A student calculated the values of the product moment correlation coefficient, \(r\), and Spearman's rank correlation coefficient, \(r _ { s }\), for two sets of bivariate data, \(A\) and \(B\). His results are given below.
$$\begin{array} { l l }
A : & r = 0.9 \text { and } r _ { s } = 1
B : & r = 1 \quad \text { and } r _ { s } = 0.9
\end{array}$$
With the aid of a diagram where appropriate, explain why the student's results for \(A\) could both be correct but his results for \(B\) cannot both be correct.
An old research paper has been partially destroyed. The surviving part of the paper contains the following incomplete information about some bivariate data from an experiment.
\includegraphics[max width=\textwidth, alt={}, center]{5c25d6cf-2c23-4b49-88fb-e4abe6c281e4-4_339_1200_1117_511}
Calculate the missing constant at the end of the equation of the second regression line.