| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2016 |
| 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 standard S1 regression question requiring calculation of least squares line from data (using formulas for Sxx, Sxy), interpretation of gradient, interpolation, and comment on residuals. All steps are routine textbook procedures with no problem-solving insight needed, making it easier than average A-level maths questions, though the arithmetic with 12 data points requires care. |
| Spec | 2.02c Scatter diagrams and regression lines5.09c Calculate regression line5.09e Use regression: for estimation in context |
| \(\boldsymbol { x }\) | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 |
| \(\boldsymbol { y }\) | 242 | 262 | 269 | 290 | 298 | 310 | 326 | 355 | 359 | 375 | 390 | 412 |
4 As part of her science project, a student found the mass, $y$ grams, of a particular compound that dissolved in 100 ml of water at each of 12 different set temperatures, $x ^ { \circ } \mathrm { C }$. The results are shown in the table.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | c | c | c | }
\hline
$\boldsymbol { x }$ & 20 & 25 & 30 & 35 & 40 & 45 & 50 & 55 & 60 & 65 & 70 & 75 \\
\hline
$\boldsymbol { y }$ & 242 & 262 & 269 & 290 & 298 & 310 & 326 & 355 & 359 & 375 & 390 & 412 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Calculate the equation of the least squares regression line of $y$ on $x$.
\item Interpret, in context, your value for the gradient of this regression line.
\item Use your equation to estimate the mass of the compound which will dissolve in 100 ml of water at $68 ^ { \circ } \mathrm { C }$.
\item Given that the values of the 12 residuals for the regression line of $y$ on $x$ lie between - 7 and + 9 , comment, with justification, on the likely accuracy of your estimate in part (c).\\[0pt]
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2016 Q4 [9]}}