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Date May Specimen paper Marks available 2 Reference code SPM.2.AHL.TZ0.4
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term Estimate Question number 4 Adapted from N/A

Question

The following table below shows the marks scored by seven students on two different mathematics tests.

Let L1 be the regression line of x on y. The equation of the line L1 can be written in the form x = ay + b.

Let L2 be the regression line of y on x. The lines L1 and L2 pass through the same point with coordinates (p , q).

Find the value of a and the value of b.

[2]
a.

Find the value of p and the value of q.

[3]
b.

Jennifer was absent for the first test but scored 29 marks on the second test. Use an appropriate regression equation to estimate Jennifer’s mark on the first test.

[2]
c.

Markscheme

a = 1.29 and b = −10.4      A1A1

[2 marks]

a.

recognising both lines pass through the mean point       (M1)

p = 28.7, q = 30.3       A2

[3 marks]

b.

substitution into their x on y equation        (M1)

x = 1.29082(29) − 10.3793

x = 27.1      A1

Note: Accept 27.

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 4—Statistics and probability » SL 4.4—Pearsons, scatter diagrams, eqn of y on x
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Topic 4—Statistics and probability » SL 4.10—X on y regression line
Topic 4—Statistics and probability

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