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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