Residuals Statistics Example 4

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

Example 4

hard
A model predicts values 18, 22, and 26 for three points, while the actual values are 20, 21, and 30. Find the residuals and identify which point has the largest underprediction.

Solution

  1. 1
    Step 1: Residuals are actual minus predicted, so the residuals are 20−18=220-18=2, 21−22=−121-22=-1, and 30−26=430-26=4.
  2. 2
    Step 2: The largest underprediction is the third point because it has the largest positive residual, 44.

Answer

Residuals: 2, -1, and 4. The third point has the largest underprediction.
Positive residuals mean the model predicted too low, while negative residuals mean it predicted too high. Comparing residuals helps identify where a model fits poorly.

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 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.

← All Residuals Examples Residuals Concept

Related Concepts

Linear Regression