21M.2.SL.TZ1.2

pestleMathematicsAASLPaper 221M· sl-4-4-pearsons-scatter-diagrams-eqn-of-y-on-xsource ↗

The following table shows the data collected from an experiment.

The data is also represented on the following scatter diagram.

The relationship between $x$ and $y$ can be modelled by the regression line of $y$ on $x$ with equation $y = a x + b$ , where $a, b \in ℝ$ .

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

[2]

Use this model to predict the value of $y$ when $x = 18$ .

[2]

Write down the value of $\bar{x}$ and the value of $\bar{y}$ .

[1]

Draw the line of best fit on the scatter diagram.

[2]

Markscheme / solution

$a = 0.433156 \dots, b = 4.50265 \dots$

$a = 0.433, b = 4.50$ A1A1

[2 marks]

attempt to substitute $x = 18$ into their equation (M1)

$y = 0.433 \times 18 + 4.50$

$= 12.2994 \dots$

$= 12.3$ A1

[2 marks]

$\bar{x} = 15, \bar{y} = 11$ A1

[1 mark]

A1A1

Note: Award marks as follows:

A1 for a straight line going through $(15, 11)$

A1 for intercepting the $y$ -axis between their $b \pm 1.5$ (when their line is extended), which includes all the data for $3.3 \leq x \leq 25.3$ .

If the candidate does not use a ruler, award A0A1 where appropriate.

[2 marks]

Examiners’ report

[N/A]