| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate regression line then predict |
| Difficulty | Moderate -0.8 This is a straightforward application of standard S1 regression formulas with clear data and direct substitution. Part (a) requires calculating summary statistics and applying the regression formulae (routine computation), while part (b) is simple substitution into the equation. No conceptual challenges or problem-solving insight required—purely mechanical calculation below average difficulty. |
| Spec | 5.09b Least squares regression: concepts5.09c Calculate regression line5.09d Linear coding: effect on regression |
| \(\boldsymbol { x }\) | 10 | 12 | 15 | 18 | 20 | 22 | 25 | 28 | 30 |
| \(\boldsymbol { y }\) | 42.9 | 40.6 | 38.5 | 35.4 | 33.0 | 30.7 | 28.0 | 25.3 | 22.6 |
1 The table shows the times taken, $y$ minutes, for a wood glue to dry at different air temperatures, $x ^ { \circ } \mathrm { C }$.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | }
\hline
$\boldsymbol { x }$ & 10 & 12 & 15 & 18 & 20 & 22 & 25 & 28 & 30 \\
\hline
$\boldsymbol { y }$ & 42.9 & 40.6 & 38.5 & 35.4 & 33.0 & 30.7 & 28.0 & 25.3 & 22.6 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Calculate the equation of the least squares regression line $y = a + b x$.
\item Estimate the time taken for the glue to dry when the air temperature is $21 ^ { \circ } \mathrm { C }$.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2008 Q1 [6]}}