Find

(i)     Pearson’s product–moment correlation coefficient, \(r\);

(ii)     the equation of the regression line \(y\) on \(x\).

Use the equation of the regression line \(y\) on \(x\) to estimate the number of mosquitoes caught in a trap that is \(28\) m from the lake.

(i)     \( - 0.998\;\;\;( - 0.997770 \ldots )\)     (A2)

Note: Award (A0)(A1) for \(0.998 (0.997770\ldots )\).

Award (A1)(A0) for \(- 0.997\).

(ii)     \(y =  - 0.470x + 81.7\;\;\;(y =  - 0.469713 \ldots x + 81.7279 \ldots )\)     (A1)(A1)     (C4)

Note: Award a maximum of (A0)(A1) if the answer is not an equation.

\( - 0.469713 \ldots (28) + 81.7279\)     (M1)

Note: Award (M1) for correct substitution of \(28\) into their equation of regression line.

\( = 68.6{\text{ (mosquitoes)}}\;\;\;(68.5759 \ldots )\)     (A1)(ft)     (C2)

Note: Accept \(68\) or \(69\) or \(68.5(4)\) from use of \(3\) sf values.

Follow through from part (a)(ii).

In part (a)(i), the majority of candidates knew how to calculate Pearson’s correlation coefficient using their GDC. The most common errors were incorrect rounding and omitting the – sign. In part (a)(ii) many candidates correctly found the equation of the regression line, again with rounding errors being the most common. A very common error was to use the second list as the frequency for the statistics.

In part (b) substitution of 28 in the regression line was done correctly by many candidates. Candidates seemed to be well prepared for this type of question.