Help with a Linear model, algebra homework help

please follow ALL written instructions given. I have also include an example for your reference, Please DON’T copy the example but only use as a reference.

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.
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 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 sport that 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: http://www.databasesports.com/ and http://www.baseball-reference.com/
(Sample) Curve-Fitting Project – Linear Model: Men’s 400 Meter Dash
Submitted by Suzanne Sands
(LR-1) Purpose: To analyze the winning times for the Olympic Men’s 400 Meter Dash using a linear model
Data: The winning times were retrieved from http://www.databaseolympics.com/sport/sportevent.htm?sp=ATH&enum=130
The winning times were gathered for the most recent 16 Summer Olympics, post-WWII. (More data was available, back to 1896.)
DATA:
(LR-2) SCATTERPLOT:
Summer Olympics: Men’s 400 Meter Dash Winning Times
50.00
45.00
40.00
35.00
30.00
Time (seconds)
25.00
Summer Olympics:
Men’s 400 Meter Dash
Winning Times
Time
Year (seconds)
1948
46.20
1952
45.90
1956
46.70
1960
44.90
1964
45.10
1968
43.80
1972
44.66
1976
44.26
1980
44.60
1984
44.27
1988
43.87
1992
43.50
1996
43.49
2000
43.84
2004
44.00
2008
43.75
20.00
15.00
10.00
5.00
0.00
1944
1952
1960
1968
1984
1992
2000
2008
1976
Year
As one would expect, the winning times generally show a downward trend, as stronger competition and training
methods result in faster speeds. The trend is somewhat linear.
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