| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Major (Further Statistics Major) |
| Year | 2023 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Direct prediction from given regression line |
| Difficulty | Easy -1.2 This is a straightforward substitution exercise requiring students to plug values into a given regression equation and comment on interpolation vs extrapolation. It tests basic understanding of regression lines but involves no derivation, calculation of the line itself, or complex statistical reasoning—purely mechanical application of a provided formula. |
| 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) | Prediction for 5C is 960 or 962 |
| Prediction for −4C is 1050 or 1054 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | 1.1 | |
| 1.1 | Only allow 1 mark max if either given to more than 4sf | |
| 2 | (b) | Although prediction for 5 °C lies within the data |
| Answer | Marks |
|---|---|
| extrapolation. | B1 |
| Answer | Marks |
|---|---|
| [3] | 2.2a |
| Answer | Marks |
|---|---|
| 3.5b | Allow first B1 for any correct comment about 5°C |
Question 2:
2 | (a) | Prediction for 5C is 960 or 962
Prediction for −4C is 1050 or 1054 | B1
B1
[2] | 1.1
1.1 | Only allow 1 mark max if either given to more than 4sf
2 | (b) | Although prediction for 5 °C lies within the data
(interpolation), the points do not lie too close to the line,
so it is not too reliable.
and the value of r2 is not too close to 1 so the estimate is
only moderately reliable.
The prediction for −4 °C is even less reliable since it is an
extrapolation. | B1
B1
B1
[3] | 2.2a
3.5b
3.5b | Allow first B1 for any correct comment about 5°C
Condone ‘Near the centre of the data’
Allow second B1 for all 3 correct comments about 5°C2 A student is investigating the link between temperature and electricity consumption in the winter months. The student finds the average minimum temperature, $x ^ { \circ } \mathrm { C }$, from across the country on a day. The student then finds the total electricity consumption for that day, $y \mathrm { GWh }$.
The scatter diagram below shows the values of $x$ and $y$ obtained from a random sample of 10 winter days. It also shows the equation of the regression line of $y$ on $x$ and the value of $r ^ { 2 }$, where $r$ is the product moment correlation coefficient.\\
\includegraphics[max width=\textwidth, alt={}, center]{c692fb20-436f-4bc1-89bd-10fdba41ceba-03_776_1043_609_244}
\begin{enumerate}[label=(\alph*)]
\item Use the regression line to estimate the electricity consumption at each of the following average minimum temperatures.
\begin{itemize}
\item $5 ^ { \circ } \mathrm { C }$
\item $- 4 ^ { \circ } \mathrm { C }$
\item Comment on the reliability of your estimates.
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Major 2023 Q2 [5]}}