Residuals Statistics Example 3

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

Example 3

hard
Given y^=20+4x\hat{y} = 20 + 4x and actual data points (2, 30), (3, 33), (4, 35), find the residual for each point.

Solution

  1. 1
    Step 1: Predictions: y^(2)=28\hat{y}(2) = 28, y^(3)=32\hat{y}(3) = 32, y^(4)=36\hat{y}(4) = 36.
  2. 2
    Step 2: Residuals: 30−28=230-28=2, 33−32=133-32=1, 35−36=−135-36=-1.

Answer

Residuals: 2, 1, −1.
Computing residuals for each data point lets us assess how well the regression line fits individual observations.

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 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