Show That the Correlation Coefficient Between Y and X Is

question 47

Essay

Show that the correlation coefficient between Y and X is unaffected if you use a linear transformation in both variables. That is, show that corr(X,Y)= corr(X^*, Y^*), where X^* = a + bX and Y^* = c + dY, and where a, b, c, and d are arbitrary non-zero constants.

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Definitions:

Kant's Philosophy

A philosophical doctrine by Immanuel Kant emphasizing rationality, ethics, and a categorical imperative guiding moral actions.

End Justifies

A philosophical principle suggesting the morality of an action can be determined by its outcome or intended result.

Means

Methods or ways employed to achieve a certain end or goal.

Rule Utilitarianism

A form of utilitarianism that suggests the best action is one that conforms to a rule that leads to the greatest good.