1. What Are Residuals?

Residuals represent the difference between observed values and predicted values in statistical models. They are a key diagnostic tool for assessing model fit and identifying potential problems with regression models.

2. How Residuals Are Calculated

The basic residual calculation formula is:

Where:

• \( \text{observed} \) — Actual measured values (unitless)
• \( \text{predicted} \) — Values predicted by the model (unitless)

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

3. Importance of Residual Analysis

Details: Examining residuals helps verify model assumptions, detect outliers, identify non-linear relationships, and check for heteroscedasticity in regression analysis.

4. Using This Calculator

Tips: Enter comma-separated lists of observed and predicted values. Both lists must have the same number of values. The calculator will compute the difference between each pair of values.

5. Frequently Asked Questions (FAQ)

Q1: What do residuals tell us about a model?
A: Residuals show how well the model fits the data. Ideally, they should be randomly distributed around zero with no discernible pattern.

Q2: What's the difference between residuals and errors?
A: Errors refer to the difference between observed values and the true (unknown) values, while residuals are the difference between observed values and model-predicted values.

Q3: How should residuals be distributed in a good model?
A: For linear regression, residuals should be normally distributed with mean zero and constant variance (homoscedasticity).

Q4: What are standardized residuals?
A: Standardized residuals are residuals divided by their standard deviation, making them scale-free for easier comparison.

Q5: Can I use this for non-linear models?
A: Yes, the residual calculation is the same regardless of model type, though interpretation may differ for non-linear models.