The volume of a sample of gas is kept constant. The gas is heated and the pressure, \(p\), is measured at 10 different temperatures, \(t\). The results are summarised below.
\(\sum p = 445 \quad \sum p ^ { 2 } = 38125 \quad \sum t = 240 \quad \sum t ^ { 2 } = 27520 \quad \sum p t = 26830\)
Find \(\mathrm { S } _ { p p }\) and \(\mathrm { S } _ { p t }\).
Given that \(\mathrm { S } _ { t t } = 21760\),
calculate the product moment correlation coefficient.
Give an interpretation of your answer to part (b).