Substitute the known value into the line: Once you have the regression line y = ax + b, predict a value of y by substituting the given x (and vice versa with the x-on-y line).
It's a one-step substitution.
Predict with the regression line — read y for a given x. Interpolation (inside the data) is reliable; far extrapolation isn't.
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IB-style question — predict y
The regression line of test score y on revision hours x is y = 2.5x + 8.
Predict the score of a student who revises for 6 hours.
Step by step
- Substitute x = 6.
- Evaluate.
Final answer
A predicted score of about 23.
Use the right line for the direction: Predicting y from x → use y on x.
Predicting x from y → use x on y.
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Inside the data is safe; outside is risky: Interpolation = predicting inside the range of the original data — generally reliable.
Extrapolation = predicting outside the range — unreliable, because the pattern may not continue.
IB-style question — judge the prediction
Data was collected for revision hours from 2 to 9.
Comment on the reliability of predicting the score for (a) 5 hours and (b) 20 hours.
Step by step
- 5 hours is inside 2–9.
- 20 hours is far outside 2–9.
Final answer
(a) Reliable (interpolation, inside the data). (b) Unreliable (extrapolation, far outside the data).
Extrapolation assumes the trend continues: Outside the data the relationship may change, so an extrapolated prediction can be far off.
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Strong correlation + inside the data: A prediction is most reliable when the correlation is strong (|r| close to 1) and the x-value is within the data range.
Weak correlation makes even interpolated predictions unreliable.
IB-style question — comment on reliability
A regression line is used to predict a value inside the data range, but the correlation coefficient is r = 0.32.
Comment on the reliability.
Step by step
- Inside the data → interpolation (good).
- But the correlation is weak.
Final answer
Although it's interpolation, the weak correlation (r = 0.32) means the prediction is still unreliable.
Check BOTH things: Mention the range (interpolation/extrapolation) and the strength of r when asked to comment.