7. A music teacher monitored the sight-reading ability of one of her pupils over a 10 week period. At the end of each week, the pupil was given a new piece to sight-read and the teacher noted the number of errors \(y\). She also recorded the
number of hours \(x\) that the pupil had practised each week. The data are shown in the table below.
| \(x\) | 12 | 15 | 7 | 11 | 1 | 8 | 4 | 6 | 9 | 3 |
| \(y\) | 8 | 4 | 13 | 8 | 18 | 12 | 15 | 14 | 12 | 16 |
- Plot these data on a scatter diagram.
- Find the equation of the regression line of \(y\) on \(x\) in the form \(y = a + b x\).
$$\text { (You may use } \left. \Sigma x ^ { 2 } = 746 , \Sigma x y = 749 . \right)$$
- Give an interpretation of the slope and the intercept of your regression line.
- State whether or not you think the regression model is reasonable
- for the range of \(x\)-values given in the table,
- for all possible \(x\)-values.
In each case justify your answer either by giving a reason for accepting the model or by suggesting an alternative model.
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