# The ROBUSTREG Procedure

### Leverage Point and Outlier Detection

The regular variable LEVERAGE is defined as

where is the cutoff value. can be set with the leverage CUTOFF= option, and can be set with the leverage CUTOFFALPHA= option.

If projected robust distances are computed for a data set that has a low-dimensional structure, the default cutoff value is where q is the dimensionality of the low-dimensional space. The LEVERAGE is then defined as

where POD is the projected off-plane distance and PRD denotes the projected robust distance. You can specify a cutoff value with the CUTOFF or the CUTOFFALPHA suboptions of the LEVERAGE option in the MODEL statement.

Residuals , based on robust regression estimates are used to detect vertical outliers. The variable OUTLIER is defined as

where is the estimated scale in the model and the multiplier of the cutoff value is specified by the CUTOFF= option in the MODEL statement. By default, k = 3.

An ODS table called Diagnostics contains the LEVERAGE and OUTLIER variables.