. The mean regression does not have the same property since

Inference

Interpretation of the slope parameters

The linear model mis-specifies the true systematic relation when is nonlinear. However, minimizes a weighted distanced to among linear models. Furthermore, the slope parameters of the linear model can be interpreted as weighted averages of the derivatives so that can be used for causal inference. Specifically, the hypothesis for all implies the hypothesis , which can be tested using the estimator

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