| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2013 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Sketch theoretical scatter diagram |
| Difficulty | Moderate -0.8 This question tests basic understanding of correlation coefficients and regression lines through sketching, requiring only recall of standard definitions (r=0 means no linear relationship, r=-1 means perfect negative linear relationship) and the textbook fact that both regression lines coincide when |r|=1. No calculation or problem-solving is needed, just visual representation of memorized concepts. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.09a Dependent/independent variables |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Sketch 6 randomly scattered points (lose B1 here if not 6 points) | B1 | |
| Sketch 6 (or more) points as if on negative gradient line | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Show on (i) line labelled \(y\) on \(x\) between points and approx. horizontal | B1 | |
| Show on (i) line labelled \(x\) on \(y\) between points and approx. vertical | B1 | |
| Show on (ii) line labelled \(y\) on \(x\) passing through points | B1 | |
| State or show on (ii) that \(x\) on \(y\) coincides with \(y\) on \(x\) | B1 |
## Question 6:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Sketch 6 randomly scattered points (lose B1 here if not 6 points) | B1 | |
| Sketch 6 (or more) points as if on negative gradient line | B1 | |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Show on (i) line labelled $y$ on $x$ between points and approx. horizontal | B1 | |
| Show on (i) line labelled $x$ on $y$ between points and approx. vertical | B1 | |
| Show on (ii) line labelled $y$ on $x$ passing through points | B1 | |
| State or show on (ii) that $x$ on $y$ coincides with $y$ on $x$ | B1 | |
**Total: 6 marks**
---6 Six pairs of values of variables $x$ and $y$ are measured. Draw a sketch of a possible scatter diagram of the data for each of the following cases:\\
(i) the product moment correlation coefficient is approximately zero;\\
(ii) the product moment correlation coefficient is exactly - 1 .
On your diagram for part (i), sketch the regression line of $y$ on $x$ and the regression line of $x$ on $y$, labelling each line.
On your diagram for part (ii), sketch the regression line of $y$ on $x$ and state its relationship to the regression line of $x$ on $y$.
\hfill \mbox{\textit{CAIE FP2 2013 Q6 [6]}}