| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Explain least squares concept |
| Difficulty | Moderate -0.3 This is a standard S1 regression question requiring conceptual understanding of regression lines (part i), residuals (part ii), calculation of PMCC using formula (part iii), and interpretation (part iv). The calculation is routine with small numbers, and the conceptual parts test basic understanding rather than deep insight. Slightly easier than average due to straightforward data and standard bookwork concepts. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08c Pearson: measure of straight-line fit5.09a Dependent/independent variables5.09b Least squares regression: concepts |
| \(x\) | 1 | 2 | 3 | 4 | 5 | 6 |
| \(y\) | 3 | 6 | 8 | 8 | 11 | 10 |
In an agricultural experiment, the relationship between the amount of water supplied, $x$ units, and the yield, $y$ units, was investigated. Six values of $x$ were chosen and for each value of $x$ the corresponding value of $y$ was measured. The results are shown in the table.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
$x$ & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
$y$ & 3 & 6 & 8 & 8 & 11 & 10 \\
\hline
\end{tabular}
\end{center}
These results, together with the regression line of $y$ on $x$, are plotted on the graph.
\includegraphics{figure_1}
\begin{enumerate}[label=(\roman*)]
\item Give a reason why the regression line of $x$ on $y$ is not suitable in this context. [1]
\item Explain the significance, for the regression line of $y$ on $x$, of the distances shown by the vertical dotted lines in the diagram. [2]
\item Calculate the value of the product moment correlation coefficient, $r$. [3]
\item Comment on your value of $r$ in relation to the diagram. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2009 Q3 [8]}}