1. What is a Residual?

A residual is the difference between an observed value and its predicted value in regression analysis. It represents the error in prediction and is a key component in assessing model fit.

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 regression model

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

3. Importance of Residuals

Details: Residual analysis helps evaluate regression model assumptions, identify outliers, and check for patterns that might suggest model misspecification.

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 (underprediction), negative means actual < predicted (overprediction).

Q2: How are residuals used in model evaluation?
A: Examining residual patterns helps assess whether linear regression assumptions are met.

Q3: What's the ideal residual value?
A: Ideally residuals should be small and randomly distributed around zero.

Q4: Can residuals be standardized?
A: Yes, standardized residuals adjust for differences in variability and are useful for outlier detection.

Q5: How do residuals relate to R-squared?
A: R-squared measures the proportion of variance explained by the model, calculated from residuals.