The correlation coefficient between two variables X and Y is found to be 0.6. All the observations on X and Y are transformed using the transformations U = 2 – 3X and V = 4Y + 1. The correlation coefficient between the transformed variables U and V will be

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The correlation coefficient between two variables X and Y is found to be 0.6. All the observations on X and Y are transformed using the transformations U = 2 – 3X and V = 4Y + 1. The correlation coefficient between the transformed variables U and V will be

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-0.6
+0.6

Answer 1

Concept:

Corr(a + bX, c +dY) = Corr(bX, dY), Where, var (X) = b & var (Y) = d
Corr(aX, bY) = (ab)Corr (X, Y) where a, b, c, and d are constants
$\begin{aligned} Corr (X, Y) & = \frac{Corr (X, Y)}{\sqrt{Var (X) Var (Y)}} \end{aligned}$

Calculation:

Given:

$\begin{aligned} Corr (X, Y) & = 0.6 \\ Corr (U, V) & = \frac{Corr (U, V)}{\sqrt{Var (U) Var (V)}} \\ = \frac{Corr (2 - 3 X, 4 Y + 1)}{\sqrt{(- 3)^{2}} \sqrt{4^{2}}} \\ = \frac{Corr (- 3 X, 4 Y)}{12} \\ = \frac{(- 3 \times 4) Corr (X, Y)}{12} \\ = \frac{(- 12) Corr (X, Y)}{12} \\ = \frac{- 12}{12} \times 0.6 \\ = - 0.6 \end{aligned}$

Hence, option (3) is correct.

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The correlation coefficient between two variables X and Y is found to be 0.6. All the observations on X and Y are transformed using the transformations U = 2 – 3X and V = 4Y + 1. The correlation coefficient between the transformed variables U and V will be

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