| Exam Board | OCR |
|---|---|
| Module | Further Statistics AS (Further Statistics AS) |
| Year | 2020 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate PMCC from raw data |
| Difficulty | Moderate -0.3 This is a straightforward application of standard PMCC and regression formulas with all summary statistics provided. Students need to recall formulas and perform arithmetic calculations, plus make basic comments about interpolation vs extrapolation. While it's a Further Maths topic, the computational and conceptual demands are routine, making it slightly easier than an average A-level question. |
| Spec | 5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09c Calculate regression line |
| Account | A | B | C | D | E | F | G | H |
| \(p\) | 1.6 | 2.1 | 2.4 | 2.7 | 2.8 | 3.3 | 5.2 | 8.4 |
| \(q\) | 1.6 | 2.3 | 2.2 | 2.2 | 3.1 | 2.9 | 7.6 | 4.8 |
| Answer | Marks |
|---|---|
| Neither | B1 [1] |
| Answer | Marks | Guidance |
|---|---|---|
| \(q = 1.13 + 0.620p\) | B1B1, B1 [3] | \(0.62(0)\) correct; both numbers correct; Fully correct answer including letters |
| Answer | Marks | Guidance |
|---|---|---|
| \(2.68\) | B1ft [1] | awrt \(2.68\), ft on their (b) if letters correct |
| Answer | Marks | Guidance |
|---|---|---|
| \(2.5\) is within data range, and points (here) are close to line/well correlated | B1, B1 [2] | At least one reason, allow "no because points not close to line"; Full argument, two reasons needed |
| Answer | Marks | Guidance |
|---|---|---|
| Not much data here/points scattered/possible outliers; So not very reliable | M1, A1 [2] | Reason for not very reliable (*not* "extrapolation"); Full argument and conclusion, not too assertive (not wholly unreliable!) |
# Question 3:
## Part (a)
Neither | **B1** [1] |
## Part (b)
$q = 1.13 + 0.620p$ | **B1B1, B1** [3] | $0.62(0)$ correct; both numbers correct; Fully correct answer including letters
## Part (c)(i)
$2.68$ | **B1ft** [1] | awrt $2.68$, ft on their **(b)** if letters correct
## Part (c)(ii)
$2.5$ is within data range, and points (here) are close to line/well correlated | **B1, B1** [2] | At least one reason, allow "no because points not close to line"; Full argument, two reasons needed
## Part (d)
Not much data here/points scattered/possible outliers; So not very reliable | **M1, A1** [2] | Reason for not very reliable (*not* "extrapolation"); Full argument and conclusion, not too assertive (not wholly unreliable!)
---3 An investor obtains data about the profits of 8 randomly chosen investment accounts over two one-year periods.
The profit in the first year for each account is $p \%$ and the profit in the second year for each account is $q \%$.
The results are shown in the table and in the scatter diagram.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | }
\hline
Account & A & B & C & D & E & F & G & H \\
\hline
$p$ & 1.6 & 2.1 & 2.4 & 2.7 & 2.8 & 3.3 & 5.2 & 8.4 \\
\hline
$q$ & 1.6 & 2.3 & 2.2 & 2.2 & 3.1 & 2.9 & 7.6 & 4.8 \\
\hline
\end{tabular}
\end{center}
$n = 8 \quad \sum \mathrm { p } = 28.5 \quad \sum \mathrm { q } = 26.7 \quad \sum \mathrm { p } ^ { 2 } = 136.35 \quad \sum \mathrm { q } ^ { 2 } = 116.35 \quad \sum \mathrm { pq } = 116.70$\\
\includegraphics[max width=\textwidth, alt={}, center]{bf1468d1-e02e-47d2-bf41-5bc8f5b4d7c4-3_782_1280_998_242}
\begin{enumerate}[label=(\alph*)]
\item State which, if either, of the variables $p$ and $q$ is independent.
\item Calculate the equation of the regression line of $q$ on $p$.
\item \begin{enumerate}[label=(\roman*)]
\item Use the regression line to estimate the value of $q$ for an investment account for which $p = 2.5$.
\item Give two reasons why this estimate could be considered reliable.
\end{enumerate}\item Comment on the reliability of using the regression line to predict the value of $q$ when $p = 7.0$.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics AS 2020 Q3 [9]}}