Question

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

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) Calculate the MSE for the regression models developed in parts (b) and (d).

If required, round your intermediate calculations and final answer to three decimal places.

Model developed in part (b) Model developed in part (d)

MSE

Answer 1

Value = 6.667 - 1*Qtr 1 - 3*Qtr 2 - 2*Qtr 3

Quarter 1 forecast	5.667
Quarter 2 forecast	3.667
Quarter 3 forecast	4.667
Quarter 4 forecast	6.667

Value = 3.417 + 0.219*Qtr 1 - 2.188*Qtr 2 - 1.594*Qtr 3 + 0.406*t

Quarter 1 forecast	8.917
Quarter 2 forecast	6.917
Quarter 3 forecast	7.917
Quarter 4 forecast	9.917

	(b)	(d)
MSE	2.833	0.220

part (d) model is more effective.

The outputs are:

	R²	0.398
	Adjusted R²	0.173
	R	0.631
	Std. Error	1.683
	n	12
	k	3
	Dep. Var.	yt
ANOVA table
Source	SS	df	MS	F	p-value
Regression	15.0000	3	5.0000	1.76	.2314
Residual	22.6667	8	2.8333
Total	37.6667	11
Regression output				confidence interval
variables	coefficients	std. error	t (df=8)	p-value	95% lower	95% upper
Intercept	6.667
Qtr 1	-1.000	1.3744	-0.728	.4876	-4.1693	2.1693
Qtr 2	-3.000	1.3744	-2.183	.0606	-6.1693	0.1693
Qtr 3	-2.000	1.3744	-1.455	.1837	-5.1693	1.1693

	R²	0.959
	Adjusted R²	0.936
	R	0.979
	Std. Error	0.469
	n	12
	k	4
	Dep. Var.	yt
ANOVA table
Source	SS	df	MS	F	p-value
Regression	36.1250	4	9.0313	41.01	.0001
Residual	1.5417	7	0.2202
Total	37.6667	11
Regression output				confidence interval
variables	coefficients	std. error	t (df=7)	p-value	95% lower	95% upper
Intercept	3.417
Qtr 1	0.219	0.4029	0.543	.6040	-0.7339	1.1714
Qtr 2	-2.188	0.3921	-5.580	.0008	-3.1146	-1.2604
Qtr 3	-1.594	0.3854	-4.135	.0044	-2.5051	-0.6824
t	0.406	0.0415	9.794	2.45E-05	0.3082	0.5043