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}
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\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).
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