3 [Figure 1, printed on the insert, is provided for use in this question.]
The table shows, for each of a sample of 12 handmade decorative ceramic plaques, the length, \(x\) millimetres, and the width, \(y\) millimetres.
| Plaque | \(\boldsymbol { x }\) | \(\boldsymbol { y }\) |
| A | 232 | 109 |
| B | 235 | 112 |
| C | 236 | 114 |
| D | 234 | 118 |
| E | 230 | 117 |
| F | 230 | 113 |
| G | 246 | 121 |
| H | 240 | 125 |
| I | 244 | 128 |
| J | 241 | 122 |
| K | 246 | 126 |
| L | 245 | 123 |
- Calculate the value of the product moment correlation coefficient between \(x\) and \(y\).
- Interpret your value in the context of this question.
- On Figure 1, complete the scatter diagram for these data.
- In fact, the 6 plaques \(\mathrm { A } , \mathrm { B } , \ldots , \mathrm { F }\) are from a different source to the 6 plaques \(\mathrm { G } , \mathrm { H } , \ldots , \mathrm { L }\). With reference to your scatter diagram, but without further calculations, estimate the value of the product moment correlation coefficient between \(x\) and \(y\) for each source of plaque.