For a random sample, \(A\), of 5 pairs of values of \(x\) and \(y\), the equations of the regression lines of \(y\) on \(x\) and \(x\) on \(y\) are respectively \(y = 4.5 + 0.3 x\) and \(x = 3 y - 13\). Four of the five pairs of data are given in the following table.
Find
- the fifth pair of values of \(x\) and \(y\),
- the value of the product moment correlation coefficient.
A second random sample, \(B\), of 5 pairs of values of \(x\) and \(y\) is summarised as follows.
$$\Sigma x = 20 \quad \Sigma x ^ { 2 } = 100 \quad \Sigma y = 17 \quad \Sigma y ^ { 2 } = 69 \quad \Sigma x y = 75$$
The two samples, \(A\) and \(B\), are combined to form a single random sample of size 10 .
- Use this combined sample to test, at the \(5 \%\) significance level, whether the population product moment correlation coefficient is different from zero.