June 28, 1998
June 28, 1998
July 1, 1998
3.157.1 - 3.157.15
Considering Numerical Error Propagation in Modeling and Regression of Data
Neima Brauner, Mordechai Shacham Tel-Aviv University/Ben-Gurion University of the Negev
Abstract The use of user-friendly interactive regression software enables undergraduate engineering students to reach a high level of sophistication in regression, correlation and analysis of data. In order to interpret correctly the results, the students must be familiar with potential causes for poor fits in correlations, should be able to recognize a poor correlation and improve it if possible. They should also be aware of the practical consequences of using a correlation which has no statistical validity.
In this paper, the harmful effects of numerical error propagation (resulting from collinearity among the independent variables) are explained and demonstrated. Simple methods for minimizing such error propagation in polynomial regression are introduced. This material can be presented, for example, as part of 3rd year undergraduate mathematical modeling and numerical methods course.
Introduction Realistic modeling and accurate correlation of experimental data are essential to sound engineering design. Many of the statistical techniques for analyzing the accuracy of the correlations have been known for several decades (see, for example, Draper and Smith, 1981, Himmelblau, 1970, Bates and Watts, 1988 and Noggle, 1993). But, until recently, those techniques have not been utilized in a significant level in undergraduate engineering education. One of the main reasons for not utilizing those techniques was that statistical tests usually yield numbers (variance, standard deviation, correlation coefficient, etc.). The meaning of these numbers can be easily misinterpreted if the statistical theory and the assumptions made in developing the tests are not well understood.
The emergence of software packages with interactive regression and statistical analysis capabilities (such as POLYMATH, MATLAB, MATHEMATICA, EXCEL) which provides both numerical and graphical output changes the situation. These software packages enable undergraduate engineering students, with moderate statistical background, to carry out rigorous regression and statistical analysis of data. They are able to select the most appropriate correlation model and test its statistical validity using residual and confidence region plots. They can analyze the quality and precision of the laboratory data by plotting one independent variable versus the others to detect hidden collinearity that may exist among the variables.
Brauner, N., & Shacham, M. (1998, June), Considering Numerical Error Propagation In Modeling And Regression Of Data Paper presented at 1998 Annual Conference, Seattle, Washington. https://peer.asee.org/6982
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