1.2.2.md

Solution to Review Question

by Qiang Gao, updated at Mar 20, 2017

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Chapter 1 Finite-Sample Properties of OLS

Section 2 The Algebra of Least Squares

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Review Question 1.2.2

Verify that $$ \mathbf{X}' \mathbf{X} / n = \frac{1}{n} \sum_i \mathbf{x}_i \mathbf{x}_i' $$ and $$ \mathbf{X}' \mathbf{y} / n = \frac{1}{n} \sum_i \mathbf{x}_i y_i $$.

Solution

By the outer-way matrix multiplication rule, noticing that $$ \mathbf{x}_i $$ is the $$ i $$th column vector of $$ \mathbf{X}' $$, above equations are obviously true.

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Copyright ©2017 by Qiang Gao