Coefficient of Determination (R²)

= −

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Calculate

Example: five students studied 1, 2, 3, 4 and 5 hours for an exam and scored 52, 58, 65, 70 and 80. How much of the variation in the scores do the hours of study explain? Change the values to work out your own case.

Values of x One value per observation, separated by spaces or commas. Values of y In the same order as the x values.

Step by step

What each term means

Coefficient of Determination (R²): The share of the variation in y that the line explains, from 0 to 1. R² = 0.9 means 90% of the variation goes away once x is taken into account.
One Minus the Residual Share: Everything except what the line doesn't explain. Since the total variation splits exactly into an explained part and a residual part, subtracting the residual share from 1 gives the explained share.
Residual Sum of Squares: The variation left after the line: the distance from each y to its predicted value ŷ, squared. It is what the least-squares line makes as small as possible.
Total Sum of Squares: The variation of y around its own mean, without using x. It is the yardstick: how much there would be to explain.