1. What is a Residual?

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

2. How to Calculate Residuals

The residual is calculated using the simple formula:

Where:

• Observed Value — The actual measured value from your data
• Predicted Value — 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 outliers, check assumptions (like linearity and homoscedasticity), and improve predictive models.

4. Using the Calculator

Tips: Enter both observed and predicted values (they can be any unit as residuals are unitless). The calculator will compute the difference between them.

5. Frequently Asked Questions (FAQ)

Q1: What do positive and negative residuals mean?
A: Positive means observed > predicted (underprediction), negative means observed < predicted (overprediction).

Q2: What's a "good" residual value?
A: There's no absolute standard - smaller residuals generally indicate better fit, but patterns in residuals are more important than individual values.

Q3: How are residuals used in regression diagnostics?
A: By examining residual plots, we can check for non-linearity, unequal error variances, and outliers.

Q4: What's the difference between residual and error?
A: Error refers to population, residual refers to sample. In practice, the terms are often used interchangeably.

Q5: Can residuals be standardized?
A: Yes, standardized residuals (divided by standard error) are often used to identify outliers (typically > ±2 or ±3).