[xadhominemx]

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

[disgruntledphd2]

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

[kyllo]

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