R-square value for model fitting

AI Thread Summary
R-square values are commonly used to assess the goodness of fit in modeling, but they can be misleading, particularly when outliers are present, as these points disproportionately influence the results. There is a concern that R-squares may not be rigorous indicators of model accuracy. Alternative methods, such as robust statistics, can provide better assessments when outliers are suspected. Many academic papers still favor R-square values despite these limitations. Understanding the impact of outliers is crucial for accurate model evaluation.
bbobb
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hi,

i make use of the r-square values quite extensively in my modeling work, mainly as an indicator of the 'goodness of fit' between data and linear/exponential models. however, i have often been told that r-squares are not rigorous indicators, especially so in cases where there exists isolated data points that are far from the main group of data as these isolated points will carry more weight in the calculation of r square.

question is, is there any other quantity that is a better quantifier of 'goodness of fit'? personally, an overwhelming majority of the papers that i have read quote r-squares as the preferred indicator.

thanks.
 
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I'd rather put this question in the probability and statistics forum.
But I'll try some answer already: These isolated points are called outliers. Sometimes there is good reason to believe that they are a result of erroneous measurements (e.g. writing up 10,000 instead of 10.000).
If you suspect to have these in your data, you may try to use so called techniques of "robust" statistics.
 
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