Regression analysis for a massive dataset I have a massive dataset, including about 5,000,000 points. There are 4 independent variables and two highly correlated dependent variables. 
How should I do the regression analysis? 
@StephanKolassa have told me to make a Cross-validation experiment and use the MAD as a measure to choose the best model from several alternatives. It is a very nice suggestion. But the problem is, how to get the "several alternative model" ?  what methods or statistical software are recommended?  Thank you!
My independent variable are the interplanetary condition components, and the dependent variable is the latitude of auroral oval boundary.  
So far, the specific relationship is still unknown in physical principle, what we want to do is to get a model from the massive data which shows how these independent variables affect the dependent variable.
 A: The main thing to keep in mind is that with this amount of data, every coefficient will probably come out as statistically significant.
In order to find out which regressors are really important (as contrasted with statistically significant), I recommend using a holdout sample: fit your model to only 4 million data points, predict the other million points and compare to the actual values. Do this for a couple of different models (using or not using regressors, transforming regressors etc.) and see which ones yield the best predictions, by e.g. calculating the Mean Absolute Deviation (MAD) between the predictions and the actual observations.
Better yet: iterate this over the entire dataset five times, using a different million points as a holdout sample each time. This is known as "cross-validation" (five-fold cross-validation in this case).
A: You have 6 variables and 5 milion data points. So your data set would take about half a gigabyte of memory ($\frac{5\cdot 10^6\cdot16}{1024^2}\cdot 6$). So it is not that big for computers which now usually have 4GB RAM as a standard. The point I am trying to make is that although your data is big it is not massive and so you can do usual regression analysis. 
