CAIE FP2 2016 June — Question 10

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2016
SessionJune
TopicLinear regression
TypeRelate two regression lines

10 For a random sample of 6 observations of pairs of values \(( x , y )\), where \(0 < x < 21\) and \(0 < y < 14\), the following results are obtained. $$\Sigma x ^ { 2 } = 844.20 \quad \Sigma y ^ { 2 } = 481.50 \quad \Sigma x y = 625.59$$ It is also found that the variance of the \(x\)-values is 36.66 and the variance of the \(y\)-values is 9.69 .
  1. Find the product moment correlation coefficient for the sample.
  2. Find the equations of the regression lines of \(y\) on \(x\) and \(x\) on \(y\).
  3. Use the appropriate regression line to estimate the value of \(x\) when \(y = 6.4\) and comment on the reliability of your estimate.