| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2013 |
| Session | November |
| Marks | 6 |
| Topic | Linear regression |
| Type | Identify response/explanatory variables |
| Difficulty | Moderate -0.8 This is a straightforward statistics question requiring identification of the independent variable (trivial) and calculation of a least squares regression line using standard formulas. While it involves multiple calculations (means, sums of products, etc.) and 5 marks for part (ii), these are routine A-level statistics procedures with no conceptual challenges or novel problem-solving required. The question is easier than average because it's purely mechanical application of learned formulas. |
| Spec | 5.09a Dependent/independent variables5.09c Calculate regression line |
| Units of alcohol consumed | 2 | 3 | 3 | 4 | 4.5 | 5.5 | 6 | 6 | 7 | 8 | 8 | 9 |
| Reaction time (seconds) | 1 | 2 | 5 | 5 | 3.8 | 5.5 | 4.8 | 8.5 | 7.2 | 6.8 | 9 | 8 |
As part of a study into the effects of alcohol, volunteers have their reaction times measured after they have consumed various fixed amounts of alcohol. For a random sample of 12 volunteers the following information was collected.
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Units of alcohol consumed & 2 & 3 & 3 & 4 & 4.5 & 5.5 & 6 & 6 & 7 & 8 & 8 & 9 \\
\hline
Reaction time (seconds) & 1 & 2 & 5 & 5 & 3.8 & 5.5 & 4.8 & 8.5 & 7.2 & 6.8 & 9 & 8 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\roman*)]
\item Which is the independent variable in this experiment? [1]
\item Find the least squares regression line of $y$ (Reaction time) on $x$ (Units of alcohol), and use it to estimate the reaction time of someone who has consumed 5 units of alcohol. [5]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2013 Q4 [6]}}