A small negative residual with a decimal slope

Question

A model predicts the fuel used in liters on a delivery run from the distance driven:

$\widehat{\text{fuel}} = 12 + 0.5 \cdot (\text{kilometers}).$

On a $20$ km run the van actually used $19$ liters.

What is the residual, and what does it say about that run?

Accepted Answer

Predict the fuel for a 20 km run: \widehat{	ext{fuel}} = 12 + 0.5 	imes 20 = 12 + 10 = 22. The residual is observed minus predicted: 	ext{residual} = 19 - 22 = -3. The residual is -3: the negative sign means the van used less fuel than the line predicted, 3 liters below expectation. That run was more efficient than the model's average (perhaps light traffic or a downhill route). The decimal slope does not complicate the residual at all, you predict as usual, then subtract from the observed value. Takeaway. Predict, then take observed minus predicted: 19 - 22 = -3, a negative residual meani…

A small negative residual with a decimal slope

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