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

Question

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

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The Answer of Show that the correlation coefficient between  Y  and  X  is unaffected if you use a linear transformation in both variables. That is, show that $\operatorname { corr } ( X , Y ) = \operatorname { corr } \left( X ^ { * } , Y ^ { * } \right) \text {, }$ where $X ^ { * } = a + b X \text { and } Y ^ { * } = c + d Y \text {, }$ and where  a, b, c , and  d  are arbitrary non-zero constants.

Show That the Correlation Coefficient Between Y and corr⁡(X,Y)=corr⁡(X∗,Y∗), \operatorname { corr } ( X , Y ) = \operatorname { corr } \left( X ^ { * } , Y ^ { * } \right) \text {, }corr(X,Y)=corr(X∗,Y∗),

Show That the Correlation Coefficient Between Y and $\operatorname { corr } ( X , Y ) = \operatorname { corr } \left( X ^ { * } , Y ^ { * } \right) \text {, }$