| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Estimate correlation from scatter diagram |
| Difficulty | Easy -1.2 This is a straightforward pattern-matching exercise requiring only visual interpretation of scatter diagrams and basic understanding of correlation coefficient signs and magnitudes. No calculations are needed, just recognition that positive slopes give positive r, negative slopes give negative r, and scattered points give values near zero. This is simpler than typical S1 questions which require actual calculations. |
| Spec | 2.02c Scatter diagrams and regression lines2.02d Informal interpretation of correlation |
| Answer | Marks |
|---|---|
| Diagram A: \(y\) & \(x\): \(r = -0.79\); As \(x\) increases, \(y\) decreases, or most points lie in the 2nd and 4th quadrant | B1; B1dep |
| Diagram B: \(v\) & \(u\): \(r = 0.08\); No real pattern. Several values of \(v\) for one value of \(u\), or points lie in all four quadrants, randomly scattered | B1; B1dep |
| Diagram C: \(t\) & \(s\): \(r = 0.68\); As \(s\) increases, \(t\) increases, or most points lie in the 1st and 3rd quadrants | B1; B1dep |
# Question 1:
**Diagram A:** $y$ & $x$: $r = -0.79$; As $x$ increases, $y$ decreases, or most points lie in the 2nd and 4th quadrant | B1; B1dep |
**Diagram B:** $v$ & $u$: $r = 0.08$; No real pattern. Several values of $v$ for one value of $u$, or points lie in all four quadrants, randomly scattered | B1; B1dep |
**Diagram C:** $t$ & $s$: $r = 0.68$; As $s$ increases, $t$ increases, or most points lie in the 1st and 3rd quadrants | B1; B1dep |
---\begin{enumerate}
\item The scatter diagrams below were drawn by a student.
\end{enumerate}
$$\begin{aligned}
& y \underset { x } { \begin{array} { l l l l }
& & \\
+ & & & \\
+ & + & + & \\
+ & + & +
\end{array} }
\end{aligned}$$
The student calculated the value of the product moment correlation coefficient for each of the sets of data.
The values were
$$\begin{array} { l l l }
0.68 & - 0.79 & 0.08
\end{array}$$
Write down, with a reason, which value corresponds to which scatter diagram.\\
(6)\\
\hfill \mbox{\textit{Edexcel S1 2005 Q1 [6]}}