Extrapolation estimates values outside the range of observed data by assuming an inferred pattern continues. Unlike interpolation, it predicts beyond the evidence and can become unreliable. section 7.8
Sports drinks beyond the data
A linear model relating temperature to sports-drink sales fitted observations above 50°F and produced an intercept of -405.26 at 0°F. That prediction is not useful: freezing temperatures were not observed, and sales behavior may change at extreme heat or cold. The fitted relationship is more defensible within the collected temperature range. section 7.7 section 7.8
Use extrapolation cautiously:
- Check whether the requested value lies outside the observed range; if it does, treat the prediction as uncertain rather than assuming the trend continues. section 7.8
- Plot the data and inspect the model before trusting statistical measures, because a fitted function can oversimplify extreme values. section 7.13
- Remember that the same problem affects more complex machine-learning and artificial-intelligence models when training data omit relevant situations. section 7.8
