**Function Fitting**

**1. Error Evaluation**

Python source code. Generates 100 points uniformly distributes between 0 and 1, and applies the function y = 2 + 3x + (Gaussian noise). SVD is used to fit y = ax + b to the data set, and the errors in the fit are estimated using:

(a) Equation 12.34 from NMM

(b) Bootstrap sampling to generate 100 data sets

(c) From fitting an ensemble of 100 independent data sets

The results are pretty much the same using all three methods. The success of the bootstap sampling surprised me. Before writing the code, I expected it would not perform nearly as well as the other two. The output from running the Python code is shown below

**2. Maximum Entropy Methods**

**3. Finding Optimal Estimators**