4 As part of her science project, a student found the mass, \(y\) grams, of a particular compound that dissolved in 100 ml of water at each of 12 different set temperatures, \(x ^ { \circ } \mathrm { C }\). The results are shown in the table.
| \(\boldsymbol { x }\) | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 |
| \(\boldsymbol { y }\) | 242 | 262 | 269 | 290 | 298 | 310 | 326 | 355 | 359 | 375 | 390 | 412 |
- Calculate the equation of the least squares regression line of \(y\) on \(x\).
- Interpret, in context, your value for the gradient of this regression line.
- Use your equation to estimate the mass of the compound which will dissolve in 100 ml of water at \(68 ^ { \circ } \mathrm { C }\).
- Given that the values of the 12 residuals for the regression line of \(y\) on \(x\) lie between - 7 and + 9 , comment, with justification, on the likely accuracy of your estimate in part (c).
[0pt]
[2 marks]