An Example using Zillow Data In order to identify outliers (outlying Y), we can take look at the values of semistudentized residuals, studentized residuals, studentized deleted residuals. a. semistudentized residuals: $\frac{e_i}{\sqrt{MSE}}$. b. studentized residuals: $\frac{e_i}{\sqrt{MSE(1-h_{ii})}}$, where $h_{ii}$ is diagonal element of Hat matrix. c. studentized deleted residuals: $d_i = Y_i - \hat{Y_{i(i)}} = \frac{e_i}{1-h_{ii}}$, redo the regression without observation i, to get $MSE_{(i)}$, so that $s^2\{d_i\} = MSE_{(i)}(1+X'_i(X'_{(i)}X_{(i)})^{-1}X_i)=\frac{MSE_{(i)}}{1-h_{ii}}$ $t_i = \frac{d_i}{s\{d_i\}}=\frac{e_i}{\sqrt{MSE_{(i)}(1-h_{ii})}}\sim t(n-p-1)$ Outlying X ( leverage ) can be identified by using Hat matrix. An observation is usually considered to be a leverage if $h_{ii} > 2p/n$. Another suggested guideline is that $h_{ii}$ exceeding 0.5 indicates very high leverage, whereas between 0.2 and 0.5 indicates moderate leverage. Influential c...