Measurements

Data Analysis Using the Least-Squares Method by John Wolberg PDF

By John Wolberg

ISBN-10: 3540256741

ISBN-13: 9783540256748

ISBN-10: 3540317201

ISBN-13: 9783540317203

The popular approach to info research of quantitative experiments is the tactic of least squares. usually, besides the fact that, the complete strength of the strategy is ignored and extremely few books take care of this topic on the point that it merits. the aim of knowledge research utilizing the tactic of Least Squares is to fill this hole and comprise the kind of info required to aid scientists and engineers follow the tactic to difficulties of their exact fields of curiosity. furthermore, graduate scholars in technology and engineering doing paintings of experimental nature can make the most of this publication. fairly, either linear and non-linear least squares, using experimental errors estimates for information weighting, methods to incorporate earlier estimates, technique for choosing and checking out versions, prediction research, and a few non-parametric tools are mentioned.

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The emphasis on neural networks as a nonparametric modeling tool is particularly attractive for time series modeling. 2. The input vector X may include any number of variables. The network includes many nonlinear elements that connect subsets of the input variables. All the internal elements are interconnected and the final output Y. There is a weighting coefficient associated with is a predicted value of Y each element. If a particular interaction has no influence on the model output, the associated weight for the element should be close to zero.

F) for various values of X. This is what is often called the prediction problem. , the ak's) and then apply the equation to calculate 34 Chapter 2 THE METHOD OF LEAST SQUARES values of y for any value of x. , xm. The least squares formulation developed in this chapter also includes the methodology for prediction problems. 2 The Objective Function The starting point for the method of least squares is the objective function. Minimization of this function yields the least squares solution. The simplest problems are those in which y (a scalar quantity) is related to an independent variable x (or variables xj's) and it can be assumed that there is no (or negligible) errors in the independent variable (or variables).

9) -1 In this equation, C is the inverse matrix of C. , unit weighting). 13) For problems in which the f function is nonlinear, the procedure is similar but is iterative. One starts with initial guesses a0k for the unknown values of ak. 15) 48 Chapter 2 THE METHOD OF LEAST SQUARES In the equation for Vk the parameter Yi is no longer the value of the dependent variable. , the a0k 's). For linear problems we don’t need to make this distinction because the initial guesses are zero and thus the computed values are zero.

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Data Analysis Using the Least-Squares Method by John Wolberg


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