632598256894

was unusually low, say, due to the effects of a business downturn or new product introductions by
competitors. Another alternative is to attempt to estimate the underlying trend in annual sales. Exhibit
11.8 presents such a graph.
In Exhibit 11.8, a statistical technique called regression analysis has been used to estimate a trend
line for Dell‟s annual sales. This line was estimated with a statistical software package called Minitab,
but the analysis is also available in Microsoft Excel and many other programs. The equation for the
trend line is Sales t = $14,330 + ($4,796 × t). This equation states that the sales for the first forecast
year are equal to $14,330 + ($4,796 × 11) (since our data ended at year 10), or $67,086 million. Our
forecasts for years 2 and 3 extend linearly with a continuation of the same slope that was estimated in
the trend line fit through the data.
A potential problem with fitting a trend line through the data with regression analysis is that each
observation is treated the same way. That is, we are not weighting the information contained in the
latest set of observations more heavily than those that occurred eight years ago. Other statistical
techniques, such as exponential smoothing, are available to address this concern. Exhibit 11.9 presents
the same annual sales data with a trend line that has been exponentially smoothed.
Notice how the estimated trend line reacts to changes in the annual sales. This technique weights
recent observations more heavily than those in the distant past. The result is a trend line whose slope
changes over time to reflect changes in sales growth. Projections for the next three years, then, begin
with the last estimate of the underlying trend and at the most recent slope indicated by the data. For
example, the estimate of Dell‟s sales for the next year is $66,241.7 million, somewhat lower than the
$67,086 million estimated for the next year‟s sales using the trend line. This reduction weights the
more recent downward trend more heavily, thus dampening the forecast.
Exhibit 11.8 Trend analysis for Dell, Inc. annual sales, 1999-2011.
Exhibit 11.9 Double exponential smoothing of Dell, Inc.’s annual sales, 1999-2011.