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Unformatted text preview: 1 Lec.33: Lec.33: Regression Models Regression Models CEE 3040 Uncertainty Analysis in Engineering (with thanks to Prof. Linda Nozick) 2 In This Unit In This Unit Motivational Example from my freight energy research Regression of energy consumption and freight value Extensions of Regression Analysis Nonlinear regression (13.113.3) Multivariate regression (13.413.5) Introduction to HW11 Q3 Resolution of motivational example on freight Overview of ANOVA (time permitting) On Friday: Lec.34 Analysis of Variance (ANOVA) Regression diagnostics and model building Readings for this Unit Main Reading: Devore, J. (2009) Chap.12, Simple Linear Regression and Correlation. Chap.13, Nonlinear and Multiple Regression Supplemental Reading: C. Khisty, and J. Mohammadi, Part of Chapter 9 in Fundamentals of Systems Engineering titled: Regression and Correlation Analysis, pp. 268283. Review from Lec.32: Fitting a, b parameters Scatter plot with linear curve fit: 1, 1 2, 4 3, 3 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1 1.5 2 2.5 3 3.5 X Value Y Value 5 Review (Cond) Review (Cond) Solving for a: x average = 2 y average = 2.67 a = y average b * x average = 2.67 1 * 2 = 0.67 1 36 42 48 54 1 2 1 2 1 1 1 = =  = = = = = = n i n i i i n i n i i i n i i i x x n y x y x n b Solve for b: Review (Cond) Review (Cond) Resulting curve: y = b*x + a = 1*x + .67 In words: The line with slope 1 and yintercept 0.67 is the line that fits the data with minimum error 6 1, 1 2, 4 3, 3 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1 1.5 2 2.5 3 3.5 X Value Y Value 7 A Motivational Example: A Motivational Example: Energy Consumption Energy Consumption and the and the Value of Freight Value of Freight 8 Nonlinear regression: Nonlinear regression: An example from my research An example from my research In many problems, data suggests form other than linear Can fit other function if shape is easily observed (e.g. log function) If not observed, fit a polynomial Example: correlation between freight energy use and value of product moved Interest in understanding nature of growing energy use 9 Trend in Relative Growth in Trend in Relative Growth in US Energy Consumption by Sector US Energy Consumption by Sector 1 1.2 1.4 1.6 1.8 2 2.2 2.4 1970 1975 1980 1985 1990 1995 2000 Relative growth (1970 = 1.00) Freight Passenger All Trans. All Energy ResComm Industrial Source: Francis Vanek and Edward Morlok; Reducing US Freight Energy Use Through Commodity Based Analysis: Justification and Implementation. Transportation Research Part D, Vol.5 No.1 pp. 1129, 2000. 10 Possible application of systems dissolution, i.e. broadening Possible application of systems dissolution, i.e. broadening the boundaries of the system in order to add new tools the boundaries of the system in order to add new tools that enable a solution(Ackoff, 1978)...
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This note was uploaded on 12/01/2010 for the course CEE 3040 at Cornell University (Engineering School).
 '08
 Stedinger

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