CAIE FP2 2018 June — Question 8

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2018
SessionJune
TopicLinear regression
TypeFind unknown values from regression

8 For a random sample of 6 observations of pairs of values \(( x , y )\), the equation of the regression line of \(y\) on \(x\) is \(y = b x + 1.306\), where \(b\) is a constant. The corresponding equation of the regression line of \(x\) on \(y\) is \(x = 0.6331 y + d\), where \(d\) is a constant. The values of \(x\) from the sample are $$\begin{array} { l l l l l l } 2.3 & 2.8 & 3.7 & p & 6.1 & 6.4 \end{array}$$ and the sum of the values of \(y\) is 46.5 . The product moment correlation coefficient is 0.9797 .
  1. Find the value of \(b\) correct to 3 decimal places.
  2. Find the value of \(p\).
  3. Use the equation of the regression line of \(x\) on \(y\) to estimate the value of \(x\) when \(y = 8.5\).