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Refers to a general estimation technique that selects the parameter value to minimize the squared difference between two quantities, such as the observed value of a variable, and the expected value of that observation conditioned on the parameter value. Gaussian linear models are fit by least squares and least squares is the idea underlying the use of mean-squared-error (MSE) as a way of evaluating an estimator.

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Is it possible for the zero conditional mean assumption to fail?

The short answer is yes, $\mathbb{E}[X_i\varepsilon_i] = 0$ by construction. A few important remarks: However, this does not imply that $\mathbb{E}[\varepsilon_i \mid X_i] = 0$. The conditional mean …
ecnmetrician's user avatar
10 votes

Why don't linear regression assumptions matter in machine learning?

A linear regression is a statistical procedure that can be interpreted from both perspectives. Instead I will tackle the question of comparing linear regression (and its assumptions) to other methods. …
ecnmetrician's user avatar