2026 EJC P2 Q10

An automotive analyst is tracking the resale price (\(P\) thousand dollars), of used cars over time (\(t\) years), after its initial purchase. The following data is collected from several used car listings:

1. Draw a scatter diagram of the data. Use your diagram to explain whether the relationship between \(P\) and \(t\) is likely to be well modelled by an equation of the form \(P=at+b\), where \(a\) and \(b\) are constants.[2]
2. The analyst proposes two models (A) and (B) for the relationship between \(P\) and \(t\), where \(a\), \(b\), \(c\), and \(d\) are constants:
   \[\text{(A)}\quad P=a+b\left(\frac1t\right)\qquad\text{(B)}\quad P=c+d\ln t.\]
   1. By calculating the relevant product moment correlation coefficients, determine whether the relationship between \(P\) and \(t\) is modelled better by (A) or (B). Explain how you decide which is the better model and state the equation in this case.[5]
   2. Use your equation in part (b)(i) to estimate the resale price of a used car 30 years after its initial purchase. Explain whether your estimation is reliable.[2]
3. The analyst wants to publish his report in a Hong Kong car magazine. Re-write your equation from part (b)(i) so that it can be used when the price is given in Hong Kong dollars. [1 Singapore dollar = 6.13 Hong Kong dollars][1]

The analyst later discovers that the prices listed are inclusive of a \(\$1000\) administrative fee.

4. Explain whether the product moment correlation coefficient would differ if the analyst removed this administrative fee from his data.[1]