# How to compare performance of multiple regression models?

I am taking a little data analysis course using SAS software and I need help with pretty much the basics.

There is this full description in the American Statistical Association page.

Basically I have the data obtained from caught fish (species, weight, length etc)

    Obs    Spec  Wt        Lt1     Lt2     Lt3     HtP    WhP    Sex
----+----1----+----2----+----3----+----4----+----5----+----6----+----7----+-
1      1     242.0     23.2    25.4    30.0    38.4   13.4   NA
2      1     290.0     24.0    26.3    31.2    40.0   13.8   NA
3      1     340.0     23.9    26.5    31.1    39.8   15.1   NA
4      1     363.0     26.3    29.0    33.5    38.0   13.3   NA
5      1     430.0     26.5    29.0    34.0    36.6   15.1   NA
...


I want to predict weight using other known characteristics. How can I prove of disprove that the same regression function would work for all fish species? Would checking hypothesis that the weight distributions (for different species) are statistically different be enough?

Then I have a bunch of models apparently suggested by experts

Weight=a+b*(Length3*Height*Width)+epsilon
Log(Weight)=a+b1*Length3+epsilon
Weight^(1/3)=a+b1*Length3+epsilon
Log(Weight)=a+b1*Length3+b2*Height+b3*Width+epsilon
Weight^(1/3)=a+b1*Length3+b2*Height+b3*Width+epsilon
Weight=a*Length3^b1*Height^b2*Width^b3+epsilon


How should I compare them? Simply look for the best root mean square error?