The line that predicts a forty-year-old is ten feet tall

Question

A pediatric study fit a straight line predicting a child's height from age, using children aged $2$ to $10$ years. Within that range each extra year added a fairly steady amount of height, and the line fit well. A parent then uses the same line to predict the height of a $40$ -year-old.

Explain why the line gives an absurd answer here, and what general lesson it illustrates.

Accepted Answer

Extending the line to age 40 produces a wildly too-tall prediction, because the straight-line relationship that held for young children simply does not continue. Growth is not linear over a lifetime. Between ages 2 and 10, children grow at a roughly constant pace, so a line describes them well. But growth slows through the teens and stops entirely in adulthood. A line has no way to know this: it assumes the same inches-per-year forever, so by age 40 it has piled on decades of growth that never actually happened. The data never covered adults. The model learned only from ages 2 to 10. Age 40 i…

The line that predicts a forty-year-old is ten feet tall

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