Chapter 3 part 5
This chapter provides information about nonlinear and multiple regression analysis, monitoring the
forecast as well as choosing a forecast technique to better understand the concept of forecasting.
Nonlinear and Multiple Regression Analysis
Simple linear regression may prove inadequate to handle certain problems because a linear
model is inappropriate or because more than one predictor variable is involved. When nonlinear
relationships are present, you should employ nonlinear regression; models that involve
more than one predictor require the use of multiple regression analysis. While these analyses
are beyond the scope of this text, you should be aware that they are often used. The computations
lend themselves more to computers than to hand calculation. Multiple regression forecasting
substantially increases data requirements. In each case, it is necessary to weigh the
additional cost and effort against potential improvements in accuracy of predictions.
MONITORING THE FORECAST
Many forecasts are made at regular intervals (e.g., weekly, monthly, quarterly). Because forecast
errors are the rule rather than the exception, there will be a succession of forecast errors.
Tracking the forecast errors and analyzing them can provide useful insight on whether forecasts
are performing satisfactorily.
There are a variety of possible sources of forecast errors, including the following:
1. The model may be inadequate due to ( a ) the omission of an important variable, ( b ) a
change or shift in the variable that the model cannot deal with (e.g., sudden appearance of
a trend or cycle), or ( c ) the appearance of a new variable (e.g., new competitor).
2. Irregular variations may occur due to severe weather or other natural phenomena, temporary
shortages or breakdowns, catastrophes, or similar events.
3. The forecasting technique may be used incorrectly, or the results misinterpreted.
4. Random variations. Randomness is the inherent variation that remains in the data after all
causes of variation have been accounted for. There are always random variations.
A forecast is generally deemed to perform adequately when the errors exhibit only random
variations. Hence, the key to judging when to reexamine the validity of a particular forecasting
technique is whether forecast errors are random. If they are not random, it is necessary to
investigate to determine which of the other sources is present and how to correct the problem.
A very useful tool for detecting nonrandomness in errors is a control chart. Errors are
plotted on a control chart in the order that they occur, such as the one depicted in Figure 3.11 .
The centerline of the chart represents an error of zero. Note the two other lines, one above
and one below the centerline. They are called the upper and lower control limits because they
represent the upper and lower ends of the range of acceptable variation for the errors.
Like the tracking signal, a control chart focuses attention on deviations that lie outside predetermined
limits. With either approach, however, it is desirable to check for possible patterns
in the errors, even if all errors are within the limits.
If nonrandomness is found, corrective action is needed. That will result in less variability
in forecast errors, and, thus, in narrower control limits. (Revised control limits must be computed
using the resulting forecast errors.) Figure 3.13 illustrates the impact on control limits
due to decreased error variability.
Comment The control chart approach is generally superior to the tracking signal approach.
A major weakness of the tracking signal approach is its use of cumulative errors: Individual
errors can be obscured so that large positive and negative values cancel each other. Conversely,
with control charts, every error is judged individually. Thus, it can be misleading to
rely on a tracking signal approach to monitor errors. In fact, the historical roots of the tracking
signal approach date from before the first use of computers in business. At that time, it was
much more difficult to compute standard deviations than to compute average deviations; for
that reason, the concept of a tracking signal was developed. Now computers and calculators
can easily provide standard deviations. Nonetheless, the use of tracking signals has persisted,
probably because users are unaware of the superiority of the control chart approach.
CHOOSING A FORECASTING TECHNIQUE
Many different kinds of forecasting techniques are available, and no single technique works
best in every situation. When selecting a technique, the manager or analyst must take a number
of factors into consideration.
The two most important factors are cost and accuracy. How much money is budgeted for
generating the forecast? What are the possible costs of errors, and what are the benefits that
might accrue from an accurate forecast? Generally speaking, the higher the accuracy, the
higher the cost, so it is important to weigh cost–accuracy trade-offs carefully. The best forecast
is not necessarily the most accurate or the least costly; rather, it is some combination of
accuracy and cost deemed best by management.
Other factors to consider in selecting a forecasting technique include the availability of
historical data; the availability of computer software; and the time needed to gather and analyze
data and to prepare the forecast. When gasoline prices increased dramatically in 2005,
due in part to hurricane damage, makers of gas-guzzling SUVs had no historical data to
predict demand for those vehicles under those conditions. Consequently, they had to resort
to qualitative approaches to predict demand. The forecast horizon is important because some
techniques are more suited to long-range forecasts while others work best for the short range.
For example, moving averages and exponential smoothing are essentially short-range techniques,
since they produce forecasts for the next period. Trend equations can be used to
project over much longer time periods. When using time-series data, plotting the data can
be very helpful in choosing an appropriate method. Several of the qualitative techniques are
well suited to long-range forecasts because they do not require historical data. The Delphi
