3 A sample of bivariate data was taken and the results were summarised as follows.
$$n = 5 \quad \Sigma x = 24 \quad \Sigma x ^ { 2 } = 130 \quad \Sigma y = 39 \quad \Sigma y ^ { 2 } = 361 \quad \Sigma x y = 212$$
- Show that the value of the product moment correlation coefficient \(r\) is 0.855 , correct to 3 significant figures.
- The ranks of the data were found. One student calculated Spearman's rank correlation coefficient \(r _ { s }\), and found that \(r _ { s } = 0.7\). Another student calculated the product moment coefficient, \(R\), of these ranks. State which one of the following statements is true, and explain your answer briefly.
(A) \(R = 0.855\)
(B) \(R = 0.7\)
(C) It is impossible to give the value of \(R\) without carrying out a calculation using the original data. - All the values of \(x\) are now multiplied by a scaling factor of 2 . State the new values of \(r\) and \(r _ { s }\).