Free Residual Calculator
Calculate the residual (prediction error) as the difference between the observed and predicted values in regression.
Residual
4.000000
Predicted Value (y-hat)41.0000
|Residual|4.000000
Squared Residual16.0000
Residual vs Observed Value (y)
How to Calculate a Residual
Formula
Residual = Observed - Predicted = y - y_hat
where y_hat = b0 + b1*x
A residual is the vertical distance between an observed data point and the regression line. Positive residuals mean the point is above the line; negative means below. In least-squares regression, the sum of all residuals is zero. Examining residuals helps detect model violations.
Example Calculation
Regression: y = 5 + 2x. At x = 18, the observed y = 45.
- 01Predicted y_hat = 5 + 2*18 = 5 + 36 = 41
- 02Residual = 45 - 41 = 4
- 03The observed value is 4 units above the regression line
- 04Squared residual = 4^2 = 16
Frequently Asked Questions
Learn More
Understanding the Normal Distribution
Learn what the normal distribution is, why it matters in statistics, and how to use the bell curve for probability calculations, z-scores, and real-world data analysis.