What is 'Regression'
Regression is a statistical measure used in finance, investing and other disciplines that attempts to determine the strength of the relationship between one dependent variable (usually denoted by Y) and a series of other changing variables (known as independent variables). Regression helps investment and financial managers to value assets and understand the relationships between variables, such as commodity prices and the stocks of businesses dealing in those commodities.
BREAKING DOWN 'Regression'
The two basic types of regression are linear regression and multiple linear regression, although there are nonlinear regression methods for more complicated data and analysis. Linear regression uses one independent variable to explain or predict the outcome of the dependent variable Y, while multiple regression uses two or more independent variables to predict the outcome.
Regression can help finance and investment professionals as well as professionals in other businesses. Regression can help predict sales for a company based on weather, previous sales, GDP growth or other conditions. The capital asset pricing model (CAPM) is an oftenused regression model in finance for pricing assets and discovering costs of capital. The general form of each type of regression is:
Linear Regression: Y = a + bX + u
Multiple Regression: Y = a + b_{1}X_{1 +} b_{2}X_{2} + b_{3}X_{3} + ... + b_{t}X_{t} + u
Where:
Y = the variable that you are trying to predict (dependent variable)
X = the variable that you are using to predict Y (independent variable)
a = the intercept
b = the slope
u = the regression residual
Regression takes a group of random variables, thought to be predicting Y, and tries to find a mathematical relationship between them. This relationship is typically in the form of a straight line (linear regression) that best approximates all the individual data points. In multiple regression, the separate variables are differentiated by using numbers with subscript.
Regression in Investing
Regression is often used to determine how many specific factors such as the price of a commodity, interest rates, particular industries or sectors influence the price movement of an asset. The aforementioned CAPM is based on regression, and it is utilized to project the expected returns for stocks and to 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 to the market or index and is reflected as the slope in the CAPM model. The expected return for the stock in question would be the dependent variable Y, while 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 model to get better estimates for returns. These additional factors are known as the FamaFrench factors, named after the professors who developed the multiple linear regression model to better explain asset returns.

Stepwise Regression
Stepwise regression is the stepbystep iterative construction ... 
Error Term
A variable in a statistical and/or mathematical model, which ... 
Heteroskedastic
Heteroskedastic refers to a condition in which the variance of ... 
Regressive Tax
A regressive tax is a tax that is applied uniformly, resulting ... 
Least Squares Method
The least squares method is a statistical technique to determine ... 
Residual Sum Of Squares  RSS
A residual sum of squares is a statistical technique used to ...

Trading
The linear regression of time and price
This investment strategy can help investors be successful by identifying price trends while eliminating human bias. 
Investing
What's the Correlation Coefficient?
The correlation coefficient is a measure of how closely two variables move in relation to one another. If one variable goes up by a certain amount, the correlation coefficient indicates which ... 
Investing
Capital Asset Pricing (CAPM) Model: Pros and Cons
CAPM, while criticized for its unrealistic assumptions, provides a more useful outcome than either the DDM or WACC in many situations. 
Financial Advisor
Calculating Beta: Portfolio Math For The Average Investor
Beta is a useful tool for calculating risk, but the formulas provided online aren't specific to you. Learn how to make your own. 
Investing
How To Calculate Beta Of A Private Company
We explain two methods for calculating the beta of a private company. 
Investing
Scenario Analysis Provides Glimpse Of Portfolio Potential
This statistical method estimates how far a stock might fall in a worstcase scenario. 
Retirement
Variable Annuities: The DoItYourself Pension Plan
Variable annuities can cost more than mutual funds, but that might be worth the protection they can add to your retirement. 
Investing
Taking Shots at CAPM
Find out why many investors think the capital asset pricing model is full of holes.

In what types of economies are regressive taxes common?
Understand the three main taxation systems, regressive, proportionate and progressive, and learn where regressive tax systems ... Read Answer >> 
What is the difference between direct costs and variable costs?
Learn about variable costs and direct costs, how direct costs and variable costs are classified and the differences between ... Read Answer >>