Comparison of close data sets I'm studying around 100 sets of temperature ($N_{sample}=500$), which depends $4$ explicative variables such as power or speed.
The dependency is always the same in each set, but sometimes the mean and the variance is different.


*

*I would like to group similar sets together and study each group separately: find a multiple regression model for each group.

*Then I would like to classify future sets I will discover in one of those groups.


I don't know if it concerns clusterisation or pattern recognition or maybe something else. But I have no idea of how to do classifiy/compare my sets, except comparing the mean and the variance one by one.
Does anybody have advices or suggestions?
Here is an example of 3 sets:


 A: Try to model the sets, for example using a multivariate Gaussian distribution, or a Gaussian Mixture Model.
Then use Kullback Leibler divergence measure to compare the models, and you should be able to use any distance-based clustering algorithm.
A: Looks like you have a clustering problem, but instead of individual observations you have entire datasets. 
What could be possible here is for each data set calculate some features, e.g. min, max, 25th and 75th percentiles, mean, median, std, linear regression coefficients, etc. And then try to use some clustering techniques to group them. It's just an idea, not sure how it's going to work, but this is what I'd do in this case. 
Once you learned the classes of your data set, you want to classify new data sets - and this is a classification problem. Here you use same set of feature (maybe new ones as well) to train your classifier, and then use it to classify new datasets. 
A: To build on the suggestion by Alexey Grigorev:   You could build some multilevel model, on level one, for each individual situation ("data set") a linear regression model, such as
$$
   y_{ij}= \alpha_j + \beta_j x_{ij} + \sigma_j \epsilon_{ij}
$$
where data sets are indexed with $j$ and observationhs within each data set is indexed by $i$.  Then on the second level, that is for the coefficients $\alpha_j, \beta_j, \sigma_j$ you can have some mixture prior.  That will probably need MCMC for estimation.  One paper which seems to do something like this is here:  http://www.southampton.ac.uk/~sks/research/papers/sahudeybranco.pdf
