OCR S1 2015 June — Question 1

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2015
SessionJune
TopicBivariate data
TypeCalculate r from summary statistics

1 For the top 6 clubs in the 2010/11 season of the English Premier League, the table shows the annual salary, \(\pounds x\) million, of the highest paid player and the number of points scored, \(y\).
ClubManchester UnitedManchester CityChelseaArsenalTottenhamLiverpool
\(x\)5.67.46.54.13.66.5
\(y\)807171686258
$$n = 6 \quad \sum x = 33.7 \quad \sum x ^ { 2 } = 200.39 \quad \sum y = 410 \quad \sum y ^ { 2 } = 28314 \quad \sum x y = 2313.9$$
  1. Use a suitable formula to calculate the product moment correlation coefficient, \(r\), between \(x\) and \(y\), showing that \(0 < r < 0.2\).
  2. State what this value of \(r\) shows in this context.
  3. A fan suggests that the data should be used to draw a regression line in order to estimate the number of points that would be scored by another Premier League club, whose highest paid player's salary is \(\pounds 1.7\) million. Give two reasons why such an estimate would be unlikely to be reliable.