Best linear unbiased estimator (BLUE)

The Best Linear Unbiased Estimator (BLUE) is a statistical method used to estimate an unknown quantity from data. It produces estimates that are straight-line-based (linear), do not systematically overguess or underguess (unbiased), and have the smallest possible average error (best) among all such estimators. Think of it as the most reliable "best guess" that is computed using a straightforward formula, ensuring accuracy and consistency, especially when dealing with noisy or incomplete data in fields like economics, engineering, and science.