| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate y on x from raw data table |
| Difficulty | Moderate -0.8 This is a straightforward S1 linear regression question requiring standard calculations (Σx, Σy, Σx², Σxy) from a data table, applying the regression formula, and making predictions. While it involves multiple parts and arithmetic with 9 data points, it follows a completely routine procedure with no conceptual challenges or novel problem-solving required. |
| Spec | 5.09c Calculate regression line5.09e Use regression: for estimation in context |
| \(\boldsymbol { x }\) days | 5 | 10 | 15 | 20 | 30 | 40 | 50 | 60 | 75 |
| \(\boldsymbol { y }\) grams | 47 | 44 | 42 | 38 | 35 | 27 | 23 | 16 | 9 |
| PART PEFRENC | |
| ..... | ............................................................................................................................................ |
| \(\_\_\_\_\) | \(\_\_\_\_\) |
| \(\_\_\_\_\) | |
| \(\_\_\_\_\) | |
| \includegraphics[max width=\textwidth, alt={}]{adf1c0d2-b0a6-4a2f-baf2-cfb45d771315-08_57_1681_2227_161} | |
| \(\_\_\_\_\) | |
4 As part of an investigation, a chlorine block is immersed in a large tank of water held at a constant temperature. The block slowly dissolves, and its weight, $y$ grams, is noted $x$ days after immersion. The results are shown in the table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | }
\hline
$\boldsymbol { x }$ days & 5 & 10 & 15 & 20 & 30 & 40 & 50 & 60 & 75 \\
\hline
$\boldsymbol { y }$ grams & 47 & 44 & 42 & 38 & 35 & 27 & 23 & 16 & 9 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Calculate the equation of the least squares regression line of $y$ on $x$.
\item Hence estimate, to the nearest gram, the initial weight of the block.
\item A company which markets the chlorine blocks claims that a block will usually dissolve completely after about 13 weeks. Comment, with justification, on this claim.
\begin{center}
\begin{tabular}{|l|l|}
\hline
PART PEFRENC & \\
\hline
& \\
\hline
..... & ............................................................................................................................................ \\
\hline
$\_\_\_\_$ & $\_\_\_\_$ \\
\hline
\multicolumn{2}{|c|}{} \\
\hline
\multicolumn{2}{|c|}{} \\
\hline
& $\_\_\_\_$ \\
\hline
& \\
\hline
& \\
\hline
& $\_\_\_\_$ \\
\hline
\multicolumn{2}{|c|}{} \\
\hline
\multicolumn{2}{|c|}{} \\
\hline
& \includegraphics[max width=\textwidth, alt={}]{adf1c0d2-b0a6-4a2f-baf2-cfb45d771315-08_57_1681_2227_161}
\\
\hline
& \\
\hline
\multicolumn{2}{|c|}{} \\
\hline
& $\_\_\_\_$ \\
\hline
& \\
\hline
\end{tabular}
\end{center}
.......... $\_\_\_\_$\\
\includegraphics[max width=\textwidth, alt={}, center]{adf1c0d2-b0a6-4a2f-baf2-cfb45d771315-09_40_118_529_159}
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2009 Q4 [8]}}