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Product No. 99813 Supplementary Print Price: FREE with membership
 

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 Ostwald’s test of the chemical Law of Mass Action are examined.

Table of Contents

1. INTRODUCTION

2. OSTWALD’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 LEAST-SQUARES 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 Least-Squares Fitted to Grouped Data
4.5 Assessment of Fits to Grouped Data

5. SOLUTIONS TO ODD-NUMBERED EXERCISES

6. APPENDIX: UNITS

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR