What is the predictor considered fixed against? I'm trying to understand Linear Regression. In wikipedia, I was confronted with the following assumption:

Weak exogeneity: This essentially means that the predictor variables x can be treated as fixed values, rather than random variables. This means, for example, that the predictor variables are assumed to be error-free—that is, not contaminated with measurement errors..

My question is regarding the "fixed" characterization of predictors. I don't understand whether X is considered to hold a single value, in the sense represented by the formula $X(Ω) = \{a\}$ where $a$ is a real number, or in the sense that, given a new universe $Ω'$ with a different experiment, $X(Ω')$ holds one value. If the latter was the case, what would the "new" universe be?
I also don't understand why the article claims that "fixed" is the same as being error-free.
 A: After that wikipedia section it actually further explains:

Although this assumption is not realistic in many settings, dropping it leads to significantly more difficult errors-in-variables models... Because the predictor variables are treated as fixed values (see above), linearity is really only a restriction on the parameters. The predictor variables themselves can be arbitrarily transformed, and in fact multiple copies of the same underlying predictor variable can be added, each one transformed differently. This technique is used, for example, in polynomial regression, which uses linear regression to fit the response variable as an arbitrary polynomial function (up to a given degree) of a predictor variable.

Thus in summary the predictor here is considered fixed against your statistical causal (linear) model. If on the contrary you view the predictor variables as random variables affected by measurement errors which are endogenous variables of your statistical model, then in addition to account for errors in response variables of your linear regression model, you may further need to employ advanced instrumental variables methods or multi-stage methods. Otherwise, simple linear regression would result in an underestimate of the coefficient known as the attenuation bias as summarized in the same reference.
