1. Men’s 200m Butterfly World Record Regression Model
By: Bella Garcia, Naomi Xu, &
Michael Brown

2. Question & Hypothesis
Question: Does this set of data show a regression model with a regression equation? Using the best fit regression equation, what should be the predicted time be in 2009, is it accurate? And what should the predicted time be this year in the 2016 Summer Olympics?
Hypothesis: We predict that the data will have a regression model and equation. We also predict that this set of data will continue to show a trend of lower values as the years go on due to new training methods and more accurate timing systems.
Assumptions: We assume that the data and alpha level we chose are accurate.

3. Data List
* We only used the fastest time each year due to the repeated years may affect data and graph.
Athlete
Country
Date
X (L1)
Y=time (L2)
Amount of decreased
Mark Spitz
USA
1972 72
2:00.70
Mike Bruner
1976 76
1:59.23
-1.47
Craig Beardsley
1980 80
1:58.21
-.02
1981 81
1:58.01
-.20
Michael Gross
Germany
1983 83
1:57.05
-.96
Jon Sieben UK
1984 84
1:57.04
-.01

4. Michael Gross
Germany
1985 85
1:56.65
-.39
1986 86
1:56.24
-.41
Melvin Stewart
USA
1991 91
1:55.69
-.55
Denis Pankratov
Russia
1995 95
1:55.22
-.47
Tom Malchow
2000
100
1:55.18
-.04
Michael Phelps
2001
101
1:54.58
-.60
2003
103
1:53.93
-.64
2006
106
1:53.80
-.13
2007
107
1:52.09
-1.71
2008
108
1:52.03
-.06
2009
109
1:51.51
-.52

5. Regression Model Alpha Level= 0.05 Significance Level: 95% n: 17
df(n-2): 15
CV: 0.482

6. Test Types and r2 values
Type of calculations r^2 rounded to three decimals
Lin Reg( ax+b)
.945
Ln Reg*
.948
Pwr Reg
.946
Quad Reg
Exp Reg

7. Calculations Ln Reg: Y= a+bLnx Predicted time for 2009:
a= Y= Ln(109)
b= Y= seconds=1’52”42
Y= Lnx Predicted time for 2016
Y= Ln(116)
Y= seconds=1’51”26

8. Final Decision
Reject The Null - We support the claim that there is significant evidence of a regression model of the men’s 200m butterfly world records and they will decrease each year due to new training methods and more accurate timing technology.

9. Summary
The predicted time for 2009 is .91 seconds slower than the actual record, which proves that our regression equation is fairly accurate, while the prediction for is 0.25 seconds faster than 2009’s record, and we will wait until the summer Olympics to see if we can achieve the predicted time.
We chose to do this particular model because of all of our water sports background like surfing and swimming. We also remember that Michael Phelps broke several world records during previous Olympics (2012 in London, 2008 in Beijing, and 2004 in Athens), which made us curious about all of his and others’ records. It was a big event in our childhood because he was like superhero to us, winning almost every one of his events.

10. Any final question?

11. We conclude our presentation
Thank you :)