2.3 Studentized

The studentized residuals are driven by the leave one out idea, which is the basis for much computationally intensive modern statistics. The leave one out idea is often called ``jackknifing''.

This ``leave one out'' residual can be used as a basis for judging the predictive ability of a model. Clearly the lower the residual the better, and the sum of the squares of the jackknifed residuals is called the PRESS statistics, or Predicted Sum of Squares.

The studentized residual, t_i, is just a standardized jackknifed residual. This is an extremely good way of judging how much of an outlier in the y-direction a point is.

From now on we will use the studentized residual plot to judge outliers in the y-direction.

A new plot. Leverage vs. studentized residual. Points that drive the regression have big leverage and extreme studentized residuals.

The delete one idea works pretty well, except when there is a second data point lying close by. In this case the second point can drive the regression line, masking the effect of the first point. This leads to the idea of ``delete two'' etc.