Given two variables described by a non-linear relationship, how do one fit a piece-wise (segmented) curve for these variables. In addition, how can one obtain the "coefficient of determination" and the "goodness-of-fit" F-values from the data.
I think you can use the optimization toolbox for that. Create an objective function that calculates the square error between the data you have and the nonlinear model you prefer. Then use least square for fitting.