written by | November 8, 2022

Regression Analysis: Useful Concepts, Types and Examples

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Table of Content


Businesses or individuals are always looking for ways to find trends in a specific pool of data collected to show them a result of all the variables available to them. Regression analysis helps to find out those data trends and identify those certain variables which have an enormous impact on the other variables. Moreover, The various types of Regression analysis are also there to find out the trends for different variables available. Now, let’s get ahead and learn more about the meaning of Regression analysis.

Did you know? The regression analysis model is used mainly in the finance and investment industries to ascertain the strengths and relationship of one variable with the other variable.

Regression Analysis and Multiple Regression analysis Formula

Regression analysis helps in finding the trends of two sets of data. It shows the relative relationship between a set of two variables, which helps determine a regression equation or formula to benefit in forecasting or predicting the variables the business requires. 

Regression analysis is a set of statistical methods used to estimate relationships between a dependent variable and one or more independent variables. It can be utilized to assess the strength of the relationship between variables and for modelling the future relationship between them.

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Given below is the Formula for Linear Regression:

Y = Bx a

  • Where, represents the value the business or the individual is trying to forecast
  • is referred to the slope of the Regression line
  •  is referred to as the value of the independent variable
  • And representing the value of the Y-intercept.     

In the above formula, a is considered as the value of Y, a dependent variable, only if the value of x, an independent variable, is “ zero” or commonly referred to as constant. It means that even if there is no or minimal change in the GDP, The company will still be making sales.

On the other hand, Multiple Regression analysis helps see a statistically significant relationship between given sets of variables. It is almost the same as linear regression. Still, the only difference between linear regression and Multiple regression analysis is that there are more independent variables (x variables ) in multiple regression analysis. Multiple regression analysis uses multiple regression independent variables or “X variables” in its equation. The equation for multiple regression analysis is given below:

Y= b0 b1x1 b0 b1x2….b0…..b1xn

  • Where Y is representing the value the business is trying to forecast from the given set of variables
  • B is the slope of the regression line and is the dependent variable here
  • X  is the independent variable here and since multiple regression analysis has more independent variables, there are more “ x variables” in this equation compared to the linear regression equation.

Regression analysis Example and constituents of Regression Analysis

Let’s understand Regression analysis through an example in Excel tools by trying to forecast sales of a particular year considering the changes in the GDP. The below gives data on the required variables: 

Year

Sales

GDP

2015

100

1.00%

     

2016

250

1.90%

     

2017

275

2.40%

     

2018

200

2.60%

     
     

2019

300

2.90%

     

In the above table, we can see that there seems to be a positive correlation between Annual sales and the GDP since both tend to go up. While using Excel, all we need to do is click on the tools drop-down menu. Then select data analysis and then choose Regression. Then a popup box will appear containing the “Y range “ as the sales column and the “X range” as the change in the GDP column. Then all you would need to do is choose the specific output range from where you want the detailed data to show up on your spreadsheet and then press OK, and finally, the GDP will show that if GDP increases by 1%, then the sales will grow by 88.12 units.

Covariance is an essential part of regression analysis. The formula to calculate Covariance is as follows:

Cov(x,y)=∑N(xn−xu)(yn−yu)

The formula mentioned above represents that if there is an increase in one variable, and the other variable also increases, then the covariance will be deemed to be positive. On the contrary, if one variable increases or goes up, and the other variable goes down, then covariance will be deemed negative.

Covariance also needs to be standardized to interpret trends better, which can be ascertained with the correlation calculation. The formula of the Correlation coefficient is:

Correlation=ρxy= Covxy/ SxSy

In the above formula, a correlation of 1 can be interpreted as suggesting that both variables are moving positively towards each other, and a -1 will imply that the variables are negatively correlated.

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Types of Regression Analysis and Use of Regression Analysis

There are various methods or types of Regression analysis used to predict or forecast business trends, which are:

  •  Linear Regression Analysis

It is the most common and extensively used kind of regression analysis method, which has an independent as well as a dependent variable. It is mostly used when the variable is considered to be in a linear pattern, and linear analysis can also be wrongly interpreted or ascertained because of fluctuations in data or various other aberrations.

Linear regression analysis is based on six fundamental assumptions:

  1. The dependent and independent variables show a linear relationship between the slope and the intercept.
  2. The independent variable is not random.
  3. The value of the residual (error) is zero.
  4. The value of the residual (error) is constant across all observations.
  5. The value of the residual (error) is not correlated across all observations.
  6. The residual (error) values follow the normal distribution.

          An example of Linear Regression analysis is to find the trends of the number of AC being sold 

  • Non-linear Regression

Non-linear regression is a regression analysis method to predict a target variable using a non-linear function consisting of parameters and one or more independent variables. Non-linear regression is often more accurate as it learns the variations and dependencies of the data.

Non-linear functions can be very confusing for beginners. For example, let’s check out the following function.

Here are a few examples of non-linear equations:

Certain nonlinear functions can be modified with algebra to mimic the linear format. For example,

This equation can be rewritten as-

Y = f(X,β) + ϵ

Where: X is a vector of P predictors. β is a vector of k parameters. F (-) is the known regression function.

Such non-linear functions that can be rewritten as linear functions are said to be intrinsically linear.

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  • Multiple linear Regression

To calculate the association between two or more independent variables and one dependent variable, utilise multiple linear regression. Multiple linear regression can be used to determine:

How closely two or more independent variables are related to one dependent variable (e.g. how rainfall, temperature, and amount of fertiliser added affect crop growth).

The dependent variable's value at a particular level of the independent variables (e.g. the expected yield of a crop at certain levels of rainfall, temperature, and fertiliser addition).

The same presumptions that underlie basic linear regression also apply to multiple linear regression:

Homogeneity of variance (homoscedasticity): Our prediction's error size does not significantly vary when the independent variable's values change.

Independence of observations: There are no unreported correlations between variables among the observations in the dataset, which were obtained using statistically sound methods.

In this case, it's plausible that some of the independent variables are in fact associated. Only one independent variable should be utilised in the regression model if the correlation between the other two is too high (r2 > 0.6).

Normality: The data exhibits normality, with a normal distribution.

Linearity: Rather than a curve or other grouping feature, a straight line provides the greatest fit through the data points.

The formula for multiple linear regression is:

 y = b1x1 + b2x2 + … + bnxn + c.

The regression coefficients, in this case, called bi's (i=1,2,..., n), show the point at which the criterion variable changes when the predictor variable does.

Use of Regression Analysis In the Following ways

  • Optimizing business

To ensure proper usage of the data collected and use it to forecast future trends in business.

  • Predictive Analysis

To stay ahead of the cutthroat competition is why regression analysis is used to predict future business trends.

  • Decision making 

For the firm since the figures or future trends collected from the data through regression analysis alert a business of possible future mishappenings, because of which a firm can make sound business decisions to ensure sustenance in the future.

  • Understanding Failures

 Regression analysis helps a business in Understanding failures in a quantitative manner, with the help of collected data and the future trends ascertained through various methods of Regression analysis. 

  • Business Success

 Regression analysis helps predict the success of a business since strong future trends from the collected aid could ensure that the business will achieve its long-term goals and be in a position of authority in the industry. 

Also Read: Understand Cash Accounting - Cash Account Meaning, Advantages And Limitations

Conclusion:

Regression analysis provides an equation for a graph so that you can make predictions about your data. Regression analysis can also be considered a way to sort out those variables mathematically and does indeed have an impact. Considering multiple variables' impact at once is one of the biggest advantages of regression analysis.

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FAQs

Q: What are the four uses of Regression analysis in today’s business world?

Ans:

The uses of regression analysis in Businesses today are as follows:

1. To help in Optimizing business

2. To Help in Predictive analysis

3. To help in the future decision-making of the firm.

4. To help the business understand failures in its policies or methods.

Q: What are the various types of Regression analysis?

Ans:

The various types of Regression analysis are

1. Linear Regression analysis

2. Logistic Regression analysis

3. Lasso Regression analysis

4. Ridge Regression analysis

5. Polynomial Regression analysis

Q: What are the constituents of Regression analysis and their formula?

Ans:

The constituents of regression analysis are 

1. Covariance, its formula is Cov(x,y)=∑N(xn−xu)(yn−yu)

2. The correlation coefficient, its formula is Correlation=ρxy= Covxy/ SxSy

Q: What does Regression analysis mean?

Ans:

Regression analysis helps in finding the trends of two sets of data. It shows the relative relationship between a set of two variables.

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Disclaimer :
The information, product and services provided on this website are provided on an “as is” and “as available” basis without any warranty or representation, express or implied. Khatabook Blogs are meant purely for educational discussion of financial products and services. Khatabook does not make a guarantee that the service will meet your requirements, or that it will be uninterrupted, timely and secure, and that errors, if any, will be corrected. The material and information contained herein is for general information purposes only. Consult a professional before relying on the information to make any legal, financial or business decisions. Use this information strictly at your own risk. Khatabook will not be liable for any false, inaccurate or incomplete information present on the website. Although every effort is made to ensure that the information contained in this website is updated, relevant and accurate, Khatabook makes no guarantees about the completeness, reliability, accuracy, suitability or availability with respect to the website or the information, product, services or related graphics contained on the website for any purpose. Khatabook will not be liable for the website being temporarily unavailable, due to any technical issues or otherwise, beyond its control and for any loss or damage suffered as a result of the use of or access to, or inability to use or access to this website whatsoever.