Residual Calculator
Calculate the residual (prediction error) for an observation from its actual and predicted values.
Residual (e)
1.5000
Residual (e) vs Actual Value (y)
Formula
## Regression Residuals A residual is the difference between an observed value and its predicted value from the regression model. Residuals are the foundation for assessing model fit and detecting problems. ### Formula **e_i = y_i - y-hat_i** Positive residuals mean the model under-predicted; negative residuals mean over-prediction. In a well-fitting model, residuals should be randomly scattered around zero with no patterns.
Exemplo Resolvido
An observation with actual y = 25 and predicted y-hat = 23.5.
- 01Residual = 25 - 23.5 = 1.5
- 02The model under-predicted by 1.5 units.
- 03Squared residual = 1.5² = 2.25
Perguntas Frequentes
What should a good residual plot look like?
Residuals should be randomly scattered around zero with constant spread (homoscedasticity). Patterns like funnels (changing variance), curves (nonlinearity), or clusters indicate model problems.
What is a standardized residual?
Standardized residual = e_i / Se, where Se is the standard error of regression. Values beyond ±2 are potential outliers; beyond ±3 are likely outliers. They make it easier to spot unusual observations.
Do residuals sum to zero?
Yes, for models with an intercept. The sum of residuals is exactly zero, and the mean residual is zero. This is a mathematical property of least-squares regression.
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