- A company wants to pay its employees according to their performance at work. The performance score \(x\) and the annual salary, \(y\) in \(\pounds 100\) s, for a random sample of 10 of its employees for last year were recorded. The results are shown in the table below.
| \(x\) | 15 | 40 | 27 | 39 | 27 | 15 | 20 | 30 | 19 | 24 |
| \(y\) | 216 | 384 | 234 | 399 | 226 | 132 | 175 | 316 | 187 | 196 |
$$\text { [You may assume } \left. \Sigma x y = 69798 , \Sigma x ^ { 2 } = 7266 \right]$$
- Draw a scatter diagram to represent these data.
- Calculate exact values of \(S _ { x y }\) and \(S _ { x x }\).
- Calculate the equation of the regression line of \(y\) on \(x\), in the form \(y = a + b x\).
Give the values of \(a\) and \(b\) to 3 significant figures.
- Draw this line on your scatter diagram.
- Interpret the gradient of the regression line.
The company decides to use this regression model to determine future salaries.
- Find the proposed annual salary for an employee who has a performance score of 35 .