| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2018 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Interpret regression line parameters |
| Difficulty | Moderate -0.8 This is a straightforward interpretation question requiring only conceptual understanding of regression parameters. Part (a) asks for correlation description (positive from positive gradient), part (b) is direct interpretation of gradient (£4.50 per point), and part (c) requires standard critique of linear models (extrapolation concerns, limited sample). No calculations needed, just recall of basic regression concepts. |
| Spec | 5.09a Dependent/independent variables5.09b Least squares regression: concepts |
| Answer | Marks | Guidance |
|---|---|---|
| Positive (correlation) | B1 (1 mark) | Allow interpretation e.g. "as points increase pay increases". Contradictory comments such as "positive correlation, as points increase pay decreases" scores B0. |
| Answer | Marks | Guidance |
|---|---|---|
| Every extra point gives £4.5(0) more on pay | B1 (1 mark) | Must convey idea of £s per point and include a correct value; must have idea of rate. Can condone missing £ sign. Accept 4.5. e.g. "every 10 points earns an extra (or increase) of £45" is B1. BUT "every point earns £4.5(0)" is B0 — *doesn't have idea of rate*. |
| Answer | Marks | Guidance |
|---|---|---|
| e.g. For points \(< 11\) it would give pay \(< 0\) which is ridiculous | B1 (1 mark) | B1 for suitable comment mentioning "points" or "pay" (o.e. e.g. "amount") or commenting on "small sample" or "range of points" used to find line. Can say that \(n\) points (for \(n < 10.4\)) would give negative pay so not suitable. Any comment suggesting some jobs would end up with negative pay scores B1. B0 for focus on "qualifications" or "hours" worked only. e.g. "Some jobs require no (or low) skills or qualifications" scores B0 (*need negative pay*). |
**Question 1:**
**(a)**
Positive (correlation) | B1 (1 mark) | Allow interpretation e.g. "as points increase pay increases". Contradictory comments such as "positive correlation, as points increase pay decreases" scores B0.
**(b)**
Every extra point gives £4.5(0) more on pay | B1 (1 mark) | Must convey idea of £s per point and include a correct value; must have idea of rate. Can condone missing £ sign. Accept 4.5. e.g. "every 10 points earns an extra (or increase) of £45" is B1. BUT "every point earns £4.5(0)" is B0 — *doesn't have idea of rate*.
**(c)**
e.g. For points $< 11$ it would give pay $< 0$ which is ridiculous | B1 (1 mark) | B1 for suitable comment mentioning "points" or "pay" (o.e. e.g. "amount") or commenting on "small sample" or "range of points" used to find line. Can say that $n$ points (for $n < 10.4$) would give negative pay so not suitable. Any comment suggesting some jobs would end up with negative pay scores B1. B0 for focus on "qualifications" or "hours" worked only. e.g. "Some jobs require no (or low) skills or qualifications" scores B0 (*need negative pay*).
**Total: 3 marks**\begin{enumerate}
\item A company is introducing a job evaluation scheme. Points ( $x$ ) will be awarded to each job based on the qualifications and skills needed and the level of responsibility. Pay ( $\pounds y$ ) will then be allocated to each job according to the number of points awarded.
\end{enumerate}
Before the scheme is introduced, a random sample of 8 employees was taken and the linear regression equation of pay on points was $y = 4.5 x - 47$\\
(a) Describe the correlation between points and pay.\\
(b) Give an interpretation of the gradient of this regression line.\\
(c) Explain why this model might not be appropriate for all jobs in the company.
\hfill \mbox{\textit{Edexcel AS Paper 2 2018 Q1 [3]}}