1. What is a Residual Plot?

A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. It helps assess whether a linear regression model is appropriate for the data.

2. How to Calculate Residuals

The residual for each data point is calculated using:

Where:

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

Explanation: Residuals represent the vertical distance between each data point and the regression line. Positive residuals indicate the observed value is above the predicted value, while negative residuals indicate it's below.

3. Importance of Residual Plots

Details: Residual plots help you verify the assumptions of linear regression:

• Linearity: Residuals should be randomly scattered around zero
• Homoscedasticity: Residuals should have constant variance
• Independence: Residuals should show no patterns or trends

4. Using the Calculator

Tips:

• Enter observed and predicted values as comma-separated lists
• Both lists must have the same number of values
• The calculator will output the residuals in the same order

5. Frequently Asked Questions (FAQ)

Q1: What does a good residual plot look like?
A: A good residual plot shows points randomly scattered around the horizontal axis with no discernible pattern.

Q2: What if my residual plot shows a pattern?
A: Patterns in residuals suggest your model may be missing important variables or the relationship isn't linear.

Q3: How large should residuals be?
A: Ideally, about 95% of residuals should fall within ±2 standard deviations from zero.

Q4: Can I use this for non-linear regression?
A: The same residual calculation applies, but interpretation of patterns differs for non-linear models.

Q5: What units do residuals have?
A: Residuals have the same units as your response (dependent) variable.