Question

6. eBook The quarterly sales data (number of copies sold) for a college textbook over the past three years follow Quarter Year 1 Year 2 Year 3 1,765 1,063 2,974 2,554 1,591 1,827 935 2,646 2,423 980 2,812 2,358 4 There appears to be a seasonal pattern in the data and perhaps amoderate upward linear trend b. Use the following dummy variables to develop an estimated regression equation to account for any seasonal effects in the data: Qtrl 1 if Quarter 1, 0 otherwise; Qtr2 1 if Quarter 2, 0 otherwise; Qtr3 1 if Quarter 3, 0 otherwise. Round your answers to whole number and enter negative value as negative number. Value = c. Compute the quarterly forecasts for next year. Round your answers to whole number Qtr1+ Qtr2 Qtr3 Quarter 1 forecast Quarter 2 forecast Quarter 3 forecast Quarter 4 forecast d. Let t= 1 to refer to the observation in quarter 1 of year 1; t=2 to refer to the observation in quarter 2 of year 1; ' . , and t=12 to refer to the observation in quarter 4 of year 3. Using the dummy variables defined in part (b) and t develop an estimated regression equation to account for seasonal effects and any linear trend in the time series Based upon the seasonal effects in the data and linear trend, compute the quarterly forecasts for next year. Round your answers to whole number and enter negative value as negative number. The regression equation is Value The quarterly forecasts for next year are as follows: Round your answers to whole number. Qtr1+ Qtr2 Qtr3 + Quarter 1 forecast Quarter 2 forecast Quarter 3 forecast Quarter 4 forecast

Answer 1

data

Actual Demand y	t	Q1	Q2	Q3
1591	1	1	0	0
935	2	0	1	0
2646	3	0	0	1
2423	4	0	0	0
1827	5	1	0	0
980	6	0	1	0
2812	7	0	0	1
2358	8	0	0	0
1765	9	1	0	0
1063	10	0	1	0
2974	11	0	0	1
2554	12	0	0	0

b)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.990525346
R Square	0.981140462
Adjusted R Square	0.974068135
Standard Error	118.374406
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	3	5831842	1943947.333	138.7295153	3.08975E-07
Residual	8	112100	14012.5
Total	11	5943942
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	2445	68.34349518	35.77516768	4.08152E-10	2287.399618
Q1	-717.3333333	96.65229778	-7.421792857	7.46248E-05	-940.2139317
Q2	-1452.333333	96.65229778	-15.02637151	3.80131E-07	-1675.213932
Q3	365.6666667	96.65229778	3.783320987	0.005362674	142.7860683

y^ = 2445 - 717 Q1 -1452 Q2 + 366 Q3

c)

Year	Quarter	Ft
4	1	1728
4	2	993
4	3	2811
4	4	2445

d)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.996654037
R Square	0.993319269
Adjusted R Square	0.989501709
Standard Error	75.31825334
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	4	5904232.125	1476058.031	260.1973997	1.09102E-07
Residual	7	39709.875	5672.839286
Total	11	5943942
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	2255	69	33	0	2092
t	24	7	4	0	8
Q1	-646	65	-10	0	-799
Q2	-1405	63	-22	0	-1554
Q3	389	62	6	0	243

y^ = 2255 -646 Q1 -1405 Q2 +389 Q3 + 24 t

e)

Year	Quarter	Period	Ft
4	1	13	1918
4	2	14	1183
4	3	15	3001
4	4	16	2635