2023 H2 Mathematics Paper 2 Question 7

Linear Correlation and Regression

Answers

(ai)
0.9281.0.9281.
(aii)
0.9697.0.9697.

(b)

ey=cx+d \mathrm{e}^y = cx + d gives a better fit to the data because the ∣r∣|r| value is closer to 1.1.
ey=376x−1880.\mathrm{e}^y = 376x -1880.

(c)

8.878.87 million.
The estimate is not reliable as x=24x=24 lies outside the given data range 4≤x≤18. 4 \leq x \leq 18.

Full solutions

(ai)
0.9281  (4 dp)  ■0.9281 \; \textrm{(4 dp)} \; \blacksquare
(aii)
0.9697  (4 dp)  ■0.9697 \; \textrm{(4 dp)} \; \blacksquare

(b)

ey=cx+d \mathrm{e}^y = cx + d gives a better fit to the data because the ∣r∣|r| value is closer to 1  ■1 \; \blacksquare

From the GC, equation of the regression line is

ey=−1881.5+375.62xey=376x−1880  ■\begin{gather*} \mathrm{e}^y = -1881.5+375.62x \\ \mathrm{e}^y = 376x -1880 \; \blacksquare \end{gather*}

(c)

In 2024,x=242024, x=24

ey=375.62(24)−1881.5=7133.3y=ln⁡7133.3=8.87\begin{align*} \mathrm{e}^y &= 375.62(24) -1881.5 \\ &= 7133.3 \\ y &= \ln 7133.3 \\ &= 8.87 \end{align*}

Hence the number of mobile phone subscriptions in 2024is2024 is estimated to be 8.878.87 million   ■\; \blacksquare

The estimate is not reliable as x=24x=24 lies outside the given data range 4≤x≤18  ■ 4 \leq x \leq 18 \; \blacksquare

Question Commentary

After the unexpectedly theoretical question last year (2022 P2Q10), we are back to a much more standard question on linear regression.

The common techniques of linearisation, GC skills and reliability of estimates will hopefully feel familiar to past practice.