Question

The following are historical demand data:

YEAR	SEASON	ACTUAL DEMAND
2 years ago	Spring	205
	Summer	140
	Fall	375
	Winter	575
last year	Spring	475
	Summer	275
	Fall	685
	Winter	965

Use regression analysis and seasonal indexes to forecast next summer’s demand. (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Answer 1

Year	Season	Actual Demand
2 years ago	Spring	205
	Summer	140
	Fall	375
	Winter	575
Last Year	Spring	475
	Summer	275
	Fall	685
	Winter	965

Quarterly average demand = (205 + 140 + 375 + 575 + 475 + 275 + 685 + 965) / 8

= 461.88

Season	Average demand	Seasonal Index
Spring	(205+475)/2 = 340	340/461.88 = 0.736
Summer	(140+275)/2 = 207.5	207.5/461.88 = 0.449
Fall	(375+685)/2 = 530	530/461.88 = 1.147
Winter	(575+965)/2 = 770	770/461.88 = 1.667
		4.0000

	Period X	Demand	Deseasonalized Demand y	XY	X^2
	1	205	278.53	278.53	1
	2	140	311.80	623.61	4
	3	375	326.94	980.82	9
	4	575	344.93	1379.72	16
	5	475	645.38	3226.90	25
	6	275	612.47	3674.83	36
	7	685	597.21	4180.47	49
	8	965	578.88	4631.07	64
Sum	36		3696.15	18975.96	204.00
Avg	4.5		462.02
Slope(b) = (N∑XY - (∑X)(∑Y)) / (N∑X2 - (∑X)2)
Slope(b) = (8*18975.96 - (36)(3696.15)) / (8*204 - (36)^2)
Slope (b)=55.79
a= Y bar - b X bar
a=462.02-55.79*4.5
a=210.965
Y=210.965+55.79x
for next summer, X=10
Y=210.965+55.79*10
Y=768.865
Forecast, summer reseasonalized =768.865*0.449 =345.22

Answer is 345.22