http://spssx-discussion.165.s1.nabble.com/Significant-regression-but-low-R-tp5722243p5722253.html
Why is R^2 seemingly low while tests are significant?
- Because the N is 830, which is large.
"Statistical significance" is a measure that compares to "random",
not to "clinically important" or "meaningful" or, more relevant to your
question, "evident with a tiny N". That's more or less the meaning of
r, if you want to be casual about it.
On the other hand, a design that collects N = 830 (instead ofa smaller
number like 50 or 100) is what is necessary when the relations have
a small r. Presumably, someone thought that effects of the observed
size would be useful and important to measure and test.
Note that r or R^2 is not, in general, a fine measure of "effect size". Yes,
it works when we know what we are expecting, mainly when we expect
something large because two things are nearly the same. The reason
that epidemiologists often collect Ns of many thousands is because their
Odds Ratios of 2.0 or more for a "big effect" may account for 1% or less
of "variance", owing to the rareness of the events being predicted.
--
Rich Ulrich
Date: Thu, 26 Sep 2013 10:39:52 +0000
From:
[hidden email]Subject: Significant regression, but low R
To:
[hidden email]
Hi
I have a question concerning the interpretation of the result of a linear regression.
N = 830
df=6
y=c + x1 + x2 + x3 + x4 +x5+ x6
corr. R2 = 0.095
Model and all independent variables (Beta) are significant.
How comes, that all the betas are significant, but the amount of explained variance is so low ? According to my poor knowledge I would have expected a higher R2…
Thanks for hints.
Tom