## 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:

- To predict future economic conditions, trends, or values
- To determine the relationship between two or more variables
- 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.

### 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 when there are only two variables.
- Multiple regression is a broader class of regressions that encompasses linear and nonlinear regressions with multiple explanatory variables.
- Whereas linear regress only has one independent variable impacting the slope of the relationship, multiple regression incorporates multiple independent variables.
- Each independent variable in multiple regression has its own coefficient to ensure each variable is weighted appropriately.

## Linear Regression

Also called simple regression, linear regression establishes the relationship between two variables. Linear regression is graphically depicted using a straight line with the slope defining how the change in one variable impacts a change in the other. The y-intercept of a linear regression relationship represents the value of one variable when the value of the other is 0.

In linear regression, every dependent value has a single corresponding independent variable that drives its value. For example, in the linear regression formula of y = 3x + 7, there is only one possible outcome of 'y' if 'x' is defined as 2.

If the relationship between two variables does not follow a straight line, nonlinear regression may be used instead. Linear and nonlinear regression are similar in that both track a particular response from a set of variables. As the relationship between the variables becomes more complex, nonlinear models have greater flexibility and capability of depicting the non-constant slope.

## Multiple Regression

For complex connections between data, the relationship might be explained by more than one variable. In this case, an analyst uses multiple regression which attempts to explain a dependent variable using more than one independent variable.

There are two main uses for multiple regression analysis. The first is to determine the dependent variable based on multiple independent variables. For example, you may be interested in determining what a crop yield will be based on temperature, rainfall, and other independent variables. The second is to determine how strong the relationship is between each variable. For example, you may be interested in knowing how a crop yield will change if rainfall increases or the temperature decreases.

Multiple regression assumes there is not a strong relationship between each independent variable. It also assumes there is a correlation between each independent variable and the single dependent variable. Each of these relationships is weighted to ensure more impactful independent variables drive the dependent value by adding a unique regression coefficient to each independent variable.

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.

## Linear Regression vs. Multiple Regression Example

Consider an analyst who wishes to establish a relationship between the daily change in a company's stock prices and the daily change in trading volume. Using linear regression, the analyst can attempt to determine the relationship between the two variables:

**Daily Change in Stock Price = (Coefficient)(Daily Change in Trading Volume) + (y-intercept)**

If the stock price increases $0.10 before any trades occur and increases $0.01 for every share sold, the linear regression outcome is:

**Daily Change in Stock Price = ($0.01)(Daily Change in Trading Volume) + $0.10**

However, the analyst realizes there are several other factors to consider including the company's P/E ratio, dividends, and prevailing inflation rate. The analyst can perform multiple regression to determine which—and how strongly—each of these variables impacts the stock price:

**Daily Change in Stock Price = (Coefficient)(Daily Change in Trading Volume) + (Coefficient)(Company's P/E Ratio) + (Coefficient)(Dividend) + (Coefficient)(Inflation Rate)**

## Is Multiple Linear Regression Better Than Simple Linear Regression?

Multiple linear regression is a more specific calculation than simple linear regression. For straight-forward relationships, simple linear regression may easily capture the relationship between the two variables. For more complex relationships requiring more consideration, multiple linear regression is often better.

## When Should You Use Multiple Linear Regression?

Multiple linear regression should be used when multiple independent variables determine the outcome of a single dependent variable. This is often the case when forecasting more complex relationships.

## How Do You Interpret Multiple Regression?

A multiple regression formula has multiple slopes (one for each variable) and one y-intercept. It is interpreted the same as a simple linear regression formula except there are multiple variables that all impact the slope of the relationship.