R-Squared (Coefficient of Determination) Calculator
Calculate R-squared from paired X and Y data to determine what proportion of the variance in your dependent variable is explained by the linear regression model. This tool also provides the adjusted R² and the Pearson correlation coefficient.
The coefficient of determination (R²) is one of the most widely reported statistics in regression analysis. It ranges from 0 to 1, where 0 means the model explains none of the variability in the response variable and 1 means it explains all of it. For example, an R² of 0.85 means 85% of the variance in Y is accounted for by the linear relationship with X.
R² is calculated as R² = 1 - (SS_res / SS_tot), where SS_res is the sum of squared residuals (the differences between observed and predicted values) and SS_tot is the total sum of squares (the differences between observed values and the mean). This approach works directly from the data without needing to compute the correlation coefficient first.
The adjusted R² corrects for the number of predictors in the model. In simple linear regression with one predictor, the adjustment is minor, but in multiple regression it prevents the false inflation of R² that occurs when adding irrelevant variables. A decreasing adjusted R² when a new variable is added is a signal that the variable does not improve the model.