Computing a residual, observed minus predicted

Question

A model predicts the number of support tickets a team closes in a day from the number of staff on shift:

$\widehat{\text{tickets}} = 20 + 3 \cdot (\text{staff on shift}).$

On one day there were $5$ staff on shift and the team actually closed $40$ tickets.

What is the residual for that day, and what does its sign tell you?

Accepted Answer

A residual is the gap between what actually happened and what the line predicted: 	ext{residual} = 	ext{observed} - 	ext{predicted}. First get the prediction for 5 staff: \widehat{	ext{tickets}} = 20 + 3 	imes 5 = 20 + 15 = 35. The team actually closed 40, so 	ext{residual} = 40 - 35 = +5. The residual is +5. The positive sign means the actual value came in above the line: the model under-predicted that day, and the team closed 5 more tickets than expected. A negative residual would mean the opposite (the line was too high, an over-prediction), and a residual of zero would mean the poin…

Computing a residual, observed minus predicted

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