7 An experiment was carried out to determine how much weedkiller to apply per \(100 \mathrm {~m} ^ { 2 }\) in a large field. Ten \(100 \mathrm {~m} ^ { 2 }\) areas of the field were randomly chosen and sprayed with predetermined volumes of the weedkiller. The volume of the weedkiller is denoted by \(x\) litres and the number of weeds that survived is denoted by \(y\). The results are given in the table.
| \(x\) | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | 0.55 |
| \(y\) | 48 | 40 | 44 | 35 | 39 | 24 | 10 | 13 | 9 | 6 |
$$\left[ \Sigma x = 3.25 , \Sigma x ^ { 2 } = 1.2625 , \Sigma y = 268 , \Sigma y ^ { 2 } = 9548 , \Sigma x y = 66.10 . \right]$$
It is given that the product moment correlation coefficient for the data is - 0.951 , correct to 3 decimal places.
- Calculate the equation of a suitable regression line, giving a reason for your choice of line.
- Estimate the best volume of weedkiller to apply, and comment on the reliability of your estimate.