R-Sq Relevance

[arkantosno1]

Hi,
I have the following figures after creating a linear regression model using mintab:

S = 2.65155 R-Sq = 31.8% R-Sq(adj) = 31.6%

PRESS = 61820.5 R-Sq(pred) = 31.29%

A few questions:
1. Considering I am using 38 independant interval variables (and that R-Sq increases with each variable) is the R-Sq a good indicator of performance? An expected random output for this model would be approx 10%.
2. The R-sq(pred), is this indicating that the model will perform almost as well predicting results as the R-Sq implies or is this an indication the any prediction results will only perform 31.29% as well as the original R-Sq of 31.8%.

Thanks for your time, sorry if this is an eas question, I am new to stats.

[noetsi]

There is no statistical answer to what is a good r squared value. That is a professional judgement that depends on the phenomenon in question. In cases where a wide range of factors contribute to the dependent variable getting 10 percent R squared might be better than the norm. In other cases you can end up with very high r squared values (eighty or more percent). I would look for studies in the literature that addressed this and see what their r square values are. I am curious how you would know that ten percent would be random, have you seen other studies in this area?

When you have a lot of variables (and 38 is a huge number of variables to have in a regression) r squared is not ideal because it gets higher as the number of variables increases. You should use adjusted R squared which adjusts for this.

I have never encountered R squared predicted before.

[derksheng]

If you have integrated vectors in your design matrix then can get highly inflated (spurious). That is, if some of your regressors aren't "stationary" (i.e. they're not at least weak white noise processes) then is unreliable.

We need more information on the variables you're regressing.

[noetsi]

r squared also only gets at linear relationships. If there are ones better described by say a quadratic term then r squared wont pick these up.