Regression Analysis with deterministic processes Is it possible (theoretically) to perform regression analysis with data that is generated deterministically? 
I know this question does not make a lot of sense, because if you know that it is generated deterministically, you probably know the underlying mechanics and therefore do not need to estimate the influencing parameters.
But are there any theoretical technical restrictions? To my knowledge, one simply assumes that the data are stochastic processes in the context of time series regression.
 A: Coin flip is also a deterministic process that can be described in terms of physics. What we denote as "random noise" is the variability that we don't control, are unaware of it's sources, or decide to ignore in our model. Randomness and probability are just useful approximations of the complicated and chaotic reality.
As about technical restrictions, regression assumes that the observations are independent and identically distributed (i.e. are of the same kind) and the variance is homoscedastic, etc., so there are assumptions about nature of the errors.
When you fit linear regression, the most basic assumption that you make is about linearity of the relationship between variables, yet in real world almost nothing would be exactly linear. We brake many of the assumption as long as statistical models serve as helpful approximations for the reality. The assumptions are important because they remind us when does the method give us guarantees about optimality of the solution, but this doesn't mean that when broken, the method is not applicable.
