21N.1.AHL.TZ0.12

pestleMathematicsAIHLPaper 121N· sl-4-4-pearsons-scatter-diagrams-eqn-of-y-on-xsource ↗

The following table shows the time, in days, from December $1 st$ and the percentage of Christmas trees in stock at a shop on the beginning of that day.

The following table shows the natural logarithm of both $d$ and $x$ on these days to $2$ decimal places.

Use the data in the second table to find the value of $m$ and the value of $b$ for the regression line, $\ln x = m (\ln d) + b$ .

[2]

Assuming that the model found in part (a) remains valid, estimate the percentage of trees in stock when $d = 25$ .

[3]

Markscheme / solution

$m = - 0.695 (- 0.695383 \dots); b = 4.63 (4.62974 \dots)$ A1A1

[2 marks]

$\ln x = - 0.695 (\ln 25) + 4.63$ M1

$\ln x = 2.39288 \dots$ (A1)

$x = 10.9 %$ A1

[3 marks]

Examiners’ report

Those candidates who did this question were often successful. There were a number, however, who found an equation of a line through two of the points instead of using their technology to find the equation of the regression line. A common problem was to introduce rounding errors at various stages throughout the problem. Some candidates failed to find the value of $x$ from that of $\ln x$ .