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All courses Math I · S-ID.6.b 55 of 59
Assess model fit informally using residuals.

Calculate a residual from an observed value and a predicted value

Problem
An observed value is 18 and the predicted value is 15. Find the residual.
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Hint

Use the residual formula \(observed - predicted\).

Residuals keep the sign of the difference. If the observed value is larger than the predicted value, the residual is positive.

Solution walkthrough

01

Write the residual definition

\[\text{residual}=\text{observed}-\text{predicted}\]

Residual subtraction always starts with the observed output so its sign has a consistent meaning.

02

Substitute the values

\[\text{residual}=18-15\]

The observed value is 18 and the model prediction is 15.

03

Compute and interpret the sign

\[18-15=3\]

The positive residual means the observed value is 3 above the prediction.

04

State the residual

\[3\]

The residual is 3.

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Another way

  1. Ask how much must be added to 15 to reach 18; the required change is positive 3.

!

Common mistake

Do not reverse the subtraction to 15-18. Residual means observed minus predicted.