| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate y on x from raw data table |
| Difficulty | Moderate -0.3 This is a standard S1 linear regression question requiring calculation of Sxx, Syy, Sxy and the regression line equation from raw data. While computationally lengthy (10 data points), it follows a completely routine algorithm with no conceptual challenges or problem-solving required. Slightly easier than average due to its purely procedural nature. |
| 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 |
| \(\boldsymbol { x }\) | 11.0 | 22.0 | 7.5 | 21.0 | 13.0 | 16.5 | 14.0 | 16.0 | 18.5 | 20.5 |
| \(\boldsymbol { y }\) | 15.0 | 35.0 | 16.0 | 23.5 | 24.0 | 17.5 | 14.5 | 27.5 | 22.5 | 34.5 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | 60 | 48 |
I appreciate you sharing this, but the content you've provided appears to be incomplete or corrupted. It shows only:
Question 4:
4 | 60 | 48
This doesn't contain any actual mark scheme content with marking annotations (M1, A1, B1, etc.) or guidance notes for me to clean up.
Could you please provide the full mark scheme content for Question 4? Once you share the complete text, I'll be happy to:
- Convert unicode symbols to LaTeX math notation
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- Remove any unnecessary commentary4 [Figure 1, printed on the insert, is provided for use in this question.]\\
Roseen is a self-employed decorator who wishes to estimate the times that it will take her to decorate bedrooms based upon their floor areas. She records the floor area, $x \mathrm {~m} ^ { 2 }$, and the decorating time, $y$ hours, for each of 10 bedrooms she has recently decorated.
\begin{center}
\begin{tabular}{ | l | l | l | r | l | l | l | l | l | l | l | }
\hline
$\boldsymbol { x }$ & 11.0 & 22.0 & 7.5 & 21.0 & 13.0 & 16.5 & 14.0 & 16.0 & 18.5 & 20.5 \\
\hline
$\boldsymbol { y }$ & 15.0 & 35.0 & 16.0 & 23.5 & 24.0 & 17.5 & 14.5 & 27.5 & 22.5 & 34.5 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item On Figure 1, plot a scatter diagram of these data.
\item Calculate the equation of the least squares regression line of $y$ on $x$.
\item Draw your regression line on Figure 1.
\item \begin{enumerate}[label=(\roman*)]
\item Use your regression equation to estimate the time that Roseen will take to decorate a bedroom with a floor area of $15 \mathrm {~m} ^ { 2 }$.
\item Making reference to Figure 1, comment on the likely reliability of your estimate in part (d)(i).
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA S1 2008 Q4 [12]}}