OCR S1 2011 June — Question 7 6 marks

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2011
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLinear regression
TypeExplain least squares concept
DifficultyModerate -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.
Spec5.08a 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}
  1. 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.
  2. Use the diagram to explain what is meant by 'least squares'.
  3. State, with a reason, the value of Spearman's rank correlation coefficient for these data.
  4. What can be said about the value of the product moment correlation coefficient for these data?

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]}}