- The scores achieved on a maths test, \(m\), and the scores achieved on a physics test, \(p\), by 16 students are summarised below.
$$\sum m = 392 \quad \sum p = 254 \quad \sum p ^ { 2 } = 4748 \quad \mathrm {~S} _ { m m } = 1846 \quad \mathrm {~S} _ { m p } = 1115$$
- Find the product moment correlation coefficient between \(m\) and \(p\)
- Find the equation of the linear regression line of \(p\) on \(m\)
Figure 1 shows a plot of the residuals.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0fcb4d83-9763-4edd-8006-93f75a44c596-02_808_1222_997_429}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure} - Calculate the residual sum of squares (RSS).
For the person who scored 30 marks on the maths test,
- find the score on the physics test.
The data for the person who scored 20 on the maths test is removed from the data set.
- Suggest a reason why.
The product moment correlation coefficient between \(m\) and \(p\) is now recalculated for the remaining 15 students.
- Without carrying out any further calculations, suggest how you would expect this recalculated value to compare with your answer to part (a).
Give a reason for your answer.
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