Question

Consider the following time series:

Quarter	Year 1	Year 2	Year 3
1	69	66	60
2	45	37	47
3	55	57	50
4	83	86	77

(a)	Choose a time series plot.
	(i) (ii) (iii) (iv)
	- Select your answer -Graph (i)Graph (ii)Graph (iii)Graph (iv)Item 1
	What type of pattern exists in the data? Is there an indication of a seasonal pattern?
	- Select your answer -Positive trend pattern, no seasonalityHorizontal pattern, no seasonalityNegative trend pattern, no seasonalityPositive trend pattern, with seasonalityHorizontal pattern, with seasonalityItem 2
(b)	Use a multiple linear regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Qtr1 = 1 if quarter 1, 0 otherwise; Qtr2 = 1 if quarter 2, 0 otherwise; Qtr3 = 1 if quarter 3, 0 otherwise. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
	ŷ =   +   Qtr1 +   Qtr2 +   Qtr3
(c)	Compute the quarterly forecasts for next year.
	Year Quarter Ft 4 1 4 2 4 3 4 4

Answer 1

a)

with seasonality Horizontal pattern

b)

year	Qurter	Y	Q1	Q2	Q3
1	1	69	1	0	0
1	2	45	0	1	0
1	3	55	0	0	1
1	4	83	0	0	0
2	1	66	1	0	0
2	2	37	0	1	0
2	3	57	0	0	1
2	4	86	0	0	0
3	1	60	1	0	0
3	2	47	0	1	0
3	3	50	0	0	1
3	4	77	0	0	0

Excel > Data > Data Analysis > Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.968245837
R Square	0.9375
Adjusted R Square	0.9140625
Standard Error	4.55521679
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	3	2490	830	40	3.65996E-05
Residual	8	166	20.75
Total	11	2656
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	82	2.62995564	31.17923313	1.21753E-09	75.93531142	88.06468858	75.93531142	88.06468858
Q1	-17	3.719318934	-4.570729292	0.001824043	-25.57676484	-8.423235158	-25.57676484	-8.423235158
Q2	-39	3.719318934	-10.48579073	5.95026E-06	-47.57676484	-30.42323516	-47.57676484	-30.42323516
Q3	-28	3.719318934	-7.528260011	6.74509E-05	-36.57676484	-19.42323516	-36.57676484	-19.42323516

Y = 82-17*Q1-39*Q2-28*Q3

c)

Year	Quarter	Ft = 82-17*Q1-39*Q2-28*Q3	Q1	Q2	Q3
4	1	65	1	0	0
4	2	43	0	1	0
4	3	54	0	0	1
4	4	82	0	0	0