19M.2.SL.TZ2.S_1

pestleMathematicsAASLPaper 219M· sl-4-4-pearsons-scatter-diagrams-eqn-of-y-on-xsource ↗

A group of 7 adult men wanted to see if there was a relationship between their Body Mass Index (BMI) and their waist size. Their waist sizes, in centimetres, were recorded and their BMI calculated. The following table shows the results.

The relationship between $x$ and $y$ can be modelled by the regression equation $y = ax + b$ .

Write down the value of $a$ and of $b$ .

[3]

a.i.

Find the correlation coefficient.

[1]

a.ii.

Use the regression equation to estimate the BMI of an adult man whose waist size is 95 cm.

[2]

Markscheme / solution

valid approach (M1)

eg correct value for $a$ or $b$ (or for correct $r$ or ${r^2}$ = 0.955631 seen in (ii))

0.141120, 11.1424

$a$ = 0.141, $b$ = 11.1 A1A1 N3

[3 marks]

a.i.

0.977563

$r$ = 0.978 A1 N1

[1 mark]

a.ii.

correct substitution into their regression equation (A1)

eg 0.141(95) + 11.1

24.5488

24.5 A1 N2

[2 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]