If x and y are two random variables and a, b, c, d are any numbers provided a…
20162021
If x and y are two random variables and a, b, c, d are any numbers provided a ≠ 0, c ≠ 0, then correlation coefficient between ax + b and cy + d is –
Answer: D. r(ax + b, cy + d) = (ac / |ac|) r(x, y) — The correlation coefficient between linear transformations ax + b and cy + d is given by (ac / |ac|)r(x, y). This result follows from the properties of…
- A.
r(ax + b, cy + d) = (ab / cd) r(x, y)
- B.
r(ax + b, cy + d) = (ac / bd) r(x, y)
- C.
r(ax + b, cy + d) = (|ac / bd|) r(x, y)
- D.
r(ax + b, cy + d) = (ac / |ac|) r(x, y)
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Correct answer: D
The correlation coefficient between linear transformations ax + b and cy + d is given by (ac / |ac|)r(x, y). This result follows from the properties of covariance and standard deviation: Cov(ax + b, cy + d) = ac·Cov(x, y), while SD(ax + b) = |a|SD(x) and SD(cy + d) = |c|SD(y). Dividing the covariance by the product of standard deviations yields (ac / |ac|)r(x, y).