A convenience store recently started to carry a new brand of soft drink. Management is interested in estimating future sales volume to determine whether it should
continue to carry the new brand or replace it with another brand. The following table provides the number of cans sold per week. Use both the trend projection with
regression and the exponential smoothing (let a=0.4 with an initial forecast for week 1 of 574) methods to forecast demand for week 13. Compare these methods by
using the mean absolute deviation and mean absolute percent error performance criteria. Does your analysis suggest that sales are trending and if so, by how much?
2
5
Period 1
3 4
574 635 652 739 679
Sales
with regression forecast.
(Enter your response rounded to the nearest whole number.)
(1) Obtain the trend projection
The forecast for week 13 is
6
637
7
723
8
691
9
773
10
718
11
656
12
729

Respuesta :

The forecast for week 13 is 9.7%

a) MAD without the forecast = 43.71

MAD with the forecast = 45.59

b) MAPE = 0.097

MAPE= 9.7%

642 602 656 747 663 618 731 726 679 737 664 740

Mean Absolute deviation is given as

MAD = [Σ|x - μ|]/N

We first calculate the mean

Mean = Σx/N

Mean = (642+602+656+747+663+618+731+726+679+737+664+740)/12

Mean = (8205/12)

Mean= 683.75

absolute deviations from the mean

|642-683.75| + |602-683.75| + |656-683.75| + |747-683.75| + |663-683.75| + |618-683.75| + |731-683.75| + |726-683.75| + |679-683.75| + |737-683.75| + |664-683.75| + |740-683.75|

Absolute deviations from the mean

41.75+81.75+27.75+63.25+20.75+65.75+47.25+42.25+4.75+53.25+19.75+56.25= 524.5.

What is the formula for absolute mean deviation?

MAD = [Σ|x - μ|]/N

MAD = (524.5/12)

MAD = 43.71

If we include the forecast for the 13th week

642 602 656 747 663 618 731 726 679 737 664 740 747

Mean = (8205+747)/13

Mean = 688.62

absolute deviations from the mean

|642-688.62| + |602-688.62| + |656-688.62| + |747-688.62| + |663-688.62| + |618-688.62| + |731-688.62| + |726-688.62| + |679-688.62| + |737-688.62| + |664-688.62| + |740-688.62| + |747-688.62|

Absolute deviations from the mean

=46.62+86.62+32.62+58.38+25.62+70.62+42.38+37.38+9.62+48.38+24.62+51.38+58.38

= 592.62

MAD = (592.62/13)

MAD = 45.59.

b) MAPE is used to check forecast errors

MAPE = (1/N) Σ [|x-f|/x]

where N = Sample size = 12

x = each variable

f = the forecasted value = 747

x = 642, 602, 656, 747, 663, 618, 731, 726, 679, 737, 664, 740

Σ[|xf|/x]=0.164+0.241+0.139+0+0.112+0.209+0.022+0.029+0.100+0.014+0.125+0.009

Σ [|x-f|/x] = 1.164

MAPE = (1.164/12)

MAPE = 0.097

MAPE=9.7%

The forecast for week 13 is 9.7%.

To learn more about the mean deviation visit:

https://brainly.com/question/447169

#SPJ1