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The correlation coefficient between two variables X and Y is 0.4. The correlation coefficient between 2X and (-Y) will be:

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SSC CGL Tier-II ( JSO ) 2016 Official Paper ( Held On : 2 Dec 2016 )
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  1. 0.4
  2. -0.8
  3. -0.4
  4. 0.8

Answer (Detailed Solution Below)

Option 3 : -0.4
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Detailed Solution

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Given

The correlation coefficient between two variables X and Y = 0.4

Concept used

The correlation coefficient (r) is independent of origin and scale and depend on the sign of variables

Calculation

The correlation coefficient between the two variables is the measure of the slope between the variables in the regression graph. It is given that the correlation coefficient between X and Y is 0.4 and the correlation coefficient is independent of change of origin and scale but it depends on variables 

∴ The correlation coefficient between 2X and (-Y) is - 0.4

 

The value of simple correlation coefficient in the interval of [-1, 1]

The regression coefficient is independent of the change of origin. But, they are not independent of the change of the scale. It means there will be no effect on the regression coefficient if any constant is subtracted from the values of x and y

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