R help - Oct 2013 - Fitting multiple horizontal lines to data

Dear R-users,
I am trying to fit my data using one or more horizontal lines. If my data
is in "y", I understand that "lm(y~1)" will fit a single
horizontal line at
mean(y). However, I want to try and fit the data with multiple horizontal
lines if that reduces the error while still keeping the number of
horizontal lines to be as small as possible.

Concretely, assume:
y=c(2,4,2,4,2,4,2,4,8,10,8,10,8,10,8,10)

lm(y~1)
fits a single horizontal line at y=6.

A better fit using multiple horizontal lines would be 2 horizontal lines at
y = 3 and y = 9.

An even better (if the objective is to solely minimize error and not
penalize the number of horizontal lines) would be 4 horizontal lines at
y=2, y=4, y=8, y=10.

kMeans works for the simple example I have shown, but I would like advice
on whether there is a better method that will work when the data does not
fit a horizontal line exactly.
Thanks,
-sashi.

	[[alternative HTML version deleted]]

Your question doesn't make much sense if you really believe that the best
fit
is to draw a horizontal line at every unique value of y.   What is the
actual problem you are trying to solve?   Clearly it's not a matter of
linear fits, so forget about using "lm" or other regression tools. 



--
View this message in context:
http://r.789695.n4.nabble.com/Fitting-multiple-horizontal-lines-to-data-tp4679324p4679345.html
Sent from the R help mailing list archive at Nabble.com.

I am not trying to fit a horizontal line at every unique value of y. I am
trying fit the y values with as few horizontal lines by trading off the
number of horizontal lines with the error. The actual problem I am trying
to solve is to smooth data in a time series. Here is a realistic example of
y

y=c(134.45,141.82,143.81,141.81,145,141.61,143.72,145.71,200,175,140,200,148.77,71.64,111.57,118.15,119.15,112.8,111.64,111.64,157.26,143.8,40.19,64.99,64.99,129.98,64.99,65,64.98,64.99)

An example fit for y using multiple horizontal lines (may not be the best
fit in terms of squared error or another error metric, but I have included
the y value for concreteness)

1. A horizontal line at approximately y=140 (to fit the first 13 values -
134.45 to 148.77)
2. A horizontal line at approximately y=110 (to fit the next 7 values -
71.64 to 111.64)
3. A horizontal line at approximately y=150 (to fit the next 2 values -
157.26 to 143.8)
4. A horizontal line at approximately y=65 (to fit the last 8 values -
40.19 to 64.99)
-sashi.

	[[alternative HTML version deleted]]