Discerning the Rsquare Value & ANOVA Table for Regression

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    I have done a linear regression run with the following results:

     Adjusted Rsquare 0.087, Std error: 3992.428; F=2.210, Sig=0.033


    I am surprised by the low Rsquare value when the Sig level is 0.033. In this case, am I able to use the subsequent results given the low explanatory power? If not, what method should I use to discern the relationship (e.g. quadratic)? Tks

    Jeremy Miles

    Don’t give us adjusted R-square, give us real R-square.  That doesn’t seem so low to me.  


    If you think you might have a quadratic relationship, you should test for it.  You should not decide to do that as a result of a poor R-squared.




    I agree with Jeremy. One should generally avoid using R2 for model selection. This, of course, depends on the purpose of the analysis, but often it is the coefficients in the model that are of interest. So focus on the coefficients in the model — what are there direction, magnitude, and significance? In addition, it is important to distinguish between the magnitude of R2 and the significance of R2. The significance depend not only on the magnitude of R2, but also on the number of observations in data. (This parallells the distinction in the effect size litterature between size and significance).

    You could, as Jeremy suggests, incorporate quadratic terms in your model to see if the fit improves. However, you should have good theoretical reasons for this, rather than statistical ones; that is, choose the functional form that suits your theory or research question, not R2.



    The real r-square value is 0.158. What would be a rule of thumb for a high r-square value ? The underlying theory supports a quadratic function, or more specifically, it first starts off as a linear before tapering. However, I was unable to find the relevant spss function to run a quadratic function.

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