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For statistical topics which involve the assumption of linearity, for example, linear regression or linear mixed models, or for the discussion of linear algebra as applied to statistics.

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Definition of a simple linear regression model

Only because it addresses the same issue, I'll mention that in his book "Extending the Linear Model with R" (page 7), Faraday claims "The construction of the least squares estimates does not require any … But once we assume linearity for the CEF, the linear projection error $u_t$ in $y_t=\beta_0+\beta_1x_t+u_t$ by definition is only uncorrelated with $x_t$, which is a weaker condition than mean-independence …
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