Closest fit data to a particular formula

R folks,
 I am somewhat new to R and have started to stumble...
I have a set of data that I am trying to model, so that I can predict
on
a much larger set - and I have been using loess to get a model.. but it
is
not what I would like to see.  For instance, I know from the nature of
the
data that the shape of this line should only decrease, and yet the
loess is
being affected by the sample outliers at 1100.  What I am interested in
is
the "best fit" of the sample data to a formula that I supply it. 
Reading
the documentation for loess - it seems that I can do this by supplying
a
formula.. but I have not had much luck.  Perhaps I am reading the
documentation incorrectly.  Here is my current loess line code:

mg.lo = loess(y ~ x, mg, span=0.25)
mg$x_c <- predict(mg.lo)

which produces a curve like the attached file loess_curve.png.

and I would like to have a curve "something like" the arccot in the
attached file arccotangent.png (from wikipedia), but all x values are
positive - meaning just the best fit of the sample data to that type of
curve.. starts high and finishes low but doesn't go below zero and only
decreases.  Looking at the arccot(x) definition I can see it as:

arccot x = pi/2 - atan(x)

So I tried to apply variations of that to the loess first "formula"
parameter with underwhelming results.

Am I even remotely on the right track?  Can loess get me there?  If not
-
another function?

Any and all comments would be greatly appreciated.

David


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Try using the lm function:

?lm
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Sent from my phone. Please excuse my brevity.

David <david at serendipityscience.com> wrote:

R folks,
 I am somewhat new to R and have started to stumble...
I have a set of data that I am trying to model, so that I can predict
on
a much larger set - and I have been using loess to get a model.. but it
is
not what I would like to see.  For instance, I know from the nature of
the
data that the shape of this line should only decrease, and yet the
loess is
being affected by the sample outliers at 1100.  What I am interested in
is
the "best fit" of the sample data to a formula that I supply it.
Reading
the documentation for loess - it seems that I can do this by supplying
a
formula.. but I have not had much luck.  Perhaps I am reading the
documentation incorrectly.  Here is my current loess line code:

mg.lo = loess(y ~ x, mg, span=0.25)
mg$x_c <- predict(mg.lo)

which produces a curve like the attached file loess_curve.png.

and I would like to have a curve "something like" the arccot in the
attached file arccotangent.png (from wikipedia), but all x values are
positive - meaning just the best fit of the sample data to that type of
curve.. starts high and finishes low but doesn't go below zero and only
decreases.  Looking at the arccot(x) definition I can see it as:

arccot x = pi/2 - atan(x)

So I tried to apply variations of that to the loess first "formula"
parameter with underwhelming results.

Am I even remotely on the right track?  Can loess get me there?  If not
-
another function?

Any and all comments would be greatly appreciated.

David


------------------------------------------------------------------------