- A teacher is monitoring the progress of students using a computer based revision course. The improvement in performance, \(y\) marks, is recorded for each student along with the time, \(x\) hours, that the student spent using the revision course. The results for a random sample of 10 students are recorded below.
| 1.0 | 3.5 | 4.0 | 1.5 | 1.3 | 0.5 | 1.8 | 2.5 | 2.3 | 3.0 |
| 5 | 30 | 27 | 10 | - 3 | - 5 | 7 | 15 | - 10 | 20 |
$$\text { [You may use } \sum x = 21.4 , \quad \sum y = 96 , \quad \sum x ^ { 2 } = 57.22 , \quad \sum x y = 313.7 \text { ] }$$
- Calculate \(S _ { x x }\) and \(S _ { x y }\).
- Find the equation of the least squares regression line of \(y\) on \(x\) in the form \(y = a + b x\).
- Give an interpretation of the gradient of your regression line.
Rosemary spends 3.3 hours using the revision course.
- Predict her improvement in marks.
Lee spends 8 hours using the revision course claiming that this should give him an improvement in performance of over 60 marks.
- Comment on Lee's claim.