Question

Consider the following time series data.

Quarter	Year	1Year2	Year 3
1	4	6	7
2	2	3	6
3	3	5	6
4	5	7	8 b.) Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend 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 (to 3 decimals if necessary). Value = ____ +____ Qtr1____ -   Qtr2____ -   Qtr3____ +   t Compute the quarterly forecasts for next year (to 2 decimals). Quarter 1 forecast Quarter 2 forecast Quarter 3 forecast Quarter 4 forecast

Answer 1

Result:

b.) Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend 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 (to 3 decimals if necessary).

Value = 3.147 +(-1)*Qtr1+(-3) *Qtr2+(-2)* Qtr3 +  1.625* t

Compute the quarterly forecasts for next year (to 2 decimals).

Quarter 1 forecast	8.92
Quarter 2 forecast	6.92
Quarter 3 forecast	7.92
Quarter 4 forecast	9.92

Recoded data

value	t	Qtr1	Qtr2	Qtr3
4	1	1	0	0
2	1	0	1	0
3	1	0	0	1
5	1	0	0	0
6	2	1	0	0
3	2	0	1	0
5	2	0	0	1
7	2	0	0	0
7	3	1	0	0
6	3	0	1	0
6	3	0	0	1
8	3	0	0	0

Regression Analysis
	R²	0.959
	Adjusted R²	0.936	n	12
	R	0.979	k	4
	Std. Error	0.469	Dep. Var.	value
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	3.4167	0.4284	7.975	.0001	2.4036	4.4297
t	1.6250	0.1659	9.794	2.45E-05	1.2327	2.0173
Qtr1	-1.0000	0.3832	-2.610	.0349	-1.9061	-0.0939
Qtr2	-3.0000	0.3832	-7.829	.0001	-3.9061	-2.0939
Qtr3	-2.0000	0.3832	-5.220	.0012	-2.9061	-1.0939
Predicted values for: value
					95% Confidence Intervals		95% Prediction Intervals
t	Qtr1	Qtr2	Qtr3	Predicted	lower	upper	lower	upper	Leverage
4	1	0	0	8.917	7.904	9.930	7.414	10.419	0.833
4	0	1	0	6.917	5.904	7.930	5.414	8.419	0.833
4	0	0	1	7.917	6.904	8.930	6.414	9.419	0.833
4	0	0	0	9.917	8.904	10.930	8.414	11.419	0.833