Question

A local moving company has collected data on the number of moves they have been asked to perform over the past three years. moving is highly saesonal so the owner operator who is both burly and highly educated decides to apply the multiplicative seasonal method based on a linear regression for total demand to forecast the number of customers for the coming year 2012. what is his forecast for each quarter of 2012?

2009
Quarter.     Demand
1.                 20
2.                 40
3.                 45
4.                 30

2010
Quarter.     Demand
1                  27
2.                 45
3.                 55
4.                 40

2011
Quarter.     Demand
1.                 33
2.                 45
3.                 55
4.                  40

Answer 1

x-bar = Sum(x)/n = 78/12 = 6.5
y-bar = Sum(y)/n = 475/12 = 39.5833

b = (Sum(xy) – n*x-bar*y-bar)/(Sum(x2) – n*x-bar*x-bar) = (3297-12*6.5*39.5833)/(650–12*6.5*6.5)
   = 209.5026/143 = 1.465053147

a = y-bar –b*x-bar
= 39.5833-1.465053147*6.5 = 30.06045454

Regression equation is y = a + bx,

y = 30.06045454+1.465053147x

	2012
Period	Quarter	Trend forecast	Seasonality adjusted trend forecast
13	1	49.10614545	34.69652536
14	2	50.5711986	56.92985539
15	3	52.03625175	66.97673624
16	4	53.50130489	46.94134645

Formula