## Notes on Regression - Method of Moments

Another way of establishing the OLS formula is through the method of moments approach. This method supposedly goes way back to Pearson in 1894. It could be thought of as replacing a population moment with a sample analogue and using it to solve for the parameter of interest.
Example 1 To find an estimator for the sample mean, \(\mu=E[X]\), one replaces the expected value with a sample analogue, \(\hat{\mu}=\frac{1}{n}\sum_{i=1}^{n} X_{i} = \bar{X}\)
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