CAIE FP2 2013 November — Question 9

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2013
SessionNovember
TopicLinear regression
TypeRelate two regression lines

9 For a random sample of 10 observations of pairs of values \(( x , y )\), the equations of the regression lines of \(y\) on \(x\) and of \(x\) on \(y\) are $$y = 4.21 x - 0.862 \quad \text { and } \quad x = 0.043 y + 6.36$$ respectively.
  1. Find the value of the product moment correlation coefficient for the sample.
  2. Test, at the \(10 \%\) significance level, whether there is evidence of non-zero correlation between the variables.
  3. Find the mean values of \(x\) and \(y\) for this sample.
  4. Estimate the value of \(x\) when \(y = 2.3\) and comment on the reliability of your answer.