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									Example 16.7b


   Estimating Seasonality with
           Regression
      COCACOLA.XLS
   We return to this data file which contains the sales
    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
    additive approach is also possible.

   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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