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Suppose I have the following regression: \begin{align*} y=\beta_0+\beta_1A+\beta_2B+\beta_3C+\beta_4(A*B)+e; \end{align*} where $A$ and $B$ are dummy variables, $C$ is a continuos variable and $A*B$ is a interaction. Suppose, too, I have this other regression: \begin{align*} y=\delta_0+\delta_1A+\epsilon; \end{align*} What is the relation between the coefficientes $(\delta_0,\delta_1)$ and the coefficientes $(\beta_0,\beta_1,\beta_2,\beta_3,\beta_4)$?.

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