# What is R-Squared?

Updated on September 25, 2023 , 718 views

R-squared (R2) is one statistical measure that signifies the variance proportion for a dependent variable that is elucidated by an independent variable. Considering that correlation talks about the relationship strength between a dependent and independent variable, R-squared is a concept that explains the extent to which the variance of one variable has explained the variance of the second variable.

Thus, if a model’s R2 is 0.50, then possibly half of the pragmatic variation is explained by the inputs of the model. In the investment domain, R-squared is basically understood as a fund’s percentage or the movements of security that can be clarified by the movements happening in the benchmark index.

### The R-squared formula is:

R2=1−Unexplained Variation/Total Variation

## How to Calculate R-Squared?

The real R-squared calculation needs different steps. This comprises taking the observation (data points) of independent and dependent variables and discovering the best fit line, generally from a regression model.

From there, you can easily find forecasted values, subtract the real values and square the outcome. This brings a list of errors squared, which is totalled and equals the unsolved variance. For calculating the total variance, you will have to minus the average real value from all of the actual values, square the outcome and total them.

Then, from there, you’d have to divide the first total of errors, which is the explained variance, by the second total, which is the total variance, minus the outcome from one and you’ll have R-squared.

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## What Does R-Squared Indicate?

The values of R-squared Range anywhere from 0 to 1. Also, they are commonly stated in the form of a percentage, which is from 0% to 100%. If an R-squared is 100%, it means that all of the security’s movements are explained in the index by the movements.

In terms of Investing, a high R-squared, which is anywhere between 85% to 100%, signifies the performance of the fund or the stock that is moving in line with the index. A fund that has a low R-squared, around 70% or lesser, signifies that the security doesn’t follow the index’s movements.

On the other hand, a high R-squared value indicates a better and useful Beta figure. For instance, if a fund or a stock has an R-squared value closer to 100% but a beta value of lesser than 1, it is likely to offer high risk-adjusted returns.

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