5 A chemical solution was gradually heated. At five-minute intervals the time, \(x\) minutes, and the temperature, \(y ^ { \circ } \mathrm { C }\), were noted.
| \(x\) | 0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 |
| \(y\) | 0.8 | 3.0 | 6.8 | 10.9 | 15.6 | 19.6 | 23.4 | 26.7 |
$$\left[ n = 8 , \Sigma x = 140 , \Sigma y = 106.8 , \Sigma x ^ { 2 } = 3500 , \Sigma y ^ { 2 } = 2062.66 , \Sigma x y = 2685.0 . \right]$$
- Calculate the equation of the regression line of \(y\) on \(x\).
- Use your equation to estimate the temperature after 12 minutes.
- It is given that the value of the product moment correlation coefficient is close to + 1 . Comment on the reliability of using your equation to estimate \(y\) when
(a) \(x = 17\),
(b) \(x = 57\).