by Qiang Gao, updated at Mar 20, 2017
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Verify that $$ \mathbf{X}' \mathbf{X} / n = \frac{1}{n} \sum_i \mathbf{x}_i \mathbf{x}_i' $$ and $$ \mathbf{X}' \mathbf{y} / n = \frac{1}{n} \sum_i \mathbf{x}_i y_i $$.
By the outer-way matrix multiplication rule, noticing that $$ \mathbf{x}_i $$ is the $$ i
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