what is regression 
regression is a statistical method used in finance investing and other disciplines that attempts to determine the strength and character of the relationship between a dependent variable and one or more independent variables linear regression is the most common form of this technique also called simple regression or ordinary least squares ols linear regression establishes the linear relationship between two variables linear regression is graphically depicted using a straight 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 nonlinear regression models also exist but are far more complex in economics regression is used to help investment managers value assets and understand the relationships between factors such as commodity prices and the stocks of businesses dealing in those commodities while a powerful tool for uncovering the associations between variables observed in data it cannot easily indicate causation regression as a statistical technique should not be confused with the concept of regression to the mean also known as mean reversion joules garcia investopediaunderstanding regressionregression captures the correlation between variables observed in a data set and quantifies whether those correlations are statistically significant or not the two basic types of regression are simple linear regression and multiple linear regression although there are nonlinear regression methods for more complicated data and analysis simple linear regression uses one independent variable to explain or predict the outcome of the dependent variable y while multiple linear regression uses two or more independent variables to predict the outcome analysts can use stepwise regression to examine each independent variable contained in the linear regression model regression can help finance and investment professionals for instance a company might use it to predict sales based on weather previous sales gross domestic product gdp growth or other types of conditions the capital asset pricing model capm is an often used regression model in finance for pricing assets and discovering the costs of capital econometrics is a set of statistical techniques used to analyze data in finance and economics an example of the application of econometrics is to study the income effect using observable data an economist may for example hypothesize that as a person increases their income their spending will also increase if the data show that such an association is present a regression analysis can then be conducted to understand the strength of the relationship between income and consumption and whether or not that relationship is statistically significant note that you can have several independent variables in an analysis for example changes to gdp and inflation in addition to unemployment in explaining stock market prices when more than one independent variable is used it is referred to as multiple linear regression this is the most commonly used tool in econometrics econometrics is sometimes criticized for relying too heavily on the interpretation of regression output without linking it to economic theory or looking for causal mechanisms it is crucial that the findings revealed in the data are able to be adequately explained by a theory calculating regressionlinear 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 in turn determined by squaring the distance between a data point and the regression line or mean value of the data set once this process has been completed usually done today with software a regression model is constructed the general form of each type of regression model is simple linear regression 1y a b x u begin aligned y a bx u end aligned y a bx u multiple linear regression 2y a b 1 x 1 b 2 x 2 b 3 x 3 b t x t u where y the dependent variable you are trying to predict or explain x the explanatory independent variable s you are using to predict or associate with y a the y intercept b beta coefficient is the slope of the explanatory variable s u the regression residual or error term 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 predictor explainx the explanatory independent variable s you 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 how regression analysis is used in financeregression 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 aforementioned capm is based on regression and it s 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 the 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 to get better estimates for returns these additional factors are known as the fama french factors named after the professors who developed the multiple linear regression model to better explain asset returns 3