Question

Consider the following time series data.

Quarter	Year 1	Year 2	Year 3
1	5	8	10
2	1	3	7
3	3	6	8
4	7	10	12

(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 t such 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.

Answer 1

data

d)

data -> data analysis -> Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.993370885
R Square	0.986785714
Adjusted R Square	0.979234694
Standard Error	0.469295318
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	4	115.125	28.78125	130.6824324	1.18135E-06
Residual	7	1.541666667	0.220238095
Total	11	116.6666667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	4.416666667	0.428406053	10.30953377	1.74932E-05	3.403647325	5.429686
t	0.65625	0.041480238	15.82078687	9.77012E-07	0.558164824	0.754335
Q1	-0.03125	0.402878254	-0.077566857	0.940343205	-0.983905691	0.921406
Q2	-4.6875	0.392055911	-11.95620285	6.51625E-06	-5.614564915	-3.76044
Q3	-3.34375	0.385416667	-8.675675676	5.41239E-05	-4.255115597	-2.43238

y^ = 4.4167 -0.03125 Q1 -4.6875 Q2 - 3.34375 Q3 + 0.65625 t

e)

Year	Quarter	Period	Ft
4	1	13	12.917
4	2	14	8.917
4	3	15	10.917
4	4	16	14.917

f)

Including t			y	t	Q1	Q2	Q3	predicted	error^2
			5	1	1	0	0	5.041667	0.001736
			1	2	0	1	0	1.041667	0.001736
			3	3	0	0	1	3.041667	0.001736
			7	4	0	0	0	7.041667	0.001736
			8	5	1	0	0	7.666667	0.111111
			3	6	0	1	0	3.666667	0.444444
			6	7	0	0	1	5.666667	0.111111
	Intercept	4.416667	10	8	0	0	0	9.666667	0.111111
	t	0.65625	10	9	1	0	0	10.29167	0.085069
	Q1	-0.03125	7	10	0	1	0	6.291667	0.501736
	Q2	-4.6875	8	11	0	0	1	8.291667	0.085069
	Q3	-3.34375	12	12	0	0	0	12.29167	0.085069
								MSE	0.128472
Excluding t
			y		Q1	Q2	Q3	predicted	error^2
Intercept	9.666667		5		1	0	0	7.666667	7.111111
Q1	-2		1		0	1	0	3.666667	7.111111
Q2	-6		3		0	0	1	5.666667	7.111111
Q3	-4		7		0	0	0	9.666667	7.111111
			8		1	0	0	7.666667	0.111111
			3		0	1	0	3.666667	0.444444
			6		0	0	1	5.666667	0.111111
			10		0	0	0	9.666667	0.111111
			10		1	0	0	7.666667	5.444444
			7		0	1	0	3.666667	11.11111
			8		0	0	1	5.666667	5.444444
			12		0	0	0	9.666667	5.444444
								MSE	4.722222

MSE

Model b = 4.722222

Model d = 0.128472

Model d is better

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