Interpolation is safe, extrapolation is not, salary by experience

Question

A firm fit a straight line predicting salary from years of experience, using employees with $1$ to $15$ years of experience. A manager wants two predictions: the salary at $8$ years, and the salary at $40$ years.

Explain why one of these predictions is far more trustworthy than the other, and name the distinction.

Accepted Answer

The two requests look the same but sit in very different places relative to the data, and that difference is the whole point. Predicting at 8 years is interpolation. Eight years sits comfortably inside the 1-to-15 range the line was fit on. There are real employees on both sides of it, so the line is describing a region it has actually seen. Interpolation, predicting inside the data range, is the safe, intended use of a regression line. This prediction is trustworthy (within the usual uncertainty). Predicting at 40 years is extrapolation. Forty years is far beyond the largest experience in th…

Interpolation is safe, extrapolation is not, salary by experience

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