2025 NJC P2 Q8

The Ministry of Health declared "War on Diabetes" in \(2016\) to rally a whole-of-nation effort to tackle diabetes. A study was conducted to investigate the effects of diabetes on one’s health, specifically to determine if the blood pressure of an adult aged between \(50\) and \(60\) years old is dependent on one’s haemoglobin level. Data from six patients in this age group from a hospital was collected. Their haemoglobin level, \(s\) mmol/mol, and blood pressure, \(p\) mmHg, are shown in the table.

1. Draw a scatter diagram of these data.[1]

It is thought that blood pressure \(p\) can be modelled by one of the formulae \[p = a + bs^2 \quad \text{or} \quad p = c + \frac{\mathrm{d}}{s}\]where \(a\), \(b\) and \(c\) are positive real numbers and \(d\) is a negative real number.

2. By using your diagram, explain which of \(p = a + bs^2\) or \(p = c + \frac{\mathrm{d}}{s}\) is the better model.[2]
3. Using the model you chose in part (ii), write down the equation for the relationship between \(s\) and \(p\), giving the numerical values of the coefficients. State the product moment correlation coefficient for this model.[2]
4. Estimate the value of \(p\) when \(s = 45\). Determine whether this estimate is reliable.[3]