1 A set of bivariate data ( \(X , Y\) ) is summarised as follows.
\(n = 25 , \sum x = 9.975 , \sum y = 11.175 , \sum x ^ { 2 } = 5.725 , \sum y ^ { 2 } = 46.200 , \sum x y = 11.575\)
- Calculate the value of Pearson's product-moment correlation coefficient.
- Calculate the equation of the regression line of \(y\) on \(x\).
It is desired to know whether the regression line of \(y\) on \(x\) will provide a reliable estimate of \(y\) when \(x = 0.75\).
- State one reason for believing that the estimate will be reliable.
- State what further information is needed in order to determine whether the estimate is reliable.