1. What is Error of Regression?

The error of regression (also called residual) is the difference between an observed value and its predicted value in a regression model. It measures how far the data points are from the regression line.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( y \) — Actual observed value
• \( \hat{y} \) — Predicted value from regression model

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

3. Importance of Regression Error

Details: Analyzing residuals helps assess model fit, identify outliers, and check assumptions of regression analysis like linearity and homoscedasticity.

4. Using the Calculator

Tips: Enter both actual 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 zero error mean?
A: A zero error means the model's prediction was exactly correct for that observation.

Q2: How are residuals used in model evaluation?
A: Residuals are analyzed to check for patterns that might indicate problems with the model, such as non-linearity or heteroscedasticity.

Q3: What's the difference between error and residual?
A: In statistics, "error" refers to the theoretical difference, while "residual" is the observed difference. They're often used interchangeably in practice.

Q4: Can errors be positive and negative?
A: Yes, positive errors occur when actual > predicted, negative when actual < predicted. The sum should be zero in ordinary least squares regression.

Q5: How do you interpret large residuals?
A: Large residuals may indicate outliers or that the model doesn't adequately capture the relationship for those observations.