Solution:
The formula for correlation coefficient is given as below:
Correlation coefficient = r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]
The calculation table is given as below:
No. |
X |
Y |
XY |
X^2 |
Y^2 |
1 |
-3 |
5 |
-15 |
9 |
25 |
2 |
-2 |
6 |
-12 |
4 |
36 |
3 |
6 |
-1 |
-6 |
36 |
1 |
4 |
7 |
3 |
21 |
49 |
9 |
Total |
8 |
13 |
-12 |
98 |
71 |
From above table, we have
n = 4
∑x = 8
∑y = 13
∑x^2 = 98
∑y^2 = 71
∑xy = -12
r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]
r = (4*(-12) - 8*13)/sqrt((4*98 - 8^2)*(4*71 - 13^2))
r = -152 / 194.2164
r = -0.78263
r = -0.783
Answer: 1) -0.783
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