WallStreetMojo

WallStreetMojo

WallStreetMojo

MENUMENU
  • Blog
  • Free Video Tutorials
  • Courses
  • All In One Bundle
  • Login
Home » Financial Modeling Tutorials » Excel Modeling » Coefficient of Determination

Coefficient of Determination

By Madhuri ThakurMadhuri Thakur | Reviewed By Dheeraj VaidyaDheeraj Vaidya, CFA, FRM

By Madhuri Thakur

What is the Coefficient of Determination?

Coefficient of determination, also known as R Squared determines the extent of the variance of the dependent variable which can be explained by the independent variable. By looking at R^2 value one can judge whether the regression equation is good enough to be used. Higher the coefficient better the regression equation as it implies that the independent variable chosen in order to determine the dependent variable is chosen properly.

Detailed Explanation

Coefficient of Determination

Coefficient of Determination Formula

Where

  • R= Correlation
  • R^2= Coefficient of determination of the regression equation
  • N= Number of observations in the regression equation
  • Xi= Independent variable of the regression equation
  • X= Mean of the independent variable of the regression equation
  • Yi= Dependent variable of the regression equation
  • Y= Mean of the dependent variable of the regression equation
  • σx = Standard deviation of the independent variable
  • σy = Standard deviation of the dependent variable

The value of the coefficient ranges from 0 to 1, where a value of 0 indicates that the independent variable does not explain the variation of the dependent variable, and a value of 1 indicates that the independent variable perfectly explains the variation in the dependent variable.

Examples

You can download this Coefficient of Determination Formula Excel Template here – Coefficient of Determination Formula Excel Template

Example #1

Let us try and understand the coefficient of determination formula with the help of an example. Let us try to find out what is the relation between the distance covered by the truck driver and the age of the truck driver. Someone actually does a regression equation to validate whether what he thinks of the relationship between two variables is also validated by the regression equation. In this particular example, we will see which variable is the dependent variable and which variable is the independent variable.

The dependent variable in this regression equation is the distance covered by the truck driver, and the independent variable is the age of the truck driver. We can find the correlation with the help of the formula and square that to get the coefficient of the regression equation. The data set and the variables are presented in the excel sheet attached.

Solution:

Below is given data for calculation of the coefficient of determination.

Popular Course in this category
Sale
All in One Financial Analyst Bundle (250+ Courses, 40+ Projects)
4.9 (1,067 ratings)
250+ Courses | 40+ Projects | 1000+ Hours | Full Lifetime Access | Certificate of Completion
View Course

Coefficient of Determination Formula Example 1

Therefore, the calculation of the coefficient of determination is as follows,

Example 1-1

R = -424520/√(683696*81071100)

R will be –

Coefficient of Determination Formula Example 1.1.2

R = -0.057020839

R^2 will be –

Example 1.2

R^2 = 0.325%

Example #2

Let us try and understand the concept of coefficient of determination with the help of another example. Let us try to find out what is the relation between the height of the students of a class and the GPA grade of those students. In this particular example, we will see which variable is the dependent variable and which variable is the independent variable.

The dependent variable in this regression equation is the GPA of the students, and the independent variable is the height of the students. We can find the correlation with the help of the formula and square that to get the R^2 of the regression equation. The data set and the variables are presented in the excel sheet attached.

Solution:

Below is given data for calculation of the coefficient of determination.

Coefficient of Determination Formula Example 2

Therefore, the calculation is as follows,

Example 2.1

R = 34.62/√(169204*3245)

Coefficient of Determination Formula Example 2.2

R = 0.000467045

Example 2.3

R^2 = 0.000000218

Interpretation

The coefficient of determination is a critical output to find out whether the data set is a good fit or not. Someone actually does a regression analysis to validate whether what he thinks of the relationship between two variables is also validated by the regression equation. The higher the coefficient better the regression equation as it implies that the independent variable chosen to determine the dependent variable is chosen properly. Ideally, a researcher will look for the coefficient of determination, which is closest to 100%.

Recommended Articles

This article has been a Guide to the Coefficient of Determination. Here we learn how to calculate the coefficient of determination using its formula with examples and a downloadable excel template. You can learn more about financing from the following articles –

  • Gini Coefficient
  • Formula of Multiple Regression
  • Formula for Coefficient of Variation
  • Formula for Correlation Coefficient
  • Payback Period Advantages and Disadvantages
0 Shares
Share
Tweet
Share
All in One Financial Analyst Bundle (250+ Courses, 40+ Projects)
  • 250+ Courses
  • 40+ Projects
  • 1000+ Hours
  • Full Lifetime Access
  • Certificate of Completion
LEARN MORE >>

Category iconExcel Modeling,  Financial Modeling Tutorials

Primary Sidebar
Footer
COMPANY
About
Reviews
Contact
Privacy
Terms of Service
RESOURCES
Blog
Free Courses
Free Tutorials
Investment Banking Tutorials
Financial Modeling Tutorials
Excel Tutorials
Accounting Tutorials
Financial Statement Analysis
COURSES
All Courses
Financial Analyst All in One Course
Investment Banking Course
Financial Modeling Course
Private Equity Course
Venture Capital Course
Excel All in One Course

Copyright © 2021. CFA Institute Does Not Endorse, Promote, Or Warrant The Accuracy Or Quality Of WallStreetMojo. CFA® And Chartered Financial Analyst® Are Registered Trademarks Owned By CFA Institute.
Return to top

WallStreetMojo

Free Investment Banking Course

IB Excel Templates, Accounting, Valuation, Financial Modeling, Video Tutorials

* Please provide your correct email id. Login details for this Free course will be emailed to you

Book Your One Instructor : One Learner Free Class
WallStreetMojo

Free Investment Banking Course

IB Excel Templates, Accounting, Valuation, Financial Modeling, Video Tutorials

* Please provide your correct email id. Login details for this Free course will be emailed to you

Let’s Get Started
Please select the batch
Saturday - Sunday 9 am IST to 5 pm IST
Saturday - Sunday 9 am IST to 5 pm IST

This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy

Login

Forgot Password?

WallStreetMojo

Download Coefficient of Determination Formula Excel Template

Special Offer - All in One Financial Analyst Bundle (250+ Courses, 40+ Projects) View More