Calcolatore Residui Avanzato
Analizza i residui della regressione con metodi avanzati per verificare il modello.
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.
Esempio Risolto
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
Domande Frequenti
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.
Impara