19M.1.SL.TZ2.T_2

pestleMathematicsAASLPaper 119M· sl-4-4-pearsons-scatter-diagrams-eqn-of-y-on-xsource ↗

Colorado beetles are a pest, which can cause major damage to potato crops. For a certain Colorado beetle the amount of oxygen, in millilitres (ml), consumed each day increases with temperature as shown in the following table.

This information has been used to plot a scatter diagram.

The mean point has coordinates (20, 230).

Find the equation of the regression line of $y$ on $x$ .

[2]

Draw the regression line of $y$ on $x$ on the scatter diagram.

[2]

In order to estimate the amount of oxygen consumed, this regression line is considered to be reliable for a temperature $x$ such that $a$ ≤ $x$ ≤ $b$ .

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

[2]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$y = 15.5x - 80$ (A1)(A1) (C2)

Note: Award (A1) for $15.5x$ ; (A1) for −80. Award at most (A1)(A0) if answer is not an equation. Award (A0)(A1)(ft) for $y = - 80x + 15.5$ .

[2 marks]

(A1)(A1) (C2)

Note: Award (A1) for a straight line using a ruler passing through (20, 230); (A1) for correct $y$ -intercept. If a ruler has not been used, award at most (A0)(A1).

[2 marks]

$a = 10$ AND $b = 30$ (A1)(A1) (C2)

Note: Accept [10, 30] or 10 ≤ $x$ ≤ 30.

[2 marks]

Examiners’ report

[N/A]