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I need to discuss the systematic component of the model in bivariate linear regression, but what is it in the first place? I have never come across this terminology in our class textbooks.

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    $\begingroup$ See stats.oecd.org/glossary/detail.asp?ID=3861. $\endgroup$ – Scortchi - Reinstate Monica Jan 17 '16 at 15:19
  • $\begingroup$ @Scortchi - and this is why I give some hints etc in the comments. I see the "graybeards" of the subject leading. $\endgroup$ – EngrStudent Feb 6 '16 at 1:47
  • $\begingroup$ "Bivariate linear regression" is potentially ambiguous. Do you mean (i) a single-x-single-y situation, (ii) a situation where $Y$ is a vector of length two, or (iii) a situation where there are two predictors (Y~X1+X2)? $\endgroup$ – Glen_b -Reinstate Monica Feb 6 '16 at 5:38
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Many models for data can be conceived as having the form

$$E(Y|\,\underline{X}=\underline{x}\,\!) = \mu(\,\!\underline{x}\,\!)+\epsilon$$

where given $x$, $\mu(x)$ is fixed; this is called the systematic component of the data-generating process, while $\epsilon$ is the random component.

We're often interested in estimating $\mu$ (as a function of $x$) and some characteristics of $\epsilon$ (such as its variance).

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