8 The yield of a particular crop on a farm is thought to depend principally on the amount of sunshine during the growing season. For a random sample of 8 years, the average yield, \(y\) kilograms per square metre, and the average amount of sunshine per day, \(x\) hours, are recorded. The results are given in the following table.
| \(x\) | 12.2 | 10.4 | 5.2 | 6.3 | 11.8 | 10.0 | 14.2 | 2.3 |
| \(y\) | 15 | 9 | 10 | 7 | 8 | 11 | 12 | 6 |
$$\left[ \Sigma x = 72.4 , \Sigma x ^ { 2 } = 769.9 , \Sigma y = 78 , \Sigma y ^ { 2 } = 820 , \Sigma x y = 761.3 . \right]$$
- Find the equation of the regression line of \(y\) on \(x\).
- Find the product moment correlation coefficient.
- Test, at the \(5 \%\) significance level, whether there is positive correlation between the average yield and the average amount of sunshine per day.