10 The mid-day temperature, \(x ^ { \circ } \mathrm { C }\), and the amount of sunshine, \(y\) hours, were recorded at a winter holiday resort on each of 12 days, chosen at random during the winter season. The results are summarised as follows.
$$\Sigma x = 18.7 \quad \Sigma x ^ { 2 } = 106.43 \quad \Sigma y = 34.7 \quad \Sigma y ^ { 2 } = 133.43 \quad \Sigma x y = 92.01$$
- Find the product moment correlation coefficient for the data.
- Stating your hypotheses, test at the \(1 \%\) significance level whether there is a non-zero correlation between mid-day temperature and amount of sunshine.
- Use the equation of a suitable regression line to estimate the number of hours of sunshine on a day when the mid-day temperature is \(2 ^ { \circ } \mathrm { C }\).