Your Textbook Discussed the Regression Model When X Is a Binary

question 29

Essay

Your textbook discussed the regression model when X is a binary variable $$Y _ { i } = \beta _ { 0 } + \beta _ { 1 } D _ { i } + u _ { i } , i = 1 , \ldots , n$$ Let $Y$ represent wages, and let $D$ be one for females, and 0 for males. Using the OLS formula for the slope coefficient, prove that $\widehat { \beta } _ { 1 }$ is the difference between the average wage for males and the average wage for females.

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Definitions:

Personal Power

Refers to the influence or authority an individual possesses that stems from within, often based on competence, skill, or personality, rather than formal position.

Referent Power

A form of influence based on the ability to inspire admiration, respect, or affection from others, often stemming from one's charisma or likability.

Coercive Power

A form of power that is based on the ability to deliver punishments or impose negative consequences on other people.

Legitimate Power

A form of authority derived from an individual's position or role within an organization, granting them the ability to influence others.