1. What is a Residual?

A residual is the difference between an observed value and the value predicted by a model. Residuals are fundamental in regression analysis and model diagnostics.

2. How Does the Calculator Work?

The calculator uses the simple residual formula:

Where:

• \( \text{observed} \) — The actual measured value
• \( \text{predicted} \) — The value predicted by your model

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

3. Importance of Residuals

Details: Residual analysis helps assess model fit, identify patterns in prediction errors, and detect outliers or violations of modeling assumptions.

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 does a residual plot show?
A: A residual plot graphs residuals against predicted values to reveal patterns that might indicate problems with the model.

Q2: What's an ideal residual pattern?
A: Ideally, residuals should be randomly scattered around zero with no discernible pattern.

Q3: What if my residuals show a pattern?
A: Patterns may suggest non-linearity, heteroscedasticity, or that important variables were omitted from the model.

Q4: How large should residuals be?
A: There's no universal standard - it depends on your data scale and measurement precision.

Q5: Can I use this for multiple residuals?
A: This calculates single residuals. For multiple points, you'd need to calculate each separately or use statistical software.