Residuals Statistics Example 1

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

Example 1

hard
A regression model predicts y^=30\hat{y} = 30 for a data point, but the actual value is y=35y = 35. Calculate the residual and interpret it.

Solution

  1. 1
    Step 1: Residual = y−y^=35−30=5y - \hat{y} = 35 - 30 = 5.
  2. 2
    Step 2: A positive residual means the model underestimated — the actual value is 5 units above the predicted value.
  3. 3
    Step 3: The data point lies above the regression line.

Answer

Residual = 5. The model underestimated by 5 units.
Residuals measure the vertical distance between observed values and the regression line. Positive residuals indicate the point is above the line; negative residuals indicate it is below.

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 2 hard

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

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