A pediatrician measures children ages 2 to 9 and fits a straight line to height — and within that window the line is superb. But a regression line only knows the data it was built from. Slide the prediction age below and watch what happens when the line is pushed past the last data point: inside the range it tracks reality almost perfectly, yet extended to adulthood it insists a grown-up should be over eleven feet tall. The line hasn't changed — only how far you dared to trust it. Every prediction, error, and reality-check is computed live.
Height vs age — the fitted line, extended
How wrong the line is, at every age
Predicting inside the dataslide the age to leave the safe zone
5.0 yr
Interpolation ages 2–9
Mild extrapolation
Extreme extrapolation
Line predicts—
Truth—
Off by—
Interpolation vs extrapolation. Predicting inside the range of the x-values used to build the line is interpolation — the data vouch for it. Predicting outside that range is extrapolation, and it rests on a promise the data never made: that the same straight-line pattern keeps going. Here the real relationship bends — children stop growing — so the further out you push, the more the line's rigid slope betrays you.
A high R² does not license extrapolation. The line fits the childhood data beautifully, and no amount of that good fit tells you what happens at age 30 — because there is no age-30 data underneath it. Trust a regression line for prediction only across the span of x it was actually shown.