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The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.?
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The coefficient of correlation between x and y is 0.6. If x and y valu...
Explanation:
When x and y values are multiplied by -1, the direction of the relationship between x and y changes, but the strength of the relationship remains the same. This is because the correlation coefficient measures the strength of the linear relationship between two variables, and multiplying both variables by a constant does not affect the linearity of the relationship.
To prove that the coefficient of correlation between x and y remains 0.6 after multiplication by -1, we can use the formula for the correlation coefficient:
r = (nΣxy - ΣxΣy) / [√(nΣx^2 - (Σx)^2) √(nΣy^2 - (Σy)^2)]
where n is the sample size, Σ is the sum of the variable, and Σxy is the sum of the product of x and y.
If we multiply both x and y by -1, the formula becomes:
r' = (nΣ(-x)(-y) - Σ(-x)Σ(-y)) / [√(nΣ(-x)^2 - (Σ(-x))^2) √(nΣ(-y)^2 - (Σ(-y))^2)]
which simplifies to:
r' = (nΣxy - ΣxΣy) / [√(nΣx^2 - (Σx)^2) √(nΣy^2 - (Σy)^2)]
This is the same as the original formula for r, which means that r' = r = 0.6.
Therefore, the correct answer is A) 0.6.
When x and y values are multiplied by -1, the direction of the relationship between x and y changes, but the strength of the relationship remains the same. This is because the correlation coefficient measures the strength of the linear relationship between two variables, and multiplying both variables by a constant does not affect the linearity of the relationship.
To prove that the coefficient of correlation between x and y remains 0.6 after multiplication by -1, we can use the formula for the correlation coefficient:
r = (nΣxy - ΣxΣy) / [√(nΣx^2 - (Σx)^2) √(nΣy^2 - (Σy)^2)]
where n is the sample size, Σ is the sum of the variable, and Σxy is the sum of the product of x and y.
If we multiply both x and y by -1, the formula becomes:
r' = (nΣ(-x)(-y) - Σ(-x)Σ(-y)) / [√(nΣ(-x)^2 - (Σ(-x))^2) √(nΣ(-y)^2 - (Σ(-y))^2)]
which simplifies to:
r' = (nΣxy - ΣxΣy) / [√(nΣx^2 - (Σx)^2) √(nΣy^2 - (Σy)^2)]
This is the same as the original formula for r, which means that r' = r = 0.6.
Therefore, the correct answer is A) 0.6.
Community Answer
The coefficient of correlation between x and y is 0.6. If x and y valu...
-0.6
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The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.?
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