How to Calculate Residual
Professional online residual calculator with step-by-step explanations. Calculate basic, standardized, and studentized residuals instantly.
Quick Residual Calculator
What is a Residual?
A residual is the difference between an observed value and the value predicted by a statistical model. In regression analysis, residuals help us understand how well our model fits the data and identify potential outliers or patterns.
Basic Residual Formula:
$$\text{Residual} = \text{Observed Value} - \text{Predicted Value}$$
$$e_i = y_i - \hat{y}_i$$
Residuals are crucial for:
- Model validation and diagnostics
- Identifying outliers and influential points
- Checking model assumptions
- Improving model performance
Our Calculator Supports
Basic Residuals
Simple difference between observed and predicted values
Standardized Residuals
Residuals divided by their standard error
Studentized Residuals
Residuals with adjusted standard errors
Batch Processing
Calculate multiple residuals at once