CAIE FP2 2019 November — Question 9

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2019
SessionNovember
TopicLinear regression
TypeFind unknown values from regression

9 A random sample of five pairs of values of \(x\) and \(y\) is taken from a bivariate distribution. The values are shown in the following table, where \(p\) and \(q\) are constants.
\(x\)12345
\(y\)4\(p\)\(q\)21
The equation of the regression line of \(y\) on \(x\) is \(y = - 0.5 x + 3.5\).
  1. Find the values of \(p\) and \(q\).
  2. Find the value of the product moment correlation coefficient.