2024 CJC H1 Q9

The crude birth rate refers to the number of live births in a given year, expressed per \(1,000\) population. The table below shows the crude birth rate, \(y\), of a certain city and the corresponding year, \(x\), for eight years.

[Data extracted from: [https://www.statista.com/statistics/977233/crude-birth-rate-in-singapore/]

1. Give a sketch of the scatter diagram for the data, as shown on your calculator.[2]
2. Find the product moment correlation coefficient and comment on its value in the context of the data.[2]
3. Find the equation of the regression line of \(y\) on \(x\), giving your answer in the form \(y = ax + b\), with the values of \(a\) and \(b\) correct to \(3\) significant figures. Explain what the value of \(a\) represents in the context of the data.[2]
4. Use the equation of your regression line to calculate an estimate for the crude birth rate in the year \(2015\). Comment on the reliability of your estimate.[2]