6 A motorist decides to check the fuel consumption, \(y\) miles per gallon, of her car at particular speeds, \(x \mathrm { mph }\), on flat roads. She carries out the check on a suitable stretch of motorway. Fig. 6 shows her results.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{880026ad-1cd3-40bb-bc87-8dcc94bd9bbd-4_707_1091_1320_477}
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{figure}
- Explain why it would not be appropriate to carry out a hypothesis test for correlation based on the product moment correlation coefficient.
- (A) One of the results is an outlier. Circle the outlier on the copy of Fig. 6 in the Printed Answer Booklet.
(B) Suggest one possible reason for the outlier in part (ii) (A) not being used in any analysis.
The motorist decides to remove this item of data from any analysis. The table below shows part of a spreadsheet that was used to analyse the 14 remaining data items (with the outlier removed). Some rows of the spreadsheet have been deliberately omitted.
| Data item | \(x\) | \(y\) | \(x ^ { 2 }\) | \(y ^ { 2 }\) | \(x y\) |
| 1 | 50 | 53.6 | 2500 | 2872.96 | 2680 |
| 2 | 50 | 53.3 | 2500 | 2840.89 | 2665 |
| | | | | | |
| 13 | 70 | 44.8 | 4900 | 2007.04 | 3136 |
| 14 | 70 | 44.2 | 4900 | 1953.64 | 3094 |
| Sum | | 840 | 686 | 51150 | 33779.7 | 40812 |
- Calculate the equation of the regression line of \(y\) on \(x\).
- Use the equation of the regression line to predict the fuel consumption of the car at
(A) 58 mph ,
(B) 30 mph . - Comment on the reliability of your predictions in part (iv).
OCR is committed to seeking permission to reproduce all third-party content that it uses in the assessment materials. OCR has attempted to identify and contact all copyright holders whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright Acknowledgements booklet. This is produced for each series of examinations and is freely available to download from our public website (\href{http://www.ocr.org.uk}{www.ocr.org.uk}) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible opportunity.
For queries or further information please contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
}\section*{}