What Is Regression?

Regression is a statistical method used in finance, investing, and other discipli⛄nes to attempt to determine the strength and character of the relationsh🐬ip between a dependent variable and one or more independent variables.

Linear regression is the most common form of this technique. It establishes the 澳洲幸运5官方开奖结果体彩网:linear relationship between two variables and is 🦩also referred to as simple 💖regression or ordinary least squares (OLS) regression.

Linear regression is graphically depicted using a straight 澳洲幸运5官方开奖结果体彩网:line of best fit, 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 the dependent variable when the value of the independent variable is zero. 澳洲幸运5官方开奖结果体彩网:Nonlinear regression models also exist but are far more complex.

Regression is used in economics to help investment managers value assets and understand the relationships between factors such as 澳洲幸运5官方开奖结果体彩网:commodity prices and the stocks of businesses dealing in those commo💟dities. It’s a powerful tool for uncovering the associations between variables observed in data, but it can’t easily indica💟te causation.

Regression as a statistical technique shouldn’t be confused with the concept of regression to the mean, also known as 澳洲幸运5官方开奖结果体彩网:mean reversion.

How Regression Works

Regression captures the correlation between variables observed in a dataset and quantifies whether those correlations are 澳洲幸运5官方开奖结果体彩网:statistically significant. The two basic types of regression are simple linear regression and 澳洲幸运5官方开奖结果体彩网:multiple linear regression, but there are nonlinear regression meth❀ods for more complicated data and 🧜analysis.

Simple linear regression uses one independent variable to explain or predict the outcome of the dependent variable Y. Multiple linear regression uses two or more independent variables to predict the outcome. Analysts can use 澳洲幸运5官方开奖结果体彩网:stepwise regression to examine each independent variable contained in⛎ the linear regꩲression model.

Regression can help finance and investment professionals. A company might use it to predict sales based on weather, previous sales, gross domestic product (GDP) growth, or other types of conditions. The 澳洲幸运5官方开奖结果体彩网:capital asset pricing model (CAPM) is a regression model that’s 𓄧often used in finance for pricing assets and discovering the costs of capital.

Regression and Econometrics

澳洲幸运5官方开奖结果体彩网:Econometrics is a set of statistical techniques that are used to analyze data in finance and economics. It effectively studies the income effect using observable data. An economist might hypothesize that a consumer’s spending will increase as they increase their income.

A ꦓregression analysis can then be conducted to understand the strengthཧ of the relationship between income and consumption if the data show that such an association is present. It can indicate whether that relationship is statistically significant.

You can have several independent variables in an analysis, such as changes to GDP and inflation in addition to unemployment in explaining stock market prices. It's referred to as multiple linear regression when more than one independent variable is used. This is the most commonly used tool in econometrics.

Calculating Regression

Linear regression models often use a least-squares approach to determine the line of best fit. The least-squares technique is determined by minimizing the sum of squares created by🃏 a mathematical function. A square is then determined by squaring the distance between a data point and the regression line or mean value of the dataset.

A regression model is constructed when this process has been completed. It✤’s usually accomplished with software. The general form of each type of regression model is:

Simple linear regression:

$\begin{aligned}&Y = a + bX + u \\\end{aligned}$​Y=a+bX+u​

Multiple linear regression:

$\begin{aligned}&Y = a + b_1X_1 + b_2X_2 + b_3X_3 + ... + b_tX_t + u \\&\textbf{where:} \\&Y = \text{The dependent variable you are trying to predict} \\&\text{or explain} \\&X = \text{The explanatory (independent) variable(s) you are } \\&\text{using to predict or associate with Y} \\&a = \text{The y-intercept} \\&b = \text{(beta coefficient) is the slope of the explanatory} \\&\text{variable(s)} \\&u = \text{The regression residual or error term} \\\end{aligned}$​Y=a+b1​X1​+b2​X2​+b3​X3​+...+bt​Xt​+uwhere:Y=The dependent variable you are trying to predi🌞ctor explainX=The explanatory (independent) variable(s) you&ﷺnbsp;are using to predict or 💝associate with Ya=The y-interceptb=(🧸beta coefficient) is the slope of the explanatoryvariable(s)u=The regression🍸 residual or error term​

Example Of Regression Analysis in Finance

Regression is often used to determine how specific factors such as the price of a commodity, interest rates, particular industries, or sectors influence the price movement of an asset. The CAPM is based on regression and is used to project the expected returns for stocks and generate costs of capital. A stock’s returns are regressed against the returns of a broader index such as the S&P 500 to generate a beta for the particular stock.

Beta is the stock’s risk in relation to𝓀 the market or index, and it’s reflected as the slope in the CAPM. The 𒆙return for the stock in question would be the dependent variable Y. The independent variable X would be the market risk premium.

Additional variables such as the market capitalization of a stock, valuation ratios, and recent returns can be added to the CAPM to get better estimates for returns. These additional factors are known as the Fama-French factors. They’re named after the professors who developed the multiple linear regression model to better explain asset returns.

Explain Regression Like I’m 5 Years Old

Regression tries to see if there’s a relationship between two things, such as whether there’s a link between how you do one thing and how you do one꧂ or more other things.

Regression helps you make educated guesses, or predictions, based on past information. It’s about finding a pattern between two or more things and using that pattern to make a good guess about what might happen in the future.

The Bottom Line

Regression is a statistical method that tries to determine the strength and character of the relationship between one dependent variable and a series of other variables. It’s u🐼sed 𝔉in finance, investing, and other disciplines.

Regression analysis uncovers the associations between variables observed in data, but it can’t easily indicate causation.