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3.5.5 Findings
So what have we learned about our product sales data? A great deal has been
revealed about the underlying behavior of the data. Some of the major findings are
summarized in the list below:
1. The products display varying levels of trend, seasonality, and cyclicality. This
can be seen in Exhibit 3.9. Not all products were examined in depth, but the
period of the cyclicality varied from seasonal for product A and E, to multi-
year for product C. Product D appeared to have no cyclicality, while product B
appears to have a cycle length of 2 quarters. These are reasonable observations,
although we should be careful given the small number of data points.
2. Our descriptive statistics are not of much value for time series data, but the mean
and the range could be of interest. Why? Because descriptive statistics generally
ignore the time dimension of the data, and this is problematic for our time series
data.
3. There are both positive (products D and E) and negative linear (products A and
E) co-relations among a number of the time series. For some (products A and B),
there is little to no linear co-relation. This variation may be valuable information
for predicting behavior of one series from the behavior of another.
4. Repeating systematic behavior is evident in varying degrees in our series. For
example, product D exhibits a small positive trend in early years. In later years
the trend appears to increase. Products B, D, and E appear to be growing in sales.
Product C might also be included, but it is not as apparent as in B, D, and E. The
opposite statement can be made for product A, although its periodic lows seem
to be very consistent. All these observations are derived from Exhibit 3.9.
5. Finally, we were able to examine an example of quarterly behavior for the series
over six years, as seen in Exhibit 3.20. In the case of product E, we fitted a
regression to the quarterly data and determined a predictive model that could be
used to forecast future Product E quarterly sales. The results were a relatively
good model fit, yet again based on a very, very small amount of data.
3.6 Analysis of Cross-Sectional Data—Forecasting/Data
Relationship Tools
Now let us return to our cross-sectional data and apply some of the Data Analysis
tools to the website data. Which tools shall we apply? We have learned a consider-
able amount about what works and why, so let us use our new found knowledge and
apply techniques that make sense.
First, recall that this is cross-sectional data; thus, the time dimension of the data
is not a factor to consider in our analysis. Let us consider the questions that we
might ask about our data:
1. Is the average number of pages higher or lower for the new website?
2. How does the frequency distribution of new versus old pages compare?
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