MCQ 11 Mark
Calculate the correlation coefficient between x and y and comment on their relationship
| X | 3 | 2 | 1 | 1 | 2 | 3 |
| Y | 9 | 4 | 1 | 1 | 4 | 9 |
- A$0.47$
- B$0.25$
- C$0.0$
- ✓$0.99$
Answer
View full question & answer→Correct option: D.
$0.99$
(d) 0.99
Explanation:
$\begin{array}{l} r =\frac{N \sum X Y-\sum X \sum Y}{\sqrt{N \sum X^2-\left(\sum X\right)^2} \sqrt{N \sum Y^2-\left(\sum Y\right)^2}} \\ =\frac{6(16)-(0)(4)}{\sqrt{6(4)-(0)^2} \sqrt{6(68)-(4)^2}}=0.99\end{array}$
Explanation:
| X | Y | dX | dY | $d X^2$ | $d Y^2$ | dXdY |
| 3 | 9 | 1 | 5 | 1 | 25 | 5 |
| 2(A) | 4(A) | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | -1 | -3 | 1 | 9 | 3 |
| 1 | 1 | -1 | -3 | 1 | 9 | 3 |
| 2 | 4 | 0 | 0 | 0 | 0 | 0 |
| 3 | 9 | 1 | 5 | 1 | 25 | 5 |
| $\sum$ | 0 | 4 | 4 | 68 | 16 |