Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): If X and Y are any two variables transformed to new variables U and V defined by , where A, B, h, K are constants and , then .
Reason (R): The correlation coefficient (r) is independent of change of origin and scale.
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If X and Y are any two variables transformed to new variables U and V defined by U = (X - A)/h, V = (Y - B)/K where A, B, h, K are constants and h, K > 0, then r_(xy) = rᵤᵥ. Reason (R): The correlation coefficient (r) is independent of change of origin and scale. (A) Both (A) and (R) are correct and (R) is the correct explanation of (A) (B) Both (A) and (R) are correct but (R) is not the correct explanation of (A) (C) (A) is correct but (R) is not correct (D) (A) is not correct but (R) is correct
Also written as: Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If X and Y are any two variables transformed to new variables U and V defined by U = (X - A)/h, V = (Y - B)/K where A, B, h, K are constants and h, K > 0, then r_(xy) = r_(uv). Reason (R): The correlation coefficient (r) is independent of change of origin and scale.
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This question is on The correlation coefficient, part of Joint distributions, covariance and correlation in Statistics.
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