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From the following data X: 2 3 5 4 7 Y:. 4 6 7 8 10 Two coefficient of correlation was found to be 0.93. what is the correlation between u and v as given below? u: -3 -2 0 -1 2 v: -4 -2 -1 0 2?
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From the following data X: 2 3 5 4 7 Y:. 4 6 7 8 10 Two coefficient of...
Correlation between u and v
Calculating the correlation coefficient:
To calculate the correlation coefficient between u and v, we need to use the formula:
r = (n∑uv - (∑u)(∑v)) / sqrt((n∑u^2 - (∑u)^2)(n∑v^2 - (∑v)^2))
Where,
n = number of observations
∑uv = sum of the product of deviations of u and v from their respective means
∑u = sum of deviations of u from its mean
∑v = sum of deviations of v from its mean
∑u^2 = sum of squares of deviations of u from its mean
∑v^2 = sum of squares of deviations of v from its mean
Calculating the values:
n = 5
∑uv = (-3*-4) + (-2*-2) + (0*-1) + (-1*0) + (2*2) = -15
∑u = -4
∑v = -5
∑u^2 = 14
∑v^2 = 14
Substituting the values in the formula, we get:
r = (5*-15 - (-4)*(-5)) / sqrt((5*14 - (-4)^2)(5*14 - (-5)^2))
r = -25 / sqrt(546)
Interpreting the result:
The value of r is approximately -0.62. This indicates a moderate negative correlation between u and v. It means that as the values of u increase, the values of v tend to decrease, and vice versa. However, since the correlation coefficient is not very close to -1, we cannot say that the correlation is very strong.
Conclusion:
The correlation coefficient between u and v is approximately -0.62, indicating a moderate negative correlation.
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From the following data X: 2 3 5 4 7 Y:. 4 6 7 8 10 Two coefficient of...
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From the following data X: 2 3 5 4 7 Y:. 4 6 7 8 10 Two coefficient of correlation was found to be 0.93. what is the correlation between u and v as given below? u: -3 -2 0 -1 2 v: -4 -2 -1 0 2?
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