Calculating R Squared By Hand

Calculating R-squared by hand is a fundamental skill in data analysis and statistics. It helps you understand the strength of the relationship between two variables and the goodness of fit of your data to a regression line.

1. Enter the X and Y values, separated by commas.
2. Enter the number of data points (N).
3. Click ‘Calculate’.

The formula for calculating R-squared (coefficient of determination) is:

R² = 1 – (∑(yi – ŷi)² / ∑(yi – ȳ)²)

Where:

• yi = actual value
• ŷi = predicted value
• ȳ = mean of actual values

Sample Data

X	Y
1	2
2	4
3	6

Calculated Values

Sum of Squares	Degrees of Freedom	Mean Square
SSM	2	R²
SSE	1	1 – R²
SST	2	Total

• Always check the assumptions of your data before calculating R-squared.
• R-squared is not the only measure of model fit. Consider other metrics like adjusted R-squared and root mean squared error.

What does R-squared represent?

R-squared represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

Learn more about R-squared

Penn State’s guide to R-squared