Your company produces a favorite summertime food product, and you have been placed in charge of forecasting shipments of this product. The historical data below represent your company's past experience with the product.
a. Since the data appear to have both seasonality and trend, you should estimate a Winters' model and calculate its root-mean-squared error.
b. You also have access to a survey of the potential purchasers of your product. This information has been collected for some time, and it has proved to be quite accurate for predicting shipments in the past. Calculate the root-mean-squared error of the purchasers' survey data.
c. After checking for bias, combine the forecasts in parts (a) and (b) and determine if a combined model may forecast better than either single model.

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Purchasers' Purchasers Date Shipments (5000) Survey (S000) Jun-2003 Jul-2003 Aug-2003 Date Shipments ($000) Survey ($000) Apr-2002 May-2002 Jun-2002 Jul-2002 Aug-2002 Sep-2002 Oct-2002 Nov-2002 Dec-2002 Jan-2003 Feb-2003 Mar-2003 Apr-2003 May-2003 13,920.32 15,052.82 26,207.69 7,237.59 7,687.23 9,788.06 7,889.46 14,679.10 17,644.48 0,436.45 6,304.89 9,354.44 11,759.15 14,971.57 21,056.00 13,509.00 9,729.00 Sep-2003 13,454.00 13,426.00 17,792.00 Dec-2003 19,026.00 9,432.00 6,356.00 12,893.00 19,379.00 4,542.00 18,043.00 0,803.00 13,838.00 15,137.00 23,713.00 24,644.20 14,224.17 9,194.77 11,971.93 17,654.14 15,580.19 9,961.98 Oct-2003 Nov-2003 10,950.00 14,752.00 18,871.00 1,329.00 Mar-2004 Apr-2004 May-2004 8,915.33 14,056.06 20,699.38 12,892.97 0,845.00 15,185.00 1 Jul-2004