[R] Curve Fitting/Regression with Multiple Observations

[Kyeong Soo (Joseph) Kim]

I recently came to realize the true power of R for statistical
analysis -- mainly for post-processing of data from large-scale
simulations -- and have been converting many of existing Python(SciPy)
scripts to those based on R and/or Perl.

In the middle of this conversion, I revisited the problem of curve
fitting for simulation data with multiple observations resulting from
repetitions.

In the past, I first processed simulation data (i.e., multiple y's
from repetitions) to get a mean with a confidence interval for a given
value of x (independent variable) and then applied spline procedure
for those mean values only (i.e., unique pairs of (x_i, y_i) for i=1,
2, ...) to get a smoothed curve. Because of rather large confidence
intervals, however, the resulting curves were hardly smooth enough for
my purpose, I had to fix the function to exponential and used least
square methods to fit its parameters for data.

>From a plot with confidence intervals, it's rather easy for one to
visually and manually(?) figure out a smoothed curve for it.
So I'm thinking right now of directly applying spline (or whatever
regression procedures for this purpose) to the simulation data with
repetitions rather than means. The simulation data in this case looks
like this (assuming three repetitions):

# x    y
1      1.2
1      0.9
1      1.3
2      2.2
2      1.7
2      2.0
...      ....

So my idea is to let spline procedure handle the fluctuations in the
data (i.e., in repetitions) by itself.
But I wonder whether this direct application of spline procedures for
data with multiple observations makes sense from the statistical
analysis (i.e., theoretical) point of view.

It may be a stupid question and quite obvious to many, but personally
I don't know where to start.
It would be greatly appreciated if anyone can shed a light on this in
this regard.

Many thanks in advance,
Joseph