EGR 103/Spring 2023/Lab 9

Submitting Work

There are Connect and Lab Assignment parts for almost every problem. The Connect parts and lab uploads are due the same day, but you will want to get the work done far earlier than that to have time to put together your own lab report.

• You can work in small groups to create the programs. Once the programs are done, you need to work individually on making the LaTeX document.
• Be sure to carefully read each problem - sometimes Connect will change a number or a prompt slightly from the book problem. Your PDF version should use the original values in the book problem so be sure to change them if needed after making calculations for Connect.
• Once you get the Connect assignment 100% correct, you will be able to look at the assignments and the explanations for the answers. Note: if there is coding involved in an answer, the solution on Connect will be presented as MATLAB code; take a look to see the similarities and differences with Python.
  • Use fig.set_size_inches(6, 4, forward=True)} to make your graphs all the same size.
  • Be sure to use tight layout and save the graph as a .png (graphics) file, not a .eps file.

Typographical Errors

None yet!

Specific Problems

• Be sure to put the appropriate version of the honor code -- if you use the examples from Pundit, the original author is either DukeEgr93 or Michael R. Gustafson II depending on how you want to cite things.

Chapra 14.5

• See Python:Fitting#Polynomial_Fitting
• Be sure to also calculate and report \(s_{y/x}\) and \(r\).

Chapra 15.10

• See Python:Fitting#General_Linear_Regression

Chapra 15.10 Alternate

• See Python:Fitting#General_Linear_Regression
• Remember what you are trying to keep track of when discussing the reasonableness of your solution.

Chapra 15.12

• See Python:Fitting#General_Linear_Regression

Quick note on nonlinear regression

You will be using nonlinear regression for the next two problems. The main Python method you will be using is:

• scipy.optimize.curve_fit

Note that generally we will bring in scipy.optimize with

import scipy.optimize as opt

so the function calls will look like

opt.curve_fit()

In the documentation on Scipy, they bring in the entire optimize package with

from scipy import optimize

so their function calls look like

optimize.curve_fit()

Chapra 15.11

• See Python:Fitting#Nonlinear_Regression
• For the initial guesses, make sure you understand the subscripts for the parameters and then figure out how to approximate their values from the information provided in the problem.

Chapra 15.22

• See Python:Fitting#Nonlinear_Regression
• For the initial guesses, mainly note that choosing $$b=0$$ would be a terrible idea.

General Concepts

General Linear Regression