Microsoft Office Tutorials and References
In Depth Information
Exhibit 3.26 Plot of fit for product E quarter 4
3.5.3 Covariance and Correlation
Recall the original questions posed about the product sales time series data, and in
particular the second question which asked: “Does one series move with another in a
predictable fashion?” The Covariance tool helps answer this question by determin-
ing how the series co-vary . We return to the original data in Table 3.1 to determine
the movement of one series with another. The Covariance tool, which is found in the
Data Analysis tool, returns a matrix of values for a set of data series that you select.
For the product sales data, it performs an exhaustive pairwise comparison of all 6
times series. As is the case with other Data Analysis tools, the dialogue box asks
for the data ranges of interest and we provide the data in Table 3.1. Each value in
the matrix represents either the variance of one time series or the covariance of one
time series compared to another. For example, in Exhibit 3.27 we see the covariance
of product A to itself (its variance) is 582.7431 and the covariance of product A
and C is –74.4896. Large positive values of covariance indicate that large values of
data observations in one series correspond to large values in the other series. Large
negative values indicate the inverse: small values in one series indicate large values
the other.
Exhibit 3.27 is relatively easy to read. The covariance of product D and E is
relatively strong at 323.649, while the same is true for product A and E at –559.77.
These values suggest that we can expect D and E moving together, or in the same
direction; while A and E also move together, but in opposite directions, due to the
negative sign of the covariance. Again, we need only refer to Exhibit 3.9 to see that
the numerical covariance values bear out the graphical evidence. Small values of
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