How to fit a smooth curve to data in order to mimic an elbow? I ran an experiment and obtained the points shown in black below. 
I would like to smooth the curve or fit (something like the red curve) in order to identify the elbow. 
The problem is that the experiment is too expensive and there is a large amount of variance in the obtained points. 
I tried fitting a second degree polynomial and an exponential curve without sucess (the curve is too smooth and the elbow is lost).  Total precision is not necessary. 
What is the best way to fit a curve in order to identify the elbow?

 A: I used the LOESS regression and it seems to do the work. Since I have a big variance for each point I wanted to smooth this curve in order to get a similar 'elbow' for each execution. 
The loess seems to do this job just fine.
A: Smoothing will tend to "smooth over" the elbow in the data. If your view, based on domain knowledge, is that the true model has a major breakpoint or elbow, then you should consider fitting a model that is not smooth.
I suggest considering regression trees or hinge functions. There are many methods for fitting these, e.g. gradient boosting and MARS. These are sometimes thought of as black box machine learning methods. That said, interpreting a model with only one independent variable is usually pretty simple. 
A: What you have are two time series that are to be impacted by unspecified deterministic series e.g. local time trends and/or level shifts and/or pulses . If you post your actual data ( i.e. pairs of Y AND X's ) I will try and help you . The composite equation could include the predictor , lags of the predictor , lags of Y and some dummies (0/1) series to provide you with the needed equation/parameters. 
