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```									Example 16.7b

Estimating Seasonality with
Regression
COCACOLA.XLS
history of Coca Cola from 1986 to quarter 2 of 1996.

   Does a regression approach provide forecasts that
are as accurate as those provided by the other
seasonal methods in this chapter?

16.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7a
Solution
   We illustrate a multiplicative approach, although an

   The data setup is as follows:

16.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7a
Solution
   Besides the Sales and Time variables, we need
dummy variables for three of the four quarters and a
Log_Sales variable.

   We then can use multiple regression, with the
Log_sales as the response variable and Time, Q1,
Q2, and Q3 as the explanatory variables.

   The regression output appears as follows:

16.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7a
Regression Output

16.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7a
Interpreting the Output
   Of particular interest are the coefficients of the
explanatory variables.
   Recall that for a log response variable, these
coefficients can be interpreted as percent changes in
the original sales variable.
   Specifically, the coefficient of Time means that
deseasonalized sales increase by 2.4% per quarter.
   This pattern is quite comparable to the pattern of
seasonal indexes we saw in the last two examples.

16.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7a
Forecast Accuracy
   To compare the forecast accuracy of this method with
earlier examples, we must go through several steps
manually.
– The multiple regression procedure in StatPro provide fitted
values and residuals for the log of sales.
– We need to take these antilogs and obtain forecasts of the
original sales data, and subtract these from the sales data to
obtain forecast errors in Column K.
– We can then use the formulas that were used in StatPro’s
forecasting procedure to obtain the summary measures
MAE, RMSE, and MAPE.

16.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7a
Forecast Errors and Summary
Measures

16.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7a
Forecast Accuracy -- continued
   From the summary measures it appears that the
forecast are not quite as accurate.

   However, looking at the plot below of the forecasts
superimposed on the original data shows us that the
method again tracks the data very well.

16.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7a

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