CAIE FP2 2012 November — Question 10

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2012
SessionNovember
TopicLinear regression
TypeCalculate y on x from raw data table

10 Delegates who travelled to a conference were asked to report the distance, \(y \mathrm {~km}\), that they had travelled and the time taken, \(x\) minutes. The values reported by a random sample of 8 delegates are given in the following table.
Delegate\(A\)\(B\)\(C\)\(D\)\(E\)\(F\)\(G\)\(H\)
\(x\)90467298526510582
\(y\)90556985455011074
$$\left[ \Sigma x = 610 , \Sigma x ^ { 2 } = 49682 , \Sigma y = 578 , \Sigma y ^ { 2 } = 45212 , \Sigma x y = 47136 . \right]$$ Find the equations of the regression lines of \(y\) on \(x\) and of \(x\) on \(y\). Estimate the time taken by a delegate who travelled 100 km to the conference. Calculate the product moment correlation coefficient for this sample.