Question

ASAP!!!!!!!!!

The monthly sales for Yazici​ Batteries, Inc., were as​ follows:                                                                                                                                         Month Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Sales 21 21 15 15 11 18 16 18 19 20 23 22 This exercise contains only parts b and c.

​b) The forecast for the next month​ (Jan) using the naive method​ = 22 sales ​(round your response to a whole​ number). The forecast for the next period​ (Jan) using a​ 3-month moving average approach​ sales ​(round your response to two decimal​ places).

The forecast for the next period​ (Jan) using a​ 6-month weighted average with weights of 0.10​, 0.10​, 0.10​, 0.20​, 0.20​, and 0.30​, where the heaviest weights are applied to the most recent month​ = sales ​(round your response to one decimal​ place).

Using exponential smoothing with alpha ​= 0.30 and a September forecast of 21.00​, the forecast for the next period​ (Jan) = nothing sales ​(round your response to two decimal​ places).

Using a method of trend​ projection, the forecast for the next month​ (Jan) = nothing sales ​(round your response to two decimal​ places). ​

c) The method that can be used for making a forecast for the month of March is ▼ a 3-month moving average a 6-month weighted moving average exponential smoothing the naive method a trend projection .

Answer 1

​b) The forecast for the next month​ (Jan) using the naive method​ = 22 sales ​(round your response to a whole​ number).

In the naive method, we simply believe that the current forecast will be the most recent trend.

So for Feb forecast it will Jan's actual data.

Naïve method
Month	Actual	Forecast
Jan	21
Feb	21	21
Mar	15	21
Apr	15	15
May	11	15
Jun	18	11
Jul	16	18
Aug	18	16
Sep	19	18
Oct	20	19
Nov	23	20
Dec	22	23
Jan (+1)		22

The forecast for the next period​ (Jan) using a​ 3-month moving average approach​ sales ​(round your response to two decimal​ places).

For this we first take the sum of most recent 3 period. Then take their average. This is the forecast for the 4th period

Eg: For May = (Feb + Mar + Apr) / 3

if it was 4 period then we would take totals of 4 periods

3-period average
Month	Actual	3 period sum	Average
Jan	21
Feb	21
Mar	15
Apr	15	57	19
May	11	51	17
Jun	18	41	13.667
Jul	16	44	14.667
Aug	18	45	15
Sep	19	52	17.333
Oct	20	53	17.667
Nov	23	57	19
Dec	22	62	20.667
Jan (+1)		65	21.667

The forecast for the next period​ (Jan) using a​ 6-month weighted average with weights of 0.10​, 0.10​, 0.10​, 0.20​, 0.20​, and 0.30​, where the heaviest weights are applied to the most recent month​ = sales ​(round your response to one decimal​ place).

For weighted average we assign different weights to different periods

This is 6 period, so the forecast will alwys be for next 7th period.

Heavier to recent weight means if for July, most recent will be June then gradually going upto Jan

July = 0.1 *(Jan + Feb + Mar) + 0.2 (Apr + May) + 0.3 * June

6-period weighted average
Month	Actual	Average
Jan	21
Feb	21
Mar	15
Apr	15
May	11
Jun	18
Jul	16	16.3
Aug	18	15.7
Sep	19	16.3
Oct	20	16.9
Nov	23	17.9
Dec	22	19.9
Jan (+1)		20.5

Using exponential smoothing with alpha ​= 0.30 and a September forecast of 21.00​, the forecast for the next period​ (Jan) = nothing sales ​(round your response to two decimal​ places).

Here the exponential smoothing gives two weights to previous actual and forecast values. Heavier is to the forecast

= 0.3

F_t = A_t-1 * + (1 - ) F_t-1

Eg; Here we begin with Sep since its forecast is given

October = 19 * 0.3 + 21 * 0.7

Exponenetial
Month	Actual	Forecast
Jan	21
Feb	21
Mar	15
Apr	15
May	11
Jun	18
Jul	16
Aug	18
Sep	19	21
Oct	20	20.4
Nov	23	20.28
Dec	22	21.096
Jan (+1)		21.37

Using a method of trend​ projection, the forecast for the next month​ (Jan) = nothing sales ​(round your response to two decimal​ places). ​

We can use the regression method for this. Where the 'x' is the year. And y is the sales. The 'x' can take values from 1 - 12 representing the number of month. We find a regression equation to predict the future values.

Month (x)	Sales (y)	x^2	y^2	xy
1	21	441	1	21
2	21	441	4	42
3	15	225	9	45
4	15	225	16	60
5	11	121	25	55
6	18	324	36	108
7	16	256	49	112
8	18	324	64	144
9	19	361	81	171
10	20	400	100	200
11	23	529	121	253
12	22	484	144	264
Total	219	4131	650	1475
Mean	18.25	344.25

Regression eq of Y on X

slope =

= 0.360

   intercept                                   

=15.909

The regression equation is

= 15.909 + 0.36x

We sub Jan = 13th month so x = 13

= 15.909 + 0.36 * 13

= 20.591

Linear regression helps to predict equation of line where when the x,y points are plotted they seem to form a linear line.

c) The method that can be used for making a forecast for the month of March is ▼ a 3-month moving average a 6-month weighted moving average exponential smoothing the naive method a trend projection

Method	Value of march
Naïve	21
moving avg	-
Weighted	-
Exponential	-
linear	16.98951

for linear trend we sub x = 3 in the regression equation.

So the methods can be used to foreast MArch are Naive and Trend projection.