When the intercept is nonsense, weight versus height

Question

A health study fits adult weight against height:

$\widehat{\text{weight in kg}} = -60 + 0.8 \cdot (\text{height in cm}).$

What weight does the model predict at a height of zero, and is that intercept a meaningful quantity?

Accepted Answer

Plug in a height of zero: \widehat{	ext{weight}} = -60 + 0.8 	imes 0 = -60 	ext{ kg.} Taken literally, the model predicts a person of height zero weighs minus 60 kilograms, which is impossible on two counts: nobody has zero height, and weight cannot be negative. So the intercept here is not meaningful as a real quantity. Why does a sensible model produce a nonsense intercept? Because the data used to fit it covered adult heights, maybe 150 to 200 cm. The line is a good description inside that range, but the intercept lives at height zero, wildly outside it. Extending a straight line all th…

When the intercept is nonsense, weight versus height

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