OCR MEI Further Statistics A AS Specimen — Question 6 12 marks

Exam BoardOCR MEI
ModuleFurther Statistics A AS (Further Statistics A AS)
SessionSpecimen
Marks12
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLinear regression
TypeAssess model appropriateness from context
DifficultyStandard +0.3 This question tests understanding of when linear regression is appropriate and basic calculation of regression lines. Part (i) requires recognizing non-linear relationships from a scatter plot (standard conceptual knowledge), parts (ii-iii) involve routine calculations using given summary statistics, and parts (iv-v) test extrapolation vs interpolation—all standard textbook material for Further Statistics. The multi-part structure and context add length but not conceptual difficulty.
Spec5.08f Hypothesis test: Spearman rank5.08g Compare: Pearson vs Spearman
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}
  1. Explain why it would not be appropriate to carry out a hypothesis test for correlation based on the product moment correlation coefficient.
  2. (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\(x\)\(y\)\(x ^ { 2 }\)\(y ^ { 2 }\)\(x y\)
    15053.625002872.962680
    25053.325002840.892665
    137044.849002007.043136
    147044.249001953.643094
    Sum8406865115033779.740812
  3. Calculate the equation of the regression line of \(y\) on \(x\).
  4. Use the equation of the regression line to predict the fuel consumption of the car at
    (A) 58 mph ,
    (B) 30 mph .
  5. Comment on the reliability of your predictions in part (iv). }{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 }\section*{}
Question 6:
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66 6
6(i) Because this test is only valid for random on random
data …
AnswerMarks
and the speeds are controlled.E1
E1
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[2]3.5a
3.5b
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6(ii) (A)
[1]1.2
6(ii) (B)
[1]2.4 N
E
E.g. differs markedly from other
values at same speed OR could be
an error
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6(iii) x = 60, y = 49
S
xy 40812(cid:16)840(cid:117)686/14 (cid:16)348
b = = =
S 51150(cid:16)8402 /14 750
xx
40812/14(cid:16)60(cid:117)49 (cid:16)24.857
OR b = =
51150/14(cid:16)492 53.571E
= –0.464
P
hence least squares regression line is:
(cid:159) y – 49 = –0.464 (x – 60)
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(cid:159) y = –0.464x + 76.84M1
C
A1
M1
A1
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[4]I
1.1a
1.1
3.3
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1.1M
For attempt at gradient (b)
For –0.464
For equation of line
FT for complete equation
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6(iv) (A)
(B)S
49.9
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62.9B1
B1
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[2]3.4
3.4
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6(v) First answer is reliable as interpolation and the points
lie close to the line
Second answer less likely to be reliable as
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extrapolationE1
E1
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[2]3.5a
3.5b
AnswerMarks Guidance
QuestionAO1 AO2
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6(i)0 0
S
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6(ii)A1 0
6(ii)B0 1
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6(iii)3 0
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6(iv)0 0
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6(v)0 0
Totals35 9
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Question 6:
6 | 6 | 6 | 6 | 6 | 6 | 6
6 | (i) | Because this test is only valid for random on random
data …
and the speeds are controlled. | E1
E1
[2] | 3.5a
3.5b
6 | (ii) | (A) | (60, 54.7) is an outlier. | B1
[1] | 1.2
6 | (ii) | (B) | Because it is not representative | E1
[1] | 2.4 | N
E
E.g. differs markedly from other
values at same speed OR could be
an error
6 | (iii) | x = 60, y = 49
S
xy 40812(cid:16)840(cid:117)686/14 (cid:16)348
b = = =
S 51150(cid:16)8402 /14 750
xx
40812/14(cid:16)60(cid:117)49 (cid:16)24.857
OR b = =
51150/14(cid:16)492 53.571E
= –0.464
P
hence least squares regression line is:
(cid:159) y – 49 = –0.464 (x – 60)
(cid:159) y = –0.464x + 76.84 | M1
C
A1
M1
A1
[4] | I
1.1a
1.1
3.3
1.1 | M
For attempt at gradient (b)
For –0.464
For equation of line
FT for complete equation
6 | (iv) | (A)
(B) | S
49.9
62.9 | B1
B1
[2] | 3.4
3.4
6 | (v) | First answer is reliable as interpolation and the points
lie close to the line
Second answer less likely to be reliable as
extrapolation | E1
E1
[2] | 3.5a
3.5b
Question | AO1 | AO2 | AO3(PS) | AO3(M) | Total
--- 6(i) ---
6(i) | 0 | 0 | 0 | 2 | 2
S
6(ii)A | 1 | 0 | 0 | 0 | 1
6(ii)B | 0 | 1 | 0 | 0 | 1
--- 6(iii) ---
6(iii) | 3 | 0 | 0 | 1 | 4
--- 6(iv) ---
6(iv) | 0 | 0 | 0 | 2 | 2
--- 6(v) ---
6(v) | 0 | 0 | 0 | 2 | 2
Totals | 35 | 9 | 3 | 13 | 60
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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]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{880026ad-1cd3-40bb-bc87-8dcc94bd9bbd-4_707_1091_1320_477}
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{center}
\end{figure}
\begin{enumerate}[label=(\roman*)]
\item Explain why it would not be appropriate to carry out a hypothesis test for correlation based on the product moment correlation coefficient.
\item (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.

\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
 & Data item & $x$ & $y$ & $x ^ { 2 }$ & $y ^ { 2 }$ & $x y$ \\
\hline
 & 1 & 50 & 53.6 & 2500 & 2872.96 & 2680 \\
\hline
 & 2 & 50 & 53.3 & 2500 & 2840.89 & 2665 \\
\hline
 &  &  &  &  &  &  \\
\hline
 & 13 & 70 & 44.8 & 4900 & 2007.04 & 3136 \\
\hline
 & 14 & 70 & 44.2 & 4900 & 1953.64 & 3094 \\
\hline
Sum &  & 840 & 686 & 51150 & 33779.7 & 40812 \\
\hline
\end{tabular}
\end{center}
\item Calculate the equation of the regression line of $y$ on $x$.
\item Use the equation of the regression line to predict the fuel consumption of the car at\\
(A) 58 mph ,\\
(B) 30 mph .
\item Comment on the reliability of your predictions in part (iv).

}{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 
}\section*{}
\end{enumerate}

\hfill \mbox{\textit{OCR MEI Further Statistics A AS  Q6 [12]}}
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