| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate y on x from raw data table |
| Difficulty | Moderate -0.8 This is a straightforward S1 linear regression question requiring standard calculations with given summary statistics. Parts (a) and (b) are routine plotting and reading from a graph, while part (c) involves direct substitution into the correlation coefficient formula with all necessary sums provided. No problem-solving insight required, just careful arithmetic and formula recall. |
| Spec | 2.02c Scatter diagrams and regression lines5.08a Pearson correlation: calculate pmcc5.09c Calculate regression line |
| Registration letter | \(K\) | \(L\) | \(M\) | \(N\) | \(P\) | \(R\) | \(S\) | \(T\) | \(V\) |
| Number of cars \(( x )\) | 6 | 7 | 9 | 11 | 15 | 14 | 12 | 10 | 7 |
| Number of vans \(( y )\) | 8 | 10 | 14 | 13 | 13 | 15 | 14 | 9 | 8 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Scatter graph showing moderate positive correlation | B5 | |
| (b) 7 or 8 | M1 A1 | |
| (c) \(\sum x = 91\), \(\sum y = 104\) | B1 | |
| \(S_{xx} = 80.89\), \(S_{yy} = 62.22\), \(S_{xy} = 54.44\), \(r = 0.767\) | M1 A1 A1 | |
| which confirms the moderate positive correlation | B1 | Total: 12 marks |
(a) Scatter graph showing moderate positive correlation | B5 |
(b) 7 or 8 | M1 A1 |
(c) $\sum x = 91$, $\sum y = 104$ | B1 |
$S_{xx} = 80.89$, $S_{yy} = 62.22$, $S_{xy} = 54.44$, $r = 0.767$ | M1 A1 A1 |
which confirms the moderate positive correlation | B1 | **Total: 12 marks**\begin{enumerate}
\item The table shows the numbers of cars and vans in a company's fleet having registrations with the prefix letters shown.
\end{enumerate}
\begin{center}
\begin{tabular}{ | l | | c | r | r | l | l | l | l | r | c | }
\hline
Registration letter & $K$ & \multicolumn{1}{|c|}{$L$} & $M$ & $N$ & $P$ & $R$ & $S$ & $T$ & $V$ \\
\hline
Number of cars $( x )$ & 6 & 7 & 9 & 11 & 15 & 14 & 12 & 10 & 7 \\
\hline
Number of vans $( y )$ & 8 & 10 & 14 & 13 & 13 & 15 & 14 & 9 & 8 \\
\hline
\end{tabular}
\end{center}
(a) Plot a scatter graph of this data, with the number of cars on the horizontal axis and the number of vans on the vertical axis.\\
(b) If there were $4 J$-registered cars, estimate the number of $J$-registered vans.
Given that $\sum x ^ { 2 } = 1001 , \sum y ^ { 2 } = 1264$ and $\sum x y = 1106$,\\
(c) calculate the product-moment correlation coefficient between $x$ and $y$. Give a brief interpretation of your answer.\\
\hfill \mbox{\textit{Edexcel S1 Q5 [12]}}