Your Textbook Discussed the Regression Model When X Is a Binary

question 52

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 intercept coefficient, prove that $\widehat { \beta } _ { 0 }$ is the average wage for males.

---

Definitions:

Iliopsoas

A composite muscle comprised of the iliacus and psoas major muscles; it is critical for flexing the hip and bending the trunk.

Sartorius

The longest muscle in the human body, running from the hip to the knee, assisting in flexing, abduction, and lateral rotation of the thigh.

Dura Mater

The outermost, tough layer of the meninges that envelops the brain and spinal cord, providing protection.

Meninx

Meninx (plural, meninges) refers to one of the three membranes (the dura mater, arachnoid mater, and pia mater) that cover the brain and spinal cord.