Question

Savings-Mart (a chain of discount department stores) sells patio and lawn furniture. Sales are seasonal, with higher sales during the spring and summer quarters and lower sales during the fall and winter quarters. The company developed the following quarterly sales forecasting model:

Yˆt=7.50+1.100t−2.75D1t+0.25D2t+3.5D3t

where

Yˆt =  = predicted sales (in millions of dollars) in quarter t
7.50 =  = quarterly sales (in millions of dollars) when t = 0
t	=  =	time period (quarter) where the fourth quarter of 2012 = 0, first quarter of 2013 = 1, second quarter of 2013 = 2, etc.
D1t	=  =	1 for first-quarter observations; 0 otherwise
D2t	=  =	1 for second-quarter observations; 0 otherwise
D3t	=  =	1 for third-quarter observations; 0 otherwise

Forecast Savings-Mart's sales of patio and lawn furniture for each quarter of 2020.

Quarter	Sales Forecast
	(Millions of dollars)
2020 First Quarter	39.15/35.90/36.65
2020 Second Quarter	40.75/45.10/43.25
2020 Third Quarter	45.10/40.25/39.20
2020 Fourth Quarter	42.70/42.45/38.10

Answer 1

The estimated equation is - Yˆt=7.50+1.100t−2.75D1t+0.25D2t+3.5D3t

a. 2020 First Quarter

In 2020 First Quarter, t = 29, D1t = 1, D2t =0 and D3t=0 the sales forecast = 7.50+1.100*29−2.75*1+0.25*0+3.5*0

=39.4 - 2.75

= 36.65

b. 2020 Second Quarter

In 2020 Second Quarter, t = 30, D1t = 0, D2t =1 and D3t=0 the sales forecast = 7.50+1.100*30−2.75*0+0.25*1+3.5*0

= 7.50 + 33 + 0.25

= 40.75

c. 2020 Third Quarter

In 2020 Third Quarter, t = 31, D1t = 0, D2t = 0 and D3t=1 the sales forecast = 7.50+1.100*31−2.75*0+0.25*0+3.5*1

= 7.5+1.1*31-2.75*0+0.25*0+3.5*1

= 7.5+1.1*31+3.5*1

= 41.6 + 3.5

= 45.10

d.  2020 Fourth Quarter: In this quarter all dummies will be equal to 0 as the effect of the fourth quarter dummy is contained in the intercept term.

In 2020 Fourth Quarter, t = 32, D1t = 0, D2t = 0 and D3t=0 the sales forecast = 7.50+1.100*32−2.75*0+0.25*0+3.5*0

= 7.50+1.100*32

= 7.50 + 35.20

=42.70

Quarter	Year	t
4	2012	0
1	2013	1
2	2013	2
3	2013	3
4	2013	4
1	2014	5
2	2014	6
3	2014	7
4	2014	8
1	2015	9
2	2015	10
3	2015	11
4	2015	12
1	2016	13
2	2016	14
3	2016	15
4	2016	16
1	2017	17
2	2017	18
3	2017	19
4	2017	20
1	2018	21
2	2018	22
3	2018	23
4	2018	24
1	2019	25
2	2019	26
3	2019	27
4	2019	28
1	2020	29
2	2020	30
3	2020	31
4	2020	32