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For example, I have the following data:

$Y = 366$ measured values

$X = 366$ measured values

$t = [ 1 : 366 ]$, representing the days of the year (index)

So at each $t$ (day), we have value of $Y$ and corresponding value of $X$. When drawing $Y$

and $X$ vs. $t$, it shows a continued curve for $Y$ with disturbances. These disturbances

are caused by the change of $X$ and it is clear that $Y$ is mainly affected by $X$, meaning

that: $Y = f(X)$

This figure is shown here:

Y and X plot

This figure shows $Y$ vs. $X$:

Y vs. X scatter plot

My aim is to find this relation between $Y$ and $X$ or in another words: $Y = f(X)$.

What I have tried and think so far is first to smooth the curve $Y$ and from the

smoothed points and smoothed curve, some function may be established.

Then, including the effect of disturbances (up and down) by some function,

may be exponential.

Could you please guide me how can I manipulate this problem to get

a final model $Y = f(X)$.

regards

  • 0
    Looks quite messy. I'm not quite sure if your data's trying to be exponential or sigmoidal in the second plot...2011-09-20
  • 0
    When you say disturbances, what exactly do you mean? For example, are these observation errors? In particular, are they equally applicable to $X$ and $Y$, or are these quantities (and their observations) fundamentally different types of processes? The reason I ask is because in classic [nonlinear regression](http://en.wikipedia.org/wiki/Nonlinear_regression#General), which models dependence as opposed to [least squares](http://en.wikipedia.org/wiki/Non-linear_least_squares) or curve fitting which model relationship, $X$ is assumed to have no error.2012-03-19
  • 0
    If you want to get a function $y=f(x)$, you must have 1 y value for each distinct x value. Looking at the second chart, taking x=20 for example, there seems to be several y-values. So is this the case or is this due to the fact that x values are so close?2012-03-19
  • 0
    To me, this looks linear with a low-end saturation.2012-08-09

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