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

question 10

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 $\operatorname { corr } ( X , Y ) = \operatorname { corr } \left( X ^ { * } , Y ^ { * } \right) \text {, }$ where $X ^ { * } = a + b X \text { and } Y ^ { * } = c + d Y \text {, }$ and where a, b, c , and d are arbitrary non-zero constants.

---

Definitions:

Organizational Resources

Assets, capabilities, and inputs that an organization utilizes to operate and achieve its objectives, including human, financial, and physical resources.

Environmental Opportunities

Circumstances in the external environment that a business can exploit to its advantage.

Organizational Weaknesses

Aspects of an organization that reduce its ability to reach its goals, including deficiencies in resources, processes, or capabilities.

Mission Statement

A concise statement that defines the purpose and guiding principles of an organization, informing its goals and strategic direction.