Consider the Following Two Models Involving Binary Variables as Explanatory $\widehat { \text { Wage } }$

question 29

Essay

Consider the following two models involving binary variables as explanatory variables: $\widehat { \text { Wage } }$ = $\widehat { \beta 0 }$ + $\widehat { \beta 1 }$ DFemme and $\widehat { \text { Wage } }$ = $\widehat { \phi _ { 1 } }$ DFemme + $\widehat { \phi _ { 2 } }$ Male
where Wage is the hourly wage rate, DFemme is a binary variable that is equal to 1 if the person is a female, and 0 if the person is a male. Male = 1 - DFemme. Even though you have not learned about regression functions with two explanatory variables (or regressions without an intercept), assume that you had estimated both models, i.e., you obtained the estimates for the regression coefficients.
What is the predicted wage for a male in the two models? What is the predicted wage for a female in the two models? What is the relationship between the ? s and the ?s? Why would you prefer one model over the other?

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Definitions:

Commission Charges

Fees paid to an agent or company for facilitating a sale, typically calculated as a percentage of the sale price.

Dollar Amount

The dollar amount refers to a monetary value expressed in units of currency, particularly in dollars.

Cumulative Preferred Stock

A type of preferred stock where dividends accumulate if not paid in a given year, and must be paid out before any dividends on common stock.

Capital Stock

The amount of shares that a company's shareholders have purchased and own, representing ownership in the company.