| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Identify response/explanatory variables |
| Difficulty | Easy -1.2 This is a straightforward introductory regression question requiring only basic terminology recall (part i), standard calculator-based regression calculation (part ii), simple substitution for interpolation (part iii), and routine interpretation of correlation coefficient (part iv). All parts are textbook exercises with no problem-solving or conceptual depth required. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09c Calculate regression line5.09e Use regression: for estimation in context |
| \(v\) | 20 | 30 | 40 | 50 | 60 | 70 |
| \(d\) | 13 | 24 | 36 | 52 | 72 | 94 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (i) | Independent and controlled |
| [1] | 1.2 | Both, no others |
| 1 | (ii) | d (cid:32)1.61v(cid:16)24.1 |
| [2] | 1.1 | |
| 3.3 | All correct including letters, 3 s.f. BC | |
| B1 Numbers right but not letters | (cid:62)d (cid:32)1.614v(cid:16)24.143(cid:64) | |
| 1 | (iii) | d (cid:32)1.61(cid:117)45(cid:16)24.1(cid:32)48to the nearest whole |
| number | B1 | |
| [1] | 3.4 | awrt 48n.5 |
| 1 | (iv) | Yes as r is close to 1 |
| and 45 is within data range | E1 |
| Answer | Marks |
|---|---|
| [2] | 3.5a |
| 3.5b | e |
| Answer | Marks | Guidance |
|---|---|---|
| 1(i) | 1 | 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 1(ii) | 1 | 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 1(iii) | 0 | 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 1(iv) | 0 | 0 |
Question 1:
1 | (i) | Independent and controlled | B1
[1] | 1.2 | Both, no others
1 | (ii) | d (cid:32)1.61v(cid:16)24.1 | B2
[2] | 1.1
3.3 | All correct including letters, 3 s.f. BC
B1 Numbers right but not letters | (cid:62)d (cid:32)1.614v(cid:16)24.143(cid:64)
1 | (iii) | d (cid:32)1.61(cid:117)45(cid:16)24.1(cid:32)48to the nearest whole
number | B1
[1] | 3.4 | awrt 48n.5
1 | (iv) | Yes as r is close to 1
and 45 is within data range | E1
E1
[2] | 3.5a
3.5b | e
Yes with one reason
Second reason
--- 1(i) ---
1(i) | 1 | 0 | 0 | 0 | 1
--- 1(ii) ---
1(ii) | 1 | 0 | 01 | 2
--- 1(iii) ---
1(iii) | 0 | 0 | 01 | 1
--- 1(iv) ---
1(iv) | 0 | 0 | 02 | 21 The table below shows the typical stopping distances $d$ metres for a particular car travelling at $v$ miles per hour.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | }
\hline
$v$ & 20 & 30 & 40 & 50 & 60 & 70 \\
\hline
$d$ & 13 & 24 & 36 & 52 & 72 & 94 \\
\hline
\end{tabular}
\end{center}
(i) State each of the following words that describe the variable $v$.
\section*{Independent Dependent Controlled Response}
(ii) Calculate the equation of the regression line of $d$ on $v$.\\
(iii) Use the equation found in part (ii) to estimate the typical stopping distance when this car is travelling at 45 miles per hour.
It is given that the product moment correlation coefficient for the data is 0.990 correct to three significant figures.\\
(iv) Explain whether your estimate found in part (iii) is reliable.
\hfill \mbox{\textit{OCR Further Statistics Q1 [6]}}