CAIE FP2 2010 June — Question 9

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2010
SessionJune
TopicLinear regression
TypeRelate two regression lines

9 A set of 20 pairs of bivariate data \(( x , y )\) is summarised by $$\Sigma x = 200 , \quad \Sigma x ^ { 2 } = 2125 , \quad \Sigma y = 240 , \quad \Sigma y ^ { 2 } = 8245 .$$ The product moment correlation coefficient is - 0.992 .
  1. What does the value of the product moment correlation coefficient indicate about a scatter diagram of the data points?
  2. Find the equation of the regression line of \(y\) on \(x\).
  3. The equation of the regression line of \(x\) on \(y\) is \(x = a ^ { \prime } + b ^ { \prime } y\). Find the value of \(b ^ { \prime }\).