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Thread: U-shaped relationship by quadratic variable. Interpreting effect size.

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    Cool U-shaped relationship by quadratic variable. Interpreting effect size.

    First post, eager to learn.

    I am trying to interpret a study that tests, among other relationships, if there is a U-shaped relationship between x (responses between 1-7) and y (dichotomous: 0 , 1). To test for the U-shaped, the author has implemented x once untransformed, once squared. Mean response (2.9) has been subtracted from the x values.

    a: b = .46*
    b: b = .68**
    c: b = .62*
    x: b = -.65**
    x^2: b = .29*

    constant: b = -6.81**

    The U-shaped relationship seems supported by the data as x is negative significant, x^2 is positive significant. My question is:

    Which (combination of) variables has to be taken into account when interpreting effect size of x on y?
    (a) I was thinking y = -6.81 -.65x + .29x^2, but the -6.81 constant makes no sense as 0<y<1 and the line would remain beneath the x axis.
    (b) Another option is y = -.65x + .29x^2, denying the constant (because seemingly trivial and accounted for by the other factors in the model). But this leaves me with a curve that has it's minimum beneath the x axis (x=1.1207; y=-0.364224).


    [update] the relevant table has now been attached
    Attached Images  
    Last edited by rj.ter.haar; 01-19-2015 at 02:02 AM.

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