7 The table shows the values of 5 observations of bivariate data \(( x , y )\).
| \(x\) | 4.6 | 5.9 | 6.5 | 7.8 | 8.3 |
| \(y\) | 15.6 | 10.8 | 10.4 | 10.1 | 9.7 |
$$n = 5 , \Sigma x = 33.1 , \Sigma y = 56.6 , \Sigma x ^ { 2 } = 227.95 , \Sigma y ^ { 2 } = 664.26 , \Sigma x y = 362.37$$
- Calculate Pearson's product-moment correlation coefficient \(r\) for the data.
- State what this value of \(r\) tells you about a scatter diagram illustrating the data.
- Test at the \(5 \%\) significance level whether there is association between \(x\) and \(y\).
- State the value of Spearman's rank correlation coefficient \(r _ { s }\) for the data.
- State whether \(r , r _ { s }\), or both or neither is changed when the values of \(x\) are replaced by
(a) \(3 x - 2\),
(b) \(\sqrt { x }\).