Line🥃ar R🔯egression vs. Multiple Regression: Overview

Linear regression, also called simple regression, is one of the most common techniques of regression analysis. Multiple regression is a broader class of regression analysis, which encompasses both linear and nonlinear regressions with m𝓀ultiple explanatory variables.

Regression analysis is a statistical method used in finance and 澳洲幸运5官方开奖结果体彩网:investing. Regression analysis pools daꩲta to help people and companies make informed decisions. There are different variables at play in this type of statistical analysis, including a dependent variable—the main variable that you're trying to understand—and an indepe💙ndent variable(s)—factors that may have an impact on the dependent variable.

People use regreℱssion analy🐈sis for several reasons:

• 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.

Linear re💜gression and multiple regression are two types of regression analysis.

Linear Regression

Also called simple regression, linear regression establishes the relationship between two variables. Linear regression is graphically depicted using a straight line; the slope defines 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, 澳洲幸运5官方开奖结果体彩网:nonlinear regression may be us⭕ed instead. Linear and nonlinear regression 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 c🎐omplex connections between data, the relationship might be explained by more than one variable. In this case, an analyst uses multiple regression. Multiple regression 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 i⛦s 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.

Lineaꦯr 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 daily changes in trading volume. Using linear regression🌼, the analyst can attempt to determine the relationship between the t𒐪wo 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 eꩵvery share so🏅ld, 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)

The Bottom Line

There are 𒆙many different types of regression analysis, including linear regression and multiple regression.🉐

Linear regression captures the relationship between two variables—for example, the relationship between the daily change in a company's stock prices and the daily change in trading volume.

Multiple linear regression is a more specific (and complex) calculation. It incorporates multiple independent variables. For example, multiple regression could capture how the daily change in a company's stock price is impacted by the company's P/E ratio, dividends, the prevailing inflation rate, and the daily change in trading volume.