Problem

Tom’s car holds $50$ litres of petrol when the fuel tank is full. For each of $10$ journeys, each starting with $50$ litres of petrol in the fuel tank, Tom records the distance travelled, $d$ kilometres, and the amount of petrol used, $p$ litres. The summary statistics for the $10$ journeys are given below.

$$\sum d=1029\qquad \sum p=50.8\qquad \sum dp=5240.8$$ $$S_{dd}=344.9\qquad S_{pp}=0.576$$

(a) Calculate the product moment correlation coefficient between $d$ and $p$

The amount of petrol remaining in the fuel tank for each journey, $w$ litres, is recorded.

(b) (i) Write down an equation for $w$ in terms of $p$

(ii) Hence, write down the value of the product moment correlation coefficient between $w$ and $p$

(c) Write down the value of the product moment correlation coefficient between $d$ and $w$