Treating extrapolation as reliable
"The Extrapolation Overreach"
The Mistake in Action
Data shows revision hours (0-10) vs test score. The line of best fit is used to predict the score for 25 hours of revision.
Wrong: "The line predicts 120% — so 25 hours would give 120%."
Why It Happens
Students apply the line of best fit beyond the data without considering that the relationship may not continue.
The Fix
Extrapolation (predicting outside the data range) is unreliable.
The relationship may not continue:
- Test scores can't exceed 100%
- There are diminishing returns to revision
- The linear pattern may change
Interpolation (within the data range) is more reliable because we have evidence the pattern holds there.
Always state: "This estimate is unreliable because it is an extrapolation beyond the data."
Spot the Mistake
Can you identify where this student went wrong?
Use line to predict for 25 hours (data is 0-10 hours)
Prediction of 120% is valid
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: