20N.2.SL.TZ0.S_2

pestleMathematicsAISLPaper 220N· sl-4-4-pearsons-scatter-diagrams-eqn-of-y-on-xsource ↗

Lucy sells hot chocolate drinks at her snack bar and has noticed that she sells more hot chocolates on cooler days. On six different days, she records the maximum daily temperature, $T$ , measured in degrees centigrade, and the number of hot chocolates sold, $H$ . The results are shown in the following table.

The relationship between $H$ and $T$ can be modelled by the regression line with equation $H = a T + b$ .

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

[3]

a.i.

Write down the correlation coefficient.

[1]

a.ii.

Using the regression equation, estimate the number of hot chocolates that Lucy will sell on a day when the maximum temperature is $12 ° C$ .

[2]

Markscheme / solution

valid approach (M1)

eg correct value for $a$ or $b$ (or for $r$ or $r^{2} = 0.962839$ seen in (ii))

$a = - 9.84636, b = 221.592$

$a = - 9.85, b = 222$ A1A1 N3

[3 marks]

a.i.

$- 0.981244$

$r = - 0.981$ A1 N1

[1 mark]

a.ii.

correct substitution into their equation (A1)

eg $- 9.85 \times 12 + 222$

$103.435$ ( $103.8$ from $3 sf$ )

$103$ (hot chocolates) A1 N2

[2 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]