5 An experiment was undertaken to collect information on the burning of a specific type of wood as a source of energy. At given fixed levels of the wood's moisture content, \(x\) per cent, its corresponding calorific value, \(y \mathrm { MWh } /\) tonne, on burning was determined. The results are shown in the table.
| \(\boldsymbol { x }\) | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 |
| \(\boldsymbol { y }\) | 5.2 | 4.7 | 4.3 | 4.0 | 3.2 | 2.8 | 2.5 | 2.2 | 1.8 | 1.5 | 1.3 | 1.0 | 0.6 |
- Explain why calorific value is the response variable.
- Calculate the equation of the least squares regression line of \(y\) on \(x\), giving your answer in the form \(y = a + b x\).
- Interpret, in context, your values for \(a\) and \(b\).
- Use your equation to estimate the wood's calorific value when it has a moisture content of 27 per cent.
- Calculate the value of the residual for the point \(( 35,2.5 )\).
- Given that the values of the 13 residuals lie between - 0.28 and + 0.23 , comment on the likely accuracy of your estimate in part (d).
- Give a general reason why your equation should not be used to estimate the wood's calorific value when it has a moisture content of 80 per cent.
- Give a specific reason, based on the context of this question and with numerical support, why your equation cannot be used to estimate the wood's calorific value when it has a moisture content of 80 per cent.