Find missing data values

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

1. the fifth pair of values of \(x\) and \(y\),
2. 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 .
3. Use this combined sample to test, at the \(5 \%\) significance level, whether the population product moment correlation coefficient is different from zero.

3. The marks obtained by ten students in a Geography test and a History test were as follows:

1. Given that \(\sum y = 547\), calculate the mark obtained by student \(E\) in History. Given further that \(\sum x ^ { 2 } = 34087 , \sum y ^ { 2 } = 31575\) and \(\sum x y = 31342\), calculate
2. the product moment correlation coefficient between \(x\) and \(y\),
3. an equation of the regression line of \(y\) on \(x\),
4. an estimate of the History mark of student \(K\), who scored 70 in Geography.
5. State, with a reason, whether you would expect your answer to part (d) to be reliable. \section*{STATISTICS 1 (A) TEST PAPER 2 Page 2}

1. 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}

1. Use the formula for \(\mathrm { S } _ { x x }\) to show that \(\mathrm { S } _ { s s } = 26.589\)
2. Find the value of the product moment correlation coefficient between \(s\) and \(d\).
3. With reference to the unfinished scatter diagram, comment on your result in part (b).