\begin{enumerate}
  \item Tomas is studying the relationship between temperature and hours of sunshine in Seapron. He records the midday temperature, $t ^ { \circ } \mathrm { C }$, and the hours of sunshine, $s$ hours, for a random sample of 9 days in October. He calculated the following statistics
\end{enumerate}

$$\sum s = 15 \quad \sum s ^ { 2 } = 44.22 \quad \sum t = 127 \quad \mathrm {~S} _ { t t } = 10.89$$

(a) Calculate $\mathrm { S } _ { s s }$

Tomas calculated the product moment correlation coefficient between $s$ and $t$ to be 0.832 correct to 3 decimal places.\\
(b) State, giving a reason, whether or not this correlation coefficient supports the use of a linear regression model to describe the relationship between midday temperature and hours of sunshine.\\
(c) State, giving a reason, why the hours of sunshine would be the explanatory variable in a linear regression model between midday temperature and hours of sunshine.\\
(d) Find $\mathrm { S } _ { s t }$\\
(e) Calculate a suitable linear regression equation to model the relationship between midday temperature and hours of sunshine.\\
(f) Calculate the standard deviation of $s$

Tomas uses this model to estimate the midday temperature in Seapron for a day in October with 5 hours of sunshine.\\
(g) State the value of Tomas' estimate.

Given that the values of $s$ are all within 2 standard deviations of the mean,\\
(h) comment, giving your reason, on the reliability of this estimate.

\hfill \mbox{\textit{Edexcel S1 2017 Q5 [15]}}