2023 H2 Maths Paper 2, Question 7

Explanation: By GC, entering the eight pairs $(x,y)$ into linear regression statistics gives the product moment correlation coefficient between $x$ and $y$.

Explanation: By GC, entering the pairs $\left( x,e^{y} \right)$ — where each $e^{y}$ is computed from the table, e.g. $e^{3.99} \approx 54.05$ and $e^{8.39} \approx 4402.82$ — gives the product moment correlation coefficient between $x$ and $e^{y}$.

Since $r = 0.9697$ (between $x$ and $e^{y}$) is closer to $1$ than $r = 0.9281$ (between $x$ and $y$), the model $e^{y} = cx + d$ gives a better (stronger linear) fit to the data than $y = ax + b$.

By GC, the regression line of $e^{y}$ on $x$ has

Note: $\bar{x} = 11$, the midpoint of the evenly spaced values $x = 4,6,\ldots,18$, as expected.

For the year $2024$, $x = 2024 - 2000 = 24$.

Since $x = 24$ lies outside the range of the given data ($x = 4$ to $x = 18$), using the regression equation here means extrapolating beyond the data range. There is no guarantee the same relationship continues to hold there, so the estimate is not necessarily reliable.