Unlock the Power of R-squared: Coefficient of Determination Calculator

Measure the goodness of fit for your regression models with our interactive R-squared calculator. Understand how well your model explains the data variance.

Data Inputs

Enter your data sets to calculate the R-squared value. Ensure both datasets are comma-separated and of equal length.

Dependent Variable (y) Data (e.g., 2,4,5,7,8)

Comma-separated numerical values.

Predicted y Values (ŷ) (e.g., 2.5,3.8,4.9,6.8,8.1)

Comma-separated predicted numerical values.

Result

R-squared Value:

The R-squared value, also known as the coefficient of determination, ranges from 0 to 1. It represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

R-squared = 1: Perfect fit. The model explains all the variance in the dependent variable.
R-squared = 0: No fit. The model explains none of the variance.
0 < R-squared < 1: Indicates the extent to which the variance in the dependent variable is predictable from the independent variable(s).

Formula: $$R^2 = 1 - \frac{SS_{res}}{SS_{tot}} = 1 - \frac{\sum_{i}(y_i - \hat{y}_i)^2}{\sum_{i}(y_i - \bar{y})^2}$$

Understanding R-squared

R-squared, or the coefficient of determination, is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. In simpler terms, it shows how well the data points fit a regression line.

It's a crucial metric in evaluating the performance of regression models. A higher R-squared value generally indicates a better fit, suggesting that the model is effective at predicting the dependent variable. However, R-squared doesn't tell the whole story and should be considered alongside other metrics and domain knowledge.

For further reading, you can explore resources like: