OCR Further Statistics 2017 Specimen — Question 1 6 marks

Exam BoardOCR
ModuleFurther Statistics (Further Statistics)
Year2017
SessionSpecimen
Marks6
TopicLinear regression
TypeIdentify response/explanatory variables
DifficultyModerate -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.
Spec5.08c Pearson: measure of straight-line fit5.09a Dependent/independent variables5.09c Calculate regression line

The table below shows the typical stopping distances \(d\) metres for a particular car travelling at \(v\) miles per hour.
\(v\)203040506070
\(d\)132436527294
  1. State each of the following words that describe the variable \(v\). Independent \quad Dependent \quad Controlled \quad Response [1]
  2. Calculate the equation of the regression line of \(d\) on \(v\). [2]
  3. Use the equation found in part (ii) to estimate the typical stopping distance when this car is travelling at 45 miles per hour. [1]
It is given that the product moment correlation coefficient for the data is 0.990 correct to three significant figures.
  1. Explain whether your estimate found in part (iii) is reliable. [2]

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]}}