Consider a linear regression model of the form Y $=$ a $+$ b X $+$ U$,$ where U is the error and a and b are coefficients that should be estimated. Suppose that X is a binary variable $($it only takes values $0$ or $1).$ Suppose also that a and b are estimated by the OLS method. 

Prove that the OLS method will give estimates for $(1)$ E$($Y$|$X$=0)$  and E$($Y$|$X$=1)-$E$($Y$=0)$

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Proof that OLS estimates EYX0 and EYX1EYX0 We are given a linear regression model YabXU where Y is the dependent variable X is a binary independent variable X 0 or 1 a and b are coefficients to be est... View the full answer