Question

Number of Certified Organic Farms in the United States, 2001–2008
Year	Farms
2001	5,974
2002	6,315
2003	7,032
2004	7,006
2005	7,486
2006	8,368
2007	9,932
2008	11,165

(a) Use Excel, MegaStat, or MINITAB to fit three trends (linear, quadratic, exponential) to the time series. (A negative value should be indicated by a minus sign. Do not round the intermediate calculations. Round your final answers to 2 decimal places.)

Exponential	yt = 5256.1e .0861x

(b) Use each of the three fitted trend equations to make numerical forecasts for the next 3 years. (Round the intermediate calculations to 2 decimal places and round your final answers to 1 decimal place.)

t		Exponential
9
10
11

I am having issue predicting the future trendlines.I got 11407.7, 12433.4, and 13551.4 and these were incorrect. Can you please help me learn what I am doing wrong.

Answer 1

a)

for exponential

Year	Farms	t	ln y
2001	5,974	1	8.695172
2002	6,315	2	8.750683
2003	7,032	3	8.858226
2004	7,006	4	8.854522
2005	7,486	5	8.92079
2006	8,368	6	9.03217
2007	9,932	7	9.203517
2008	11,165	8	9.320539

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.969205598
R Square	0.939359491
Adjusted R Square	0.92925274
Standard Error	0.057858065
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.311134412	0.311134412	92.94376074	7.13297E-05
Residual	6	0.020085334	0.003347556
Total	7	0.331219746
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	8.56713967	0.045082641	190.0318949	1.4327E-12	8.456826422
t	0.08606952	0.008927693	9.64073445	7.13297E-05	0.064224241

e^(8.5671) = 5256.074

y^= 5256.074 e^(0.08607 t)

t	forecast
9	11404.52341
10	12429.58585
11	13546.78305

rounding to 2 decimal

t	forecast
9	11404.52
10	12429.59
11	13546.78