Prove That the Regression $R ^ { 2 }$ Is Identical to the Square of the Correlation Coefficient Between

question 28

Essay

Prove that the regression $R ^ { 2 }$ is identical to the square of the correlation coefficient between two variables Y and X . Regression functions are written in a form that suggests causation running from X to Y . Given your proof, does a high regression $R ^ { 2 }$ present supportive evidence of a causal relationship? Can you think of some regression examples where the direction of causality is not clear? Is without a doubt?

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Environmental Scanning

The process of collecting, analyzing, and using information about trends, events, and relationships in an organization's external environment to assist in planning.

Firm's Control

The extent to which a business can influence or dictate its operational environment, including internal processes and external market conditions.

Sociocultural Changes

Alterations in the social and cultural aspects of a society, which can impact consumer behavior, business practices, and market trends.

Two-Income Families

Households in which both partners are employed, contributing to the family's total income and economic status.