This coefficient of determination calculator tool will help you determine the proportion of variance in the dependent variable that can be predicted from the independent variable.

## How it Works

The Coefficient of Determination (R^{2}) Calculator computes the proportion of the variance in the dependent variable (Y) that is predictable from the independent variable(s). It is a key output of regression analysis and ranges from 0 to 1.

## How to Use the Calculator

Enter the actual Y values and the predicted Y values separated by commas in their respective fields and click “Calculate”. The calculator will return the R^{2} value which represents the goodness of fit of the regression model. Higher values indicate a better fit.

## How the Result is Calculated

The calculator computes the sum of squares total (SST), which is the total variance in Y. It also calculates the sum of squares due to error (SSE), which represents the variance in Y not explained by the model. R^{2} is then calculated as *1 – SSE/SST*. If SSE is 0, the R^{2} will be 1, indicating a perfect fit.

## Limitations

The calculator assumes that the input data are numerical and that the length of Y values and predicted Y values are the same. Non-numerical values or mismatched lengths will cause erroneous calculations. Furthermore, a high R^{2} value does not necessarily mean the model is the best fit, as it does not account for the complexity of the model or the number of predictors.