Assessing how good a model is

#1
I have a model that predicts speed at points along a roadway. Additionally I have measured speeds along the roadway (not used to make the model). The data sets have 3000+ matched points. I want to be able to say something about how good the model is (we have added an extra module to the model and changing some of the parameters so ultimately we want to be able to say which parameters result in the best model). What is the best statistical test for this?

We tried comparing the 2 data sets using Pearson correlation coefficients (RSQ in excel) and they were always below 0.2. Perhaps the model is just really bad, but hoping that maybe we are just using the wrong test...
 
#2
Did you use a regression model?

You check a random phenomenon. so by definition, not all of it will be explained by any model.
If for example R=0.2 and R^2 =0.04, it says that only 0.04 of the variance will be explained by your model and this is very low ...
On the other hand, it doesn't say you model is not significant. but I assume a significant model that explains so little is not good.

Did you look at the residual plots?
should distribute symmetrically around the zero. (not skewed)
should have the same variance (homoscedasticity)

If not you may need to transform some of the dependent variables.
 
#3
The speed model is a regression model (things such as posted speed limit, width of road, slope... are the input variables). But it is not a model that we have developed, we've just developed the driver behavior part, and the speed model itself has been generally well established in practice, although there hasn't really been much documentation about that...

We'll take a look into what you suggest and try and go from there. Thanks!