# 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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Access Free Writing Tools**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

**Answer** **and Explanation**

**:** *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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