| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2019 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Interpret regression line parameters |
| Difficulty | Easy -1.2 This question tests basic interpretation of regression coefficients (gradient = rate of change) and understanding model limitations. Part (b) requires simple arithmetic (0.5 × 5.60) and contextual interpretation. Part (c) is open-ended recall of standard limitations (extrapolation, correlation ≠ causation, etc.). No complex calculations or novel problem-solving required—straightforward application of AS-level statistics concepts. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc5.09a Dependent/independent variables5.09c Calculate regression line5.09e Use regression: for estimation in context |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Label each year group | B1 | For a suitable numbered/labelled/ordered list/database/register for each year group. Condone poor numbering but if just one list, Year 12s must be distinguishable from Year 13s |
| Use random numbers to select a... | B1 | For use of random numbers/sample/selection to choose students |
| Simple random sample of \(24\) Year 12s and \(16\) Year 13s | B1 | For 24 Year 12s and 16 Year 13s |
| (3) | Note: A description of a systematic sample: only allow access to first mark, maximum B1B0B0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Increase by \(2.8\) marks | B1 | Must include increase (o.e.) and \(2.8\). 'Increase by approximately 3 marks' is B0 but isw if 2.8 is seen. \(5.6 \div 2\) is not sufficient |
| (1) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| e.g. 'the best performance is predicted for students who never wake up' | B1 | For any suitable limitation of the model, e.g. the longer you sleep the better performance; only valid between 0 and 24 hours; only valid within range of data; only takes sleep into consideration; cannot score below 26.1 marks; model might not be linear over entire range; model might predict more than maximum mark. B0: e.g. might not be correlation between \(s\) and \(p\), or individual student performance may vary |
| (1) |
## Question 1:
### Part (a)
| Answer/Working | Mark | Guidance |
|---|---|---|
| Label **each** year group | B1 | For a suitable numbered/labelled/ordered list/database/register for **each** year group. Condone poor numbering but if just one list, Year 12s must be distinguishable from Year 13s |
| Use random numbers to select a... | B1 | For use of random numbers/sample/selection to choose students |
| Simple random sample of $24$ Year 12s and $16$ Year 13s | B1 | For 24 Year 12s and 16 Year 13s |
| | **(3)** | Note: A description of a systematic sample: only allow access to first mark, maximum B1B0B0 |
### Part (b)
| Answer/Working | Mark | Guidance |
|---|---|---|
| Increase by $2.8$ marks | B1 | Must include increase (o.e.) and $2.8$. 'Increase by approximately 3 marks' is B0 but isw if 2.8 is seen. $5.6 \div 2$ is not sufficient |
| | **(1)** | |
### Part (c)
| Answer/Working | Mark | Guidance |
|---|---|---|
| e.g. 'the best performance is predicted for students who never wake up' | B1 | For any suitable limitation of the model, e.g. the longer you sleep the better performance; only valid between 0 and 24 hours; only valid within range of data; only takes sleep into consideration; cannot score below 26.1 marks; model might not be linear over entire range; model might predict more than maximum mark. B0: e.g. might not be correlation between $s$ and $p$, or individual student performance may vary |
| | **(1)** | |
---\begin{enumerate}
\item A sixth form college has 84 students in Year 12 and 56 students in Year 13
\end{enumerate}
The head teacher selects a stratified sample of 40 students, stratified by year group.\\
(a) Describe how this sample could be taken.
The head teacher is investigating the relationship between the amount of sleep, s hours, that each student had the night before they took an aptitude test and their performance in the test, $p$ marks.\\
For the sample of 40 students, he finds the equation of the regression line of $p$ on $s$ to be
$$p = 26.1 + 5.60 s$$
(b) With reference to this equation, describe the effect that an extra 0.5 hours of sleep may have, on average, on a student's performance in the aptitude test.\\
(c) Describe one limitation of this regression model.
\hfill \mbox{\textit{Edexcel AS Paper 2 2019 Q1 [5]}}