6 Tom has read in a newspaper that you can tell the air temperature by counting how often a cricket chirps in a period of 20 seconds. (A cricket is a type of insect.) He wants to know exactly how the temperature can be predicted. On 8 randomly selected days, when Tom can hear crickets chirping, he records the number of chirps, $x$, made by a cricket in a 20-second interval, and also the temperature, $y ^ { \circ } \mathrm { C }$, at that time. The data are summarised as follows.\\
$n = 8 \quad \sum x = 268 \quad \sum y = 141.9 \quad \sum x ^ { 2 } = 9618 \quad \sum y ^ { 2 } = 2630.55 \quad \sum \mathrm { xy } = 5009.1$\\
These data are illustrated below.\\
\includegraphics[max width=\textwidth, alt={}, center]{8f1e0c68-a334-4657-823e-386ab0994c02-5_661_1035_699_242}
\begin{enumerate}[label=(\alph*)]
\item Determine the equation of the regression line of $y$ on $x$. Give your answer in the form $\mathrm { y } = \mathrm { ax } + \mathrm { b }$, giving the values of $a$ and $b$ correct to $\mathbf { 3 }$ significant figures.
\item Use the equation of the regression line to predict the temperature for the following values of $x$.

\begin{itemize}
  \item 35
  \item 10
\item Comment on the reliability of your predictions in part (b).
\item State the coordinates of the point of intersection of the line whose equation you have calculated with the regression line of $x$ on $y$.
\end{itemize}
\end{enumerate}

\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2022 Q6 [10]}}