Suppose that \(x_{i}\) only takes on the values 0 and 1. Out of the \(n\) observations, \(n_{1}\) take on the value \(x=0\). The \(n_{1}\) observations have an average \(y\) value of \(\bar{y}_{1}\). The remaining \(n-n_{1}\) observations have value \(x=1\) and an average \(y\) value of \(\bar{y}_{2}\). Use Exercise 2.8 to show that \(b_{1}=\bar{y}_{2}-\bar{y}_{1}\).