What an ad-spend slope predicts for new signups

Question

A gym models weekly new signups against its advertising budget:

$\widehat{\text{signups}} = 40 + 3 \cdot (\text{ad spend in thousands of dollars}).$

If the gym raises ad spend by $2{,}000, how many extra signups does the model predict, and state what the slope of 3 means.

Accepted Answer

The slope 3 means: each extra \1{,}000 of advertising is associated with about 3 more signups. It is the predicted change in signups per one unit of the input, and here one unit is one thousand dollars. A \2{,}000 increase is two units, so multiply the slope by two: 3 	imes 2 = 6 	ext{ extra signups.} The baseline 40 (the intercept) does not appear, because the question asks only about the change from spending more, not the total number of signups. Keep the units straight: the input is measured in thousands, so \2{,}000 is 2, not 2{,}000. Getting that wrong is the most common slip in slope …

What an ad-spend slope predicts for new signups

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