SPM.2.AHL.TZ0.4

pestleMathematicsAAHLPaper 2SPM· sl-4-4-pearsons-scatter-diagrams-eqn-of-y-on-xsource ↗

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]

Find the value of p and the value of q.

[3]

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]

Markscheme / solution

a = 1.29 and b = −10.4 A1A1

[2 marks]

recognising both lines pass through the mean point (M1)

p = 28.7, q = 30.3 A2

[3 marks]

substitution into their $x$ on $y$ equation (M1)

$x$ = 1.29082(29) − 10.3793

$x$ = 27.1 A1

Note: Accept 27.

[2 marks]

Examiners’ report

[N/A]