FORECASTING A major source of revenue in Jacksonville is a county sales tax on certain types...

FORECASTING

A major source of revenue in Jacksonville is a county sales tax on certain types of goods and services. For the most recent 4 years (2015 to 2018), quarterly sales tax revenue (in millions of dollars) has been collected. These values are shown in the following table:

Year	Quarter	Sales Tax Revenue ($1,000,000)
2015	1	218
2015	2	247
2015	3	243
2015	4	292
2016	1	225
2016	2	254
2016	3	255
2016	4	299
2017	1	234
2017	2	265
2017	3	264
2017	4	327
2018	1	250
2018	2	283
2018	3	389
2018	4	356

Use multiple regression to estimate the trend and seasonal components of this time series. Explain the meaning of each estimated coefficient that results from the regression procedure. Then, provide a forecast for each quarter of 2019.

Expert Solution

data

y	t	Q1	Q2	Q3
218	1	1	0	0
247	2	0	1	0
243	3	0	0	1
292	4	0	0	0
225	5	1	0	0
254	6	0	1	0
255	7	0	0	1
299	8	0	0	0
234	9	1	0	0
265	10	0	1	0
264	11	0	0	1
327	12	0	0	0
250	13	1	0	0
383	14	0	1	0
389	15	0	0	1
356	16	0	0	0

Excel regression output

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.86072103
R Square	0.740840692
Adjusted R Square	0.646600944
Standard Error	32.58867274
Observations	16

ANOVA
	df	SS	MS	F	Significance F
Regression	4	33395.2	8348.8	7.861233775	0.0030201
Residual	11	11682.2375	1062.021591
Total	15	45077.4375

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	244.0625	24.44150455	9.985575948	7.50039E-07	190.2671112	297.8578888
t	7.44375	1.821762189	4.086016302	0.001801683	3.434078458	11.45342154
Q1	-64.41875	23.68290845	-2.720052317	0.01992959	-116.54448	-12.29302
Q2	-16.3625	23.32993925	-0.701352019	0.497652968	-67.71135007	34.98635007
Q3	-23.30625	23.11557079	-1.008248951	0.334999183	-74.18327827	27.57077827

y^= 244.0625 + 7.44375 t -64.41875 Q1 -16.3625 Q2 -23.30625 Q3

t	predicted
17	306.1875
18	361.6875
19	362.1875
20	392.9375

orchestra answered 2 years ago

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