Reading a regression slope, cold brew and temperature

Question

A campus cart sells cold brew. Fitting daily cups sold against the day's high temperature gives the line

$\widehat{\text{cups}} = 18 + 7 \cdot (\text{temperature in }^\circ\text{C}).$

If tomorrow is 4°C warmer than today, how many more cups does the model predict, and what does the slope of 7 mean in plain words?

Accepted Answer

The slope is the number multiplying the input. Here it is 7, and its plain meaning is: for every extra 1^\circC, the model expects about 7 more cups sold. That is the whole job of a slope, it is the predicted change in the output per one-unit change in the input. To go from a 1^\circC step to a 4^\circC step, just multiply. A 4^\circC rise predicts 7 	imes 4 = 28 	ext{ more cups.} Two things worth noting. First, you did not need the intercept (18) at all: the intercept only matters when you want an actual level of sales, not a change. For a change, the slope alone does the work. Second, "pr…

Reading a regression slope, cold brew and temperature

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