10 For each month of a certain year, a weather station recorded the average rainfall per day, \(x \mathrm {~mm}\), and the average amount of sunshine per day, \(y\) hours. The results are summarised below.
$$n = 12 , \quad \Sigma x = 24.29 , \quad \Sigma x ^ { 2 } = 50.146 , \quad \Sigma y = 45.8 , \quad \Sigma y ^ { 2 } = 211.16 , \quad \Sigma x y = 88.415 .$$
- Find the mean values, \(\bar { x }\) and \(\bar { y }\).
- Calculate the gradient of the line of regression of \(y\) on \(x\).
- Use the answers to parts (i) and (ii) to obtain the equation of the line of regression of \(y\) on \(x\).
- Find the product moment correlation coefficient and comment, in context, on its value.
- Stating your hypotheses, test at the \(1 \%\) level of significance whether there is negative correlation between average rainfall per day and average amount of sunshine per day.