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This part is incorrect: “ The main practical reason why square error is minimized in ordinary linear regression is that it has an analytical solution”

OLS is popular because it gives correct answers as a result of the CLT

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And it has an analytical solution, which was important before computing (and still makes it quicker today).

In other words, as economists say, because OLS is provably the BLUE (Best Linear Unbiased Estimator) aka the Gauss-Markov Theorem.

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