1. What is a Residual?

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

2. How Does the Calculator Work?

The calculator uses the simple residual formula:

Where:

• Observed Value — The actual measured value from your data
• Predicted Value — The value predicted by your statistical model

Explanation: A positive residual means the observed value is higher than predicted, while a negative residual means it's lower than predicted.

3. Importance of Residuals

Details: Residual analysis helps assess model fit, identify outliers, check assumptions (like homoscedasticity), and improve predictive models. Small, randomly distributed residuals indicate a good model fit.

4. Using the Calculator

Tips: Enter both observed and predicted values. The values can be any real numbers (positive, negative, or zero) and can have decimal places.

5. Frequently Asked Questions (FAQ)

Q1: What do positive and negative residuals mean?
A: Positive residuals indicate the model underestimated the actual value, while negative residuals indicate overestimation.

Q2: What's the difference between residual and error?
A: Error refers to the difference between observed and true (unknown) values, while residual is between observed and model-predicted values.

Q3: How are residuals used in regression diagnostics?
A: Patterns in residual plots can reveal non-linearity, heteroscedasticity, or outliers that violate regression assumptions.

Q4: What are standardized residuals?
A: Residuals scaled by their standard deviation, making them comparable across different models or datasets.

Q5: Can residuals be zero?
A: Yes, when the model perfectly predicts an observation, though this is rare in real-world data.