To study the relationship between income and person’s gender you decide to fit the following regression model:

1. To study the relationship between income and person’s gender you decide to fit the following regression model:
Y i=β 0 + β 1 d i +ui i=1, … , N
where d i is a binary variable which is one for females, that constitute n f
observations out of N, and zero for male, that make up nm observations. n f +nm =N .
Suppose that the observations in your sample were sorted so that d i=1 for i=1,… , n f and
d i=0 for i=n f +1, … , nm . Show that the OLS estimate of the slope equals to the
difference in the average income for female and male.
^
β 1= y´ f − y´m
´ n f , you can express any mean as
Hints: d=
N
N
N x´ =∑ x i
i=1
 
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