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Question
(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.)
Instructions
For this assignment, collect data exhibiting a relatively linear
trend, fnd the line o± best ft, plot the data and the line, interpret
the slope, and use the linear equation to make a prediction. Also,
fnd
r
2
(coe²cient o± determination) and
r
(correlation coe²cient).
Discuss your fndings. Your topic may be that is related to sports,
your work, a hobby, or something you fnd interesting. I± 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 di³erent data.)
The idea with the discussion posting is two-±old: (1) To share your interesting
project idea with your classmates, and (2) To give me a chance to give you a
brie± thumbs-up or thumbs-down about your proposed topic and data.
Sometimes students get o³ on the wrong ±oot or misunderstand the intent o±
the project, and your posting provides an opportunity ±or some ±eedback.
Remark:
Students may choose similar topics, but must have
diFerent
data sets
. For example, several students may be interested in a particular
Olympic sport, and that is fne, but they must collect di³erent data, perhaps
±rom di³erent events or di³erent gen
der.
(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 care±ully. Visually judge whether the data points exhibit a
relatively linear trend. (I± so, proceed. I± not, try a di³erent topic or data set.)
(LR-3) Find the line o± best ft (regression line) and graph it on the
scatterplot. State the equation o± the line.
(LR-4) State the slope o± the line o± best ft. Care±ully interpret the
meaning o± the slope in a sentence or two.
(LR-5) Find and state the value o±
r
2
, the coe²cient o±
determination, and r, the correlation coe²cient. Discuss your
fndings in a ±ew sentences. Is r positive or negative? Why? Is a
line a good curve to ft to this data? Why or why not? Is the linear
relationship very strong, moderately strong, weak, or
nonexistent?
(LR-6) Choose a value o± interest and use the line o± best ft to
make an estimate or prediction. Show calculation work.
(LR-7) Write a brief narrative of a paragraph or two. Summarize
your Fndings 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.
Here are some possible topics:
•
Choose an
Olympic sport
-- an event that interests you. Go
to
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 di±erent event.) After you Fnd the line of best Ft, 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: ²ish sandwich at fast-food chains, cheese pizza,
breakfast cereal) ²or 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 di±erent type of food.) After you Fnd the line of best
Ft, 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
sport
that particularly interests you and Fnd two variables that may exhibit a linear
relationship. ²or instance, for each team for a particular season in baseball, Fnd the total runs
scored and the number of wins. Excellent websites:
http://www.databasesports.com/
and
http://www.baseball-reference.com/
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