1. What is Standardized Residual?

The standardized residual is a statistical measure that indicates how many standard deviations an observed value deviates from its predicted value in regression analysis. It helps identify outliers and assess model fit.

2. How Does the Calculator Work?

The calculator uses the standardized residual formula:

Where:

• \( res \) — Residual (observed - predicted value)
• \( MSE \) — Mean squared error of the regression model
• \( h \) — Leverage value (0 ≤ h < 1)

Explanation: The formula adjusts the raw residual by the model's overall error (MSE) and the observation's leverage, providing a standardized measure of deviation.

3. Importance of Standardized Residuals

Details: Standardized residuals are crucial for diagnosing regression models, identifying outliers, checking homoscedasticity assumptions, and validating model appropriateness.

4. Using the Calculator

Tips: Enter the residual value (can be positive or negative), the model's MSE (must be positive), and the leverage value (between 0 and 1). All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: What's a "large" standardized residual?
A: Typically, values beyond ±2 are considered potentially unusual, and beyond ±3 are likely outliers.

Q2: How is this different from studentized residuals?
A: Studentized residuals use a modified MSE calculation that excludes the current observation, making them more sensitive to outliers.

Q3: When should I check standardized residuals?
A: Always examine them after fitting a regression model to check assumptions and identify problematic observations.

Q4: What does high leverage (h) indicate?
A: High leverage points are observations with unusual predictor values that can disproportionately influence the regression results.

Q5: Can standardized residuals be used for model comparison?
A: While primarily diagnostic, patterns in residuals can suggest one model fits better than another for certain data characteristics.