| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 6 |
| Topic | Linear regression |
| Type | Identify response/explanatory variables |
| Difficulty | Moderate -0.8 This is a straightforward regression question requiring standard calculations (finding regression line equation, making a prediction, interpreting correlation). All parts are routine textbook exercises with no problem-solving insight needed. The interpolation and high correlation make part (iv) trivial. Easier than average A-level due to its purely procedural nature. |
| Spec | 5.08c Pearson: measure of straight-line fit5.09a Dependent/independent variables5.09c Calculate regression line |
| \(v\) | 20 | 30 | 40 | 50 | 60 | 70 |
| \(d\) | 13 | 24 | 36 | 52 | 72 | 94 |
The table below shows the typical stopping distances $d$ metres for a particular car travelling at $v$ miles per hour.
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
$v$ & 20 & 30 & 40 & 50 & 60 & 70 \\
\hline
$d$ & 13 & 24 & 36 & 52 & 72 & 94 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\roman*)]
\item State each of the following words that describe the variable $v$.
Independent \quad Dependent \quad Controlled \quad Response [1]
\item Calculate the equation of the regression line of $d$ on $v$. [2]
\item Use the equation found in part (ii) to estimate the typical stopping distance when this car is travelling at 45 miles per hour. [1]
\end{enumerate}
It is given that the product moment correlation coefficient for the data is 0.990 correct to three significant figures.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{3}
\item Explain whether your estimate found in part (iii) is reliable. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2017 Q1 [6]}}