## Quick Reference

A method of regression that is not greatly affected by discordant observations. The most usual method for obtaining regression estimates is ordinary least squares (OLS), which is quite sensitive to the presence of outliers. One example of a robust alternative to OLS is iteratively reweighted least squares.

When there is a single *x*-variable a simple alternative robust method is as follows.*x*-values. Call the groups L (low), M (medium), and H (High). Find the medians of the *x*-values and *y*-values in each group: (*x** _{L}*,

*y*

*), (*

_{L}*x*

*,*

_{M}*y*

*), and (*

_{M}*x*

*,*

_{H}*y*

*).*

_{H}*β̃*=

*y*

*−*

_{H}*y*

_{L}*x*

*−*

_{H}*x*

*.*

_{L}*y*

*−*

_{H}*β̃*

*x*

*) + (*

_{H}*y*

*−*

_{M}*β̃*

*x*

*) + (*

_{M}*y*

*−*

_{L}*β̃*

*x*

*)}.The resulting line is known as the median-median line or the resistant line.*

_{L}*x*-values. Call the groups L (low), M (medium), and H (High). Find the medians of the *x*-values and *y*-values in each group: (*x** _{L}*,

*y*

*), (*

_{L}*x*

*,*

_{M}*y*

*), and (*

_{M}*x*

*,*

_{H}*y*

*).*

_{H}*β̃* = *y** _{H}* −

*y*

_{L}*x*

*−*

_{H}*x*

*.*

_{L}*y** _{H}* −

*β̃*

*x*

*) + (*

_{H}*y*

*−*

_{M}*β̃*

*x*

*) + (*

_{M}*y*

*−*

_{L}*β̃*

*x*

*)}.*

_{L}
*Subjects:*
Probability and Statistics.

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