# Obtain the OLS estimators of the simple model from the multiple model

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In the context of the simple regression model (two variables) we know that the estimators of OLS are given from:

$$\hat{\beta}_{1}=\frac{Cov(x_i.y_i)}{Var(x_i} \quad and \quad \hat{\beta_0}=\bar{y_i}-\hat{\beta}_{1}\bar{x_i}$$

Use the correct matrix $$X$$ so that from the OLS estimator of a multiple regression $$\hat{\beta}=(X´X)^{-1} X´y$$, obtain the estimators of the simple regression model.

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