| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Explain least squares concept |
| Difficulty | Moderate -0.8 This question tests basic conceptual understanding of regression terminology (independent variable, least squares definition, correlation coefficients) with minimal calculation. Parts require only recall and diagram interpretation—no problem-solving or multi-step reasoning. Easier than average A-level statistics questions. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08e Spearman rank correlation5.09a Dependent/independent variables5.09b Least squares regression: concepts |
7 The diagram shows the results of an experiment involving some bivariate data. The least squares regression line of $y$ on $x$ for these results is also shown.\\
\includegraphics[max width=\textwidth, alt={}, center]{48ffcd44-d933-40e0-818a-20d6db607298-5_748_919_390_612}\\
(i) Given that the least squares regression line of $y$ on $x$ is used for an estimation, state which of $x$ or $y$ is treated as the independent variable.\\
(ii) Use the diagram to explain what is meant by 'least squares'.\\
(iii) State, with a reason, the value of Spearman's rank correlation coefficient for these data.\\
(iv) What can be said about the value of the product moment correlation coefficient for these data?
\hfill \mbox{\textit{OCR S1 2011 Q7 [6]}}