You are doing regression with one explanatory variable and so consider the basic linear regression model \(y_{i}=\beta_{0}+\beta_{1} x_{i}+\varepsilon_{i}\).

a. Show that the \(i\) th leverage can be simplified to

\[h_{i i}=\frac{1}{n}+\frac{\left(x_{i}-\bar{x}\right)^{2}}{(n-1) s_{x}^{2}}\]

b. Show that \(\bar{h}=2 / n\).

c. Suppose that \(h_{i i}=6 / n\). How many standard deviations is \(x_{i}\) away (either above or below) from the mean?