1 Five salesmen from a certain firm were selected at random for a survey. For each salesman, the annual income, $x$ thousand pounds, and the distance driven last year, $y$ thousand miles, were recorded. The results were summarised as follows.

$$n = 5 \quad \Sigma x = 251 \quad \Sigma x ^ { 2 } = 14323 \quad \Sigma y = 65 \quad \Sigma y ^ { 2 } = 855 \quad \Sigma x y = 3247$$
\begin{enumerate}[label=(\roman*)]
\item (a) Show that the product moment correlation coefficient, $r$, between $x$ and $y$ is - 0.122 , correct to 3 significant figures.\\
(b) State what this value of $r$ shows about the relationship between annual income and distance driven last year for these five salesmen.\\
(c) It was decided to recalculate $r$ with the distances measured in kilometres instead of miles. State what effect, if any, this would have on the value of $r$.
\item Another salesman from the firm is selected at random. His annual income is known to be $\pounds 52000$, but the distance that he drove last year is unknown. In order to estimate this distance, a regression line based on the above data is used. Comment on the reliability of such an estimate.
\end{enumerate}

\hfill \mbox{\textit{OCR S1 2011 Q1 [7]}}