1) How many people were present for the signing of the Declaration of Independence?

Expert Solution

a)

b)

c)

Answers to a),b) and c)

year	Demand	3 MA	weighted average	Exponential alpha = 0.03
1	4			5
2	6			4.7000
3	5			5.0900
4	5	5	5	5.0630
5	10	5.3333	5.25	5.0441
6	9	6.6667	7.5	6.5309
7	13	8	8.25	7.2716
8	15	10.6667	11.25	8.9901

Formula in Excel

year	Demand	3 MA	weighted average	Exponential alpha = 0.03
1	4			5
=1+A2	6			=E2+0.3*(B2-E2)
=1+A3	5			=E3+0.3*(B3-E3)
=1+A4	5	=AVERAGE(B2:B4)	=0.5B4+0.25B3+0.25*B2	=E4+0.3*(B4-E4)
=1+A5	10	=AVERAGE(B3:B5)	=0.5B5+0.25B4+0.25*B3	=E5+0.3*(B5-E5)
=1+A6	9	=AVERAGE(B4:B6)	=0.5B6+0.25B5+0.25*B4	=E6+0.3*(B6-E6)
=1+A7	13	=AVERAGE(B5:B7)	=0.5B7+0.25B6+0.25*B5	=E7+0.3*(B7-E7)
=1+A8	15	=AVERAGE(B6:B8)	=0.5B8+0.25B7+0.25*B6	=E8+0.3*(B8-E8)

d)

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.9246
R Square	0.8548
Adjusted R Square	0.8306
Standard Error	1.6744
Observations	8

ANOVA
	df	SS	MS	F	Significance F
Regression	1	99.0536	99.0536	35.3312	0.0010
Residual	6	16.8214	2.8036
Total	7	115.8750

	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	1.4643	1.3047	1.1223	0.3046	-1.7281
year	1.5357	0.2584	5.9440	0.0010	0.9035

Observation	Predicted Demand
1	3
2	4.5357
3	6.0714
4	7.6071
5	9.1429
6	10.6786
7	12.2143
8	13.75

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