On the Use of Equivalent Numbers in the Method of Least Squares - Softcover

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9781333402822: On the Use of Equivalent Numbers in the Method of Least Squares

Synopsis

This book is an innovative study that challenges the conventional wisdom that has dominated the application of the method of least squares for fitting an empirical function to a series of observed facts. In mathematics, the method of least squares is a standard technique for solving problems where there are more unknowns than equations, and while it is recognized that the pursuit of accuracy can be carried to unreasonable lengths, the current practice is to adhere strictly to the rigorous precepts of least squares to an extent that is theoretically incorrect and unnecessarily laborious. The author demonstrates that a more nuanced approach that allows for scalar modifications to the computational factors used in the method, can achieve nearly equivalent results with exceptional numerical facilitation. While the core of the book is mathematical in nature, the author offers a clear account of the principles governing the application of the method of least squares in practice, and makes the case that scientists should not be bound by an overly strict interpretation of its tenets when seeking to extract meaningful insights from observations. This pragmatic analysis will appeal to researchers, scientists, and students employing statistical models.

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