Statistics & Probability
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Residual Calculator.
Calculate the difference between an observed value and its entered prediction.
Set your values
Results update as you type.
Residual = observed − predicted. This calculator does not fit a regression model or provide residual diagnostics; both values are supplied directly.
Results update automatically as you type.
Use Cases
Evaluate model accuracy
Use residuals to assess how well a regression model fits your data. Smaller residuals indicate better predictions.
Example: After fitting a linear model, compute residuals for each data point to spot outliers.
Check assumptions in regression
Residual analysis helps verify that model assumptions like homoscedasticity and normality hold.
Example: Plot residuals vs. fitted values to detect patterns that suggest model misspecification.
Frequently Asked Questions
- What is a residual in statistics?
- A residual is the difference between an observed value and the value predicted by a model. It shows how far off the prediction is for a single data point. A positive residual means the observed value is higher than predicted, while a negative residual means it is lower.
- How do I calculate a residual?
- Enter the observed value and the predicted value into the calculator. The residual is simply the observed value minus the predicted value. The calculator also shows the absolute error, which is the magnitude of the residual without the sign.
- What does the absolute error tell me?
- The absolute error is the absolute value of the residual. It tells you the size of the prediction error regardless of direction. For example, a residual of -5 and +5 both have an absolute error of 5, meaning the prediction was off by 5 units.
Tips & Common Mistakes
Tips
- Ensure you enter the observed and predicted values in the same units to get a meaningful residual.
- Use the absolute error to compare prediction accuracy across different data points without worrying about sign.
- If you have many data points, compute residuals for each to identify which predictions are most off.
- Remember that a residual of zero means the prediction exactly matches the observed value.
Common Mistakes to Avoid
- Swapping the observed and predicted values, which changes the sign of the residual.
- Forgetting that the residual is observed minus predicted, not the other way around.
- Ignoring the absolute error when you only need the magnitude of the error.
Last updated: August 13, 2026