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Mathematical formula for R-sq adjusted

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  • August 7, 2006 at 12:31 pm #44248

    chhabra
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    Can some one explain me the significance of R-sq adjusted as compared to R-sq in regression analysis ? What is the mathematical formula for R-sq adjusted ? how it is different from R-sq ?
     
     

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    August 7, 2006 at 12:57 pm #141483

    EdG
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    R2 and R2-Adjusted represent the proportion of variation in the response data explained by the predictors.  So, if your error is small (all of the points are “close” to the regression model – the line) then your R2 value approaches 1. 
     
    It is possible to artificially make R2 approach 1 buy adding more X’s to your model.  But, R2-Adjusted takes into account the number of X’s and number of data points being analyzed and there for mitigates this impact on your value.
     
    Hope that this helps.
     
    BTW.  R2-Adjusted = 1 – [(SSERROR / dfERROR) / (SSTOTAL / dfTOTAL)] 
    as opposed to
    R2 = SSERROR / SSTOTAL

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    August 17, 2006 at 5:26 am #141837

    Jonathon Andell
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    In simple terms:If your model has lots of X’s but not a lot of data points, adjusted R^2 will be significantly lower than R^2.

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