A Level Maths Notes: S2 – Prediction and Extrapolation

Extrapolation is a bad idea. It involves using a set of data to make predictions for data outside the range used to construct a statistical model. Suppose for example that a drug is being tested. The drug is designed to lower cholesterol. The drug is tested on healthy people first to minimise the risks of damage to health, and at first the dose will be restricted. A graph is drawn of cholesterol against dose.

The graph may be used to estimate cholesterol level levels for doses between d-1 and d-2 but not outside this range. Doses outside the range may have unpredictable consequences, either reducing the cholesterol BELOW a safe level, or possibly even raising cholesterol by causing damage to the mechanism which raises cholesterol.

Predictions of future values may be extrapolate from past experience in the same way. For instance, when things are good, people imagine things will get better. They look at their increasing income for the past few years and imagine themselves on the escalator to prosperity. If income increased 5% each year for the past 5 years, they may think it will increase by 5% next year. In fact income is subject to the business cycle. Income goes up every year for several years and then down for a couple.

Don't extrapolate if you can avoid it. If you can't avoid it, leave a large margin for error. And bear in mind that the further you extrapolate outside the range of data for which you have a model, the larger the errors you may find yourself making.