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R – Squared Formula

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R - Squared Formula

R – Squared Formula (Table of Contents)

  • R – Squared Formula
  • Examples of R – Squared Formula (With Excel Template)
  • R – Squared Calculator

R – Squared Formula

The R-squared formula is also known as the coefficient of determination; it is a statistical measure which determines the correlation between an investor performance and the return or the performance of the benchmark index. It basically shows what degree to a stock or portfolio performance can be attributed to a specific benchmark index. This formula is slightly different from a correlation of variable because the correlation formula shows the relationship between the dependent and the independent variable, whereas on the other hand, the R -squared formula shows to what extent the variance of one variable explains the variance of the second variable.

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A formula for R – Squared is given by:

R – Squared = 1 – (Sum of First Errors / Sum of Second Errors)

Examples of R – Squared Formula (With Excel Template)

Let’s take an example to understand the calculation of R – Squared in a better manner.

You can download this R – Squared Formula Template here – R – Squared Formula Template

Example #1

Consider the following information, and calculate the R Squared.

Example 1-1

Square of error X will be calculated as:

R - Squared Formula Example 1-2

The result will be as given below.

R - Squared Formula Example 1-3

Square of error X for all the data as given below.

R - Squared Formula Example 1-4

Similarly, We have to calculate the Square of error Y for all the data.

R - Squared Formula Example 1-5

R – Squared is calculated using the formula given below

R – Squared = 1 – (Sum of First Errors / Sum of Second Errors)

Result of Example 1

Here first, we have squared the error of the following points and have done a summation of the above problems. After that, the sum of the first error is divided by the sum of the second error and is subtracted by 1.

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The R-squared lies within the range of 0 to 1. An r -squared off 1 or 100% signifies that all the movements in the index are completely explained by the movements in the benchmark index.

Example #2

Consider the following information, and calculate the R Squared.

Example 2-1

Square of error X will be calculated as:

R - Squared Formula Example 2-2

The result will be as given below.

R - Squared Formula Example 2-3

Squared of error X for all the data as given below.

R - Squared Formula Example 2-4

Similarly, We have to calculate the Squared of error Y for all the data.

R - Squared Formula Example 2-5

R – Squared is calculated using the formula given below

R – Squared = 1 – (Sum of First Errors / Sum of Second Errors)

Result of Example 2

Example #3

Consider the following information, and calculate the R Squared.

Example 3-1

Squared of error X will be calculated as:

R - Squared Formula Example 3-2

The result will be as given below.

R - Squared Formula Example 3-3

Squared of error X for all the data as given below.

R - Squared Formula Example 3-4

Similarly, We have to calculate the Squared of error Y for all the data.

R - Squared Formula Example 3-5

R – Squared is calculated using the formula given below

R – Squared = 1 – (Sum of First Errors / Sum of Second Errors)

Result of Example 3

Relevance and Uses

  • This formula is widely being used by portfolio managers and fund managers as a measure that tells how the funds movements correlate with the benchmark index.
  • This formula is also used in the stock market industry, which tells the broker or the investor how well the stock is correlating with the overall movement of the market.
  • This formula has its own limitations as it cannot judge whether the coefficient estimates and the predictions are biased or not; hence, you just need to assess the residual plots.
  • Where R – Squared does not serve as a good comparison model to compare the goodness of the two variable, an R- Squared adjusted is used most of the time to do multiple linear regressions.
  • A low or high R- the squared number cannot always be good or bad as it does not tell the user the reliability of the model.
  • If the user has a low R-squared value, but the independent variables are statistically significant, the user can still draw important conclusions about the relationships between the variables.

R – Squared Calculator

You can use the following R – Squared Calculator

Sum of First Errors
Sum of Second Errors
R - Squared Formula
 

R - Squared Formula = 1 -(Sum of First Errors / Sum of Second Errors)
= 1 -(0 / 0) = 0

Recommended Articles

This has been a guide to R – Squared Formula. Here we discuss how to calculate R – Squared along with practical examples. We also provide R – Squared calculator with a downloadable excel template. You may also look at the following articles to learn more –

  1. Guide To Expected Return Formula
  2. How To Calculate PEG Ratio?
  3. Examples of Solvency Ratio Formula
  4. Calculator For Leverage Ratio Formula
  5. PEG Ratio | Examples | Excel Template

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