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99813 
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Data Analysis with Examples from Chemistry
Yves Nievergelt

Mathematics Topic: Modeling, Statistics 
Application Areas: Chemistry, Weighted least squares linear regression 
Prerequisites: Extremum of a quadratic polynomial, linear inequalities,
and summation notation.
TARGET AUDIENCE:
Students studying statistics, numerical analysis, chemistry,
or any other science using measured data. 

 ©2014 by COMAP, Inc.  UMAP Journal 35.4  40 pages 

This Module shows how methods for various analyses
of data reduce to the calculation of a weighted mean
to minimize a weighted sum of squares. As examples,
data from Wilhelm Ostwaldâ€™s test of the chemical Law
of Mass Action are examined.
Table of Contents
1. INTRODUCTION
2. OSTWALDâ€™S DATA
3. PRECISION AND ACCURACY
3.1 Precision and Accuracy of Data
3.2 Precision and Accuracy of Computations
3.3 Fitting One Point to Data
3.4 Sensitivity ofWeighted Means to Perturbations of Data
3.5 Analyses of Variances ofWeighted Means
4. WEIGHTED LEASTSQUARES REGRESSION
4.1 Weighted Regression through a Fixed Point
4.2 Weighted RegressionWith a Fixed Slope
4.3 Sensitivity of the Slope to Perturbations of the Data
4.4 Lines ofWeighted LeastSquares Fitted to Grouped Data
4.5 Assessment of Fits to Grouped Data
5. SOLUTIONS TO ODDNUMBERED EXERCISES
6. APPENDIX: UNITS
REFERENCES
ACKNOWLEDGMENTS
ABOUT THE AUTHOR



