2024 EJC H1 Q11

A random sample of \(8\) employees at a particular company is selected. Their monthly earnings, \(y\) thousand dollars, and their length of service in the company, \(x\) years, are given in the table below.

The human resource manager checks the job scope of the \(8\) employees. She realises that employee \(D\) with \(x=10\) and \(y=8.33\) is a supervisor in the company and holds many extra responsibilities.

1. Explain why the data relating to employee \(D\) should not be used in any analysis of the data.[1]

In the rest of this question you should not include the data for employee \(D\).

2. Give a sketch of the scatter diagram for the data, as shown on your calculator.[2]
3. Find the product moment correlation coefficient.[1]
4. Find the equation of the regression line of \(y\) on \(x\), giving your answer in the form of \(y=mx+c\), with the values of \(m\) and \(c\) correct to \(3\) significant figures. Sketch this line on your scatter diagram in part (b).[2]
5. Use the equation of your regression line to calculate an estimate for the monthly earnings of an employee who has worked in the company for \(24\) years. Explain why you would expect this estimate to be unreliable.[2]

Due to a financial crisis, all employees at this company are given a salary reduction of \(\$500\) per month.

6. Without any further calculations, state any change you would expect in the values of your constants \(m\) and \(c\) found in part (d).[2]