I have two different regression models with same predictand (y) but different sets of predictors in two models. Let the models are as following:
y=a0+a1x1+a2x2+a3x3
y=b0+b1z1+b2z2+b3z3+b4z4
now I got two multiple R^2 values for two models say R1^2 and R2^2 respectively. I want check whether difference between two R^2 values are statistically significant or not.
Please note these two models are not nested models and there is no relation between two predictor sets x’s and z’s.
Also these two models contain atmospheric/meteorological data.
So, please suggest some suitable statistical tests.
Thanks.
I suggest that along with R^2 Statistic you also compute the R^2 adjusted statistic, even if R^2 of the two models are very close or turns out to be identical, R^2 adjusted addresses the issue of over fitting to certain extent.
it is quite possible that these two models have very different R^2 adjusted values.
@Mehmet ...to check whether two models are same or not at a given significance level (say 0.05).
You could use the coxtest. For explanation in R, see https://www.rdocumentation.org/packages/lmtest/versions/0.9-35/topics/coxtest. The links also holds a literature reference.
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