Question

The following time series shows the sales of a clothing store over a 10-week period. Compute the mean square error (MSE) for a 4-week moving average forecast for the time series. Week Sales($1,000s) 1 15 2 16 3 19 4 18 5 19 6 20 7 19 8 22 9 15 10 21 Group of answer choices 21.50 7.67 15.00 16.90 2.33

Answer 1

Answer:

7.67

Step-by-step explanation:

Given the data :

Week_sales_Forecast ___|error|_ |error|²

1 _____15

2 ____ 16

3 ____ 19

4 ____ 18

5 ____ 19 ____ 17 _______ 2____4

6 ____ 20 ___ 18 ________2____4

7 ____ 19 ____19 ________0____0

8 ___ 22 ____ 19 ________3____9

9 ___ 15 ____ 20 ________5___ 25

10 __ 21 _____19 ________ 2 ___ 4

Mean squared error :

(4 + 4 + 0 + 9 + 25 + 4) / 6

= 46 / 6

= 7.666

= 7.67

Answer 2

The mean square error for a 4-week moving average forecast for the time series will be:

"7.67".

Statistics

Period    Data    Forecasts         Abs. Error        Error²        Abs. % Error

1               15

2              16

3              19

4              18

5              19            17                [19-17] = 2           4                    10.53%

6              20           18               [20-18] = 2           4                      10%

7              19             19               [19-19] = 0           0                       0%

8              22            19              [22-19] = 3           9                    13.64%

9              15             20             [15-20] = 5          25                   33.33%

10             21             19              [21-19] = 2           4                      9.52%                              

Now,

The mean squared error will be:

= $\frac{\Sigma |error|^2}{Number \ of \ forecasted \ weeks}$

By substituting the values,

= $\frac{46}{6}$

= 7.67

Thus the response above is correct.

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