| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Minor (Further Statistics Minor) |
| Year | 2021 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Interpret features of scatter diagram |
| Difficulty | Moderate -0.8 This is a straightforward linear regression question testing basic concepts: identifying independent/dependent variables, calculating regression line equation (likely using calculator/formula), making predictions, understanding extrapolation issues, computing residuals, and explaining when regression is appropriate. All parts are standard textbook exercises requiring recall and routine application rather than problem-solving or insight. While it's Further Maths content, these are foundational regression concepts that are easier than typical A-level questions. |
| Spec | 5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09c Calculate regression line5.09e Use regression: for estimation in context |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (a) | a is the independent variable since the values of a are |
| not subject to random variation | B1 | |
| [1] | 2.4 | B1: values of a are controlled |
| B0: d is dependent on a | Explanation required | |
| 2 | (b) | d = –1.104a + 197.1 |
| Answer | Marks |
|---|---|
| [2] | 3.3 |
| 1.1 | For either –1.104(a) or 197.1 |
| BC | y = –1.104x + 197.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (c) | estimate = 130.9 (m) |
| [1] | 1.1 | FT from (b) if the value is plausible |
| from the scatter diagram. | Accept 130 as rounded |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (d) | Because this would be extrapolation and it is possible |
| that the relationship is different for young children | B1 |
| Answer | Marks |
|---|---|
| [2] | 2.2b |
| 2.4 | For ‘extrapolation’ |
| Answer | Marks |
|---|---|
| to read yet | B0 for comment about |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (e) | Residual = 150 – (–1.104… × 40+197.1…) |
| = −3.0 | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | Subtraction other way around scores |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (f) | Because the values of a are non-random so it makes no |
| sense to try to predict them. | B1 | |
| [1] | 3.2b | Should show understanding of a |
Question 2:
2 | (a) | a is the independent variable since the values of a are
not subject to random variation | B1
[1] | 2.4 | B1: values of a are controlled
B0: d is dependent on a | Explanation required
2 | (b) | d = –1.104a + 197.1 | M1
A1
[2] | 3.3
1.1 | For either –1.104(a) or 197.1
BC | y = –1.104x + 197.1
scores M1 A0
2 | (c) | estimate = 130.9 (m) | B1FT
[1] | 1.1 | FT from (b) if the value is plausible
from the scatter diagram. | Accept 130 as rounded
to 2 significant figures.
2 | (d) | Because this would be extrapolation and it is possible
that the relationship is different for young children | B1
B1
[2] | 2.2b
2.4 | For ‘extrapolation’
B1: a 5-year-old child may not be able
to read yet | B0 for comment about
child not being able to
drive
2 | (e) | Residual = 150 – (–1.104… × 40+197.1…)
= −3.0 | M1
A1FT
[2] | 1.1
1.1 | Subtraction other way around scores
M1 only
Allow –2.9 (using 1.104 and 197.1)
FT from (b)
2 | (f) | Because the values of a are non-random so it makes no
sense to try to predict them. | B1
[1] | 3.2b | Should show understanding of a
purpose of a regression line being to
make predictions.2 A road transport researcher is investigating the link between the age of a person, a years, and the distance, $d$ metres, at which the person can read a large road sign. The researcher selects 13 individuals of different ages between 20 and 80 and measures the value of $d$ for each of them. The spreadsheet below shows the data which the researcher obtained, together with a scatter diagram which illustrates the data.\\
\includegraphics[max width=\textwidth, alt={}, center]{691e8b55-e9a1-4fff-b9ee-a71ff1f73ead-3_725_1566_495_251}
\begin{enumerate}[label=(\alph*)]
\item Explain which of the two variables $a$ and $d$ is the independent variable.
\item Find the equation of the regression line of $d$ on $a$.
\item Use the regression line to predict the average distance at which a 60-year-old person can read the road sign.
\item Explain why it might not be sensible to use the regression line to predict the average distance at which a 5 -year-old child can read the road sign.
\item Determine the value of the residual for $a = 40$.
\item Explain why it would not be useful to find the equation of the regression line of $a$ on $d$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Minor 2021 Q2 [9]}}