Goodness-of-fit statistics

Comparison of Goodness of Fit Statistics for Linear Regression Part 1 - Introduction... 

Workman, J. and Mark, H., Chemometrics in Spectroscopy Comparison of Goodness of Fit Statistics for Linear Regression - Part 1, Introduction , Spectroscopy 19(4), 32-35 (2004). 

The attached worksheet from MathCad ( 1986-2001 MathSoft Engineering Education, Inc., 101 Main Street Cambridge, MA 02142-1521) is used for computing the statistical parameters and graphics discussed in Chapters 58 through 61, in references [b-l-b-4]. It is recommended that the statistics incorporated into this series of Worksheets be used for evaluations of goodness of fit statistics such as the correlation coefficient, the coefficient of determination, the standard error of estimate and the useful range of calibration standards used in method development. If you would like this Worksheet sent to you, please request this by e-mail from the authors. 

Default distributions can be evaluated at 2 levels 1) in comparative studies, one may compare how often alternative distributions better describe the data, e.g., based on goodness-of-fit statistics, and 2) before applying a default distribution in a particular situation, one should evaluate whether the distribution agrees with whatever data are available for that situation. 

Regression analysis as described in Section 6.5.2 will fail. The autocorrelation affects the significance levels and the goodness of fit statistics. If one of the explanatory variables is itself autocorrelated, the regression will fail. 

Using the information obtained (from the literature) or provided (by the proponent of the QSAR) in step 1, there should be an independent confirmation of the QSAR. This means that someone with statistical expertise should apply the specified statistical method to the training set of data, to check that the same QSAR model and (goodness-of-fit) statistics are obtained. If the QSAR model is confirmed, step 3 should be initiated. Alternatively, the proposed QSAR could be modified, so that the modified QSAR is subjected to independent assessment. 

Discuss the methods and report the goodness-of-fit statistics for any parametric distributions for input variables that were fitted quantitatively to measured data. 

The goodness of fit statistic measures how well a model fits the data of the - training set, e.g. how well a regression model (or a classification model) accounts for the variance of the response variable. 

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