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If the two lines of regression are 5x + 3y = 55 and 7x + y = 45, then the correlation coefficient between x and y is
  • a)
    + 1
  • b)
    - 1
  • c)
    - √(5/21)
  • d)
    - √(21/5)
Correct answer is option 'C'. Can you explain this answer?
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If the two lines of regression are 5x + 3y = 55 and 7x + y = 45, then ...
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If the two lines of regression are 5x + 3y = 55 and 7x + y = 45, then ...
Given lines of regression:

Line 1: 5x - 3y = 55
Line 2: 7x - y = 45

To find the correlation coefficient between x and y, we need to find the slope of the lines of regression.

Finding the slope of Line 1:
Rearranging Line 1 to the slope-intercept form (y = mx + c):
-3y = -5x + 55
Dividing both sides by -3:
y = (5/3)x - 55/3

The slope of Line 1 is 5/3.

Finding the slope of Line 2:
Rearranging Line 2 to the slope-intercept form (y = mx + c):
y = 7x - 45

The slope of Line 2 is 7.

The correlation coefficient (r) between x and y is given by the ratio of the slopes of the lines of regression.

r = slope of Line 1 / slope of Line 2
r = (5/3) / 7
r = 5/3 * 1/7
r = 5/21

Therefore, the correlation coefficient between x and y is √(5/21), which corresponds to option C.
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If the two lines of regression are 5x + 3y = 55 and 7x + y = 45, then the correlation coefficient between x and y isa)+ 1b)- 1c)- √(5/21)d)- √(21/5)Correct answer is option 'C'. Can you explain this answer?
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