Consider the Following Two Models Involving Binary Variables as Explanatory

question 43

Essay

Consider the following two models involving binary variables as explanatory
variables: $$\widehat { \text { Wage } } = \widehat { \beta } _ { 0 } + \widehat { \beta } _ { 1 } D \text { Femme and } \widehat { \text { Wage } } = \widehat { \phi } _ { 1 } D \text { Femme } + \widehat { \phi } _ { 2 } \text { Male }$$ 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 $\beta \mathrm { s }$ and the $\phi s$ ? Why would you prefer one model over the other?

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Definitions:

Crutches

Mobility aids consisting of two long sticks with crosspieces for a person to place under their arms and use for support while walking.

Physical Therapist

A healthcare professional specialized in diagnosing and treating individuals of all ages, who have medical problems or health-related conditions that limit their abilities to move and perform functional activities in their daily lives.

Range-Of-Motion Exercises

Physical activities designed to improve or maintain the flexibility and mobility of joints through stretching and movement.

ROM

ROM stands for Range of Motion, which is the full movement potential of a joint, usually its range of flexion and extension.