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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