| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 9 |
| 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 regression question requiring standard formula application (b = S_wl/S_ll, a = w̄ - bl̄) with summary statistics provided, followed by routine substitution for prediction and a basic reliability comment about extrapolation. Below average difficulty as it's purely procedural with no conceptual challenges. |
| Spec | 5.09b Least squares regression: concepts5.09c Calculate regression line5.09e Use regression: for estimation in context |
| \(l\) | 49.0 | 52.0 | 53.0 | 54.5 | 54.1 | 53.4 | 50.0 | 51.6 | 49.5 | 51.2 |
| \(w\) | 29 | 32 | 34 | 39 | 38 | 35 | 30 | 31 | 29 | 30 |
5. The weight, $w$ grams, and the length, $l \mathrm {~mm}$, of 10 randomly selected newborn turtles are given in the table below.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | l | l | l | }
\hline
$l$ & 49.0 & 52.0 & 53.0 & 54.5 & 54.1 & 53.4 & 50.0 & 51.6 & 49.5 & 51.2 \\
\hline
$w$ & 29 & 32 & 34 & 39 & 38 & 35 & 30 & 31 & 29 & 30 \\
\hline
\end{tabular}
\end{center}
$$\text { (You may use } \mathrm { S } _ { l l } = 33.381 \quad \mathrm {~S} _ { w l } = 59.99 \quad \mathrm {~S} _ { w w } = 120.1 \text { ) }$$
\begin{enumerate}[label=(\alph*)]
\item Find the equation of the regression line of $w$ on $l$ in the form $w = a + b l$.
\item Use your regression line to estimate the weight of a newborn turtle of length 60 mm .
\item Comment on the reliability of your estimate giving a reason for your answer.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2009 Q5 [9]}}