- A company wants to pay its employees according to their performance at work. Last year's performance score \(x\) and annual salary \(y\), in thousands of dollars, were recorded for a random sample of 10 employees of the company.
The performance scores were
$$\begin{array} { l l l l l l l l l l }
15 & 24 & 32 & 39 & 41 & 18 & 16 & 22 & 34 & 42
\end{array}$$
(You may use \(\sum x ^ { 2 } = 9011\) )
- Find the mean and the variance of these performance scores.
The corresponding \(y\) values for these 10 employees are summarised by
$$\sum y = 306.1 \quad \text { and } \quad \mathrm { S } _ { y y } = 546.3$$
- Find the mean and the variance of these \(y\) values.
The regression line of \(y\) on \(x\) based on this sample is
$$y = 12.0 + 0.659 x$$
- Find the product moment correlation coefficient for these data.
- State, giving a reason, whether or not the value of the product moment correlation coefficient supports the use of a regression line to model the relationship between performance score and annual salary.
The company decides to use this regression model to determine future salaries.
- Find the proposed annual salary, in dollars, for an employee who has a performance score of 35