R-square value for model fitting

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SUMMARY

The discussion centers on the use of R-square values as indicators of 'goodness of fit' in modeling, particularly in linear and exponential models. Participants highlight the limitations of R-square, especially when outliers disproportionately influence the results. The conversation suggests exploring "robust statistics" as an alternative approach to better quantify model fit, especially in the presence of outliers. The consensus indicates that while R-square is commonly cited in literature, its reliability can be compromised by isolated data points.

PREREQUISITES
  • Understanding of R-square values in statistical modeling
  • Familiarity with linear and exponential models
  • Knowledge of outliers and their impact on statistical analysis
  • Basic concepts of robust statistics
NEXT STEPS
  • Research robust statistical techniques for handling outliers
  • Explore alternative goodness-of-fit measures such as Adjusted R-square and AIC
  • Learn about linear regression diagnostics and their implications
  • Investigate the impact of outliers on model performance using simulation studies
USEFUL FOR

Data scientists, statisticians, and researchers involved in statistical modeling and analysis, particularly those working with datasets that may contain outliers.

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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