S1 June 2010 Q1
1. Gary compared the total attendance, \(x\), at home matches and the total number of goals, \(y\), scored at home during a season for each of 12 football teams playing in a league. He correctly calculated:
\[S_{xx} = 1\,022\,500 \qquad S_{yy} = 130.9 \qquad S_{xy} = 8825\]Helen was given the same data to analyse. In view of the large numbers involved she decided to divide the attendance figures by 100. She then calculated the product moment correlation coefficient between \(\dfrac{x}{100}\) and \(y\).
| Scheme | Marks |
|---|---|
| \(r = \dfrac{8825}{\sqrt{1022500 \times 130.9}}\), = awrt 0.763 | M1 A1 |
| (2) |
Notes
M1 for a correct expression, square root required
Correct answer award 2/2
| Scheme | Marks |
|---|---|
| Teams with high attendance scored more goals (oe, statement in context) | B1 |
| (1) |
Notes
Context required (attendance and goals). Condone causality.
B0 for ‘strong positive correlation between attendance and goals’ on its own oe
| Scheme | Marks |
|---|---|
| 0.76(3) | B1ft |
| (1) | |
| (4 marks) |
Notes
Value required.
Must be a correlation coefficient between -1 and +1 inclusive.
B1ft for 0.76 or better or same answer as their value from part (a) to at least 2 d.p.