If the relation between x and u is 3x + 4u + 7=0 and the correlation coefficient bw tween x and y is -0.6, then what is the correlation coefficient between u and y?

Question

Answer

Correlation Coefficient Between u and y:
To find the correlation coefficient between u and y, we need to first express u in terms of x using the given relation 3x + 4u + 7 = 0.

Expressing u in terms of x:
4u = -3x - 7
u = (-3x - 7) / 4
Now that we have u in terms of x, we can relate u to y through x and y's correlation coefficient of -0.6.

Relation between u and y:
Since u = (-3x - 7) / 4, we can express u in terms of y:
u = (-3(1/4)y - 7/4)
This allows us to find the correlation coefficient between u and y:
Corr(u, y) = Corr(u, x) * Corr(x, y)
Given that Corr(x, y) = -0.6, we can substitute into the formula:
Corr(u, y) = Corr(u, x) * (-0.6)
To find Corr(u, x), we can use the formula:
Corr(u, x) = Cov(u, x) / (σu * σx)
However, since we are not provided with the standard deviations of u and x, we cannot directly calculate Corr(u, y) using this method. We would need additional information to fully determine the correlation coefficient between u and y.

Answer

-0.6 ,0.8, 0.6, or -0.8

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