A chart can make next year's college figures look almost settled. Draw a straight line through a few past observations, extend it to the application year, and the software produces a precise number. That number is a calculation under a model, not another observed record. Its apparent precision can hide the change in evidential status.

NIST's engineering statistics handbook distinguishes predictions within the observed domain from predictions outside it and stresses checking model predictions against additional observations. This article applies that general statistical distinction to a fictional college-planning example. NIST's page is not a study of university prices or a source of the invented figures below.

Mark the last observed year

Suppose an imaginary college reports an annual charge of 10,000 units in year 1, 11,000 in year 2 and 12,000 in year 3. The figures cover the same charge definition and student category. A simple linear rule reproduces them: charge = 9,000 + 1,000 × year number.

Year number Value Evidential status
1 10,000 Fictional observed input
2 11,000 Fictional observed input
3 12,000 Fictional observed input
4 13,000 Linear extrapolation
5 14,000 Linear extrapolation

The last two rows were not reported by the imaginary college. They inherit an assumption that the same absolute annual increment continues. Write that assumption beside the values, rather than displaying all five rows with the same visual treatment.

An estimate at year 2.5 would fall within the time range, making it interpolation in this numerical model. That does not create a meaningful half-year tuition quotation: the real charging schedule might be discrete or use different billing rules. Mathematical location and practical interpretation are separate checks.

Test the shape rather than just the fit

The three inputs fit the linear rule perfectly. That alone cannot prove what happens after year 3. Consider two alternative fictional policies: a freeze after year 3, producing 12,000 in year 4, or an exceptional increase to 15,000. Both are compatible with the same historical three values because they describe future events not contained in those values.

The linear year-4 estimate differs from those scenarios by 1,000 and 2,000 respectively. Those are scenario gaps, not a confidence interval and not probabilities. Without an appropriate statistical model and its assumptions, the range 12,000–15,000 should not be labelled a 95% interval or a likely outcome.

The relevant practical question is often whether the programme has published its actual future fee policy. A binding published figure or a clearly applicable policy can provide evidence that a trend extension lacks. Check the student's entry cohort, currency, fee category and academic year before replacing an estimate with a reported value.

Keep an assumption register

Record the source dates, covered years, units and exact variable definition. State whether the model uses absolute increments, percentage growth or another relationship. A percentage-growth rule and a fixed-increment rule can diverge even when their initial predictions look similar. Do not choose a shape solely because it produces a reassuring budget.

Also record the conditions that would trigger revision: a new official schedule, a change in programme length, a different fee category or a break in the historical definition. When the next actual observation becomes available, retain the earlier forecast and compare it with the outcome. Replacing the forecast silently removes the opportunity to learn whether the method was useful.

A responsible planning sheet can contain observed values, explicit scenarios and a model output together, provided their labels remain distinct. The decision should reflect the consequences of being wrong and the availability of better evidence. Extending a line is easy; knowing which assumptions have crossed beyond the data is the essential part of using it.