**Definition: ****Definition of OLS / Ordinary Least Squares**: OLS stands for Ordinary Least Squares, the standard linear regression procedure. One estimates a parameter from data and applying the linear model

y = Xb + e

where y is the dependent variable or vector, X is a matrix of independent variables, b is a vector of parameters to be estimated, and e is a vector of errors with mean zero that make the equations equal.

The estimator of b is: (X'X)^{-1}X'y

A common derivation of this estimator from the model equation (1) is:

y = Xb + e

Multiply through by X'. X'y = X'Xb + X'e

Now take expectations. Since the e's are assumed to be uncorrelated to the X's the last term is zero, so that term drops. So now:

E[X'Xb] = E[X'y]

Now multiply through by (X'X)^{-1}

E[(X'X)^{-1}X'Xb] = E[(X'X)^{-1}X'y]

E** = E[(X'X) ^{-1}X'y]**

Since the X's and y's are data the estimate of b can be calculated.(Econterms)

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