Solutions to Review Question

by Qiang Gao, updated at Mar 20, 2017

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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