5 A doctor is investigating the relationship between the levels in the blood of a particular hormone and of calcium in healthy adults. The levels of the hormone and of calcium, each measured in suitable units, are denoted by $x$ and $y$ respectively.

The doctor selects a random sample of 14 adults and measures the hormone and calcium levels in each of them. The spreadsheet in Fig. 5 shows the values obtained, together with a scatter diagram which illustrates the data. The equation of the regression line of $y$ on $x$ is shown on the scatter diagram, together with the value of the square of the product moment correlation coefficient.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{ba3fcd3c-6834-4116-be0e-d5b27aed0a7e-5_801_1644_646_255}
\captionsetup{labelformat=empty}
\caption{Fig. 5}
\end{center}
\end{figure}
\begin{enumerate}[label=(\alph*)]
\item Use the equation of the regression line to estimate the mean calcium level of people with the following hormone levels.

\begin{itemize}
  \item 150
  \item 250
\item Explain which of your two estimates is likely to be more reliable.
\item Comment on the goodness of fit of the regression line.
\item Explain whether it would be appropriate to plot the scatter diagram the other way around with calcium level on the horizontal axis and hormone level on the vertical axis.
\item Calculate the equation of a regression line which would be suitable for estimating the mean hormone level of people with a known calcium level.
\end{itemize}
\end{enumerate}

\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2020 Q5 [8]}}