# Interpretation of $R^2$ in simple regression

I have run a linear regression with five independent variables and two dependent variable I am using EPS and ROE as my dependent variable and Board meeting, Board size, leadership, Independend Non-Executive, Audit committee as my Independent variable and my resulting Model is shown as:

Model Summary 1    (Dv: ROE)

R. Square 0.39
Error of the Estimate = 19.4807565
a. Predictors: (Constant), Board meeting, Board size, leadership,
Independent Non-Executive, Audit committee.

Model Summary 2    (Dv: EPS)
R   .308a
R Square = .095
Std. Error of the Estimate = 35.308797
a. Predictors: (Constant), Board meeting, Board size, leadership,
Independent Non-Executive, Audit committee


I got confused regarding how to explain the correlation of my independent and dependent variables. I'm also wondering if my results are any good. Thanks.

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Both model 1 and model 2 seem to be poor as the adjusted $R^2$ indicates that less than $10\%$ of the variance is explained by the model. The first model looks like it fits ROE better than the second one fits EPS but the adjusted $R^2$ is small $(1.4\%)$ even though the $R^2$ is $39\%$. There is probably overfitting in that case.
Did you notice that the two models involve different dependent variables? It therefore makes little sense to say one is a "better fit." Also, it's clear there is no $R^2$ equal to 39% (it couldn't possibly be consistent with an adjusted $R^2$ of just 0.014): the second line of output is likely corrupted. – whuber Aug 18 '12 at 15:45