| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2020 |
| Session | November |
| Marks | 10 |
| 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 basic substitution into given equations, finding a line through two points, and making simple comparisons. All techniques are routine A-level methods with no conceptual challenges or novel problem-solving required. |
| Spec | 5.09a Dependent/independent variables5.09c Calculate regression line |
| 2016 | 2017 |
| \(\pounds 290000\) | \(\pounds 300000\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| house prices are generally higher in London boroughs (than elsewhere in the country), so Dr Procter's suggestion is probably wrong | B1 [1] (2.2a) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(214\,505\) | B1 (3.4) | |
| \(219\,402\) | B1 [2] (1.1) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P = 28\,500Y - 57\,184\,000\) (where \(Y\) is the calendar year) | B1 (3.3) | gradient; allow both marks for correct equation in any form isw |
| or \(P = 28\,500y + 215\,000\) (where \(y\) is the number of years after 2014) | B1 [2] (1.1) | intercept; allow e.g. \(y = 28\,500x - 57\,184\,000\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 2016: \(272\,000\) | B1 (3.4) | FT their straight line model provided this gives values \(> 250\,000\) |
| 2017: \(300\,500\) | B1 [2] (1.1) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Dr Procter's model is a (very) poor fit | B1 (2.2a) | dependent on correct values in (b) |
| Prof Jackson's is a good fit, or works well for 2017, but not 2016 | B1 [2] (2.2a) | FT comment for their values \(> 250\,000\); dependent on having calculated values in part (d) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| neither – extrapolation oe | B1 [1] (3.5b) |
## Question 11:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| house prices are generally higher in London boroughs (than elsewhere in the country), so Dr Procter's suggestion is probably wrong | B1 [1] (2.2a) | |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $214\,505$ | B1 (3.4) | |
| $219\,402$ | B1 [2] (1.1) | |
### Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P = 28\,500Y - 57\,184\,000$ (where $Y$ is the calendar year) | B1 (3.3) | gradient; allow both marks for correct equation in any form isw |
| or $P = 28\,500y + 215\,000$ (where $y$ is the number of years after 2014) | B1 [2] (1.1) | intercept; allow e.g. $y = 28\,500x - 57\,184\,000$ |
### Part (d):
| Answer | Marks | Guidance |
|--------|-------|----------|
| 2016: $272\,000$ | B1 (3.4) | FT their straight line model provided this gives values $> 250\,000$ |
| 2017: $300\,500$ | B1 [2] (1.1) | |
### Part (e):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Dr Procter's model is a (very) poor fit | B1 (2.2a) | dependent on correct values in (b) |
| Prof Jackson's is a good fit, or works well for 2017, but not 2016 | B1 [2] (2.2a) | FT comment for their values $> 250\,000$; dependent on having calculated values in part (d) |
### Part (f):
| Answer | Marks | Guidance |
|--------|-------|----------|
| neither – extrapolation oe | B1 [1] (3.5b) | |
---11 The pre-release material contains information concerning median house prices over the period 2004-2015. A spreadsheet has been used to generate a time series graph for two areas: the London borough of "Barking and Dagenham" and "North West". This is shown together with the raw data in Fig. 11.1.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{cea67565-8074-4703-8e1a-09b98e380baf-12_572_1751_447_159}
\captionsetup{labelformat=empty}
\caption{Fig. 11.1}
\end{center}
\end{figure}
Dr Procter suggests that it is unusual for median house prices in a London borough to be consistently higher than those in other parts of the country.
\begin{enumerate}[label=(\alph*)]
\item Use your knowledge of the large data set to comment on Dr Procter's suggestion.
Dr Procter wishes to predict the median house price in Barking and Dagenham in 2016. She uses the spreadsheet function LINEST to find the equation of the line of best fit for the given data. She obtains the equation\\
$P = 4897 Y - 9657847$, where $P$ is the median house price in pounds and $Y$ is the calendar year, for example 2015.
\item Use Dr Procter's equation to predict the median house price in Barking and Dagenham in
\begin{itemize}
\item 2016
\item 2017.
\end{itemize}
Professor Jackson uses a simpler model by using the data from 2014 and 2015 only to form a straight-line model.
\item Find the equation Professor Jackson uses in her model.
\item Use Professor Jackson's equation to predict the median house price in Barking and Dagenham in
\begin{itemize}
\item 2016
\item 2017.
\end{itemize}
Professor Jackson carries out some research online. She finds some information about median house prices in Barking and Dagenham, which is shown in Fig. 11.2.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | l | l | }
\hline
2016 & 2017 \\
\hline
$\pounds 290000$ & $\pounds 300000$ \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 11.2}
\end{center}
\end{table}
\item Comment on how well
\begin{itemize}
\item Dr Procter's model fits the data,
\item Professor Jackson's model fits the data.
\item Explain which, if any, of the models is likely to be more reliable for predicting median house prices in Barking and Dagenham in 2020.
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2020 Q11 [10]}}