Question

  Quarterly billing for water usage is shown below. Assume the time series has seasonality with a long term trend.

	Year
Quarter	1	2	3	4
Winter	64	66	68	73
Spring	103	103	104	120
Summer	152	160	162	176
Fall	73	72	78	88

Forecast the next four quarters:

FWinter = 81.625, FSpring = 126.375, FSummer= 175.375, FFall= 92.625

FWinter = 80.625, FSpring = 120.375, FSummer= 175.375, FFall= 90.625

FWinter = 82.625, FSpring = 120.375, FSummer= 174.375, FFall= 90.625

FWinter = 80.625, FSpring = 120.375, FSummer= 174.375, FFall= 95.625

Answer 1

data

Quarter	1	winter	spring	summer	t
Winter	64	1	0	0	1
Spring	103	0	1	0	2
Summer	152	0	0	1	3
Fall	73	0	0	0	4
	66	1	0	0	5
	103	0	1	0	6
	160	0	0	1	7
	72	0	0	0	8
	68	1	0	0	9
	104	0	1	0	10
	162	0	0	1	11
	78	0	0	0	12
	73	1	0	0	13
	120	0	1	0	14
	176	0	0	1	15
	88	0	0	0	16

here winter, spring and summer are three dummy variable

t = 1 to 16

result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.995917324
R Square	0.991851316
Adjusted R Square	0.988888158
Standard Error	4.079327039
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	4	22280.7	5570.175	334.7278066	2.09358E-11
Residual	11	183.05	16.64090909
Total	15	22463.75
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	64.875	3.059495279	21.20447789	2.85131E-10	58.14109629
winter	-6.1375	2.964537083	-2.070306368	0.062739758	-12.66240213
spring	32.325	2.92035373	11.06886459	2.65619E-07	25.89734478
summer	86.0375	2.893519896	29.73454585	7.34358E-12	79.66890565
t	1.2875	0.228041314	5.645906775	0.000149723	0.785584452

using regression result

17	80.625
18	120.375
19	175.375
20	90.625

formula

17	=B17+B18+B21*17
18	=B17+B19+B21*18
19	=B17+B20+B21*19
20	=B17+B21*20

B17 is

64.875

B18 slope of winter , B19 - spring , B20 for summer , B21 for t

option B) is correct