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R squared adjusted in DOE

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  • #42590

    Tierradentro
    Participant

    Hi
    I have 2 significant X’s that impact the Y. I am trying to manipulate the input data  when running a one way anova to achieve a >80% R Square adjusted figure. When ‘playing’ around with the individual inputs and then running the anova I am getting a p value <0.05 though a low R squared adjusted figure OR a higher (though not high enough) R squared adjusted figure and a p value >0.05.
    I am trying to understand how to manipulate the input data to influence the output and achieve >80% R square adjusted
    Really, really need to understand from a learning perspective
    HELP !!
    John

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    #134572

    NATZIC
    Participant

    Hi John,
    you need to be careful with the R-sq & R-sq adjusted values. You probably know that R-sq describes the amount of variation in Y that is explained by your X’s. It is possible to over inflate this by having an excess amount of X’s in your model, hence R-sq adj is used. R-sq adjusted is adjusted by the amount of X’s in your model. I’d be more concerned about getting your R-sq adjusted to within 5% of R-sq. We were told this is the “Monkey” test, because any monkey can get a high R-sq, but not a high R-sq adjusted. I’d much prefer to have a R-sq =0.6, and an R-sq adjusted = 0.55 then an R-sq=0.9 and an R-sq adjusted = 0.6.

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    #134687

    Tierradentro
    Participant

    Hi Pat
    In experimenting with my figures I am finding that once I start to increase the adjusted R-sq % result then the p-value becomes >0.05
    I am told that  I need an adjusted r-sq fiqure of >80%, I am getting nowhere near that. I have only 2 significant X’s to work with
    ???
    John

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    #134688

    NATZIC
    Participant

    Hi John,
    an Rsq value less then 80% means that less then 80% of the variation in your Y is explained by your chosen X’s. It doesn’t mea your model is inadequate, remember the other checks you need to do such as residual analysis.What Rsq values are you getting?. Possible reasons why Rsq is low

    External noise in DOE caused variation in Y
    Your model did not include all significant X’s
    You cannot mess around with your model to artificially inflate Rsq values.

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    #134701

    Robert Butler
    Participant

    John,
      Pat has given you good advice.  As he said, you need to look at your residual plots – they will tell you what you need to know with respect to missing X’s, influential data points and noise.  As was noted, you can make the R2 go as high as you want by just throwing terms in the model.  Assuming you have no replicates you can drive it all the way to 1 if you want – of course the model won’t mean a thing.
      As for the assertion that you need “adjusted r-sq fiqure of >80%” Whoever offered that advice doesn’t know what they are talking about.  There are many processes with a level of ordinary variation so high that you will be lucky to get an R2 of 30%.  Does this make a model invalid or useless – no – it just means the uncertainty associated with its predictions will be large.  It is nice to have a good predictive model with a high R2 but a high R2, by itself, guarantees nothing.

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