| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Minor (Further Statistics Minor) |
| Year | 2023 |
| Session | June |
| Marks | 8 |
| 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 requiring standard calculations (finding regression line equation, making predictions, commenting on interpolation/extrapolation). The only slightly elevated aspect is part (d) discussing the distinction between regressing m on w versus w on m, but this is a standard textbook point in Further Statistics. Overall, this is routine application of well-rehearsed techniques with no novel problem-solving required. |
| 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 |
|---|---|---|
| 5 | (a) | 𝑚 = 0.914𝑤−64.1 |
| Answer | Marks |
|---|---|
| [2] | 3.3 |
| 1.1 | First B1 for either coefficient |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (b) | Prediction for 99 is 26(.4) |
| Prediction for 110 is 36(.4) | B1 FT |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | Allow only 1 mark if either prediction is given to more than |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (c) | The prediction for 99 is (moderately) reliable as it is |
| Answer | Marks |
|---|---|
| straight line. | B1 |
| Answer | Marks |
|---|---|
| [2] | 3.5a |
| 3.5b | First B1 for a correct conclusion and reference to at least |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (d) | It would not be sensible/appropriate |
| Answer | Marks |
|---|---|
| the wing length for a given value of the mass. | B1 |
| Answer | Marks |
|---|---|
| [2] | 2.2a |
| 2.2a | Correct conclusion (may be implied by rest of comment) |
Question 5:
5 | (a) | 𝑚 = 0.914𝑤−64.1 | B1
B1
[2] | 3.3
1.1 | First B1 for either coefficient
Second for both given correct to 3sf and 𝑚 and 𝑤 used in an
equation, not just stated separately
(so 𝑦 = 0.914𝑥−64.1 scores B1 B0)
5 | (b) | Prediction for 99 is 26(.4)
Prediction for 110 is 36(.4) | B1 FT
B1 FT
[2] | 1.1
1.1 | Allow only 1 mark if either prediction is given to more than
1 decimal place
5 | (c) | The prediction for 99 is (moderately) reliable as it is
interpolation although the points do not appear to be close
to a straight line.
The prediction for 110 is not (at all) reliable as it is
extrapolation and the points do not appear to be close to a
straight line. | B1
B1
[2] | 3.5a
3.5b | First B1 for a correct conclusion and reference to at least
one of interpolation/extrapolation/not close to a straight line
Use of ‘accurate’ for ‘reliable’ is incorrect.
Second B1 for all 3
5 | (d) | It would not be sensible/appropriate
For example:
• Because this is the equation of the w on m
regression line, not m on w.
• Because this is found by minimising the squares
of the horizontal (𝑤)residuals.
• Since this line should only be used to estimate
wing length from the mass of a bird.
• Since this line only measures the average value of
the wing length for a given value of the mass. | B1
B1
[2] | 2.2a
2.2a | Correct conclusion (may be implied by rest of comment)
Must be linked with a correct conclusion5 An ornithologist is investigating the link between the wing length and the mass of small birds, in order to try to predict the mass from the wing length without having to weigh birds. The ornithologist takes a random sample of 9 birds and measures their wing lengths $w \mathrm {~mm}$ and their masses $m g$. The spreadsheet below shows the data, together with a scatter diagram which illustrates the data.\\
\includegraphics[max width=\textwidth, alt={}, center]{72215d69-c3e6-492d-bb3e-bdc28aeb4613-5_719_1424_495_246}
\begin{enumerate}[label=(\alph*)]
\item Find the equation of the regression line of $m$ on $w$, giving the coefficients correct to $\mathbf { 3 }$ significant figures.
\item Use the equation which you found in part (a) to estimate the mass for each of the following wing lengths.
\begin{itemize}
\item 99 mm
\item 110 mm
\item Comment on the reliability of your estimates.
\item The equation of the regression line of $w$ on $m$ is $w = 0.473 m + 87.5$. A friend of the ornithologist suggests that this equation could also be used to estimate the masses of birds from their wing lengths.
\end{itemize}
Comment on this suggestion.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Minor 2023 Q5 [8]}}