2023 H2 Mathematics Paper 2 Question 7

Linear Correlation and Regression

Answers

{{0.9281.}}

{{0.9697.}}

{{ \mathrm{e}^y = cx + d}}

gives a better fit to the data because the

{{|r|}}

value is closer to

{{1.}}

{{\mathrm{e}^y = 376x -1880.}}

{{8.87}}

million.
The estimate is not reliable as

{{x=24}}

lies outside the given data range

{{ 4 \leq x \leq 18.}}

(ai)

{{0.9281 \; \textrm{(4 dp)} \; \blacksquare}}

(aii)

{{0.9697 \; \textrm{(4 dp)} \; \blacksquare}}

{{ \mathrm{e}^y = cx + d}}

gives a better fit to the data because the

{{|r|}}

value is closer to

{{1 \; \blacksquare}}

From the GC, equation of the regression line is

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

In ${{2024, x=24}}$

\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 ${{2024 is}}$ estimated to be ${{8.87 }}$ million ${{\; \blacksquare}}$

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

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.