The second decision flowchart links regression direction, fit and the observed range. Its final judgement must refer to the actual data and conditions.
Is the input
controlled?
Fit response on
controlled input.
Solve that model for
a target if justified.
Two measured variables:
fit the variable to predict
on the given variable.
Check scatter, relevant r and
the variables actually fitted.
If fit is unsuitable, reconsider model.
Given input inside
observed range?
Interpolation:
assess fit and
comparable conditions.
Extrapolation:
continuation of the trend
has not been checked.
Give a contextual judgement.
Range and large |r| alone
do not guarantee accuracy.
Bridge the judgement
A fitted model uses input values from 10 to 40. An estimate at 25 is interpolation; at 60 it is extrapolation. Interpolation avoids extending the fitted trend beyond the data, but may still be poor if the scatter is curved, spread widely, or drawn from different conditions.
Exam wording for interpolation: “The input lies within the observed range, and the relevant scatter shows a strong approximately linear association, so the estimate may be reasonably reliable under comparable conditions.”
Exam wording for extrapolation: “The input lies outside the observed range, so the estimate extrapolates. The observed data do not establish that the fitted trend continues there.” A large magnitude of correlation alone does not remove that limitation.

The second decision flowchart links regression direction, fit and the observed range. Its final judgement must refer to the actual data and conditions.

Fit response on
controlled input.
Solve that model for
a target if justified.

Two measured variables:
fit the variable to predict
on the given variable.

Check scatter, relevant r and
the variables actually fitted.
If fit is unsuitable, reconsider model.

Interpolation:
assess fit and
comparable conditions.

Extrapolation:
continuation of the trend
has not been checked.

Give a contextual judgement.
Range and large |r| alone
do not guarantee accuracy.

A fitted model uses input values from 10 to 40. An estimate at 25 is interpolation; at 60 it is extrapolation. Interpolation avoids extending the fitted trend beyond the data, but may still be poor if the scatter is curved, spread widely, or drawn from different conditions.

Exam wording for interpolation: “The input lies within the observed range, and the relevant scatter shows a strong approximately linear association, so the estimate may be reasonably reliable under comparable conditions.”

Exam wording for extrapolation: “The input lies outside the observed range, so the estimate extrapolates. The observed data do not establish that the fitted trend continues there.” A large magnitude of correlation alone does not remove that limitation.

Deciding Whether a Regression Estimate Is Reliable

Deciding Whether a Regression Estimate Is Reliable