17M.2.SL.TZ2.S_2

pestleMathematicsAASLPaper 217M· sl-4-4-pearsons-scatter-diagrams-eqn-of-y-on-xsource ↗

The maximum temperature $T$ , in degrees Celsius, in a park on six randomly selected days is shown in the following table. The table also shows the number of visitors, $N$ , to the park on each of those six days.

M17/5/MATME/SP2/ENG/TZ2/02

The relationship between the variables can be modelled by the regression equation $N = aT + b$ .

Find the value of $a$ and of $b$ .

[3]

a.i.

Write down the value of $r$ .

[1]

a.ii.

Use the regression equation to estimate the number of visitors on a day when the maximum temperature is 15 °C.

[3]

Markscheme / solution

evidence of set up (M1)

eg $\,\,\,\,\,$ correct value for $a$ or $b$

0.667315, 22.2117

$a = 0.667,{\text{ }}b = 22.2$ A1A1 N3

[3 marks]

a.i.

0.922958

$r = 0.923$ A1 N1

[1 marks]

a.ii.

valid approach (M1)

eg $\,\,\,\,\,$ $0.667(15) + 22.2,{\text{ }}N(15)$

32.2214 (A1)

32 (visitors) (must be an integer) A1 N2

[3 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]