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Physical Sciences and Mathematics Commons™
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- Generalized least-squares regression (2)
- Geometric mean regression (2)
- Least-squares (2)
- Orthogonal regression (2)
- Symmetric least-squares (2)
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- Weighted ordinary least-squares (2)
- Common Core State Standards for Mathematics (1)
- Curricular reform (1)
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- Geometry (1)
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- Mathematical modeling (1)
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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
A Primer For Mathematical Modeling, Marla A. Sole
A Primer For Mathematical Modeling, Marla A. Sole
Publications and Research
With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school with the mathematics they will use outside of school. Instructors have found mathematical modeling difficult to teach. To successfully incorporate modeling activities I believe that curricular changes should be accompanied by professional development for curriculum developers, classroom teachers, and higher education professionals. This article serves as an introduction to modeling by …
The Use Of Statistics In Experimental Physics, Thomas J. Pfaff, Maksim Sipos, M. C. Sullivan, B. G. Thompson, Max Tran
The Use Of Statistics In Experimental Physics, Thomas J. Pfaff, Maksim Sipos, M. C. Sullivan, B. G. Thompson, Max Tran
Publications and Research
Most mathematicians are aware of the importance of statistics in biological sciences, business, and economics, but are less aware that statistics is used every day in experimental physics. This paper gives three interesting examples of how statistics plays a vital role in physics. These examples use the basic statistical tools of residuals analysis and goodness of fit.
Generalized Least-Squares Regressions I: Efficient Derivations, Nataniel Greene
Generalized Least-Squares Regressions I: Efficient Derivations, Nataniel Greene
Publications and Research
Ordinary least-squares regression suffers from a fundamental lack of symmetry: the regression line of y given x and the regression line of x given y are not inverses of each other. Alternative symmetric regression methods have been developed to address this concern, notably: orthogonal regression and geometric mean regression. This paper presents in detail a variety of least squares regression methods which may not have been known or fully explicated. The derivation of each method is made efficient through the use of Ehrenberg's formula for the ordinary least-squares error and through the extraction of a weight function g(b) which characterizes …
Generalized Least-Squares Regressions Ii: Theory And Classification, Nataniel Greene
Generalized Least-Squares Regressions Ii: Theory And Classification, Nataniel Greene
Publications and Research
In the first paper of this series, a variety of known and new symmetric and weighted least-squares regression methods were presented with efficient derivations. This paper continues and generalizes the previous work with a theory for deriving, analyzing, and classifying all symmetric and weighted least-squares regression methods.
Elementary College Geometry, Henry Africk
Elementary College Geometry, Henry Africk
Open Educational Resources
This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra.
The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem-proving or formal methods of reasoning. However the topics are …