A large positive residual in a sales model

Question

A model predicts a booth's daily sales in units from the number of flyers handed out:

$\widehat{\text{sales}} = 50 + 4 \cdot (\text{flyers in hundreds}).$

On a day when $300$ flyers were handed out (that is, $3$ hundreds), the booth sold $70$ units.

What is the residual, and interpret its size and sign.

Accepted Answer

The input is measured in hundreds of flyers, so 300 flyers is 3. Predict: \widehat{	ext{sales}} = 50 + 4 	imes 3 = 50 + 12 = 62. Then the residual is observed minus predicted: 	ext{residual} = 70 - 62 = +8. The residual is +8: a positive sign, so the booth beat the prediction, selling 8 more units than the line expected for that many flyers. The size (8) tells you how big the miss was; a residual of +1 would be a near-perfect fit, while +8 is a noticeably good day the model did not anticipate (maybe a promotion or good weather). Watch the units, using 300 instead of 3 for the input would t…

A large positive residual in a sales model

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