What is Regression Analysis?
Regression analysis is a set of statistical methods used for the estimation of relationships between a dependent variable and one or more independent variablesIndependent VariableAn independent variable is an input, assumption, or driver that is changed in order to assess its impact on a dependent variable (the outcome). Think of the independent variable as the input and the dependent variable as the output. In financial modeling and analysis, an analyst typically performs sensitivity analysis. It can be utilized to assess the strength of the relationship between variables and modeling the future relationship between them.
Regression analysis includes several variations, such as linear, multiple linear, and nonlinear. The most common models are simple linear and multiple linear. Nonlinear regression analysis is usually used for more complicated data sets in which the dependent and independent variables show a nonlinear relationship.
Regression analysis offers numerous applications in various disciplines, including finance.
Linear model assumptions
Linear regression analysis is based on six fundamental assumptions:
- The dependent and independent variables show a linear relationship between the slope and the intercept.
- The independent variable is not random.
- The value of the residual (error) is zero.
- The value of the residual (error) is constant across all observations.
- The value of the residual (error) is not correlated across all observations.
- The residual (error) values follow the normal distribution.
Simple linear regression
Simple linear regression is a model that assesses the relationship between a dependent variable and one independent variable. The simple linear model is based on the following assumptions:
The simple linear regression model is expressed using the following equation:
Y = a + bX + ϵ
Where:
Y – dependent variable
X – independent (explanatory) variable
a – intercept
b – slope
ϵ – residual (error)
Multiple linear regression
Multiple linear analysis is essentially similar to the simple linear model, with the exception of multiple independent variables used in the model. The mathematical representation of the multiple linear regression is:
Y = a + bX_{1} + cX_{2 }+ dX_{3} + ϵ
Where:
Y – dependent variable
X_{1}, X_{2}, X_{3 }– independent (explanatory) variables
a – intercept
b, c, d – slopes
ϵ – residual (error)
Multiple linear regression follows the same conditions as the simple linear model. However, since there are several independent variables in multiple linear analysis, there is another mandatory condition for the model:
- Non-collinearity: Independent variables should show a minimum correlation with each other. If the independent variables are highly correlated with each other, it will be difficult to assess the true relationships between the dependent and independent variables.
Regression analysis in finance
Regression analysis offers several applications in finance. For example, the statistical method is fundamental to the Capital Asset Pricing Model (CAPM)Capital Asset Pricing Model (CAPM)The Capital Asset Pricing Model (CAPM) is a model that describes the relationship between expected return and risk of a security. CAPM formula shows the return of a security is equal to the risk-free return plus a risk premium, based on the beta of that security. This guide explains the CAPM concept with examples. Essentially, the CAPM equation is a model that determines the relationship between the expected return of an asset and the market risk premium.
The analysis is also used to forecast the returns of securities based on different factors, or forecast the performance of a business. Learn more forecasting methods in CFI’s Budgeting and Forecasting Course!
1. Beta and CAPM
In finance, regression is used to calculate the BetaBetaThe beta (β) of an investment security (i.e. a stock) is a measurement of its volatility of returns relative to the entire market. It is used as a measure of risk and is an integral part of the Capital Asset Pricing Model (CAPM). A company with a higher beta has greater risk and also greater expected returns. (volatility of returns relative to the market) for a stock. It can be done in Excel using the Slope functionSLOPE FunctionThe SLOPE Function is categorized under Statistical functions. It will return the slope of the linear regression line through the data points in known_y's and known_x's. In financial analysis, SLOPE can be useful in calculating beta for a stock. Formula = LOPE(known_y's, known_x's) The function uses the.
Download CFI’s free beta calculatorBeta CalculatorThis beta calculator allows you to measure the volatility of returns of an individual stock relative to the entire market. The beta (β) of an investment security (i.e. a stock) is a measurement of its volatility of returns relative to the entire market. It is used as a measure of risk and is an integral part of the Cap!
2. Forecasting Revenues and Expenses
When forecasting financial statementsFinancial ForecastingFinancial forecasting is the processing or estimating or predicting how a business will perform in the future. The most common type of financial forecast is an income statement, however, in a complete financial model all three statements are foretasted. In this guide on how to build a financial forecast, we build the for a company, it may be useful to do a multiple regression analysis to determine how changes in certain assumptions or drivers of the business will impact revenue or expenses in the future. For example, there may be a very high correlation between the number of salespeople employed by a company, the number of stores they operate, and the revenue the business generates.
The above example shows how to use the Forecast functionFORECAST FunctionThe FORECAST Function is categorized under Statistical functions. It will calculate or predict for us a future value using existing values. In financial modeling, the forecast function can be useful in calculating the statistical value of a forecast made. For example, if we know the past earnings and in Excel to calculate a company’s revenue based on the number of ads it runs.
Learn more forecasting methods in CFI’s Budgeting and Forecasting Course!
Additional resources
CFI offers the Financial Modeling & Valuation Analyst (FMVA)™FMVA™ CertificationThe Financial Modeling & Valueation Analyst (FMVA)™ accreditation is a global standard for financial analysts that covers finance, accounting, financial modeling, valuation, budgeting, forecasting, presentations, and strategy. certification program for those looking to take their careers to the next level. To learn more about related topics, check out the following resources:
- Cost Behavior AnalysisCost Behavior AnalysisCost behavior analysis refers to management’s attempt to understand how operating costs change in relation to a change in an organization’s level of activity. These costs may include direct materials, direct labor, and overhead costs that are incurred from developing a product.
- Financial Modeling SkillsFinancial Modeling SkillsLearn what the 10 most important financial modeling skills are and what's required to be good at financial modeling in Excel. he most important skills are 1 accounting, 2 Excel, 3 linking the financial statements, 4 forecasting, 5 problem-solving, 6 attention to detail, 7 simplicity, 8 esthetics, 9 presentations, 10
- Forecasting MethodsForecasting MethodsTop Forecasting Methods. There is a wide range of frequently used quantitative budget forecasting tools. In this article, we will explain four types of revenue forecasting methods that financial analysts use to predict future revenues. Four Types of revenue forecasting include straight-line, moving average, regression
- High-Low MethodHigh-Low MethodIn cost accounting, the high-low method is a technique used to split mixed costs into variable and fixed costs. Although the high-low method is easy to apply, it is seldom used, as it can distort costs due to its reliance on two extreme values from a given data set. Formula for the High-Low Method The formula for