- Over a period of time, researchers took 10 blood samples from one patient with a blood disease. For each sample, they measured the levels of serum magnesium, \(s \mathrm { mg } / \mathrm { dl }\), in the blood and the corresponding level of the disease protein, \(d \mathrm { mg } / \mathrm { dl }\). One of the researchers coded the data for each sample using \(x = 10 s\) and \(y = 10 ( d - 9 )\) but spilt ink over his work.
The following summary statistics and unfinished scatter diagram are the only remaining information.
$$\sum d ^ { 2 } = 1081.74 \quad \mathrm {~S} _ { d s } = 59.524$$
and
$$\sum y = 64 \quad \mathrm {~S} _ { x x } = 2658.9$$
\(d \mathrm { mg } / \mathrm { dl }\)
\includegraphics[max width=\textwidth, alt={}, center]{e777c787-0d39-4d84-a0f9-fc4a6712184f-22_983_1534_840_303}
- Use the formula for \(\mathrm { S } _ { x x }\) to show that \(\mathrm { S } _ { s s } = 26.589\)
- Find the value of the product moment correlation coefficient between \(s\) and \(d\).
- With reference to the unfinished scatter diagram, comment on your result in part (b).