Question

Consider the following time series data.

Quarter	Year 1	Year 2	Year 3
1	2	5	7
2	0	2	6
3	5	8	10
4	5	8	10

b)	Use a multiple 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.
	If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) If the constant is "1" it must be entered in the box. Do not round intermediate calculation.
	ŷ =   +  Qtr1 +  Qtr2 +  Qtr3
(c)	Compute the quarterly forecasts for next year based on the model you developed in part (b).
	If required, round your answers to three decimal places. Do not round intermediate calculation.
	Year Quarter Ft 4 1 4 2 4 3 4 4
(d)	Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part (b) to capture seasonal effects and create a variable tsuch that t = 1 for Quarter 1 in Year 1, t = 2 for Quarter 2 in Year 1,… t = 12 for Quarter 4 in Year 3.
	If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
	ŷ =  +  Qtr1 +  Qtr2 +  Qtr3 +  t
(e)	Compute the quarterly forecasts for next year based on the model you developed in part (d).
	Do not round your interim computations and round your final answer to three decimal places.
	Year Quarter Period Ft 4 1 13 4 2 14 4 3 15 4 4 16
(f)	Is the model you developed in part (b) or the model you developed in part (d) more effective?
	If required, round your intermediate calculations and final answer to three decimal places.
	Model developed in part (b) Model developed in part (d) MSE
	- Select your answer -Model developed in part (b)Model developed in part (d)Item 22
	Justify your answer.
	The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Please show steps to solve using Excel.

Answer 1

b)

data

y	q1	q2	q3
2	1	0	0
0	0	1	0
5	0	0	1
5	0	0	0
5	1	0	0
2	0	1	0
8	0	0	1
8	0	0	0
7	1	0	0
6	0	1	0
10	0	0	1
10	0	0	0

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.698535473
R Square	0.487951807
Adjusted R Square	0.295933735
Standard Error	2.661453237
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	3	54	18	2.541176471	0.129679966
Residual	8	56.66666667	7.083333333
Total	11	110.6666667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	7.666666667	1.536590743	4.98940053	0.001066868	4.123282059
q1	-3	2.173067468	-1.38053698	0.204763892	-8.011102568
q2	-5	2.173067468	-2.300894967	0.050400371	-10.01110257
q3	6.28037E-16	2.173067468	2.89009E-16	1	-5.011102568

y^= 7.6667 -3 Q1 -5 Q +0 Q3

c)

Year	Quarter	Ft
4	1	4.6667
4	2	2.6667
4	3	7.6667
4	4	7.6667

d)

data

y	q1	q2	q3	t
2	1	0	0	1
0	0	1	0	2
5	0	0	1	3
5	0	0	0	4
5	1	0	0	5
2	0	1	0	6
8	0	0	1	7
8	0	0	0	8
7	1	0	0	9
6	0	1	0	10
10	0	0	1	11
10	0	0	0	12

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.99301021
R Square	0.986069277
Adjusted R Square	0.978108864
Standard Error	0.469295318
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	4	109.125	27.28125	123.8716216	1.42033E-06
Residual	7	1.541666667	0.220238095
Total	11	110.6666667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	2.416666667	0.428406053	5.641065646	0.000781715	1.403647325
q1	-1.03125	0.402878254	-2.559706285	0.037567703	-1.983905691
q2	-3.6875	0.392055911	-9.405546243	3.19973E-05	-4.614564915
q3	0.65625	0.385416667	1.702702703	0.132407607	-0.255115597
t	0.65625	0.041480238	15.82078687	9.77012E-07	0.558164824

y^= 2.4167 -1.03125 *q1 -3.6875 *q2 +0.65625 q3 + 0.65625 t

d)

Year	Quarter	Period	Ft
4	1	13	9.9167
4	2	14	7.9167
4	3	15	12.9167
4	4	16	12.9167