How To Calculate R2 By Hand

R-squared, also known as 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. Calculating R-squared by hand is crucial for understanding the strength of the relationship between variables and the goodness of fit of your model.

1. Enter the values for X and Y in the respective input fields.
2. Enter the number of data points (N) in the provided field.
3. Click the ‘Calculate’ button to compute the R-squared value.

The formula for calculating R-squared by hand is:

R² = 1 – [(Σ(y_i – ŷ_i)²) / (Σ(y_i – ȳ)²)]

Where:

• y_i is each individual data point.
• ŷ_i is the predicted value for each data point.
• ȳ is the mean of all y values.

Comparison of R-squared values for different models

Model	R-squared
Linear Regression	0.85
Polynomial Regression (degree 2)	0.92
Polynomial Regression (degree 3)	0.95

• Interpretation: An R-squared value of 1 indicates a perfect fit, while 0 indicates no fit. Values between 0 and 1 suggest varying degrees of fit.
• Avoid overfitting: Be cautious of models with high R-squared values but poor predictive power due to overfitting.

What does a high R-squared value mean?

A high R-squared value indicates that the independent variables explain a large proportion of the variance in the dependent variable.

For more information, see the following authoritative sources:

• Stack Exchange – What does R-squared really tell us?
• Nature – The meaning and interpretation of R-squared (R²)