# R-squared (R2) – Formula | Example | Calculation

## R-squared (R2)

R-squared, known as the coefficient of determination. For the statistical measurement of the correlation between the performance of the investment and the specific benchmark index, this calculation is used.

#### Definition: What is R-squared (R2)?

At the model comparing time, R-squared is used for the determination that how will the line fits with the data set of observations. In the following figures, we can see how well the line follow variation within the set of data.

## Formula

We can calculate the R-square (R2) formula by subtracting the derivation of the first sum of errors and the second sum of errors from 1.

#### R-square = 1 – ( First sum of errors – Second sum of errors)

For the set of the data point, this is the last step in calculating the R-squared. Before getting to this point there are many steps.

## Analysis and Interpretation

#### What is R-squared use for?

For the comparing of the performance of the portfolio with the broader market, Investor use this ratio mostly. Also, it predicts the trend which might occur in the future.

We take the example of investors now which purchase the investment fund that is correlated with S&P 500 strongly. The investor will look that fund which r-square value close to 1. if the value is closer to 1 then it is more correlated.

Assume that there are 3 funds with R2 values of 0.5, 0.7, and 0.9. Investor chooses the 0.9 value because it is close to 1 so it is more correlated to the S&P 500.