The best-fit line, straight from the GDC: The regression line of y on x is the best-fit line y = ax + b.
On Paper 2 you get a (gradient) and b (intercept) from the calculator's linear regression — no hand calculation.
The regression line of best fit passes through the mean point (x̄, ȳ); use it to predict y from x.
Interactive diagram
Explore the labelled diagram, charts and maps for this topic in full study mode.
IB-style question — find the line
Hours studied x and score y are (1,40), (2,50), (3,55), (4,70), (5,80).
Find the regression line of y on x.
Step by step
- Enter the pairs and run linear regression.
- Write the line.
Final answer
y = 10x + 29 (to 3 s.f. if needed).
GDC walkthrough
Step through the exact calculator keystrokes, screen by screen, in study mode.
Free preview
This is the free notes preview
You're reading the free notes. Aimnova Pro unlocks the full study experience — and you can try it with your first topic free to keep:
- FlashcardsLock in vocabulary and key terms with spaced repetition.
- Practice questionsAnswer exam-style questions and get instant AI marking.
- Mock exams & past-paper vaultSit full mocks and see exactly how examiners award marks.
- Personalised study planA daily plan built around your exam date and weak areas.
a = change per unit, b = value at x = 0: In y = ax + b, the gradient a is the change in y for each 1-unit increase in x, and the intercept b is the predicted y when x = 0.
Always read them in context.
IB-style question — interpret a and b
A regression line for plant height y cm against weeks x is y = 1.8x + 4.
Interpret the gradient and the intercept.
Step by step
- Gradient = change in y per 1 unit of x.
- Intercept = y when x = 0.
Final answer
The plant grows about 1.8 cm per week, and was about 4 cm tall at the start (week 0).
Use the units: State the gradient with units ('per week', 'per °C') and the intercept as the starting value.
Feeling unprepared for exams?
Get a clear study plan, practice with real questions, and know exactly where you stand before exam day. No more guessing.
Every regression line passes through (x̄, ȳ): The regression line always passes through the mean point (x̄, ȳ).
So if you know the line and one mean, you can find the other — and the point of the two means is guaranteed to be on the line.
IB-style question — use the mean point
A regression line is y = 10x + 29 and the mean of x is x̄ = 3.
Find the mean of y.
Step by step
- The mean point (x̄, ȳ) lies on the line.
- Substitute x̄ = 3.
Final answer
ȳ = 59.
A quick check: Substituting (x̄, ȳ) into the regression line should always work exactly — a handy way to check your line.
y on x to predict y; the two lines cross at the mean point: To predict y from x, use the line of y on x; to predict x from y, use x on y.
Both lines pass through (x̄, ȳ), so solving them simultaneously gives the two means.
IB-style question — find the means
The regression line of y on x is y = 2x + 1, and the line of x on y is x = 0.4y + 0.2.
Find the mean of x and the mean of y.
Step by step
- Both lines meet at the mean point — solve simultaneously.
- Solve for x̄, then ȳ.
Final answer
x̄ = 3, ȳ = 7.
Match the line to the direction: Use the line whose subject is the variable you want to predict — y on x for y, x on y for x.
Using the wrong one loses accuracy and marks.
IB-style question — two regression lines
For a data set, the regression line of y on x is y = 0.8x + 2, and the line of x on y is x = 0.9y − 1.
(a) Which line should be used to estimate y from a given x?
(b) Find the mean point (x̄, ȳ).
Step by step
- (a) To predict y FROM x, use the y-on-x line. (Using x-on-y the wrong way round loses marks.)
- (b) Both lines pass through the mean point, so solve them simultaneously.
- Back-substitute for ȳ.
Final answer
(a) the y-on-x line. (b) mean point ≈ (2.86, 4.29).
The two regression lines cross at the mean point (x̄, ȳ). Use y-on-x to predict y, and x-on-y to predict x — never the other way round.
Interactive diagram
Explore the labelled diagram, charts and maps for this topic in full study mode.