Abstract
We have seen how ideas from linear algebra can give insight into the sample cor relation coefficient. They can also provide intuition in the study of correlation and covariance of distributions. While none of these ideas are new or deep, they should enable the reader to appreciate the explanatory power of a linear algebra approach in a statistical context. Sadly, while some linear algebra texts like [2] include applications to statistics, available statistics texts, perhaps in an effort to reduce prerequisites, do not seem to relate concepts in statistics to ideas from linear algebra. Even [3], which uses ideas from matrix theory in the context of analysis of variance and which proves and names a version of the Cauchy-Schwartz inequality in the context of the covari ance of distributions, does not point out the relationship between the inner product and covariance. This is an unfortunate loss of a helpful tool for understanding covariance and correlation. It is always a good idea to find ways to reference, use, and reinforce ideas studied in other courses.
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