Question

# Savings-Mart (a chain of discount department stores) sells patio and lawn furniture. Sales are seasonal, with...

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=9.50+0.600t−2.75D1t+0.25D2t+3.5D3tY^t=9.50+0.600t−2.75D1t+0.25D2t+3.5D3t

where

 YˆtY^t = = predicted sales (in millions of dollars) in quarter tpredicted sales (in millions of dollars) in quarter t 9.509.50 = = quarterly sales (in millions of dollars) when t = 0quarterly sales (in millions of dollars) when t = 0 tt = = time period (quarter) where the fourth quarter of 2012 = 0, first quarter of 2013 = 1, second quarter of 2013 = 2, etc.time period (quarter) where the fourth quarter of 2012 = 0, first quarter of 2013 = 1, second quarter of 2013 = 2, etc. D1tD1t = = 1 for first-quarter observations; 0 otherwise1 for first-quarter observations; 0 otherwise D2tD2t = = 1 for second-quarter observations; 0 otherwise1 for second-quarter observations; 0 otherwise D3tD3t = = 1 for third-quarter observations; 0 otherwise1 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 selector 1
• 24.15
• 26.65
• 23.40
2020 Second Quarter selector 2
• 31.60
• 30.25
• 27.75
2020 Third Quarter selector 3
• 31.60
• 25.20
• 27.25
2020 Fourth Quarter selector 4
• 28.70
• 24.60
• 28.45

As per linear model forecasting concept , by use of given equation

Value of t for fourth quarter 2012 = 0 , 1st quarter 2013 = 1 , the series of value changes as +1,

value of t at 1st quarter 2020 = 29

value of t at 2nd quarter 2020 = 30

value of t at 3rd quarter 2020 = 31

value of t at 4th quarter 2020 = 32

 1 st Quarter 2020 t=29 Yt = 29*6+ 9.5 -2.75 17.4 D1=1 26.9 24.15 D2=0 Option 1 D3=0 2nd Quarter 2020 t=30 Yt = 30*6+ 9.5 +0.25 18 D1=0 27.5 27.75 D2=1 Option C D3=0 3rd Quarter 2020 t=31 Yt = 31*6+ 9.5 +3.5 18.6 D1=0 28.1 31.6 D2=0 Option A D3=1 4th Quarter 2020 t=32 Yt = 31*6+ 9.5 19.2 D1=0 28.7 28.7 D2=0 Option A D3=0