Let \(X_{i}\) denote a binary variable, and consider the regression \(Y_{i}=\beta_{0}+\) \(\beta_{1} X_{i}+u_{i}\). Let \(\bar{Y}_{0}\) denote the sample mean for observations with \(X=0\), and let \(\bar{Y}_{1}\) denote the sample mean for observations with \(X=1\). Show that \(\hat{\beta}_{0}=\bar{Y}_{0}, \hat{\beta}_{0}+\hat{\beta}_{1}=\bar{Y}_{1}\), and \(\hat{\beta}_{1}=\bar{Y}_{1}-\bar{Y}_{0}\).