or more explanatory variables have a linear relationship with the dependent variable, the regression is called a multiple linear regression.

Many data relationships do not follow a straight line, so statisticians use nonlinear regression instead. The two are similar in that both track a particular response from a set of variables graphically. But nonlinear models are more complicated than linear models because the function is created through a series of assumptions that may stem from trial and error.

Multiple Regression

It is rare that a dependent variable is explained by only one variable. In this case, an analyst uses multiple regression, which attempts to explain a dependent variable using more than one independent variable. Multiple regressions can be linear and nonlinear.

Multiple regressions are based on the assumption that there is a linear relationship between both the dependent and independent variables. It also assumes no major correlation between the independent variables.

As mentioned above, there are several different advantages to using regression analysis. These models can be used by businesses and economists to help make practical decisions.

A company can not only use regression analysis to understand certain situations like why customer service calls are dropping, but also to make forward-looking predictions like sales figures in the future, and make important decisions like special sales and promotions.

Linear Regression vs. Multiple Regression: Example

Consider an analyst who wishes to establish a linear relationship between the daily change in a company's stock prices and other explanatory variables such as the daily change in trading volume and the daily change in market returns. If he runs a regression with the daily change in the company's stock prices as a dependent variable and the daily change in trading volume as an independent variable, this would be an example of a simple linear regression with one explanatory variable.

If the analyst adds the daily change in market returns into the regression, it would be a multiple linear regression.

Key Takeaways

  • Regression analysis is a common statistical method used in finance and investing.
  • Linear regression is one of the most common techniques of regression analysis.
  • Multiple regression is a broader class of regressions that encompasses linear and nonlinear regressions with multiple explanatory variables.