CAIE FP2 2018 November — Question 9

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2018
SessionNovember
TopicLinear regression
TypeRelate two regression lines

9 For a random sample of 5 observations of pairs of values \(( x , y )\), the equation of the regression line of \(y\) on \(x\) is \(y = 4.2 + c x\) and the equation of the regression line of \(x\) on \(y\) is \(x = 10.8 + d y\), where \(c\) and \(d\) are constants. The product moment correlation coefficient is - 0.7214 and the mean value of \(x\) is 7.018.
  1. Test at the \(5 \%\) significance level whether there is evidence of non-zero correlation between the variables.
  2. Find the values of \(c\) and \(d\).
  3. Use an appropriate regression line to estimate the value of \(x\) when \(y = 3.5\), and comment on the reliability of your estimate.