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If the relationship between two variables x and y in given by 2x + 3y + 4 = 0, then the value of the correlation coefficient between x and y is
  • a)
    0
  • b)
    1
  • c)
    – 1
  • d)
    negative
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the relationship between two variables x and y in given by 2x + 3y ...
y = -2/3 x - 4/3 .. (1) which is regression equation of y on x and
x = -3/2 y -2 ...(2) which is regression of x on y. From (1), regression coefficient of y on x i.e. b (yx) = -2/3 & from (2) regression coefficient of x on y i.e. b (xy) = -3/2
We know, b(yx) * b (xy) = r^2 where r is the correlation coefficient of x & y. Hence r^2 = 1 Or, r = +/ - 1
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Most Upvoted Answer
If the relationship between two variables x and y in given by 2x + 3y ...
Given equation: 2x + 3y + 4 = 0

Solving for y:
3y = -2x - 4
y = (-2/3)x - (4/3)

This is the equation of a straight line in slope-intercept form, where the slope is -2/3.

Therefore, we can conclude the following:

1. The correlation coefficient between x and y is equal to the slope of the line.
2. The slope of the line is negative.
3. Therefore, the correlation coefficient between x and y is negative.

Option (d) is incorrect because it only states that the correlation coefficient is negative, without specifying the value of the coefficient. Option (a) is incorrect because a correlation coefficient of zero would mean there is no linear relationship between x and y, which is not the case here. Option (b) is incorrect because a correlation coefficient of 1 would mean there is a perfect positive linear relationship between x and y, which is also not the case here.

Therefore, the correct answer is option (c), which states that the correlation coefficient is negative, without specifying the exact value.
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Community Answer
If the relationship between two variables x and y in given by 2x + 3y ...
Two discrete random· variable X and Y are .
connected by the relation 2X + 3 Y + 4 = 0. Prove
that the correlation coefficient between X and Y
is - 1.
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If the relationship between two variables x and y in given by 2x + 3y + 4 = 0, then the value of the correlation coefficient between x and y isa)0b)1c)– 1d)negativeCorrect answer is option 'C'. Can you explain this answer?
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