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Exhibit 3.27 Covariance matrix for product A–E
covariance like those for product A and B (and C also) indicate little co-variation.
The problem with this analysis is that it is not a simple matter to know what we
mean by large or small values—large or small relative to what.
Fortunately, statisticians have a solution for this problem— Correlation analysis.
Correlation analysis will make understanding the linear co-variation or co-relation
between two variables much easier, because it is measured in values that are stan-
dardized between the range of –1 and 1. A correlation coefﬁcient of 1 for two
data series indicates that the two series are perfectly positively correlated :as
one variable increases so does the other. If correlation coefﬁcient of –1 is found,
then the series are perfectly negatively correlated : as one variable increases the
other decreases. Two series are said to be independent if their correlation is 0. The
calculation of correlation coefﬁcients involves the covariance of two data series.
In Exhibit 3.28 we see a correlation matrix which is very similar the covariance
matrix. You can see that the strongest positive correlation in the matrix is between
products D and E, 0.725793, and the strongest negative correlation is between A
and E, where the coefﬁcient of correlation is –0.65006. There are also some values
that indicate near linear independence; for example, products A and B with a coef-
ﬁcient of 0.118516. Clearly this is a more direct method of determining the linear
correlation of one data series with another than the covariance matrix.
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