In regression analysis, is unexplained variation inherently inevitable? I am quite confused as to why unexplained variation is always present in every regression. 
I understand that the best model you could create out of a sample of response (a model of only Y, without any dependent variables) is the mean of the response or a horizontal line and that the variation of the resulting model is purely unexplained. However, if you identify a dependent variable and incorporate it in the model, you would reduce the initial amount of unexplained variation because some of that initial variation would turn into 'explained variation' (sum of squares regression), hence leaving a smaller amount of unexplained variation (sum of squares of residuals).
Hypothetically, if you identify every possible relevant variable and incorporate it as dependent variables in the model, and create the 'true' regression model, you would still receive errors/residuals following the normal distribution. Why so? And if it is indeed inevitable to have these unexplained variations, is there a way to minimize them?
Please point out if I have said anything incorrect.
 A: This may be overly philosophical, but here is my take. There are three concepts that need to be distinguished: 1) the data-generating process, 2) a scientist's (necessarily simplified) model of the phenomenon, and 3) the statistical method a researcher uses to extract knowledge about the phenomenon from the data they have available (e.g., linear regression). Your question can be applied to any of these three concepts.
Why is there inherent unexplained variability in the data-generating process?
We don't know that there is. We could live in a completely deterministic world with no random processes. This seems unlikely given what we know about quantum mechanics. If we did live in a deterministic world, then there would be no random process, conditional on all observable phenomena, and the premise of the question is rejected. If we didn't live in a deterministic world and there was a truly random component to every phenomenon, then your question amounts to "why are things the way they are?" which is a question philosophy and religion have sought to answer for millennia.
Why is there an unexplained component in scientific models of phenomena?
For most phenomena, we simply don't have good enough scientific models to completely explain the observed variation. While the quest of science is to further explain the unexplained, it's unclear that that quest will ever be fully realized because of the limits (at least at this stage) of human knowledge. For example, it may be impossible to fully describe complex (in the complexity science sense) phenomena, even if we know they are governed by deterministic processes. For example, human behavior is so complex because it is due both to chemical fluctuations in the brain and to the interactions among members in a society; it is a multi-layered, complex, dynamic system that likely no model will ever fully explain without some unexplained variation. Even for simple physical systems, noise due error in the measurement of the phenomena may not ever be explained because it depends on a complex dynamic system outside the simple system under study.
Why is there a nonzero residual term in linear regression models?
There doesn't have to be. If you have one measurement for each person and a variable that represents that person's identity (e.g., participant ID), regressing any outcome on participant identity will yield a model with zero residual variance. Likewise, if every participant had a unique value of a continuous variable, regressing the outcome on that variable treated as categorical would yield zero residual variance, or regressing the outcome on a polynomial with one fewer degree than the number of participants would yield zero residual variance. Nonzero residual variance is not a necessary feature in a statistical model applied to data; it is a feature we choose to impose because we believe it is a better representation of the data-generating process or it allows us to better estimate the parameters of the scientific model we propose.

In short, there is unexplained variability because 1) there is likely fundamentally unexplainable variability in the data-generating process; 2) even if there isn't, our scientific models will never be adequate enough to fully explain any phenomenon; and 3) statistical models that include unexplained variability are better at serving their purpose (estimating the parameters of a scientific model).
