| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | June |
| Marks | 14 |
| 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 standard S1 linear regression question with all summations provided. Students follow a routine algorithm: calculate Sdd and Sfd using given summations, find b and a using formulas, then solve a simple inequality. No conceptual challenges or novel problem-solving required—purely mechanical application of memorized procedures. |
| Spec | 2.02c Scatter diagrams and regression lines5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09c Calculate regression line5.09e Use regression: for estimation in context |
| Destination | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) |
| \(d\) | 2.2 | 4.0 | 6.0 | 2.5 | 8.0 | 5.0 |
| \(f\) | 18 | 20 | 25 | 23 | 32 | 28 |
**Question 6(c):** M1 for a correct method seen for either - a correct expression. 1st A1 for $S_{dd}$ awrt 24.2. 2nd A1 for $S_{fd}$ awrt 49.1.
**Question 6(d):** 1st M1 for a correct expression for $b$ - can follow through their answers from (c). 2nd M1 for a correct method to find $a$ - follow through their $b$ and their means. 2nd A1 for $f = \ldots$ in terms of $d$ and all values awrt given expressions. Accept 15 as rounding from correct answer only.
**Question 6(f):** M1 for an attempt to find the intersection of the 2 lines. Value of $t$ in range 500 to 505 seen award M1. Value of $d$ in range 5 to 5.05 award M1. Accept $t$ greater than 500 to 505 inclusive to include graphical solution for M 1A1.6. A travel agent sells flights to different destinations from Beerow airport. The distance $d$, measured in 100 km , of the destination from the airport and the fare $\pounds f$ are recorded for a random sample of 6 destinations.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | }
\hline
Destination & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ \\
\hline
$d$ & 2.2 & 4.0 & 6.0 & 2.5 & 8.0 & 5.0 \\
\hline
$f$ & 18 & 20 & 25 & 23 & 32 & 28 \\
\hline
\end{tabular}
\end{center}
$$\text { [You may use } \sum d ^ { 2 } = 152.09 \quad \sum f ^ { 2 } = 3686 \quad \sum f d = 723.1 \text { ] }$$
\begin{enumerate}[label=(\alph*)]
\item Using the axes below, complete a scatter diagram to illustrate this information.
\item Explain why a linear regression model may be appropriate to describe the relationship between $f$ and $d$.
\item Calculate $S _ { d d }$ and $S _ { f d }$
\item Calculate the equation of the regression line of $f$ on $d$ giving your answer in the form $f = a + b d$.
\item Give an interpretation of the value of $b$.
Jane is planning her holiday and wishes to fly from Beerow airport to a destination $t \mathrm {~km}$ away. A rival travel agent charges 5 p per km.
\item Find the range of values of $t$ for which the first travel agent is cheaper than the rival.\\
\includegraphics[max width=\textwidth, alt={}, center]{039e6fcf-3222-40cc-95ea-37b8dc4a4ddb-11_1013_1701_1718_116}
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2010 Q6 [14]}}