IB · Mathematics: Analysis & Approaches SL & HL · Statistics & probability

Correlation & regression: IB Mathematics: Analysis & Approaches questions with answers

Free Correlation & regression questions for IB Mathematics: Analysis & Approaches (SL & HL), part of Statistics & probability. Each question has the answer and the marking points an examiner would look for.

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Correlation & regression practice questions

Question 1Structured · 7 marks

The table shows the time x hours spent revising and the score y obtained by a sample of students.

x	3	6	8	11	15	20	23	25
y	17.4	31.8	33.6	43.9	55.8	69	81.4	84.1

Table 1.1

(a)

Find the value of Pearson’s product-moment correlation coefficient, r.

[2]

(b)

Find the equation of the regression line of y on x.

[2]

(c)

Use your regression line to estimate the score of a student who revises for 15 hours.

[2]

(d)

Explain why it would not be appropriate to use the line to estimate the score of a student who revises for 45 hours.

[1]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	0.997 use of GDC (M1) r = 0.997 A1	2
(b)	y = 2.99x + 10.7 use of GDC (M1) y = 2.99x + 10.7 A1	2
(c)	55.5 2.99(15) + 10.7 (M1) 55.5 A1	2
(d)	extrapolation 45 is outside the range of the data (extrapolation) R1	1

Question 2Structured · 6 marks

The table shows the hours of revision, x, and test scores, y, of six students.

x	2	4	7	9	11	13
y	5	10	18	21	21	25

Table 2.1

(a)

Find the value of Pearson’s product-moment correlation coefficient and interpret it.

[2]

(b)

Find the equation of the regression line of y on x.

[2]

(c)

Use your equation to estimate the score of a student who revised for 7 hours, and comment on the reliability.

[2]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	r = 0.971 r = 0.971 A1 strong positive correlation A1	2
(b)	y = 1.77x + 3.12 a = 1.77 A1 b = 3.12 A1	2
(c)	15.5 15.5 A1 interpolation with strong r so reliable R1	2

Question 3Structured · 7 marks

The table shows the time x hours spent revising and the score y obtained by a sample of students.

x	5	10	15	19	23	27	31	36
y	18.7	35	46.4	55.8	68	79	87.3	100.6

Table 3.1

(a)

Find the value of Pearson’s product-moment correlation coefficient, r.

[2]

(b)

Find the equation of the regression line of y on x.

[2]

(c)

Use your regression line to estimate the score of a student who revises for 20 hours.

[2]

(d)

Explain why it would not be appropriate to use the line to estimate the score of a student who revises for 59 hours.

[1]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	0.999 use of GDC (M1) r = 0.999 A1	2
(b)	y = 2.61x + 7.17 use of GDC (M1) y = 2.61x + 7.17 A1	2
(c)	59.4 2.61(20) + 7.17 (M1) 59.4 A1	2
(d)	extrapolation 59 is outside the range of the data (extrapolation) R1	1

Question 4Structured · 7 marks

The table shows the time x hours spent revising and the score y obtained by a sample of students.

x	7	10	15	18	20	24
y	7.8	4.8	−3.6	−8.3	−12.2	−18.2

Table 4.1

(a)

Find the value of Pearson’s product-moment correlation coefficient, r.

[2]

(b)

Find the equation of the regression line of y on x.

[2]

(c)

Use your regression line to estimate the score of a student who revises for 16 hours.

[2]

(d)

Explain why it would not be appropriate to use the line to estimate the score of a student who revises for 46 hours.

[1]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	−0.998 use of GDC (M1) r = −0.998 A1	2
(b)	y = −1.57x + 19.7 use of GDC (M1) y = −1.57x + 19.7 A1	2
(c)	−5.47 −1.57(16) + 19.7 (M1) −5.47 A1	2
(d)	extrapolation 46 is outside the range of the data (extrapolation) R1	1

Question 5Structured · 7 marks

The table shows the time x hours spent revising and the score y obtained by a sample of students.

x	8	13	17	19	23	28	32
y	46.5	68.1	80.7	89.3	106.6	122.7	139.5

Table 5.1

(a)

Find the value of Pearson’s product-moment correlation coefficient, r.

[2]

(b)

Find the equation of the regression line of y on x.

[2]

(c)

Use your regression line to estimate the score of a student who revises for 19 hours.

[2]

(d)

Explain why it would not be appropriate to use the line to estimate the score of a student who revises for 54 hours.

[1]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	0.999 use of GDC (M1) r = 0.999 A1	2
(b)	y = 3.83x + 16.7 use of GDC (M1) y = 3.83x + 16.7 A1	2
(c)	89.5 3.83(19) + 16.7 (M1) 89.5 A1	2
(d)	extrapolation 54 is outside the range of the data (extrapolation) R1	1

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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in