2024 ASRJC H1 Q11
2024 ASRJC H1 Q11
10 marks
A random sample of \(8\) employees at a tech company is taken. Their years of experience, denoted as \(t\), and their annual salaries in thousand dollars, denoted as \(y\), are provided in the following table:
| Employee | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| \(t\) | \(1\) | \(2\) | \(3\) | \(5\) | \(7\) | \(10\) | \(20\) | \(15\) |
| \(y\) | \(50\) | \(55\) | \(62\) | \(69\) | \(81\) | \(105\) | \(120\) | \(114\) |
- Give a sketch of the scatter diagram for the data, as shown on your calculator.[2]
- Find the value of the product moment correlation coefficient and comment on its value in the context of the data.[2]
- Find the equation of the regression line of \(y\) on \(t\), giving your answer in the form \(y = mt + c\), with the values of \(m\) and \(c\) correct to \(3\) decimal places. Sketch this line on your scatter diagram.[2]
- Use the equation of your regression line to calculate an estimate for the salary of an employee with \(90\) months of experience. Give two reasons whether you would expect this to be a reliable estimate.[3]
- If all employees receive a raise in their annual salary by a fixed amount, explain without further calculations how the value of \(m\) from part (c) will be affected.[1]
Solution:
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Answer:
(a) Scatter shown. (b) \(r\approx0.964\), strong positive linear correlation.
(c) \(y\approx3.951t+50.885\), coefficients to 3 decimal places.
(d) \(80.5\) thousand dollars; reasonably reliable interpolation with strong correlation.
(e) \(m\) is unchanged.
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