Least squares methods basic assumption

A graphical method can be applied to problems of this nature and has the same basic assumptions as the least-squares method, namely that the x variables do not interact with one another. 

While the least squares estimator appeared several centuries ago as an independent method giving good results under certain assumptions, we have to dig deeper into mathematical statistics to see its roots, and, in particular, its limitations. This general subject is the maximum likelihood principle, one of the basic concepts of mathematical statistics. The principle is simple ... 

The next step in the protocol answers the question about what is the best method to estimate the reactivity ratios. Historically, because of its simplicity, linearization techniques such as the Fineman-Ross, Kelen-Tudos, and extended Kelen-Tudos methods have been used. Easily performed on a simple calculator, these techniques suffer from inaccuracies due to the linearization of the inherently nonlinear Mayo-Lewis model. Such techniques violate basic assumptions of linear regression and have been repeatedly shown to be invalid [117, 119, 126]. Nonlinear least squares (NLLS) techniques and other more advanced nonlinear techniques such as the error-in-variables-model (EVM) method have been readily available for several decades [119, 120, 126, 127]. 

Standard curves are calculated according to the method of least squares. Appropriate algorithms are provided with scientific calculators and most spreadsheet programs for personal computers. It is better to compute the standard curves employing the single readings instead of means. Be aware of the basic assumptions made in... 

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