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Regression

Regression. What is a Regression?.

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Regression

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  1. Regression

  2. What is a Regression? • In statistics, regression analysis refers to techniques for the modeling and analysis of numerical data consisting of values of a dependent variable (also called a response variable) and of one or more independent variables (also known as explanatory variables or predictors). The dependent variable in the regression equation is modeled as a function of the independent variables, corresponding parameters ("constants"), and an error term. The error term is treated as a random variable and represents unexplained variation in the dependent variable. Parameters are estimated to give a "best fit" of the data. Most commonly the best fit is evaluated by using the least squares method, but other criteria have also been used. • Regression can be used for prediction (including forecasting of time-series data), inference, hypothesis testing, and modeling of causal relationships. These uses of regression rely heavily on the underlying assumptions being satisfied. Regression analysis has been criticized as being misused for these purposes in many cases where the appropriate assumptions cannot be verified to hold. One factor contributing to the misuse of regression is that it can take considerably more skill to critique a model than to fit a model. [1]

  3. Linear Quadratic Cubic Quartic Exponential Logarithmic Power Logistic Sine Types(on TI-83/84)

  4. Linear Methods: • Least Squares • Calculus • Calculator, computer software, free online tools • http://calculator.maconstate.edu/

  5. Linear Problems • [1] Basic Line • [2] Fertilizer • [3] Population • http://www.google.com/publicdata?ds=uspopulation&met=population&idim=county:13193&q=Population+of+Macon+Georgia#met=population&idim=county:13151:13021:13207:13153

  6. Quadratic Popular applications: • Area • Trajectory • Maximizing revenue or materials • Minimizing cost

  7. Cubic • TI-82 Mini-Labs: Algebraic Investigations by Phil DeMarois, MathWare, 1994, p. 130 • http://phe.rockefeller.edu/green_mobility/ • http://www.bts.gov/

  8. Quartic

  9. Power On a recent episode of Mythbusters, they got a “lead balloon off the ground. Of course a regular balloon is spherical, but: Find the equation that compares the volume to surface area of a “cubic” balloon as the volume increases.

  10. Exponential M & Ms Logarithmic Earthquakes pH Decible levels Learning and forgetting

  11. Logistic Heights Sine Wave Temperatures http://climate.engr.uga.edu/state/ga_temp.html

  12. Internet Resources: • http://mdk12.org/share/clgtoolkit/lessonplans/SlopeInterceptTastyTacos.pdf • http://illuminations.nctm.org/ • (also a link from the Georgia DOE web site)

  13. Internet References • [1] http://en.wikipedia.org/wiki/Regression_analysis • [2] http://www.thinkanddone.com/ge/Reg.html • [3] http://video.msn.com/video.aspx?mkt=en-us&vid=a3e00446-2bf7-4bc9-99ff-097ec2b382cc Print Sources • Animals as Our Companions, WLME 6 (NCTM), 2000 • Graphing Calculator Activities, Exploring Topics in Algebra I and Algebra II, by Charles Lund & Edwin Andersen, Dale Seymour Publications, 1998

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