5. Franca is the manager of an accountancy firm. She is investigating the relationship between the salary, $\pounds x$, and the length of commute, $y$ minutes, for employees at the firm. She collected this information from 9 randomly selected employees.

The salary of each employee was then coded using $w = \frac { x - 20000 } { 1000 }$

The table shows the values of $w$ and $y$ for the 9 employees.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | }
\hline
$w$ & 6 & 8 & 8 & - 1 & 25 & 15 & 3 & - 2 & 19 \\
\hline
$y$ & 45 & 50 & 35 & 65 & 25 & 40 & 50 & 75 & 20 \\
\hline
\end{tabular}
\end{center}

(You may use $\sum w = 81 \quad \sum y = 405 \quad \sum w y = 2490 \quad S _ { w w } = 660 \quad S _ { y y } = 2500$ )
\begin{enumerate}[label=(\alph*)]
\item Calculate the salary of the employee with $w = - 2$
\item Show that, to 3 significant figures, the value of the product moment correlation coefficient between $w$ and $y$ is - 0.899
\item State, giving a reason, the value of the product moment correlation coefficient between $x$ and $y$

The least squares regression line of $y$ on $w$ is $y = 60.75 - 1.75 w$
\item Find the equation of the least squares regression line of $y$ on $x$ giving your answer in the form $y = a + b x$
\item Estimate the length of commute for an employee with a salary of $\pounds 21000$

Franca uses the regression line to estimate the length of commute for employees with salaries between $\pounds 25000$ and $\pounds 40000$
\item State, giving a reason, whether or not these estimates are reliable.
\end{enumerate}

\hfill \mbox{\textit{Edexcel S1 2018 Q5 [12]}}