Kctm Conference 09 Regression Analysis

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.



Where do you see algebra outside of your classroom?





When looking for a data source, what are you looking for?



GRE Score Concentrations in 28 Fields of PhD Study

http://www.swivel.com/data_sets/show/1016902

http://www.swivel.com/data_sets/show/1016902



Cost/month in US $

Electricity Gas



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

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Height of teachers in schoolH

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ms

60 65 70 75 80150

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f(x) = 2.56873978184328 x − 1.788905737173

Height in inches



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/

http://www.swivel.com/graphs

http://www.the-numbers.com/charts/thisweek.php

http://www.swivel.com/graphs

http://zipskinny.com/



Example 1



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?



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



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?



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

f(x) = − 1283924.11188811 x + 35634284.8939394R² = 0.548253054622562

Why do these points behave differently?

1/16/98

2/13/98

12/19/97



Creating a Regression Analysis• Identify regression equation• Display trend line and data set• Interpolate/Extrapolate

– Trace function– Point of intersection

• What is interesting to you? What is connects to what you have already studied/taught?

• What questions can we ask?



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…



What did we find?

How can we use it?



Example 2



What’s the problem here?

How can you handle this kind of problem?

y= -3,107,000 x + 16,063,000r2 = 0.9442



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



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



1920 1930 1940 1950 1960 1970 1980 1990 2000220

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Questions?

Next Steps?

Link to Presentation Materials:http://ctlonline.pbworks.com/Regression-Analysis



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)Piulet (Daniel)NfalseyMonkeyc.netJarkkoSDegreezero2000Sanjibm



What algebra do you see in this graph?



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



Notes



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 = 0.548253054622561



Patent Data with Trend Line

0 5 10 15 20 25 3030000

40000

50000

60000

70000

80000

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100000

f(x) = 2069.92939609236 x + 37148.3246003553R² = 0.857632250143874

U.S. OriginU.S. Origin

Years Since 1980

Pat

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in

Th

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Education

Kctm Conference 09 Regression Analysis