5 Bob, a gardener, measures the time taken, \(y\) minutes, for 60 grams of weedkiller pellets to dissolve in 10 litres of water at different set temperatures, \(x ^ { \circ } \mathrm { C }\). His results are shown in the table.
| \(\boldsymbol { x }\) | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56 |
| \(\boldsymbol { y }\) | 4.7 | 4.3 | 3.8 | 3.5 | 3.0 | 2.7 | 2.4 | 2.0 | 1.8 | 1.6 | 1.1 |
- State why the explanatory variable is temperature.
- Calculate the equation of the least squares regression line \(y = a + b x\).
- Interpret, in the context of this question, your value for \(b\).
- Explain why no sensible practical interpretation can be given for your value of \(a\).
- Estimate the time taken to dissolve 60 grams of weedkiller pellets in 10 litres of water at \(30 ^ { \circ } \mathrm { C }\).
- Show why the equation cannot be used to make a valid estimate of the time taken to dissolve 60 grams of weedkiller pellets in 10 litres of water at \(75 ^ { \circ } \mathrm { C }\). (2 marks)