Residuals Statistics Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

hard
A residual plot shows a clear U-shaped pattern. What does this indicate about the regression model?

Solution

  1. 1
    Step 1: Ideally, residuals should be randomly scattered around zero with no pattern.
  2. 2
    Step 2: A U-shaped pattern indicates the relationship is not linear — a curved model may fit better.
  3. 3
    Step 3: The linear model systematically overestimates in some regions and underestimates in others.

Answer

A U-shaped residual plot indicates the linear model is inappropriate; the data has a non-linear relationship.
Residual plots are diagnostic tools. Random scatter confirms a linear model is appropriate; patterns (curves, fans) signal violations of assumptions.

About Residuals

A residual is the difference between an observed data value and the value predicted by a statistical model, calculated as residual=yobserved−ypredicted\text{residual} = y_{\text{observed}} - y_{\text{predicted}}. Positive residuals mean the model underestimated; negative residuals mean it overestimated.

Learn more about Residuals →

More Residuals Examples

Example 1 hard

A regression model predicts [formula] for a data point, but the actual value is [formula]. Calculate

Example 3 hard

Given [formula] and actual data points (2, 30), (3, 33), (4, 35), find the residual for each point.

Example 4 hard

A model predicts values 18, 22, and 26 for three points, while the actual values are 20, 21, and 30.

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Related Concepts

Linear Regression