ENGR 132
Spring 2023
A11 ∙ Linear Regression
Introduction
Assignment Goals
This assignment uses Excel to build on the least squares analysis you learned in ENGR 131 and then adds two
MATLAB linear regression problems with engineering contexts.
Successful Completion
This assignment has 3 problems. All problems go with Classes A and B.
1.
Read Notes Before You Start, on Page 1.
2.
Read each problem carefully. You are responsible for following all instructions within each problem.
a.
The deliverables list within each problem contains everything you are expected to submit.
3.
Complete the problems using the problem-specific templates when a template is provided in the assignment
download.
4.
For any file, replace template or login in the filename with your Purdue Career Account login.
5.
Review your work using the learning objective evidences.
6.
When your work is complete, confirm your deliverables are submitted to Gradescope.
a.
Note the three different assignments in Gradescope.
i. A11 – All Problems: submit your deliverables for all problems. Help link.
ii. A11 – Team Planning: submit your team plan for Problem 3 as a team. Help link.
7.
b.
You can resubmit your work as many times as you want; only the final submission will be graded.
c.
Do NOT upload any document not listed in the deliverables. Do not upload temporary versions of mfiles (*.m~ or *.asv) – these files will be ignored by Gradescope.
d.
You must submit an m-file or xlsx file when one is requested; failing to do so will result in a 0 on the
problem.
Late submissions will be accepted up to 24 hours after the due date and will result in a 25% penalty.
Learning Objectives & Grading
This course uses learning objectives (LOs) to assess your work. You can find a full list of the course LOs here.
Review the grading outline at the end of each problem in this assignment to see each problem’s LOs.
Notes Before You Start
Helpful MATLAB Commands
Learn about the following built-in MATLAB commands, which might be useful in your solutions:
polyfit, polyval
Publishing code
You will publish m-files as PDF documents in this assignment. See detailed instructions on publishing here.
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ENGR 132
Spring 2023
Problem 1:
Excel Linear Regression
Introduction
This problem has you using Excel to determine least squares model and goodness of fit for a data set. You will
compare models and discuss their differences. You will use your knowledge of your data set to make reasonable
predictions using your model.
Submission
Gradescope Assignment
A11 – All Problems
Deliverables
 Requested results and information
Assignment Type
Individual
 A11Prob1_wireBonds_login.xlsx
 A11Prob1_figure_login.png
Problem
Wire bonding is a method that uses thin wires and heat to attach and connect integrated circuits in
microelectronic devices. The wire bonds the semiconductor to a terminal on the chip package. These circuits are
used in electronic applications across all
engineering disciplines. For some applications, the
strength of the connections must be quantified and
confirmed. The United States military has a
standard method for testing wire bond strength for
critical aviation and space components. The
National Aeronautics and Space Administration
(NASA) also uses this standard for testing mission
critical components. The method can be done
destructively or non-destructively. For the destructive test, a machine hooks onto a wire in the circuit and pulls up
until the bond fails and the connection between the semiconductor and the terminal is broken.
You work as a quality control engineer for a microprocessor manufacturer that sells components for aviation and
space applications. Your team selected random circuits from production batches and conducted destructive wire
bond testing on them. You placed the circuits in a testing machine that places a hook on the wire and pulls with an
upward force until the wire bond fails. The machine reports the applied force and the height of the hook (i.e., a
measure of wire stretch) at the point of failure. Your company has been using a model, 𝐹 = 21.9ℎ + 3.3 to
predict wire strength in the circuits, where ℎ is the hook height above its starting point (mm) and 𝐹 is the pull
strength at which the bond fails (grams-force).
You must perform least-squares regression to find a new model for the pull strength as a function of hook height
at failure. You will find the data in the CALCULATIONS sheet of the provided Excel template.
Instructions
Excel Calculations
Using the CALCULATIONS sheet in the Excel template, you must
1.
Use the data and the least-squares equations to determine the least-square line for the data.
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ENGR 132
2.
3.
Spring 2023
Plot the data and confirm your least-squares line using Excel’s “add a trendline” feature. Show both
the model equation and the r-squared value. Update the equation display using clear and appropriate
variable names in place of 𝑥 and 𝑦. Format the plot for technical presentation.
Determine the goodness of fit (SSE, SST, and r2) for both the provided model and your least-squares
model.
Save a plot image
After you have completed the calculations and created the plot, you need to save an image of your Excel plot that
shows the data, the trendline, and the least-squares model (as described in Step 2 above). Save an image of your
Excel plot with the trendline and r-squared value visible.
•
If you have a Mac, right click the chart and select “Save as picture”.
•
If you have Windows, you may need to Copy the figure, paste into Powerpoint as an image, right click the
image in Powerpoint and select “Save as picture”.
*You can use any image file type (png, jpg, tiff, etc.) that will render in Gradescope but name the file appropriately.
Answer Questions & Submit to Gradescope
After you complete the calculations, open Gradescope and select the assignment A11 – All Problems. You will find
5 parts within Q1. Excel – Linear Regression. Answer all the questions and their parts. Save your answers
periodically in case you lose internet connection or need to stop working on the assignment before it is complete.
a.
Submit your XLSX file, with the appropriate file name.
b.
Submit your plot image, with the appropriate file name.
c.
Answer the questions presented in Gradescope.
Note: Failure to submit the XLSX worksheet will result in a 0 on this problem.
References
National Aeronautics and Space Administration. (n.d.). Wirebond – Basic Information. https://nepp.nasa.gov/index.cfm/20911
National Institute of Standards and Technology. (1976). The destructive bond pull test.
https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nbsspecialpublication400-18.pdf
Grading
LOs: PC05, MAT03, MOD01, EPS01, EPS02
Point value: 10 points. Problem is graded by question. Partial credit is available and is based on evidences in MAT03,
MOD01, EPS01, EPS02. If you do not meet the PC05 expectations, you will lose additional credit.
Q.1.(1)
Q.1.(2)
Q.1.(3)
Q.1.(4)
Q.1.(5)
Figure
Points
2
1
1
2
2
2
PC05 (1)
PC05 (2)
PC05 (4)
PC05 (8)
Points
-100%
-25%
-15%
-100%
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Spring 2023
Grading Process
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ENGR 132
Spring 2023
Problem 2:
MATLAB Linear Regression
Introduction
You will write script that performs least squares regression using MATLAB and use the model you find to make
reasonable predictions with justifications. You will learn to publish your MATLAB file as a PDF.
Submission
Individual
Gradescope Assignment
A11 – All Problems
Deliverables
 A11Prob2_oxygenLevels_login.m
Assignment Type
Individual
Supporting files:
 A11Prob2_oxygenLevels_login.pdf
 Data_DO_concentrations.csv
Problem
A large focus within biological engineering is limnology, the study of inland bodies of water. Besides water itself,
the second most important factor for living organisms underwater is dissolved oxygen (DO). DO is an important
measure for water quality and has a big impact on the living creatures in natural waters. Too little oxygen in the
water can cause aquatic plants and animals to die, and prolonged low oxygen levels can destroy an ecosystem.
There are a lot of factors that influence the DO levels in water, but the one that we are concentrating on is
temperature. Warmer water holds less DO, while colder water tends to hold more DO.
You are working with a team of biological engineers to predict the concentration of dissolved oxygen in the
Colorado river at different temperatures based on samples that were collected by your team. The data collected
can be found in the data file Data_DO_concentrations.csv. The temperature is measured in degrees Celsius (°C)
and the dissolved oxygen concentration is measured in milligrams per liter (mg/l).
Using linear regression, you need to create a model that can estimate the concentration of dissolved oxygen at a
given temperature. You will create a script that must do the following:
•
Perform least squares analysis and goodness of fit calculations:
o
Perform linear regression on the data to get the least-squares coefficients.
o
Determine the predicted values of the linear model.
o
Calculate SSE, SST, and r2 values for the model.
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ENGR 132
•
Spring 2023
Display information to the Command Window, using professional communication standards for all displays:
o
The linear model equation with clear, descriptive variable names in the format 𝑦 = 𝑎𝑥 + 𝑏.
o
The goodness of fit results for SSE, SST, and r2.
•
Create a figure that displays the raw data and the model line on the same axes. Format the figure for
technical presentation.
•
Use the least-squares model to calculate the predicted dissolved oxygen levels at 17 deg C and 45 deg C.
Publish your code
When your code is working properly, publish your m-file as a PDF. When you publish, MATLAB will run your code
and will create a PDF file that has your code with all outputs and displays it produces. Be sure to suppress
commands and variable assignments so that only the requested displays (text and figure) are visible in the PDF.
1.
2.
3.
Open your m-file in the MATLAB Editor and then click on the Publish tab.
Click the bottom half of the Publish button and then click Edit Publishing Options…
Set the Output Format to pdf and click Publish.
Detailed instructions and videos for publishing are on this website for both MATLAB Online and MATLAB desktop.
If you encounter an issue while publishing, check the Troubleshooting section.
Answer questions & submit to Gradescope
Open the Gradescope assignment.
•
•
•
•
Enter your predicted values for 17 and 45 deg C in the appropriate space in Gradescope. Do not just enter
values alone. Use your knowledge of the data to justify your prediction for each value. Use professional
communication standards in both answers.
Copy-paste your Command Window text display into Gradescope (equation and goodness of fit results).
Submit your published PDF that shows your code, text display, and figure all in one document.
Submit your m-file and data file.
References
Oxygen Saturation Technology. (n.d.). Solitude Lake Management. Retrieved September 30, 2022, from
https://www.solitudelakemanagement.com/blog/oxygen-saturation-technology-blog/
La Hee, J. (September 8, 2020). Stop pond and lake odors at the source. Vertex Aquatic Solutions.
https://vertexaquaticsolutions.com/aeration-for-pond-lake-odors/
Grading
LOs: PC05, MAT03, MOD01, EPS01, EPS02
Point value: 10 points. Partial credit is available and is based on evidences in MAT03, MOD01, EPS01, EPS02. If you
do not meet the PC05 expectations, you will lose additional credit.
Evidence
Penalty
Graded item
LOs
Points
PC05 (1)
PC05 (2)
PC05 (3)
PC05 (4)
Lose full credit on problem
Lose 25% of full credit on problem
Lose 25% of full credit on problem
Lose 15% of full credit on problem
Predictions
Model and goodness of
fit values and display
EPS01
MAT03,
MOD01,
EPS01
2.5
4.5
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Spring 2023
Figure Display
Problem 3:
EPS02
3
Greenhouse Gas Analysis
Introduction
This problem will allow you to apply linear regression concepts to data sets that contain environmental data used
in news, commercial, academic, and scientific settings. You will discuss what you know about the models using
your knowledge of the data.
Submission
Individual
Gradescope Assignment
A11 – All Problems
Deliverables
 A11Prob3_airPollution_login.m
Assignment Type
Individual
Supporting files:
 A11Prob3_airPollution_login.pdf
 Data_NOAA_ESRL_co2_trend_1980-2022-global.csv
 Data_NOAA_ESRL_n2o_trend_2001-2022.txt
Team Plan
Gradescope Assignment
A11 – Team Planning
Deliverables
 Requested information
Assignment Type
Team
Problem
Greenhouse gases cause the Earth’s atmosphere to retain heat
by absorbing infrared radiation and blocking it from being
reemitted back into space. Earth is habitable due to naturally
occurring greenhouse gases that form a carbon exchange cycle,
but industrial production of these gases well exceeds what the
natural environment’s cycle can manage. Fossil fuel emissions
and wildfires are primary sources of greenhouse gases and
contribute more carbon to the atmosphere than the land and
ocean carbon sinks can remove, which leads to unnatural and
dangerous warming on a global scale. Greenhouse gases and
their effects are studied in almost all engineering disciplines,
including environmental, agricultural, mechanical, chemical,
construction, aerospace, and civil engineering.
Carbon dioxide (CO2) and nitrous oxide (N2O) emissions are
two significant greenhouse gases. The National Oceanic and
Atmospheric Administration’s Earth System Research Laboratory (ESRL) maintains records of atmospheric
greenhouse gas concentrations.
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Spring 2023
For this problem, you must model the global averages in CO2 and N2O atmospheric concentrations. You will find
the CO2 data, with its complete NOAA header, in the file named Data_NOAA_ESRL_co2_trend_1980-2022global.csv and the N2O data in the file Data_NOAA_ESRL_n2o_trend_2001-2022.txt.
Write a MATLAB no-input, no-output function to perform least squares regression on the provided data. You will
model average CO2 (in ppm) as a function of decimal year and then model average N2O (in ppb) as a function of
decimal year. Your function must
•
Perform linear regression on the data to get the least-squares coefficients, first for CO2 and then for N2O.
•
Determine the predicted values of each linear model.
•
Calculate SSE, SST, and r2 values for each model.
•
Display the linear model equation (with clear variable names), SSE, SST, and r2 to the Command Window
for each model. Make sure you can differentiate between the information for CO2 and N2O.
•
Generate one figure with two subplots stacked vertically. On the top subplot, display the data and the
trend line on the same axes for CO2. On the bottom subplot, display the data and trend line on the same
axes for N2O. Format both subplots and the figure for technical presentation.
o
Learn about the xlim function to set the x-axis limits of both subplots. Make your subplots have
identical axes limits on the x-axis and show all data in both subplots.
Enter information and answer analysis questions in Gradescope
In Gradescope, you will need to enter your Command Window text display, and you find two questions to answer.
Copy and paste your equations and goodness of fit displays for both gases.
For the analysis questions, your answers must meet course communication expectations.
Q1. From your analyses, can you draw a conclusion about the accuracy of the data measurements? Provide
justification for your answer.
Q2. For which data set does a linear model best explain the variation that exists in the data? Clearly state the
basis of your reasoning and provide justification for your answer.
Publish your code
When your code is working properly, publish your m-file as a PDF. When you publish, MATLAB will run your code
and will create a PDF file that has your code with all outputs and displays it produces. Be sure to suppress
commands and variable assignments so that only the requested displays (text and figure) are visible in the PDF.
1.
2.
3.
Open your m-file in the MATLAB Editor and then click on the Publish tab.
Click the bottom half of the Publish button and then click Edit Publishing Options…
Set the Output Format to pdf and click Publish.
Detailed instructions and videos for publishing are on this website for both MATLAB Online and MATLAB desktop.
If you encounter an issue while publishing, check the Troubleshooting section.
Instructions
1.
Read through the entire problem statement.
2.
Team Planning: As a team, outline a plan to solve this problem that has at least 2-3 steps, is not highly
detailed, and does not contain code. Submit the plan to Gradescope. Link to thorough instructions.
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ENGR 132
Spring 2023
o
3.
All teammates confirm that you get a submission email and verify that you can see the team
plan submission in your Gradescope.
Individually:
a.
Complete your m-file and run it to get your results.
o
The team plan is an initial start on the problem. It may not be completely correct, and you
may find flaws in the plan once you start coding. You should make any individual changes
that are necessary to obtain the best solution. You will be assessed on your individual
solution to the problem.
b.
Cite any peers you worked with in your script header if their help changed how you decided to
solve the problem. Make sure you also completed the rest of the script header.
c.
Answer the questions and submit your properly named files to the individual Gradescope
assignment (see the submission list at the beginning of this problem).
o
Do not submit any other files.
References
Ed Dlugokencky, NOAA/GML (gml.noaa.gov/ccgg/trends_n2o/)
Ed Dlugokencky and Pieter Tans, NOAA/GML (www.esrl.noaa.gov/gmd/ccgg/trends/)
https://gml.noaa.gov/ccgg/carbontracker/
Grading
LOs: PC05, MAT03, MOD01, EPS01, EPS02
Team planning: 1 points
Point value: 10 points. Problem is graded by question. Partial credit is available and is based on evidences in MAT03,
MOD01, EPS01, EPS02. If you do not meet the PC05 expectations, you will lose additional credit.
LO Table
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
PC05
-100%
-25%
-10%
-15%
0
0
0
0
EPS02
0.4
0.4
0.4
0.4
0.4
0.4
0.5
0
MAT08
0.5
1.5
0.5
0
0
0
0
0
MAT03
0.6
0.6
0.6
0.6
0
0
0
0
Analysis
Q1
Q2
Points*
1
1.2
* Assessment of analysis questions is based on LOs in EPS01
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Spring 2023
Grading Process
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