Dear Experts,
It is stated: for 15 pairs of data, with 5% significance level, R2 values should be higher than 0.2601.
how can I know such R2 value for 540 pairs? how can I find this certain value for a different number of pairs?
Is it understandable using SPSS?
Thank you
You can generate 540 pairs from approximately the same distribution and then see how R2 will looks like.
Hello Majid,
For ordinary, bivariate correlations, the minimal value of r (or r-squared) for statistical significance with N = 540, at the .05 level (non-directional) would be: r = .0844 (rounded to 4 decimal places), and r-squared = .000712.
You can find this by some simple trial and error via the formula for testing significance of r, which is via a t-statistic with N - 2 df. Since you've fixed the N, the critical t-value is easily found (e.g., = IDF.T(..975, 538) in SPSS).
If you're talking about a multiple regression equation (with more than 1 IV in the model), then the minimal value for R (or R^2) depends on the number of IVs included in the model. For example, for a model with 2 IVs, the minimal R for model significance at the .05 level would be .1054 (R^2 = .0111).
Good luck with your work.
https://stats.stackexchange.com/questions/130069/what-is-the-distribution-of-r2-in-linear-regression-under-the-null-hypothesis
Indeed, you want to check the significance of the regression model.
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