1. What is a Statistical Residual?

A residual is the difference between an observed value and the value predicted by a statistical model. It represents the error in the prediction and is a fundamental concept in regression analysis.

2. How Does the Calculator Work?

The calculator uses the simple residual formula:

Where:

• \( y \) — Observed value
• \( \hat{y} \) — Predicted value from the model
• \( res \) — Residual (difference between observed and predicted)

Explanation: Positive residuals indicate the model underestimated the actual value, while negative residuals indicate overestimation.

3. Importance of Residual Calculation

Details: Residuals are crucial for assessing model fit, identifying outliers, checking assumptions in regression analysis, and improving predictive models.

4. Using the Calculator

Tips: Enter both observed and predicted values. The calculator will compute the difference (residual). Values can be positive or negative.

5. Frequently Asked Questions (FAQ)

Q1: What do positive and negative residuals mean?
A: Positive means actual > predicted (underestimation), negative means actual < predicted (overestimation).

Q2: What's considered a "good" residual?
A: Smaller residuals generally indicate better model fit, but interpretation depends on context and scale of the data.

Q3: How are residuals used in model diagnostics?
A: Patterns in residuals can reveal non-linearity, heteroscedasticity, or other model deficiencies.

Q4: What's the difference between residual and error?
A: Error refers to population-level discrepancies, while residuals are sample-level differences between observed and predicted values.

Q5: Can residuals be standardized?
A: Yes, standardized residuals adjust for differences in scale and are useful for comparing across different models.