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st: resistant line or median median line


From   Faith Anne <faithanne.myers@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: resistant line or median median line
Date   Wed, 9 Feb 2005 07:47:44 -0500

Hi!

I need to calculate a specific type of line through a two-variable
dataset. In exploratory data analysis, what I need is called a
resistant line. In my high school classes, we called it a
median-median line. The way it's calculated is to divide the data into
three groups, find the x-median and y-median values (called the
summary point) for each group, and then use those three summary points
to determine the line.  The outer two summary points determine the
slope, and an average of all of them determines the intercept.

As far as I can tell, this isn't quite the same as the quantile
regression command, because the resistant line doesn't necessarily go
through the median of the whole dataset.  In the resistant line
calculation, you ignore all information besides the summary points, so
you don't actually take into account the absolute deviations and try
to minimize them. Someone please correct me if I have misunderstood
this!

I'm aware of the pros and cons of this method as compared to least
squares linear regression, but I am required to do this analysis and
compare it to least squares. Minitab can do this through its menu of
EDA commands, but I'm deeply frustrated with Minitab's data management
and graphing, so I'd really like to know how to do this with Stata.

Thank you!
Faith Anne Myers
Ohio State University
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