The field of Artificial Intelligence and machine learning is set to conquer most of the human disciplines; from art and literature to commerce and sociology; from computational biology and decision analysis to games and puzzles.” ~Anand Krish
Regression analysis is a way to find trends in data.
For example, you might guess that there’s a connection between how much you eat and how much you weigh; regression analysis can help you quantify that equation.
Regression analysis will provide you with an equation for a graph so that you can make predictions about your data.
For example, if you’ve been putting on weight over the last few years, it can predict how much you’ll weigh in ten years time if you continue to put on weight at the same rate.
It will also give you a slew of statistics (including a p-value and a correlation coefficient) to tell you how accurate your model is.
Introduction to Regression Analysis
Regression analysis is a statistical technique for analysing and comprehending the connection between two or more variables of interest. The methodology used to do regression analysis aids in understanding which elements are significant, which may be ignored, and how they interact with one another.
Regression is a statistical approach used in finance, investment, and other fields to identify the strength and type of a connection between one dependent variable (typically represented by Y) and a sequence of other variables (known as independent variables).
Regression analysis is a mathematical method for determining which of those factors has an effect. It provides answers to the following questions:
Which factors are most important
Which of these may we disregard
How do those elements interact with one another, and perhaps most significantly, how confident are we in all of these variables
These elements are referred to as variables in regression analysis. You have your dependent variable, which is the key aspect you're attempting to understand or forecast. Then there are your independent variables, which are the elements you assume have an effect on your dependent variable.
(Most related blog: 7 Types of Regression Techniques in ML)
Types of Regression Analysis
Types of regression analysis
The relationship between a dependent variable and a single independent variable is described using a basic linear regression methodology. A Simple Linear Regression model reveals a linear or slanted straight line relation, thus the name.
The simple linear model is expressed using the following equation:
Y = a + bX + ϵ
- Y – variable that is dependent
- X – Independent (explanatory) variable
- a – Intercept
- b – Slope
- ϵ – Residual (error)
The dependent variable needs to be continuous/real, which is the most crucial component of Simple Linear Regression. On the other hand, the independent variable can be evaluated using either continuous or categorical values.
Multiple linear regression
Multiple linear regression (MLR), often known as multiple regression, is a statistical process that uses multiple explanatory factors to predict the outcome of a response variable.
MLR is a method of representing the linear relationship between explanatory (independent) and response (dependent) variables.
The mathematical representation of multiple linear regression is:
y=ß0+ ß1 x1+ …………..ßn xn + ϵ
Where, y = the dependent variable’s predicted value
B0 = the y-intercept
B1X1= B1 is the coefficient for regression of the first independent variable X1 (The effect of increasing the independent variable's value on the projected y value is referred to as X1.)
… = Repeat for as many independent variables as you're testing.
BnXn = the last independent variable's regression coefficient
ϵ = model error (i.e. how much flexibility is there in our y estimate)
Multiple linear regression uses the same criteria as single linear regression. Due to the huge number of independent variables in multiple linear regression, there is an extra need for the model:
The absence of a link between two independent variables with a low correlation is referred to as non-collinearity. It would be hard to determine the true correlations between the dependent and independent variables if the independent variables were strongly correlated.
(Related blog: Pearson’s Correlation Coefficient ‘r’)
A sort of regression analysis in which data is fitted to a model and then displayed numerically is known as nonlinear regression.
Simple linear regression connects two variables (X and Y) in a straight line (y = mx + b), whereas nonlinear regression connects two variables (X and Y) in a nonlinear (curved) relationship.
The goal of the model is to minimise the sum of squares as much as possible. The sum of squares is a statistic that tracks how much Y observations differ from the nonlinear (curved) function that was used to anticipate Y.
In the same way that linear regression modelling aims to graphically trace a specific response from a set of factors, nonlinear regression modelling aims to do the same.
Because the function is generated by a series of approximations (iterations) that may be dependent on trial-and-error, nonlinear models are more complex to develop than linear models.
The Gauss-Newton methodology and the Levenberg-Marquardt approach are two well-known approaches used by mathematicians.
(Must check: Statistical Data Analysis)
What are applications of Regression Analysis?
Most of the regression analysis is done to carry out processes in finances. So, here are 5 applications of Regression Analysis in the field of finance and others relating to it.
Applications of regression analysis
The most common use of regression analysis in business is for forecasting future opportunities and threats. Demand analysis, for example, forecasts the amount of things a customer is likely to buy.
When it comes to business, though, demand is not the only dependent variable. Regressive analysis can anticipate significantly more than just direct income.
For example, we may predict the highest bid for an advertising by forecasting the number of consumers who would pass in front of a specific billboard.
Insurance firms depend extensively on regression analysis to forecast policyholder creditworthiness and the amount of claims that might be filed in a particular time period.
The Capital Asset Pricing Model (CAPM), which establishes the link between an asset's projected return and the related market risk premium, relies on the linear regression model.
It is also frequently used in financial analysis by financial analysts to anticipate corporate returns and operational performance.
The beta coefficient of a stock is calculated using regression analysis. Beta is a measure of return volatility in relation to total market risk.
Because it reflects the slope of the CAPM regression, we can rapidly calculate it in Excel using the SLOPE tool.
Comparing with competition:
It may be used to compare a company's financial performance to that of a certain counterpart.
It may also be used to determine the relationship between two firms' stock prices (this can be extended to find correlation between 2 competing companies, 2 companies operating in an unrelated industry etc).
It can assist the firm in determining which aspects are influencing their sales in contrast to the comparative firm. These techniques can assist small enterprises in achieving rapid success in a short amount of time.
Regression is useful not just for providing factual evidence for management choices, but also for detecting judgement mistakes.
A retail store manager, for example, may assume that extending shopping hours will significantly boost sales.
However, RA might suggest that the increase in income isn't enough to cover the increase in operational cost as a result of longer working hours (such as additional employee labour charges).
As a result, this research may give quantitative backing for choices and help managers avoid making mistakes based on their intuitions.
Many businesses and their top executives are now adopting regression analysis (and other types of statistical analysis) to make better business decisions and reduce guesswork and gut instinct.
Regression enables firms to take a scientific approach to management. Both small and large enterprises are frequently bombarded with an excessive amount of data.
Managers may use regression analysis to filter through data and choose the relevant factors to make the best decisions possible.
For a long time, regression analysis has been utilised extensively by enterprises to transform data into useful information, and it continues to be a valuable asset to many leading sectors.
The significance of regression analysis lies in the fact that it is all about data: data refers to the statistics and statistics that identify your company.
The benefits of regression analysis are that it allows you to essentially crunch the data to assist you make better business decisions now and in the future.