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Mathematical formula for R-sq adjusted

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  • #44248

    chhabra
    Participant

    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 ?ย how it is different from R-sq ?
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    #141483

    EdG
    Participant

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

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    #141837

    Jonathon Andell
    Participant

    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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