# ALGEBRA 212-The monthly sales for Yazici Batteries, Inc., were as follows

## 1. The monthly sales for Yazici Batteries, Inc., were as follows:

Month Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec

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Sales 20 20 16 12 15 15 16 17 22 22 20 23??

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

The forecast for the next? period? (Jan) using? a? 3-month moving average? approach? = ______sales? ?(round 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 to one? decimal? place).

Using exponential smoothing with? ? ?= 0.40 and a September forecast of? 20.00?, the forecast for the next?period? (Jan)? =_____ sales? ?(round two? decimal? places).

Using a method of? trend? projection, the forecast for the next? month? (Jan)? =_____sales? ?(round two? decimal? places).

The method that can be used for making a forecast for the month of March? is:

A exponential smoothing

B a 3-month moving average

C a trend projection

D the naive method

E a 6-month weighted moving average

: a trend projection

This method enables us to compute the trend equation which can be applied to make future forecasts.

The months are an independent variable (X)

The sales are the dependent variable (Y)

MonthMonth(X)Sales (Y)X^2XYJan120120

Feb221442

Mar315945

Apr4121648

May5132565

Jun6163696

Jul71749119

Aug81764136

Sep92281198

Oct1021100210

Nov1123121253

Dec12231442767822065015086.5018.3333

¯Xi=∑ni=1Xn=7812=6.5 X¯i=∑i=1nXn=7812=6.5

¯Yi=∑ni=1Yn=22012=18.3333 Y¯i=∑i=1nYn=22012=18.3333

Estimate the value of the slope

b=∑XY−n¯X¯Y∑X2−n¯X2=1,508−(12∗6.5∗18.3333)650−(12∗6.52)=78.0026143=0.5455 b=∑XY−nX¯Y¯∑X2−nX¯2=1,508−(12∗6.5∗18.3333)650−(12∗6.52)=78.0026143=0.5455

Estimate the value of the intercept

a=¯Y−b¯X=18.3333−(0.5455∗6.5)=14.7876 a=Y¯−bX¯=18.3333−(0.5455∗6.5)=14.7876

The trend equation is

^Y=a+bX=14.7876+0.5455XY^=a+bX=14.7876+0.5455X

• Using a method of trend projection, the forecast for the next month (Jan) = 21.88 sales

January is the 13th month we, therefore, compute it as:

^Y=14.7726+0.5473X=14.7876+(0.5455∗13)=21.88

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