Homework 11

CHE 116: Numerical Methods and Statistics

Version 1.0 (3/14/2016)

Problem 1 (100 Points)

Write a module to package your CHE 116 methods. You will create two files: stats.py and regression.py. Your stats.py file will contain the confidence interval function from Unit 13, Lecture 1. You will write two regression functions in regression.py: linear_regress and nonlinear_regress. Here are their attributes:

linear_regress:

1. Takes in an x matrix of data and y values
2. Performs a regression and return standard errors of the fit coefficients and standard error in residual
3. Takes in a True/False variable which indicates whether or not to create plots
4. If creating plots, it should create a single plot (!) with as many subplots as needed to justify the regression
5. Takes in a pvalue variable, which if True computes and returns $p$-values for each of the coefficients using a t-test hypothesis test

nonlinear_regress:

1. Takes in an x matrix of data, a function which takes in (beta, x, y), an initial guess for beta, and y values
2. Performs a regression and return standard errors of the fit coefficients and standard error in residual
3. Takes in a True/False variable which indicates whether or not to create plots
4. If creating plots, it should create a single plot (!) with as many subplots as needed to justify the regression
5. Takes in a pvalue variable, which if True computes and returns $p$-values for each of the coefficients using a t-test hypothesis test
6. Take in a nonconvex variable, which if True causes the method to use basin_hopping for minimizing SSR

You should be able to install your resulting CHE 116 module using the pip command as shown in lecture.

I have been intentionally vague on the specifications. It is up to you to write detailed documentation and specifications about your function. You will be graded according to the following:

1. Your module can be installed and imported [20 Points]
2. Your module and functions are well-documented, including examples, returns and parameters descriptions. [20 Points]
3. Your functions behave correctly on usual data and perform plots/statistics [50 Points]
4. Your functions respond gracefully to bad inputs and give warnings/notice if it fails to fit for any reason [10 Points]

You should submit a zipped folder containing your module and notebook demonstrating how to use your function.

Useful code snippets