Question

If u + 5x = 6 and 3y - 7v = 20 and the correlation coefficient between x and y is 0.58 then what
would be the correlation coefficient between u and v?
(a) 0.58
(b) -0.58
(c) -0.84
(d) 0.84​

Answer 1

Answer:

b)-0.58

Step-by-step explanation:

As correlation coefficient is unaffected by change of scale and origin the absolute value of 'r' will not change .

Whereas sign will change as sign of scales are different.

I.e -5 and 3/7 from :-

u=6-5x and v=3/7y-20

Answer 2

Given : u + 5x = 6 and 3y - 7v = 20 and the correlation coefficient between x and y is 0.58

To Find : what  would be the correlation coefficient between u and v

Solution:

correlation coefficient between x and y is 0.58  

u + 5x = 6

=> u  = 6 - 5x

-5 is the factor    ( constant does not have any impact)

3y - 7v = 20

=> 7v   = 3y - 20

=> v = (3/7)y - 20/7

(3/7) is the factor  ( constant does not have any impact)

correlation coefficient between u and v =  0.58 * (-5)(3/7) / √(-5)²√(3/7)²

= -0.58

correlation coefficient between u and v = -0.58

option b is correct

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