CAIE FP2 2019 June — Question 10 4 marks

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2019
SessionJune
Marks4
TopicLinear regression
TypeCalculate y on x from summary statistics

10 The means and variances for a random sample of 8 pairs of values of \(x\) and \(y\) taken from a bivariate distribution are given in the following table.
MeanVariance
\(x\)3.31253.3086
\(y\)6.73757.9473
The product moment correlation coefficient for the sample is 0.5815 , correct to 4 decimal places.
  1. Find the equation of the regression line of \(y\) on \(x\).
  2. Test at the \(5 \%\) significance level whether there is evidence of positive correlation between \(x\) and \(y\). [4]
  3. Calculate an estimate of \(y\) when \(x = 6.0\) and comment on the reliability of your estimate.