Question

if karl Pearson coefficient of correlation between X and Y js 0.4 then the corresponding value between 2x and 2y is​

Answer 1

Answer:

0.5

Explanation:

Pearson correlation coefficient is invariant to the change of origin but it get affected by the change of scale. If we multiply X and Y with opposite signed scaler, then sign of the Pearson correlation coefficient changes to the opposite sign to the original one. Hence the correlation coefficient between 2x-4 and 3–2y is -0.5

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Answer 2

Karl Pearson's coefficient of correlation between 2X and 2Y is 0.4

Given:

Karl Pearson's coefficient of correlation between X and Y is 0.4

To Find:

corresponding Karl Pearson coefficient of correlation value between 2x and 2y

Solution:

1. Karl Pearson's correlation coefficient does not depend on the change of origin but it gets affected by the change of scale.

2. If we multiply X and Y with an oppositely signed scaler then the sign of the Karl Pearson correlation coefficient changes to the opposite sign of the original one with no change in magnitude.

3. If we multiply X and Y with the same signed scaler then the sign of the Karl Pearson correlation coefficient remains the same as the original one with no change in magnitude.

Coming to the numerical, since X and Y are multiplied with the same signed scalar ( i.e 2 ) so  Karl Pearson's coefficient of correlation does not change.

Hence, Karl Pearson's coefficient of correlation between 2X and 2Y = 0.4

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