using regression analysis to develop algebraic understanding
DESCRIPTION
Using Regression Analysis to Develop Algebraic Understanding. KCTM Fall 2009 Conference Roland O’Daniel. Standards for the Presentation. Participants will understand how to create learning experiences that: Make connections and develop a framework for algebraic reasoning - PowerPoint PPT PresentationTRANSCRIPT
Using Regression Analysis to Develop
Algebraic Understanding
KCTM Fall 2009 ConferenceRoland O’Daniel
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Standards for the Presentation
Participants will understand how to create learning experiences that:
• Make connections and develop a framework for algebraic reasoning
• Identify and describe patterns in data using functions that approximate the data.
• Flexibly move between multiple representations of functions to model mathematical ideas, solve problems, and communicate understandings.
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Where do you see algebra outside of your classroom?
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
When looking for a data source, what are you looking for?
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
GRE Score Concentrations in 28 Fields of PhD Study
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Cost/month in US $
Electricity Gas
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
U.S. Origin Patent Data
0 5 10 15 20 25 3030000
40000
50000
60000
70000
80000
90000
100000
Years Since 1980
Pat
ents
in
Th
ou
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The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Height of teachers in schoolH
eig
ht
in c
ms
60 65 70 75 80150
160
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Height in inches
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Finding a Source of Data• Gather your own!
– Measure/CBR/Go Motion
• Swivel– http://www.swivel.com/graphs
• The Numbers– http://www.the-numbers.com/charts/thisweek.php
• ZIPskinny – http://zipskinny.com/
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Example 1
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Determining a Relationship
• Choose the tool you wish to use– TI graphing calculator– Excel spreadsheet
• Create a representation of the data set
• What are the kinds of questions that we can ask students regarding the representation of data?
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Titanic W.B.O. Gross 12/97- 3/98Date Weekend B.O. Gross
12/19/1997 1 $28,638,131 12/26/1997 2 $35,455,673
1/2/1998 3 $33,315,278 1/9/1998 4 $28,716,310
1/16/1998 5 $36,014,544 1/23/1998 6 $25,238,720 1/30/1998 7 $25,907,172
2/6/1998 8 $23,027,838 2/13/1998 9 $32,876,424 2/20/1998 10 $21,036,343 2/27/1998 11 $19,633,056
3/6/1998 12 $17,605,849
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Titanic Weekend Box Office Gross December ‘97 thru March ‘98
What questions do you have about the graphs? What information, is necessary for the graphs to be more understandable?
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Researching a Data Set: Titanic WBO Gross 12/97-3/98
1 3 5 7 9 11 13$15,000,000
$20,000,000
$25,000,000
$30,000,000
$35,000,000
$40,000,000 Why do these points behave differently?
1/16/98
2/13/98
12/19/97
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Creating a Regression Analysis
• Identify regression equation• Display trend line and data set• Interpolate/Extrapolate
– Trace function– Point of intersection
• What questions can we ask?
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
What did we find?
How can we use it?
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Kinds of Tasks/Questions to Ask• Describe what the values in the regression
equation mean in terms of this problem.
• What does ( , ) mean in terms of this data?• What would happen to the model if the data
were changed by ….?
• Compare trend lines…
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Titanic Data w/ Trend Line
0 2 4 6 8 10 12 14$10.00
$15.00
$20.00
$25.00
$30.00
$35.00
$40.00
f(x) = − 1.28392411188811 x + 35.6342848939394R² = 0.548253054622562
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Patent Data with Trend Line
0 5 10 15 20 25 3030000
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f(x) = 2069.92939609236 x + 37148.3246003553R² = 0.857632250143874
U.S. OriginU.S. Origin
Years Since 1980
Pat
ents
in
Th
ou
san
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The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Example 2
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
What’s the problem here?
How can you handle this kind of problem?
y= -3,107,000 x + 16,063,000r2 = 0.9442
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
0 1 2 3 4 5 6 7$0
$2,000,000
$4,000,000
$6,000,000
$8,000,000
$10,000,000
$12,000,000
$14,000,000
$16,000,000
$18,000,000
$20,000,000
f(x) = 19159230.9629448 exp( − 0.436289780450987 x )R² = 0.983739067493835
Gross
Exponential (Gross)
Predicted Gross
Weekend Since March 20, 2009
y = 19,160,000∙0.646x
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Another Example of a System
y1 = -1.3x + 305y2 = -0.31x + 248
What kind of questions could your students ask about this system?
Olympic Men 400 Meter Free Style Swimming Winning Times Since 1924
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
What algebra do you see in this graph?
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Questions?
Next Steps?
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Photo Acknowledgements
LushTraffic JamHey, I'm all Bundled upDon’t Bother MeTodavía hay esperanzaBrooklyn Bridgemotion study experimentstopped in motionLadder of KnowledgeSteps to Knowledge
...-Wink-... (taking a break)
...-Wink-... (taking a break)
...-Wink-... (taking a break)
...-Wink-... (taking a break)Piulet (Daniel)NfalseyMonkeyc.netJarkkoSDegreezero2000Sanjibm
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Number of Patents Granted in US by Origin
Year Year from 1980 U.S. Origin Foreign Origin
2008 28 92000 93244
2005 25 82586 75155
2000 20 97011 79072
1995 15 64510 49445
1990 10 52977 46243
1985 5 43393 33880
1980 0 40764 25455Full Data Set from Swivel.com
The Collaborative for Teaching and Learning Regression Analysis
Roland O’Daniel September 2009
Notes