Posted: May 12th, 2024

UMUC MATH107 Curve-fitting Project – Linear Model

Curve-fitting
Project - Linear Model(due at the end of Week 5)
Instructions
For this assignment, collect data exhibiting a
relatively linear trend, find the line of best fit, plot the data and the line,
interpret the slope, and use the linear equation to make a prediction. Also,
find r2 (coefficient of determination) and r (correlation
coefficient). Discuss your findings. Your topic may be that is related to
sports, your work, a hobby, or something you find interesting. If you choose,
you may use the suggestions described below.
A Linear Model Example and Technology Tips are provided in separate documents.
Tasks for
Linear Regression Model (LR)
(LR-1) Describe your topic, provide
your data, and cite your source. Collect at least 8 data points. Label
appropriately. (Highly recommended: Post this information in
the Linear Model Project discussion as well as in your completed project. Include
a brief informative description in the title of your posting. Each
student must use different data.)

The idea with the discussion posting is two-fold:
(1) To share your interesting project idea with your classmates, and (2) To
give me a chance to give you a brief thumbs-up or thumbs-down about your
proposed topic and data. Sometimes students get off on the wrong foot or
misunderstand the intent of the project, and your posting provides an opportunity
for some feedback. Remark: Students may choose similar topics, but must
have different data sets. For example, several students may be
interested in a particular Olympic sport, and that is fine, but they must
collect different data, perhaps from different events or different gender.
(LR-2) Plot the points (x, y) to obtain
a scatterplot. Use an appropriate scale on the horizontal and vertical
axes and be sure to label carefully.Visually
judge whether the data points exhibit a relatively linear trend. (If so,
proceed. If not, try a different topic or data set.)
(LR-3) Find the line of best
fit (regression line) and graph it on the
scatterplot. State the equation of the line.
(LR-4) State the slope of the line
of best fit. Carefully interpret the meaning of the slope in a
sentence or two.
(LR-5) Find and state the value of r2,
the coefficient of determination, and r, the correlation coefficient.
Discuss your findings in a few sentences. Is r positive or negative?
Why? Is a line a good curve to fit to this data? Why or why not? Is the linear
relationship very strong, moderately strong, weak, or nonexistent?
(LR-6) Choose a value of interest and use the
line of best fit to make an estimate or prediction. Show calculation work.
(LR-7) Write a brief narrative of a paragraph
or two. Summarize your findings and be sure to mention any aspect of the linear
model project (topic, data, scatterplot, line, r, or estimate, etc.) that
you found particularly important or interesting.
You may submit all of your project in one document
or a combination of documents, which may consist of word processing documents
or spreadsheets or scanned handwritten work, provided it is clearly labeled
where each task can be found. Be sure to include your name. Projects are graded
on the basis of completeness, correctness, ease in locating all of the
checklist items, and strength of the narrative portions.

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Here are some possible topics:
Choose an Olympic sport-- an event that interests
you. Go to .databaseolympics.com/">http://www.databaseolympics.com/ and
collect data for winners in the event for at least 8 Olympic games (dating
back to at least 1980). (Example: Winning times in Men's 400 m dash). Make
a quick plot for yourself to "eyeball" whether the data points
exhibit a relatively linear trend. (If so, proceed. If not, try a
different event.) After you find the line of best fit, use your line to
make a prediction for the next Olympics (2014 for a winter
event, 2016 for a summer event ).Choose a particular type of food. (Examples: Fish
sandwich at fast-food chains, cheese pizza, breakfast cereal) For at least
8 brands, look up the fat content and the associated calorie total per
serving. Make a quick plot for yourself to "eyeball" whether the
data exhibit a relatively linear trend. (If so, proceed. If not, try a
different type of food.) After you find the line of best fit, use your
line to make a prediction corresponding to a fat amount not occurring in
your data set.) Alternative: Look up carbohydrate content and associated
calorie total per serving.Choose a sportthat particularly interests you and
find two variables that may exhibit a linear relationship. For instance,
for each team for a particular season in baseball, find the total runs
scored and the number of wins. Excellent websites: .databasesports.com/">http://www.databasesports.com/
and .baseball-reference.com/">http://www.baseball-reference.com/

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