Statistics Homework Solutions
Problem
#5340

Time Line Series Forecasting

The table attached presents 4 years of quarterly sales for Mary’s Mongoose Menagerie.  Marty wants to know what quarterly sales will be in 2002.  Project quarterly sales for 2002 using trend analysis.  Now, project quarterly sales for 2002.  Revise quarterly sales number for season of the year.

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table 5.doc
The table below presents 4 years of quarterly sales for Mary’s
Mongoose Menagerie. Marty wants to know what quarterly sales will be in
2002. Project quarterly sales for 2002 using trend analysis. Now,
project quarterly sales for 2002. Revise quarterly sales number for
season of the year.

Winter 1998 20000 Winter 1999 22000 Winter 2000 23000 Winter 2001 23000
3 year

Winter 88000

Spring

1998 24000 Spring

1999 25000 Spring

2000 26000 Spring

2001 30000 3 year

Spring 105000

Summer 1998 35000 Summer 1999 36000 Summer 2000 37000 Summer 2001 38000
3 year

Summer 146000

Fall 1998 32000 Fall 1999 32000 Fall 2000 34000 Fall 2001 35000 3 year

Fall 133000

Total 111000

115000

120000

126000 3 year total 472000



My Answer:

1998 1999 2000 2001 Total

Winter 20000 22000 23000 23000 88000

Spring 24000 25000 26000 30000 105000

Summer 35000 36000 37000 38000 146000

Fall 32000 32000 34000 35000 133000

Total 111000 115000 120000 126000 472000

X Y XY X2 Indexes

1 11000 111000 1 0.745 118000/88000

2 115000 230000 4 0.889

3 120000 360000 9 1.237

4 126000 504000 16 1.127

10 472000 205000 30

X=10/4=2.5 Y=472000/4=118000

_ _

B=sum of XY (-) N X Y 120500-(10)(2.5)(118000) = 59369.23

Sum X2 (-) N X2 30-(10)(2.5)2(squared)

B= 59369.23

A= _ _

Y(-) Bx =118000-59369.23(2.5) =30423.07

A= 30423.07

^

Y= 30,423.07 +59369.23X

Sales in 2002 = 30423.07 + 59369.23 (5) =327269.22

Seasonal Average 327269.22/3 = 109089.72

109089.72 +0.745=???????

Solution Summary

This solution looks at using the least squares line.

Solution
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