Sales of Volkswagen\'s popular Beetle have grown steadily at auto dealerships in

Question

Sales of Volkswagen's popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years (see table below) Sales 455 502 518 566 585 ear a) Forecasted sales for year 6 using a 3-year moving average is 556.3 sales (round your response to one decimal place). b) The MAD for a 3-year moving average based forecast is 65.3 sales (round your response to one decimal place). c) The MSE for a 3-year moving average based forecast is sales round your response to the nearest whole number

Explanation / Answer

a) A three period moving average method averages the actual value for the previous three periods to generate the forecast for the next period. This can be calculated using the following formula : Sum of the actual value for the previous three periods / 3

So using the above formula,

the forecast for year 6 = (518 + 566 + 585) / 3 = 1669/3 = 556.3

b) using the formula used in part a, the forecast for year 4 and 5 are

Calculation of MAD

Deviation = actual value - forecasted value

Absolute deviation = absolute value of deviation

Using the above formula the deviation and absolute deviation for year 4 and 5 are

MAD = Sum of the absolute deviation for all the periods / number of periods

= (74.33+56.33) / 2

= 130.66/2

= 65.3

c) Error = deviation = actual value - forecasted value

Here the deviation or error for year 4 and 5 is calculated in part b. So using the errors calculated in part b, the squared errors are:

MSE = Sum of the squared errors for all the periods / number of periods

= (5524.95 + 3173.07) / 2

= 8698.02/2

=4349.01 or rounded to 4349

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