Module-8-Curve-Fitting

Module-8 Curve Fitting

Curve fitting, including linear regression, is a powerful way to assess whether signals you observe behave in a predictable manner.

Objectives

At the end of this module, you will be able to

• Determine the correlation between measurements and independent variables
• Fit data to any function
• Use a general linear model to analyze data

Materials

• The main MLX ./docs/curveFitting.mlx explains various approaches to curve fitting in Matlab.
• ./docs/errorSurface.mlx visualizes a so-called error surface associated with curve fitting.

Assignments

As discussed in ./docs/curveFitting.mlx for nonlinear curve fitting there is no guarantee that the fit function finds the global optimum. While there are some fancy tools (e.g. simulated annealing) to improve the likelihood of finding a global optimum, in this assignment you'll create a function that uses a brute-force technique.

Your assignment is to write a function that runs a nonlinear fit (using the fit.m function in the Curve Fitting Toolbox) from a range of starting positions and returns the best overall fit.

Start from the ./code/iterateFit.m function in the code folder.

Steps:

1. The function should be documented and commented appropriately.
2. iterateFit should return the same output as fit
3. iterateFit should accept the same inputs as fit (including all its parameter/value pairs)
4. iterateFit should also accept the following parameter/value pair:

• min (a vector with the lowest starting point for each parameter)
• max (a vector with largest starting point for each parameter )
• n (the total number of starting points to try).

1. iterateFit should generate n random starting positions distributed randomly between min and max for each parameter, loop over those, and return the best overall solution. Hint use rand.