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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 22 Nov 2012 09:28:40 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/22/t1353594544elzs8mcyqhp9toe.htm/, Retrieved Thu, 02 May 2024 09:56:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=191800, Retrieved Thu, 02 May 2024 09:56:15 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

111

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Exponential Smoothing] [WS 8 - exponentio...] [2012-11-22 13:48:01] [b952eaabb01bdc8fc50f908b86502128]
- R P     [Exponential Smoothing] [WS 8 - single exp...] [2012-11-22 14:28:40] [fd3c35a156f52433b5d6e23e16a12a78] [Current]
- R  D      [Exponential Smoothing] [WS 8 - double exp...] [2012-11-22 14:30:09] [b952eaabb01bdc8fc50f908b86502128] 
- R  D      [Exponential Smoothing] [WS 8 - triple exp...] [2012-11-22 14:31:26] [b952eaabb01bdc8fc50f908b86502128] 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191800&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191800&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191800&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999922436590606
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999922436590606 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191800&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.999922436590606[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191800&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191800&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999922436590606
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	8.89	8.64	0.25
3	8.87	8.88998060914765	-0.0199806091476535
4	8.81	8.87000154976417	-0.0600015497641664
5	8.87	8.81000465392477	0.0599953460752296
6	9.06	8.86999534655641	0.190004653443591
7	9.12	9.05998526259128	0.0600147374087214
8	8.66	9.11999534505235	-0.459995345052352
9	8.17	8.66003567880727	-0.490035678807269
10	8.04	8.17003800883797	-0.130038008837975
11	7.71	8.04001008619132	-0.330010086191316
12	7.55	7.71002559670742	-0.16002559670742
13	7.52	7.55001241213087	-0.0300124121308709
14	7.38	7.52000232786501	-0.140002327865009
15	7.52	7.38001085905787	0.139989140942127
16	7.31	7.51998914196495	-0.20998914196495
17	6.92	7.31001628747379	-0.390016287473786
18	7.09	6.92003025099298	0.169969749007024
19	7.05	7.08998681656677	-0.0399868165667732
20	7.37	7.05000310151382	0.319996898486177
21	7.05	7.36997517994956	-0.319975179949558
22	6.79	7.05002481836588	-0.260024818365879
23	6.35	6.79002016841144	-0.44002016841144
24	6.44	6.35003412946446	0.0899658705355364
25	6.89	6.43999302194035	0.450006978059647
26	7.16	6.88996509592453	0.27003490407547
27	7.46	7.15997905517218	0.300020944827815
28	7.91	7.45997672935263	0.450023270647371
29	7.86	7.90996509466082	-0.0499650946608217
30	8.02	7.86000387546309	0.159996124536907
31	8.38	8.01998759015509	0.360012409844909
32	8.5	8.37997207621007	0.120027923789932
33	8.4	8.49999069022501	-0.0999906902250078
34	8.24	8.40000775561884	-0.160007755618842
35	8.33	8.24001241074706	0.089987589252944
36	8.28	8.32999302025577	-0.0499930202557746
37	8.15	8.2800038776291	-0.130003877629097
38	8.06	8.15001008354398	-0.0900100835439837
39	7.79	8.06000698148896	-0.270006981488961
40	7.28	7.79002094266204	-0.510020942662044
41	7.52	7.28003955896318	0.239960441036824
42	7.23	7.51998138785007	-0.289981387850072
43	7.13	7.2300224919451	-0.100022491945103
44	7.21	7.13000775808549	0.0799922419145087
45	6.99	7.20999379552899	-0.219993795528992
46	6.77	6.99001706346883	-0.220017063468828
47	6.69	6.77001706527357	-0.0800170652735668
48	6.39	6.69000620639639	-0.300006206396393
49	6.85	6.39002326950421	0.459976730495792
50	6.74	6.84996432263654	-0.10996432263654
51	6.56	6.74000852920778	-0.180008529207776
52	6.62	6.56001396207524	0.0599860379247552
53	6.71	6.61999534727838	0.0900046527216176
54	6.67	6.70999301893227	-0.0399930189322735
55	6.54	6.6700031019949	-0.1300031019949
56	6.14	6.54001008348382	-0.400010083483822
57	6.13	6.14003102614587	-0.0100310261458674
58	5.86	6.13000077804059	-0.270000778040587
59	5.88	5.86002094218088	0.0199790578191159
60	5.75	5.87999845035616	-0.129998450356159
61	5.53	5.75001008312303	-0.220010083123025
62	5.86	5.53001706473215	0.329982935267852
63	5.9	5.8599744053985	0.0400255946015013
64	5.95	5.89999689547842	0.0500031045215801
65	5.69	5.94999612158873	-0.259996121588733
66	5.53	5.69002016618562	-0.16002016618562
67	5.71	5.53001241170966	0.179987588290339
68	5.6	5.709986039549	-0.109986039549004
69	5.73	5.60000853089221	0.129991469107788
70	5.6	5.72998991741846	-0.129989917418465
71	5.41	5.60001008246118	-0.190010082461181
72	5.13	5.41001473782982	-0.280014737829815
73	5	5.13002171889775	-0.130021718897747
74	5.04	5.00001008492781	0.0399899150721872
75	5.1	5.03999689824585	0.0600031017541536
76	4.96	5.09999534595485	-0.139995345954853
77	4.9	4.96001085851633	-0.060010858516331
78	4.8	4.90000465464679	-0.100004654646788
79	4.48	4.80000775670197	-0.320007756701969
80	4.29	4.48002482089264	-0.190024820892643
81	4.27	4.29001473897298	-0.0200147389729786
82	4.18	4.27000155241139	-0.0900015524113931
83	4.02	4.18000698082726	-0.160006980827256
84	3.82	4.02001241068696	-0.20001241068696
85	4.13	3.82001551364449	0.309984486355506
86	4.16	4.12997595654638	0.0300240434536212
87	3.98	4.15999767123283	-0.179997671232826
88	4.26	3.98001396123306	0.279986038766936
89	4.7	4.25997828332825	0.44002171667175
90	4.96	4.69996587041545	0.260034129584552
91	5.13	4.95997983086635	0.170020169133649
92	5.35	5.12998681265602	0.220013187343984
93	5.41	5.34998293502708	0.0600170649729224
94	5.42	5.40999534487182	0.0100046551281805
95	5.51	5.41999922400484	0.0900007759951613
96	5.75	5.50999301923297	0.240006980767035
97	5.67	5.74998138424029	-0.079981384240293
98	5.46	5.67000620362885	-0.21000620362885
99	5.56	5.46001628879715	0.0999837112028521
100	5.56	5.55999224492247	7.75507752504012e-06
101	5.54	5.55999999939849	-0.0199999993984896
102	5.53	5.54000155126814	-0.0100015512681413
103	5.65	5.53000077575442	0.119999224245585
104	5.58	5.64999069245104	-0.0699906924510429
105	5.57	5.58000542871673	-0.0100054287167319
106	5.36	5.57000077605516	-0.210000776055164
107	5.23	5.36001628837617	-0.130016288376166
108	5.11	5.2300100845066	-0.120010084506603
109	5.07	5.11000930839132	-0.0400093083913164
110	5.04	5.07000310325837	-0.030003103258367
111	5.34	5.04000232714298	0.299997672857018
112	5.43	5.33997673115768	0.0900232688423168
113	5.31	5.42999301748834	-0.119993017488344
114	5.12	5.31000930706754	-0.190009307067539
115	4.97	5.12001473776967	-0.150014737769673
116	5	4.97001163565452	0.0299883643454795
117	4.64	4.99999767400022	-0.359997674000219
118	4.8	4.64002792264697	0.15997207735303
119	5.1	4.79998759202027	0.300012407979727
120	5.11	5.09997673001478	0.0100232699852238
121	5.12	5.10999922256101	0.010000777438993
122	5.36	5.11999922430561	0.240000775694395
123	5.26	5.35998138472158	-0.0999813847215805
124	5.27	5.26000775489707	0.00999224510292507
125	5.1	5.2699992249674	-0.169999224967402
126	4.94	5.10001318571948	-0.160013185719482
127	4.68	4.94001241116823	-0.260012411168233
128	4.41	4.68002016744909	-0.270020167449094
129	4.6	4.41002094368479	0.189979056315207
130	4.53	4.59998526457668	-0.0699852645766779
131	4.18	4.53000542829573	-0.350005428295728
132	4	4.18002714761433	-0.180027147614325
133	3.87	4.00001396351935	-0.130013963519352
134	4.09	3.87001008432628	0.21998991567372
135	4.13	4.08998293683211	0.040017063167892
136	3.74	4.12999689614015	-0.389996896140146
137	3.81	3.74003024948892	0.0699697505110821
138	4.11	3.8099945729076	0.300005427092404
139	4.14	4.10997673055624	0.0300232694437614
140	3.99	4.13999767129286	-0.14999767129286
141	4.28	3.99001163433079	0.289988365669213
142	4.37	4.27997750751367	0.0900224924863258
143	4.24	4.36999301754856	-0.129993017548561
144	4.19	4.24001008270164	-0.0500100827016388
145	4.01	4.19000387895252	-0.180003878952519
146	3.95	4.01001396171456	-0.0600139617145556
147	4.3	3.95000465488748	0.349995345112518
148	4.37	4.29997285316776	0.0700271468322393
149	4.4	4.36999456845574	0.0300054315442591
150	4.29	4.39999767267643	-0.109997672676429
151	4.12	4.29000853179452	-0.170008531794518
152	4.07	4.12001318644135	-0.050013186441352
153	3.93	4.07000387919326	-0.140003879193256
154	3.79	3.9300108591782	-0.140010859178199
155	3.67	3.79001085971959	-0.12001085971959
156	3.53	3.67000930845144	-0.140009308451444
157	3.69	3.53001085959931	0.15998914040069
158	3.69	3.6899875906968	1.24093031956818e-05
159	3.48	3.68999999903749	-0.209999999037492
160	3.31	3.4800162883159	-0.170016288315898
161	3.16	3.31001318704297	-0.150013187042974
162	3.25	3.16001163553424	0.0899883644657589
163	3.14	3.24999302019565	-0.109993020195646
164	3.19	3.14000853143366	0.0499914685663438
165	3.43	3.18999612249126	0.240003877508743
166	3.45	3.42998138448099	0.0200186155190076
167	3.31	3.44999844728793	-0.139998447287929
168	3.51	3.31001085875688	0.199989141243118
169	3.53	3.50998448816036	0.0200155118396368
170	3.83	3.52999844752866	0.300001552471339
171	4.02	3.82997673085677	0.190023269143233
172	3.99	4.01998526114738	-0.0299852611473801
173	4.11	3.99000232575909	0.119997674240914
174	3.96	4.10999069257127	-0.149990692571267
175	3.83	3.96001163378949	-0.130011633789493
176	3.71	3.83001008414558	-0.120010084145578
177	3.81	3.71000930839129	0.0999906916087121
178	3.73	3.80999224438105	-0.0799922443810512
179	3.99	3.7300062044712	0.259993795528801
180	4.17	3.9899798339948	0.180020166005202
181	4	4.16998603702216	-0.169986037022165
182	4.1	4.00001318469658	0.0999868153034189
183	4.24	4.09999224468171	0.14000775531829
184	4.45	4.23998914052116	0.210010859478844
185	4.62	4.44998371084173	0.170016289158271
186	4.49	4.61998681295696	-0.12998681295696
187	4.45	4.49001008222039	-0.0400100822203893
188	4.49	4.45000310331839	0.0399968966816129
189	4.36	4.48999689770433	-0.129996897704328
190	4.32	4.3600100830026	-0.0400100830025965
191	4.45	4.32000310331845	0.129996896681552
192	4.13	4.44998991699748	-0.319989916997483
193	4.14	4.13002481950893	0.00997518049106549
194	4.3	4.13999922629099	0.160000773709008
195	4.42	4.29998758979449	0.120012410205515
196	4.67	4.41999069142829	0.250009308571705
197	4.96	4.66998060842565	0.290019391574353
198	4.73	4.9599775051072	-0.229977505107199
199	4.52	4.73001783783938	-0.210017837839381
200	4.36	4.52001628969954	-0.160016289699536
201	4.15	4.36001241140899	-0.210012411408988
202	3.92	4.15001628927864	-0.230016289278645
203	3.88	3.92001784084761	-0.0400178408476126
204	4.2	3.88000310392017	0.319996896079827
205	3.95	4.19997517994974	-0.249975179949744
206	3.78	3.95001938892722	-0.170019388927221
207	3.69	3.78001318728347	-0.0900131872834682
208	3.77	3.6900069817297	0.0799930182703039
209	3.66	3.76999379546878	-0.109993795468775
210	3.53	3.66000853149379	-0.130008531493789
211	3.5	3.53001008390495	-0.0300100839049526
212	3.14	3.50000232768442	-0.360002327684424
213	3.42	3.14002792300793	0.279972076992075
214	3.3	3.41997828441117	-0.119978284411173
215	2.81	3.30000930592479	-0.490009305924792
216	3.15	2.8100380067924	0.339961993207597
217	3.37	3.14997363138874	0.220026368611258
218	4.05	3.36998293400469	0.680017065995306
219	4	4.04994725555791	-0.0499472555579148
220	4.2	4.00000387407943	0.19999612592057
221	4.21	4.19998448761861	0.0100155123813916
222	4.24	4.20999922316271	0.0300007768372872
223	4.24	4.23999767303746	2.3269625355482e-06
224	4.17	4.23999999981951	-0.0699999998195135
225	4.12	4.17000542943864	-0.0500054294386434
226	4.35	4.1200038785916	0.229996121408404
227	3.98	4.34998216071668	-0.369982160716675
228	3.62	3.9800286970778	-0.3600286970778
229	4.39	3.62002792505323	0.769972074946774
230	5.01	4.38994027834073	0.620059721659271
231	4.07	5.00995190605396	-0.93995190605396
232	3.7	4.0700729058745	-0.3700729058745
233	3.59	3.7000287041163	-0.110028704116305
234	3.44	3.59000853420142	-0.150008534201422
235	3.33	3.44001163517335	-0.110011635173351
236	2.98	3.3300085328775	-0.350008532877497
237	3.14	2.98002714785513	0.159972852144873
238	2.55	3.13998759196018	-0.589987591960178
239	2.49	2.55004576144913	-0.0600457614491323
240	2.53	2.49000465735398	0.039995342646022
241	2.43	2.52999689782486	-0.0999968978248642

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 8.89 & 8.64 & 0.25 \tabularnewline
3 & 8.87 & 8.88998060914765 & -0.0199806091476535 \tabularnewline
4 & 8.81 & 8.87000154976417 & -0.0600015497641664 \tabularnewline
5 & 8.87 & 8.81000465392477 & 0.0599953460752296 \tabularnewline
6 & 9.06 & 8.86999534655641 & 0.190004653443591 \tabularnewline
7 & 9.12 & 9.05998526259128 & 0.0600147374087214 \tabularnewline
8 & 8.66 & 9.11999534505235 & -0.459995345052352 \tabularnewline
9 & 8.17 & 8.66003567880727 & -0.490035678807269 \tabularnewline
10 & 8.04 & 8.17003800883797 & -0.130038008837975 \tabularnewline
11 & 7.71 & 8.04001008619132 & -0.330010086191316 \tabularnewline
12 & 7.55 & 7.71002559670742 & -0.16002559670742 \tabularnewline
13 & 7.52 & 7.55001241213087 & -0.0300124121308709 \tabularnewline
14 & 7.38 & 7.52000232786501 & -0.140002327865009 \tabularnewline
15 & 7.52 & 7.38001085905787 & 0.139989140942127 \tabularnewline
16 & 7.31 & 7.51998914196495 & -0.20998914196495 \tabularnewline
17 & 6.92 & 7.31001628747379 & -0.390016287473786 \tabularnewline
18 & 7.09 & 6.92003025099298 & 0.169969749007024 \tabularnewline
19 & 7.05 & 7.08998681656677 & -0.0399868165667732 \tabularnewline
20 & 7.37 & 7.05000310151382 & 0.319996898486177 \tabularnewline
21 & 7.05 & 7.36997517994956 & -0.319975179949558 \tabularnewline
22 & 6.79 & 7.05002481836588 & -0.260024818365879 \tabularnewline
23 & 6.35 & 6.79002016841144 & -0.44002016841144 \tabularnewline
24 & 6.44 & 6.35003412946446 & 0.0899658705355364 \tabularnewline
25 & 6.89 & 6.43999302194035 & 0.450006978059647 \tabularnewline
26 & 7.16 & 6.88996509592453 & 0.27003490407547 \tabularnewline
27 & 7.46 & 7.15997905517218 & 0.300020944827815 \tabularnewline
28 & 7.91 & 7.45997672935263 & 0.450023270647371 \tabularnewline
29 & 7.86 & 7.90996509466082 & -0.0499650946608217 \tabularnewline
30 & 8.02 & 7.86000387546309 & 0.159996124536907 \tabularnewline
31 & 8.38 & 8.01998759015509 & 0.360012409844909 \tabularnewline
32 & 8.5 & 8.37997207621007 & 0.120027923789932 \tabularnewline
33 & 8.4 & 8.49999069022501 & -0.0999906902250078 \tabularnewline
34 & 8.24 & 8.40000775561884 & -0.160007755618842 \tabularnewline
35 & 8.33 & 8.24001241074706 & 0.089987589252944 \tabularnewline
36 & 8.28 & 8.32999302025577 & -0.0499930202557746 \tabularnewline
37 & 8.15 & 8.2800038776291 & -0.130003877629097 \tabularnewline
38 & 8.06 & 8.15001008354398 & -0.0900100835439837 \tabularnewline
39 & 7.79 & 8.06000698148896 & -0.270006981488961 \tabularnewline
40 & 7.28 & 7.79002094266204 & -0.510020942662044 \tabularnewline
41 & 7.52 & 7.28003955896318 & 0.239960441036824 \tabularnewline
42 & 7.23 & 7.51998138785007 & -0.289981387850072 \tabularnewline
43 & 7.13 & 7.2300224919451 & -0.100022491945103 \tabularnewline
44 & 7.21 & 7.13000775808549 & 0.0799922419145087 \tabularnewline
45 & 6.99 & 7.20999379552899 & -0.219993795528992 \tabularnewline
46 & 6.77 & 6.99001706346883 & -0.220017063468828 \tabularnewline
47 & 6.69 & 6.77001706527357 & -0.0800170652735668 \tabularnewline
48 & 6.39 & 6.69000620639639 & -0.300006206396393 \tabularnewline
49 & 6.85 & 6.39002326950421 & 0.459976730495792 \tabularnewline
50 & 6.74 & 6.84996432263654 & -0.10996432263654 \tabularnewline
51 & 6.56 & 6.74000852920778 & -0.180008529207776 \tabularnewline
52 & 6.62 & 6.56001396207524 & 0.0599860379247552 \tabularnewline
53 & 6.71 & 6.61999534727838 & 0.0900046527216176 \tabularnewline
54 & 6.67 & 6.70999301893227 & -0.0399930189322735 \tabularnewline
55 & 6.54 & 6.6700031019949 & -0.1300031019949 \tabularnewline
56 & 6.14 & 6.54001008348382 & -0.400010083483822 \tabularnewline
57 & 6.13 & 6.14003102614587 & -0.0100310261458674 \tabularnewline
58 & 5.86 & 6.13000077804059 & -0.270000778040587 \tabularnewline
59 & 5.88 & 5.86002094218088 & 0.0199790578191159 \tabularnewline
60 & 5.75 & 5.87999845035616 & -0.129998450356159 \tabularnewline
61 & 5.53 & 5.75001008312303 & -0.220010083123025 \tabularnewline
62 & 5.86 & 5.53001706473215 & 0.329982935267852 \tabularnewline
63 & 5.9 & 5.8599744053985 & 0.0400255946015013 \tabularnewline
64 & 5.95 & 5.89999689547842 & 0.0500031045215801 \tabularnewline
65 & 5.69 & 5.94999612158873 & -0.259996121588733 \tabularnewline
66 & 5.53 & 5.69002016618562 & -0.16002016618562 \tabularnewline
67 & 5.71 & 5.53001241170966 & 0.179987588290339 \tabularnewline
68 & 5.6 & 5.709986039549 & -0.109986039549004 \tabularnewline
69 & 5.73 & 5.60000853089221 & 0.129991469107788 \tabularnewline
70 & 5.6 & 5.72998991741846 & -0.129989917418465 \tabularnewline
71 & 5.41 & 5.60001008246118 & -0.190010082461181 \tabularnewline
72 & 5.13 & 5.41001473782982 & -0.280014737829815 \tabularnewline
73 & 5 & 5.13002171889775 & -0.130021718897747 \tabularnewline
74 & 5.04 & 5.00001008492781 & 0.0399899150721872 \tabularnewline
75 & 5.1 & 5.03999689824585 & 0.0600031017541536 \tabularnewline
76 & 4.96 & 5.09999534595485 & -0.139995345954853 \tabularnewline
77 & 4.9 & 4.96001085851633 & -0.060010858516331 \tabularnewline
78 & 4.8 & 4.90000465464679 & -0.100004654646788 \tabularnewline
79 & 4.48 & 4.80000775670197 & -0.320007756701969 \tabularnewline
80 & 4.29 & 4.48002482089264 & -0.190024820892643 \tabularnewline
81 & 4.27 & 4.29001473897298 & -0.0200147389729786 \tabularnewline
82 & 4.18 & 4.27000155241139 & -0.0900015524113931 \tabularnewline
83 & 4.02 & 4.18000698082726 & -0.160006980827256 \tabularnewline
84 & 3.82 & 4.02001241068696 & -0.20001241068696 \tabularnewline
85 & 4.13 & 3.82001551364449 & 0.309984486355506 \tabularnewline
86 & 4.16 & 4.12997595654638 & 0.0300240434536212 \tabularnewline
87 & 3.98 & 4.15999767123283 & -0.179997671232826 \tabularnewline
88 & 4.26 & 3.98001396123306 & 0.279986038766936 \tabularnewline
89 & 4.7 & 4.25997828332825 & 0.44002171667175 \tabularnewline
90 & 4.96 & 4.69996587041545 & 0.260034129584552 \tabularnewline
91 & 5.13 & 4.95997983086635 & 0.170020169133649 \tabularnewline
92 & 5.35 & 5.12998681265602 & 0.220013187343984 \tabularnewline
93 & 5.41 & 5.34998293502708 & 0.0600170649729224 \tabularnewline
94 & 5.42 & 5.40999534487182 & 0.0100046551281805 \tabularnewline
95 & 5.51 & 5.41999922400484 & 0.0900007759951613 \tabularnewline
96 & 5.75 & 5.50999301923297 & 0.240006980767035 \tabularnewline
97 & 5.67 & 5.74998138424029 & -0.079981384240293 \tabularnewline
98 & 5.46 & 5.67000620362885 & -0.21000620362885 \tabularnewline
99 & 5.56 & 5.46001628879715 & 0.0999837112028521 \tabularnewline
100 & 5.56 & 5.55999224492247 & 7.75507752504012e-06 \tabularnewline
101 & 5.54 & 5.55999999939849 & -0.0199999993984896 \tabularnewline
102 & 5.53 & 5.54000155126814 & -0.0100015512681413 \tabularnewline
103 & 5.65 & 5.53000077575442 & 0.119999224245585 \tabularnewline
104 & 5.58 & 5.64999069245104 & -0.0699906924510429 \tabularnewline
105 & 5.57 & 5.58000542871673 & -0.0100054287167319 \tabularnewline
106 & 5.36 & 5.57000077605516 & -0.210000776055164 \tabularnewline
107 & 5.23 & 5.36001628837617 & -0.130016288376166 \tabularnewline
108 & 5.11 & 5.2300100845066 & -0.120010084506603 \tabularnewline
109 & 5.07 & 5.11000930839132 & -0.0400093083913164 \tabularnewline
110 & 5.04 & 5.07000310325837 & -0.030003103258367 \tabularnewline
111 & 5.34 & 5.04000232714298 & 0.299997672857018 \tabularnewline
112 & 5.43 & 5.33997673115768 & 0.0900232688423168 \tabularnewline
113 & 5.31 & 5.42999301748834 & -0.119993017488344 \tabularnewline
114 & 5.12 & 5.31000930706754 & -0.190009307067539 \tabularnewline
115 & 4.97 & 5.12001473776967 & -0.150014737769673 \tabularnewline
116 & 5 & 4.97001163565452 & 0.0299883643454795 \tabularnewline
117 & 4.64 & 4.99999767400022 & -0.359997674000219 \tabularnewline
118 & 4.8 & 4.64002792264697 & 0.15997207735303 \tabularnewline
119 & 5.1 & 4.79998759202027 & 0.300012407979727 \tabularnewline
120 & 5.11 & 5.09997673001478 & 0.0100232699852238 \tabularnewline
121 & 5.12 & 5.10999922256101 & 0.010000777438993 \tabularnewline
122 & 5.36 & 5.11999922430561 & 0.240000775694395 \tabularnewline
123 & 5.26 & 5.35998138472158 & -0.0999813847215805 \tabularnewline
124 & 5.27 & 5.26000775489707 & 0.00999224510292507 \tabularnewline
125 & 5.1 & 5.2699992249674 & -0.169999224967402 \tabularnewline
126 & 4.94 & 5.10001318571948 & -0.160013185719482 \tabularnewline
127 & 4.68 & 4.94001241116823 & -0.260012411168233 \tabularnewline
128 & 4.41 & 4.68002016744909 & -0.270020167449094 \tabularnewline
129 & 4.6 & 4.41002094368479 & 0.189979056315207 \tabularnewline
130 & 4.53 & 4.59998526457668 & -0.0699852645766779 \tabularnewline
131 & 4.18 & 4.53000542829573 & -0.350005428295728 \tabularnewline
132 & 4 & 4.18002714761433 & -0.180027147614325 \tabularnewline
133 & 3.87 & 4.00001396351935 & -0.130013963519352 \tabularnewline
134 & 4.09 & 3.87001008432628 & 0.21998991567372 \tabularnewline
135 & 4.13 & 4.08998293683211 & 0.040017063167892 \tabularnewline
136 & 3.74 & 4.12999689614015 & -0.389996896140146 \tabularnewline
137 & 3.81 & 3.74003024948892 & 0.0699697505110821 \tabularnewline
138 & 4.11 & 3.8099945729076 & 0.300005427092404 \tabularnewline
139 & 4.14 & 4.10997673055624 & 0.0300232694437614 \tabularnewline
140 & 3.99 & 4.13999767129286 & -0.14999767129286 \tabularnewline
141 & 4.28 & 3.99001163433079 & 0.289988365669213 \tabularnewline
142 & 4.37 & 4.27997750751367 & 0.0900224924863258 \tabularnewline
143 & 4.24 & 4.36999301754856 & -0.129993017548561 \tabularnewline
144 & 4.19 & 4.24001008270164 & -0.0500100827016388 \tabularnewline
145 & 4.01 & 4.19000387895252 & -0.180003878952519 \tabularnewline
146 & 3.95 & 4.01001396171456 & -0.0600139617145556 \tabularnewline
147 & 4.3 & 3.95000465488748 & 0.349995345112518 \tabularnewline
148 & 4.37 & 4.29997285316776 & 0.0700271468322393 \tabularnewline
149 & 4.4 & 4.36999456845574 & 0.0300054315442591 \tabularnewline
150 & 4.29 & 4.39999767267643 & -0.109997672676429 \tabularnewline
151 & 4.12 & 4.29000853179452 & -0.170008531794518 \tabularnewline
152 & 4.07 & 4.12001318644135 & -0.050013186441352 \tabularnewline
153 & 3.93 & 4.07000387919326 & -0.140003879193256 \tabularnewline
154 & 3.79 & 3.9300108591782 & -0.140010859178199 \tabularnewline
155 & 3.67 & 3.79001085971959 & -0.12001085971959 \tabularnewline
156 & 3.53 & 3.67000930845144 & -0.140009308451444 \tabularnewline
157 & 3.69 & 3.53001085959931 & 0.15998914040069 \tabularnewline
158 & 3.69 & 3.6899875906968 & 1.24093031956818e-05 \tabularnewline
159 & 3.48 & 3.68999999903749 & -0.209999999037492 \tabularnewline
160 & 3.31 & 3.4800162883159 & -0.170016288315898 \tabularnewline
161 & 3.16 & 3.31001318704297 & -0.150013187042974 \tabularnewline
162 & 3.25 & 3.16001163553424 & 0.0899883644657589 \tabularnewline
163 & 3.14 & 3.24999302019565 & -0.109993020195646 \tabularnewline
164 & 3.19 & 3.14000853143366 & 0.0499914685663438 \tabularnewline
165 & 3.43 & 3.18999612249126 & 0.240003877508743 \tabularnewline
166 & 3.45 & 3.42998138448099 & 0.0200186155190076 \tabularnewline
167 & 3.31 & 3.44999844728793 & -0.139998447287929 \tabularnewline
168 & 3.51 & 3.31001085875688 & 0.199989141243118 \tabularnewline
169 & 3.53 & 3.50998448816036 & 0.0200155118396368 \tabularnewline
170 & 3.83 & 3.52999844752866 & 0.300001552471339 \tabularnewline
171 & 4.02 & 3.82997673085677 & 0.190023269143233 \tabularnewline
172 & 3.99 & 4.01998526114738 & -0.0299852611473801 \tabularnewline
173 & 4.11 & 3.99000232575909 & 0.119997674240914 \tabularnewline
174 & 3.96 & 4.10999069257127 & -0.149990692571267 \tabularnewline
175 & 3.83 & 3.96001163378949 & -0.130011633789493 \tabularnewline
176 & 3.71 & 3.83001008414558 & -0.120010084145578 \tabularnewline
177 & 3.81 & 3.71000930839129 & 0.0999906916087121 \tabularnewline
178 & 3.73 & 3.80999224438105 & -0.0799922443810512 \tabularnewline
179 & 3.99 & 3.7300062044712 & 0.259993795528801 \tabularnewline
180 & 4.17 & 3.9899798339948 & 0.180020166005202 \tabularnewline
181 & 4 & 4.16998603702216 & -0.169986037022165 \tabularnewline
182 & 4.1 & 4.00001318469658 & 0.0999868153034189 \tabularnewline
183 & 4.24 & 4.09999224468171 & 0.14000775531829 \tabularnewline
184 & 4.45 & 4.23998914052116 & 0.210010859478844 \tabularnewline
185 & 4.62 & 4.44998371084173 & 0.170016289158271 \tabularnewline
186 & 4.49 & 4.61998681295696 & -0.12998681295696 \tabularnewline
187 & 4.45 & 4.49001008222039 & -0.0400100822203893 \tabularnewline
188 & 4.49 & 4.45000310331839 & 0.0399968966816129 \tabularnewline
189 & 4.36 & 4.48999689770433 & -0.129996897704328 \tabularnewline
190 & 4.32 & 4.3600100830026 & -0.0400100830025965 \tabularnewline
191 & 4.45 & 4.32000310331845 & 0.129996896681552 \tabularnewline
192 & 4.13 & 4.44998991699748 & -0.319989916997483 \tabularnewline
193 & 4.14 & 4.13002481950893 & 0.00997518049106549 \tabularnewline
194 & 4.3 & 4.13999922629099 & 0.160000773709008 \tabularnewline
195 & 4.42 & 4.29998758979449 & 0.120012410205515 \tabularnewline
196 & 4.67 & 4.41999069142829 & 0.250009308571705 \tabularnewline
197 & 4.96 & 4.66998060842565 & 0.290019391574353 \tabularnewline
198 & 4.73 & 4.9599775051072 & -0.229977505107199 \tabularnewline
199 & 4.52 & 4.73001783783938 & -0.210017837839381 \tabularnewline
200 & 4.36 & 4.52001628969954 & -0.160016289699536 \tabularnewline
201 & 4.15 & 4.36001241140899 & -0.210012411408988 \tabularnewline
202 & 3.92 & 4.15001628927864 & -0.230016289278645 \tabularnewline
203 & 3.88 & 3.92001784084761 & -0.0400178408476126 \tabularnewline
204 & 4.2 & 3.88000310392017 & 0.319996896079827 \tabularnewline
205 & 3.95 & 4.19997517994974 & -0.249975179949744 \tabularnewline
206 & 3.78 & 3.95001938892722 & -0.170019388927221 \tabularnewline
207 & 3.69 & 3.78001318728347 & -0.0900131872834682 \tabularnewline
208 & 3.77 & 3.6900069817297 & 0.0799930182703039 \tabularnewline
209 & 3.66 & 3.76999379546878 & -0.109993795468775 \tabularnewline
210 & 3.53 & 3.66000853149379 & -0.130008531493789 \tabularnewline
211 & 3.5 & 3.53001008390495 & -0.0300100839049526 \tabularnewline
212 & 3.14 & 3.50000232768442 & -0.360002327684424 \tabularnewline
213 & 3.42 & 3.14002792300793 & 0.279972076992075 \tabularnewline
214 & 3.3 & 3.41997828441117 & -0.119978284411173 \tabularnewline
215 & 2.81 & 3.30000930592479 & -0.490009305924792 \tabularnewline
216 & 3.15 & 2.8100380067924 & 0.339961993207597 \tabularnewline
217 & 3.37 & 3.14997363138874 & 0.220026368611258 \tabularnewline
218 & 4.05 & 3.36998293400469 & 0.680017065995306 \tabularnewline
219 & 4 & 4.04994725555791 & -0.0499472555579148 \tabularnewline
220 & 4.2 & 4.00000387407943 & 0.19999612592057 \tabularnewline
221 & 4.21 & 4.19998448761861 & 0.0100155123813916 \tabularnewline
222 & 4.24 & 4.20999922316271 & 0.0300007768372872 \tabularnewline
223 & 4.24 & 4.23999767303746 & 2.3269625355482e-06 \tabularnewline
224 & 4.17 & 4.23999999981951 & -0.0699999998195135 \tabularnewline
225 & 4.12 & 4.17000542943864 & -0.0500054294386434 \tabularnewline
226 & 4.35 & 4.1200038785916 & 0.229996121408404 \tabularnewline
227 & 3.98 & 4.34998216071668 & -0.369982160716675 \tabularnewline
228 & 3.62 & 3.9800286970778 & -0.3600286970778 \tabularnewline
229 & 4.39 & 3.62002792505323 & 0.769972074946774 \tabularnewline
230 & 5.01 & 4.38994027834073 & 0.620059721659271 \tabularnewline
231 & 4.07 & 5.00995190605396 & -0.93995190605396 \tabularnewline
232 & 3.7 & 4.0700729058745 & -0.3700729058745 \tabularnewline
233 & 3.59 & 3.7000287041163 & -0.110028704116305 \tabularnewline
234 & 3.44 & 3.59000853420142 & -0.150008534201422 \tabularnewline
235 & 3.33 & 3.44001163517335 & -0.110011635173351 \tabularnewline
236 & 2.98 & 3.3300085328775 & -0.350008532877497 \tabularnewline
237 & 3.14 & 2.98002714785513 & 0.159972852144873 \tabularnewline
238 & 2.55 & 3.13998759196018 & -0.589987591960178 \tabularnewline
239 & 2.49 & 2.55004576144913 & -0.0600457614491323 \tabularnewline
240 & 2.53 & 2.49000465735398 & 0.039995342646022 \tabularnewline
241 & 2.43 & 2.52999689782486 & -0.0999968978248642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191800&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]8.89[/C][C]8.64[/C][C]0.25[/C][/ROW]
[ROW][C]3[/C][C]8.87[/C][C]8.88998060914765[/C][C]-0.0199806091476535[/C][/ROW]
[ROW][C]4[/C][C]8.81[/C][C]8.87000154976417[/C][C]-0.0600015497641664[/C][/ROW]
[ROW][C]5[/C][C]8.87[/C][C]8.81000465392477[/C][C]0.0599953460752296[/C][/ROW]
[ROW][C]6[/C][C]9.06[/C][C]8.86999534655641[/C][C]0.190004653443591[/C][/ROW]
[ROW][C]7[/C][C]9.12[/C][C]9.05998526259128[/C][C]0.0600147374087214[/C][/ROW]
[ROW][C]8[/C][C]8.66[/C][C]9.11999534505235[/C][C]-0.459995345052352[/C][/ROW]
[ROW][C]9[/C][C]8.17[/C][C]8.66003567880727[/C][C]-0.490035678807269[/C][/ROW]
[ROW][C]10[/C][C]8.04[/C][C]8.17003800883797[/C][C]-0.130038008837975[/C][/ROW]
[ROW][C]11[/C][C]7.71[/C][C]8.04001008619132[/C][C]-0.330010086191316[/C][/ROW]
[ROW][C]12[/C][C]7.55[/C][C]7.71002559670742[/C][C]-0.16002559670742[/C][/ROW]
[ROW][C]13[/C][C]7.52[/C][C]7.55001241213087[/C][C]-0.0300124121308709[/C][/ROW]
[ROW][C]14[/C][C]7.38[/C][C]7.52000232786501[/C][C]-0.140002327865009[/C][/ROW]
[ROW][C]15[/C][C]7.52[/C][C]7.38001085905787[/C][C]0.139989140942127[/C][/ROW]
[ROW][C]16[/C][C]7.31[/C][C]7.51998914196495[/C][C]-0.20998914196495[/C][/ROW]
[ROW][C]17[/C][C]6.92[/C][C]7.31001628747379[/C][C]-0.390016287473786[/C][/ROW]
[ROW][C]18[/C][C]7.09[/C][C]6.92003025099298[/C][C]0.169969749007024[/C][/ROW]
[ROW][C]19[/C][C]7.05[/C][C]7.08998681656677[/C][C]-0.0399868165667732[/C][/ROW]
[ROW][C]20[/C][C]7.37[/C][C]7.05000310151382[/C][C]0.319996898486177[/C][/ROW]
[ROW][C]21[/C][C]7.05[/C][C]7.36997517994956[/C][C]-0.319975179949558[/C][/ROW]
[ROW][C]22[/C][C]6.79[/C][C]7.05002481836588[/C][C]-0.260024818365879[/C][/ROW]
[ROW][C]23[/C][C]6.35[/C][C]6.79002016841144[/C][C]-0.44002016841144[/C][/ROW]
[ROW][C]24[/C][C]6.44[/C][C]6.35003412946446[/C][C]0.0899658705355364[/C][/ROW]
[ROW][C]25[/C][C]6.89[/C][C]6.43999302194035[/C][C]0.450006978059647[/C][/ROW]
[ROW][C]26[/C][C]7.16[/C][C]6.88996509592453[/C][C]0.27003490407547[/C][/ROW]
[ROW][C]27[/C][C]7.46[/C][C]7.15997905517218[/C][C]0.300020944827815[/C][/ROW]
[ROW][C]28[/C][C]7.91[/C][C]7.45997672935263[/C][C]0.450023270647371[/C][/ROW]
[ROW][C]29[/C][C]7.86[/C][C]7.90996509466082[/C][C]-0.0499650946608217[/C][/ROW]
[ROW][C]30[/C][C]8.02[/C][C]7.86000387546309[/C][C]0.159996124536907[/C][/ROW]
[ROW][C]31[/C][C]8.38[/C][C]8.01998759015509[/C][C]0.360012409844909[/C][/ROW]
[ROW][C]32[/C][C]8.5[/C][C]8.37997207621007[/C][C]0.120027923789932[/C][/ROW]
[ROW][C]33[/C][C]8.4[/C][C]8.49999069022501[/C][C]-0.0999906902250078[/C][/ROW]
[ROW][C]34[/C][C]8.24[/C][C]8.40000775561884[/C][C]-0.160007755618842[/C][/ROW]
[ROW][C]35[/C][C]8.33[/C][C]8.24001241074706[/C][C]0.089987589252944[/C][/ROW]
[ROW][C]36[/C][C]8.28[/C][C]8.32999302025577[/C][C]-0.0499930202557746[/C][/ROW]
[ROW][C]37[/C][C]8.15[/C][C]8.2800038776291[/C][C]-0.130003877629097[/C][/ROW]
[ROW][C]38[/C][C]8.06[/C][C]8.15001008354398[/C][C]-0.0900100835439837[/C][/ROW]
[ROW][C]39[/C][C]7.79[/C][C]8.06000698148896[/C][C]-0.270006981488961[/C][/ROW]
[ROW][C]40[/C][C]7.28[/C][C]7.79002094266204[/C][C]-0.510020942662044[/C][/ROW]
[ROW][C]41[/C][C]7.52[/C][C]7.28003955896318[/C][C]0.239960441036824[/C][/ROW]
[ROW][C]42[/C][C]7.23[/C][C]7.51998138785007[/C][C]-0.289981387850072[/C][/ROW]
[ROW][C]43[/C][C]7.13[/C][C]7.2300224919451[/C][C]-0.100022491945103[/C][/ROW]
[ROW][C]44[/C][C]7.21[/C][C]7.13000775808549[/C][C]0.0799922419145087[/C][/ROW]
[ROW][C]45[/C][C]6.99[/C][C]7.20999379552899[/C][C]-0.219993795528992[/C][/ROW]
[ROW][C]46[/C][C]6.77[/C][C]6.99001706346883[/C][C]-0.220017063468828[/C][/ROW]
[ROW][C]47[/C][C]6.69[/C][C]6.77001706527357[/C][C]-0.0800170652735668[/C][/ROW]
[ROW][C]48[/C][C]6.39[/C][C]6.69000620639639[/C][C]-0.300006206396393[/C][/ROW]
[ROW][C]49[/C][C]6.85[/C][C]6.39002326950421[/C][C]0.459976730495792[/C][/ROW]
[ROW][C]50[/C][C]6.74[/C][C]6.84996432263654[/C][C]-0.10996432263654[/C][/ROW]
[ROW][C]51[/C][C]6.56[/C][C]6.74000852920778[/C][C]-0.180008529207776[/C][/ROW]
[ROW][C]52[/C][C]6.62[/C][C]6.56001396207524[/C][C]0.0599860379247552[/C][/ROW]
[ROW][C]53[/C][C]6.71[/C][C]6.61999534727838[/C][C]0.0900046527216176[/C][/ROW]
[ROW][C]54[/C][C]6.67[/C][C]6.70999301893227[/C][C]-0.0399930189322735[/C][/ROW]
[ROW][C]55[/C][C]6.54[/C][C]6.6700031019949[/C][C]-0.1300031019949[/C][/ROW]
[ROW][C]56[/C][C]6.14[/C][C]6.54001008348382[/C][C]-0.400010083483822[/C][/ROW]
[ROW][C]57[/C][C]6.13[/C][C]6.14003102614587[/C][C]-0.0100310261458674[/C][/ROW]
[ROW][C]58[/C][C]5.86[/C][C]6.13000077804059[/C][C]-0.270000778040587[/C][/ROW]
[ROW][C]59[/C][C]5.88[/C][C]5.86002094218088[/C][C]0.0199790578191159[/C][/ROW]
[ROW][C]60[/C][C]5.75[/C][C]5.87999845035616[/C][C]-0.129998450356159[/C][/ROW]
[ROW][C]61[/C][C]5.53[/C][C]5.75001008312303[/C][C]-0.220010083123025[/C][/ROW]
[ROW][C]62[/C][C]5.86[/C][C]5.53001706473215[/C][C]0.329982935267852[/C][/ROW]
[ROW][C]63[/C][C]5.9[/C][C]5.8599744053985[/C][C]0.0400255946015013[/C][/ROW]
[ROW][C]64[/C][C]5.95[/C][C]5.89999689547842[/C][C]0.0500031045215801[/C][/ROW]
[ROW][C]65[/C][C]5.69[/C][C]5.94999612158873[/C][C]-0.259996121588733[/C][/ROW]
[ROW][C]66[/C][C]5.53[/C][C]5.69002016618562[/C][C]-0.16002016618562[/C][/ROW]
[ROW][C]67[/C][C]5.71[/C][C]5.53001241170966[/C][C]0.179987588290339[/C][/ROW]
[ROW][C]68[/C][C]5.6[/C][C]5.709986039549[/C][C]-0.109986039549004[/C][/ROW]
[ROW][C]69[/C][C]5.73[/C][C]5.60000853089221[/C][C]0.129991469107788[/C][/ROW]
[ROW][C]70[/C][C]5.6[/C][C]5.72998991741846[/C][C]-0.129989917418465[/C][/ROW]
[ROW][C]71[/C][C]5.41[/C][C]5.60001008246118[/C][C]-0.190010082461181[/C][/ROW]
[ROW][C]72[/C][C]5.13[/C][C]5.41001473782982[/C][C]-0.280014737829815[/C][/ROW]
[ROW][C]73[/C][C]5[/C][C]5.13002171889775[/C][C]-0.130021718897747[/C][/ROW]
[ROW][C]74[/C][C]5.04[/C][C]5.00001008492781[/C][C]0.0399899150721872[/C][/ROW]
[ROW][C]75[/C][C]5.1[/C][C]5.03999689824585[/C][C]0.0600031017541536[/C][/ROW]
[ROW][C]76[/C][C]4.96[/C][C]5.09999534595485[/C][C]-0.139995345954853[/C][/ROW]
[ROW][C]77[/C][C]4.9[/C][C]4.96001085851633[/C][C]-0.060010858516331[/C][/ROW]
[ROW][C]78[/C][C]4.8[/C][C]4.90000465464679[/C][C]-0.100004654646788[/C][/ROW]
[ROW][C]79[/C][C]4.48[/C][C]4.80000775670197[/C][C]-0.320007756701969[/C][/ROW]
[ROW][C]80[/C][C]4.29[/C][C]4.48002482089264[/C][C]-0.190024820892643[/C][/ROW]
[ROW][C]81[/C][C]4.27[/C][C]4.29001473897298[/C][C]-0.0200147389729786[/C][/ROW]
[ROW][C]82[/C][C]4.18[/C][C]4.27000155241139[/C][C]-0.0900015524113931[/C][/ROW]
[ROW][C]83[/C][C]4.02[/C][C]4.18000698082726[/C][C]-0.160006980827256[/C][/ROW]
[ROW][C]84[/C][C]3.82[/C][C]4.02001241068696[/C][C]-0.20001241068696[/C][/ROW]
[ROW][C]85[/C][C]4.13[/C][C]3.82001551364449[/C][C]0.309984486355506[/C][/ROW]
[ROW][C]86[/C][C]4.16[/C][C]4.12997595654638[/C][C]0.0300240434536212[/C][/ROW]
[ROW][C]87[/C][C]3.98[/C][C]4.15999767123283[/C][C]-0.179997671232826[/C][/ROW]
[ROW][C]88[/C][C]4.26[/C][C]3.98001396123306[/C][C]0.279986038766936[/C][/ROW]
[ROW][C]89[/C][C]4.7[/C][C]4.25997828332825[/C][C]0.44002171667175[/C][/ROW]
[ROW][C]90[/C][C]4.96[/C][C]4.69996587041545[/C][C]0.260034129584552[/C][/ROW]
[ROW][C]91[/C][C]5.13[/C][C]4.95997983086635[/C][C]0.170020169133649[/C][/ROW]
[ROW][C]92[/C][C]5.35[/C][C]5.12998681265602[/C][C]0.220013187343984[/C][/ROW]
[ROW][C]93[/C][C]5.41[/C][C]5.34998293502708[/C][C]0.0600170649729224[/C][/ROW]
[ROW][C]94[/C][C]5.42[/C][C]5.40999534487182[/C][C]0.0100046551281805[/C][/ROW]
[ROW][C]95[/C][C]5.51[/C][C]5.41999922400484[/C][C]0.0900007759951613[/C][/ROW]
[ROW][C]96[/C][C]5.75[/C][C]5.50999301923297[/C][C]0.240006980767035[/C][/ROW]
[ROW][C]97[/C][C]5.67[/C][C]5.74998138424029[/C][C]-0.079981384240293[/C][/ROW]
[ROW][C]98[/C][C]5.46[/C][C]5.67000620362885[/C][C]-0.21000620362885[/C][/ROW]
[ROW][C]99[/C][C]5.56[/C][C]5.46001628879715[/C][C]0.0999837112028521[/C][/ROW]
[ROW][C]100[/C][C]5.56[/C][C]5.55999224492247[/C][C]7.75507752504012e-06[/C][/ROW]
[ROW][C]101[/C][C]5.54[/C][C]5.55999999939849[/C][C]-0.0199999993984896[/C][/ROW]
[ROW][C]102[/C][C]5.53[/C][C]5.54000155126814[/C][C]-0.0100015512681413[/C][/ROW]
[ROW][C]103[/C][C]5.65[/C][C]5.53000077575442[/C][C]0.119999224245585[/C][/ROW]
[ROW][C]104[/C][C]5.58[/C][C]5.64999069245104[/C][C]-0.0699906924510429[/C][/ROW]
[ROW][C]105[/C][C]5.57[/C][C]5.58000542871673[/C][C]-0.0100054287167319[/C][/ROW]
[ROW][C]106[/C][C]5.36[/C][C]5.57000077605516[/C][C]-0.210000776055164[/C][/ROW]
[ROW][C]107[/C][C]5.23[/C][C]5.36001628837617[/C][C]-0.130016288376166[/C][/ROW]
[ROW][C]108[/C][C]5.11[/C][C]5.2300100845066[/C][C]-0.120010084506603[/C][/ROW]
[ROW][C]109[/C][C]5.07[/C][C]5.11000930839132[/C][C]-0.0400093083913164[/C][/ROW]
[ROW][C]110[/C][C]5.04[/C][C]5.07000310325837[/C][C]-0.030003103258367[/C][/ROW]
[ROW][C]111[/C][C]5.34[/C][C]5.04000232714298[/C][C]0.299997672857018[/C][/ROW]
[ROW][C]112[/C][C]5.43[/C][C]5.33997673115768[/C][C]0.0900232688423168[/C][/ROW]
[ROW][C]113[/C][C]5.31[/C][C]5.42999301748834[/C][C]-0.119993017488344[/C][/ROW]
[ROW][C]114[/C][C]5.12[/C][C]5.31000930706754[/C][C]-0.190009307067539[/C][/ROW]
[ROW][C]115[/C][C]4.97[/C][C]5.12001473776967[/C][C]-0.150014737769673[/C][/ROW]
[ROW][C]116[/C][C]5[/C][C]4.97001163565452[/C][C]0.0299883643454795[/C][/ROW]
[ROW][C]117[/C][C]4.64[/C][C]4.99999767400022[/C][C]-0.359997674000219[/C][/ROW]
[ROW][C]118[/C][C]4.8[/C][C]4.64002792264697[/C][C]0.15997207735303[/C][/ROW]
[ROW][C]119[/C][C]5.1[/C][C]4.79998759202027[/C][C]0.300012407979727[/C][/ROW]
[ROW][C]120[/C][C]5.11[/C][C]5.09997673001478[/C][C]0.0100232699852238[/C][/ROW]
[ROW][C]121[/C][C]5.12[/C][C]5.10999922256101[/C][C]0.010000777438993[/C][/ROW]
[ROW][C]122[/C][C]5.36[/C][C]5.11999922430561[/C][C]0.240000775694395[/C][/ROW]
[ROW][C]123[/C][C]5.26[/C][C]5.35998138472158[/C][C]-0.0999813847215805[/C][/ROW]
[ROW][C]124[/C][C]5.27[/C][C]5.26000775489707[/C][C]0.00999224510292507[/C][/ROW]
[ROW][C]125[/C][C]5.1[/C][C]5.2699992249674[/C][C]-0.169999224967402[/C][/ROW]
[ROW][C]126[/C][C]4.94[/C][C]5.10001318571948[/C][C]-0.160013185719482[/C][/ROW]
[ROW][C]127[/C][C]4.68[/C][C]4.94001241116823[/C][C]-0.260012411168233[/C][/ROW]
[ROW][C]128[/C][C]4.41[/C][C]4.68002016744909[/C][C]-0.270020167449094[/C][/ROW]
[ROW][C]129[/C][C]4.6[/C][C]4.41002094368479[/C][C]0.189979056315207[/C][/ROW]
[ROW][C]130[/C][C]4.53[/C][C]4.59998526457668[/C][C]-0.0699852645766779[/C][/ROW]
[ROW][C]131[/C][C]4.18[/C][C]4.53000542829573[/C][C]-0.350005428295728[/C][/ROW]
[ROW][C]132[/C][C]4[/C][C]4.18002714761433[/C][C]-0.180027147614325[/C][/ROW]
[ROW][C]133[/C][C]3.87[/C][C]4.00001396351935[/C][C]-0.130013963519352[/C][/ROW]
[ROW][C]134[/C][C]4.09[/C][C]3.87001008432628[/C][C]0.21998991567372[/C][/ROW]
[ROW][C]135[/C][C]4.13[/C][C]4.08998293683211[/C][C]0.040017063167892[/C][/ROW]
[ROW][C]136[/C][C]3.74[/C][C]4.12999689614015[/C][C]-0.389996896140146[/C][/ROW]
[ROW][C]137[/C][C]3.81[/C][C]3.74003024948892[/C][C]0.0699697505110821[/C][/ROW]
[ROW][C]138[/C][C]4.11[/C][C]3.8099945729076[/C][C]0.300005427092404[/C][/ROW]
[ROW][C]139[/C][C]4.14[/C][C]4.10997673055624[/C][C]0.0300232694437614[/C][/ROW]
[ROW][C]140[/C][C]3.99[/C][C]4.13999767129286[/C][C]-0.14999767129286[/C][/ROW]
[ROW][C]141[/C][C]4.28[/C][C]3.99001163433079[/C][C]0.289988365669213[/C][/ROW]
[ROW][C]142[/C][C]4.37[/C][C]4.27997750751367[/C][C]0.0900224924863258[/C][/ROW]
[ROW][C]143[/C][C]4.24[/C][C]4.36999301754856[/C][C]-0.129993017548561[/C][/ROW]
[ROW][C]144[/C][C]4.19[/C][C]4.24001008270164[/C][C]-0.0500100827016388[/C][/ROW]
[ROW][C]145[/C][C]4.01[/C][C]4.19000387895252[/C][C]-0.180003878952519[/C][/ROW]
[ROW][C]146[/C][C]3.95[/C][C]4.01001396171456[/C][C]-0.0600139617145556[/C][/ROW]
[ROW][C]147[/C][C]4.3[/C][C]3.95000465488748[/C][C]0.349995345112518[/C][/ROW]
[ROW][C]148[/C][C]4.37[/C][C]4.29997285316776[/C][C]0.0700271468322393[/C][/ROW]
[ROW][C]149[/C][C]4.4[/C][C]4.36999456845574[/C][C]0.0300054315442591[/C][/ROW]
[ROW][C]150[/C][C]4.29[/C][C]4.39999767267643[/C][C]-0.109997672676429[/C][/ROW]
[ROW][C]151[/C][C]4.12[/C][C]4.29000853179452[/C][C]-0.170008531794518[/C][/ROW]
[ROW][C]152[/C][C]4.07[/C][C]4.12001318644135[/C][C]-0.050013186441352[/C][/ROW]
[ROW][C]153[/C][C]3.93[/C][C]4.07000387919326[/C][C]-0.140003879193256[/C][/ROW]
[ROW][C]154[/C][C]3.79[/C][C]3.9300108591782[/C][C]-0.140010859178199[/C][/ROW]
[ROW][C]155[/C][C]3.67[/C][C]3.79001085971959[/C][C]-0.12001085971959[/C][/ROW]
[ROW][C]156[/C][C]3.53[/C][C]3.67000930845144[/C][C]-0.140009308451444[/C][/ROW]
[ROW][C]157[/C][C]3.69[/C][C]3.53001085959931[/C][C]0.15998914040069[/C][/ROW]
[ROW][C]158[/C][C]3.69[/C][C]3.6899875906968[/C][C]1.24093031956818e-05[/C][/ROW]
[ROW][C]159[/C][C]3.48[/C][C]3.68999999903749[/C][C]-0.209999999037492[/C][/ROW]
[ROW][C]160[/C][C]3.31[/C][C]3.4800162883159[/C][C]-0.170016288315898[/C][/ROW]
[ROW][C]161[/C][C]3.16[/C][C]3.31001318704297[/C][C]-0.150013187042974[/C][/ROW]
[ROW][C]162[/C][C]3.25[/C][C]3.16001163553424[/C][C]0.0899883644657589[/C][/ROW]
[ROW][C]163[/C][C]3.14[/C][C]3.24999302019565[/C][C]-0.109993020195646[/C][/ROW]
[ROW][C]164[/C][C]3.19[/C][C]3.14000853143366[/C][C]0.0499914685663438[/C][/ROW]
[ROW][C]165[/C][C]3.43[/C][C]3.18999612249126[/C][C]0.240003877508743[/C][/ROW]
[ROW][C]166[/C][C]3.45[/C][C]3.42998138448099[/C][C]0.0200186155190076[/C][/ROW]
[ROW][C]167[/C][C]3.31[/C][C]3.44999844728793[/C][C]-0.139998447287929[/C][/ROW]
[ROW][C]168[/C][C]3.51[/C][C]3.31001085875688[/C][C]0.199989141243118[/C][/ROW]
[ROW][C]169[/C][C]3.53[/C][C]3.50998448816036[/C][C]0.0200155118396368[/C][/ROW]
[ROW][C]170[/C][C]3.83[/C][C]3.52999844752866[/C][C]0.300001552471339[/C][/ROW]
[ROW][C]171[/C][C]4.02[/C][C]3.82997673085677[/C][C]0.190023269143233[/C][/ROW]
[ROW][C]172[/C][C]3.99[/C][C]4.01998526114738[/C][C]-0.0299852611473801[/C][/ROW]
[ROW][C]173[/C][C]4.11[/C][C]3.99000232575909[/C][C]0.119997674240914[/C][/ROW]
[ROW][C]174[/C][C]3.96[/C][C]4.10999069257127[/C][C]-0.149990692571267[/C][/ROW]
[ROW][C]175[/C][C]3.83[/C][C]3.96001163378949[/C][C]-0.130011633789493[/C][/ROW]
[ROW][C]176[/C][C]3.71[/C][C]3.83001008414558[/C][C]-0.120010084145578[/C][/ROW]
[ROW][C]177[/C][C]3.81[/C][C]3.71000930839129[/C][C]0.0999906916087121[/C][/ROW]
[ROW][C]178[/C][C]3.73[/C][C]3.80999224438105[/C][C]-0.0799922443810512[/C][/ROW]
[ROW][C]179[/C][C]3.99[/C][C]3.7300062044712[/C][C]0.259993795528801[/C][/ROW]
[ROW][C]180[/C][C]4.17[/C][C]3.9899798339948[/C][C]0.180020166005202[/C][/ROW]
[ROW][C]181[/C][C]4[/C][C]4.16998603702216[/C][C]-0.169986037022165[/C][/ROW]
[ROW][C]182[/C][C]4.1[/C][C]4.00001318469658[/C][C]0.0999868153034189[/C][/ROW]
[ROW][C]183[/C][C]4.24[/C][C]4.09999224468171[/C][C]0.14000775531829[/C][/ROW]
[ROW][C]184[/C][C]4.45[/C][C]4.23998914052116[/C][C]0.210010859478844[/C][/ROW]
[ROW][C]185[/C][C]4.62[/C][C]4.44998371084173[/C][C]0.170016289158271[/C][/ROW]
[ROW][C]186[/C][C]4.49[/C][C]4.61998681295696[/C][C]-0.12998681295696[/C][/ROW]
[ROW][C]187[/C][C]4.45[/C][C]4.49001008222039[/C][C]-0.0400100822203893[/C][/ROW]
[ROW][C]188[/C][C]4.49[/C][C]4.45000310331839[/C][C]0.0399968966816129[/C][/ROW]
[ROW][C]189[/C][C]4.36[/C][C]4.48999689770433[/C][C]-0.129996897704328[/C][/ROW]
[ROW][C]190[/C][C]4.32[/C][C]4.3600100830026[/C][C]-0.0400100830025965[/C][/ROW]
[ROW][C]191[/C][C]4.45[/C][C]4.32000310331845[/C][C]0.129996896681552[/C][/ROW]
[ROW][C]192[/C][C]4.13[/C][C]4.44998991699748[/C][C]-0.319989916997483[/C][/ROW]
[ROW][C]193[/C][C]4.14[/C][C]4.13002481950893[/C][C]0.00997518049106549[/C][/ROW]
[ROW][C]194[/C][C]4.3[/C][C]4.13999922629099[/C][C]0.160000773709008[/C][/ROW]
[ROW][C]195[/C][C]4.42[/C][C]4.29998758979449[/C][C]0.120012410205515[/C][/ROW]
[ROW][C]196[/C][C]4.67[/C][C]4.41999069142829[/C][C]0.250009308571705[/C][/ROW]
[ROW][C]197[/C][C]4.96[/C][C]4.66998060842565[/C][C]0.290019391574353[/C][/ROW]
[ROW][C]198[/C][C]4.73[/C][C]4.9599775051072[/C][C]-0.229977505107199[/C][/ROW]
[ROW][C]199[/C][C]4.52[/C][C]4.73001783783938[/C][C]-0.210017837839381[/C][/ROW]
[ROW][C]200[/C][C]4.36[/C][C]4.52001628969954[/C][C]-0.160016289699536[/C][/ROW]
[ROW][C]201[/C][C]4.15[/C][C]4.36001241140899[/C][C]-0.210012411408988[/C][/ROW]
[ROW][C]202[/C][C]3.92[/C][C]4.15001628927864[/C][C]-0.230016289278645[/C][/ROW]
[ROW][C]203[/C][C]3.88[/C][C]3.92001784084761[/C][C]-0.0400178408476126[/C][/ROW]
[ROW][C]204[/C][C]4.2[/C][C]3.88000310392017[/C][C]0.319996896079827[/C][/ROW]
[ROW][C]205[/C][C]3.95[/C][C]4.19997517994974[/C][C]-0.249975179949744[/C][/ROW]
[ROW][C]206[/C][C]3.78[/C][C]3.95001938892722[/C][C]-0.170019388927221[/C][/ROW]
[ROW][C]207[/C][C]3.69[/C][C]3.78001318728347[/C][C]-0.0900131872834682[/C][/ROW]
[ROW][C]208[/C][C]3.77[/C][C]3.6900069817297[/C][C]0.0799930182703039[/C][/ROW]
[ROW][C]209[/C][C]3.66[/C][C]3.76999379546878[/C][C]-0.109993795468775[/C][/ROW]
[ROW][C]210[/C][C]3.53[/C][C]3.66000853149379[/C][C]-0.130008531493789[/C][/ROW]
[ROW][C]211[/C][C]3.5[/C][C]3.53001008390495[/C][C]-0.0300100839049526[/C][/ROW]
[ROW][C]212[/C][C]3.14[/C][C]3.50000232768442[/C][C]-0.360002327684424[/C][/ROW]
[ROW][C]213[/C][C]3.42[/C][C]3.14002792300793[/C][C]0.279972076992075[/C][/ROW]
[ROW][C]214[/C][C]3.3[/C][C]3.41997828441117[/C][C]-0.119978284411173[/C][/ROW]
[ROW][C]215[/C][C]2.81[/C][C]3.30000930592479[/C][C]-0.490009305924792[/C][/ROW]
[ROW][C]216[/C][C]3.15[/C][C]2.8100380067924[/C][C]0.339961993207597[/C][/ROW]
[ROW][C]217[/C][C]3.37[/C][C]3.14997363138874[/C][C]0.220026368611258[/C][/ROW]
[ROW][C]218[/C][C]4.05[/C][C]3.36998293400469[/C][C]0.680017065995306[/C][/ROW]
[ROW][C]219[/C][C]4[/C][C]4.04994725555791[/C][C]-0.0499472555579148[/C][/ROW]
[ROW][C]220[/C][C]4.2[/C][C]4.00000387407943[/C][C]0.19999612592057[/C][/ROW]
[ROW][C]221[/C][C]4.21[/C][C]4.19998448761861[/C][C]0.0100155123813916[/C][/ROW]
[ROW][C]222[/C][C]4.24[/C][C]4.20999922316271[/C][C]0.0300007768372872[/C][/ROW]
[ROW][C]223[/C][C]4.24[/C][C]4.23999767303746[/C][C]2.3269625355482e-06[/C][/ROW]
[ROW][C]224[/C][C]4.17[/C][C]4.23999999981951[/C][C]-0.0699999998195135[/C][/ROW]
[ROW][C]225[/C][C]4.12[/C][C]4.17000542943864[/C][C]-0.0500054294386434[/C][/ROW]
[ROW][C]226[/C][C]4.35[/C][C]4.1200038785916[/C][C]0.229996121408404[/C][/ROW]
[ROW][C]227[/C][C]3.98[/C][C]4.34998216071668[/C][C]-0.369982160716675[/C][/ROW]
[ROW][C]228[/C][C]3.62[/C][C]3.9800286970778[/C][C]-0.3600286970778[/C][/ROW]
[ROW][C]229[/C][C]4.39[/C][C]3.62002792505323[/C][C]0.769972074946774[/C][/ROW]
[ROW][C]230[/C][C]5.01[/C][C]4.38994027834073[/C][C]0.620059721659271[/C][/ROW]
[ROW][C]231[/C][C]4.07[/C][C]5.00995190605396[/C][C]-0.93995190605396[/C][/ROW]
[ROW][C]232[/C][C]3.7[/C][C]4.0700729058745[/C][C]-0.3700729058745[/C][/ROW]
[ROW][C]233[/C][C]3.59[/C][C]3.7000287041163[/C][C]-0.110028704116305[/C][/ROW]
[ROW][C]234[/C][C]3.44[/C][C]3.59000853420142[/C][C]-0.150008534201422[/C][/ROW]
[ROW][C]235[/C][C]3.33[/C][C]3.44001163517335[/C][C]-0.110011635173351[/C][/ROW]
[ROW][C]236[/C][C]2.98[/C][C]3.3300085328775[/C][C]-0.350008532877497[/C][/ROW]
[ROW][C]237[/C][C]3.14[/C][C]2.98002714785513[/C][C]0.159972852144873[/C][/ROW]
[ROW][C]238[/C][C]2.55[/C][C]3.13998759196018[/C][C]-0.589987591960178[/C][/ROW]
[ROW][C]239[/C][C]2.49[/C][C]2.55004576144913[/C][C]-0.0600457614491323[/C][/ROW]
[ROW][C]240[/C][C]2.53[/C][C]2.49000465735398[/C][C]0.039995342646022[/C][/ROW]
[ROW][C]241[/C][C]2.43[/C][C]2.52999689782486[/C][C]-0.0999968978248642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191800&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191800&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	8.89	8.64	0.25
3	8.87	8.88998060914765	-0.0199806091476535
4	8.81	8.87000154976417	-0.0600015497641664
5	8.87	8.81000465392477	0.0599953460752296
6	9.06	8.86999534655641	0.190004653443591
7	9.12	9.05998526259128	0.0600147374087214
8	8.66	9.11999534505235	-0.459995345052352
9	8.17	8.66003567880727	-0.490035678807269
10	8.04	8.17003800883797	-0.130038008837975
11	7.71	8.04001008619132	-0.330010086191316
12	7.55	7.71002559670742	-0.16002559670742
13	7.52	7.55001241213087	-0.0300124121308709
14	7.38	7.52000232786501	-0.140002327865009
15	7.52	7.38001085905787	0.139989140942127
16	7.31	7.51998914196495	-0.20998914196495
17	6.92	7.31001628747379	-0.390016287473786
18	7.09	6.92003025099298	0.169969749007024
19	7.05	7.08998681656677	-0.0399868165667732
20	7.37	7.05000310151382	0.319996898486177
21	7.05	7.36997517994956	-0.319975179949558
22	6.79	7.05002481836588	-0.260024818365879
23	6.35	6.79002016841144	-0.44002016841144
24	6.44	6.35003412946446	0.0899658705355364
25	6.89	6.43999302194035	0.450006978059647
26	7.16	6.88996509592453	0.27003490407547
27	7.46	7.15997905517218	0.300020944827815
28	7.91	7.45997672935263	0.450023270647371
29	7.86	7.90996509466082	-0.0499650946608217
30	8.02	7.86000387546309	0.159996124536907
31	8.38	8.01998759015509	0.360012409844909
32	8.5	8.37997207621007	0.120027923789932
33	8.4	8.49999069022501	-0.0999906902250078
34	8.24	8.40000775561884	-0.160007755618842
35	8.33	8.24001241074706	0.089987589252944
36	8.28	8.32999302025577	-0.0499930202557746
37	8.15	8.2800038776291	-0.130003877629097
38	8.06	8.15001008354398	-0.0900100835439837
39	7.79	8.06000698148896	-0.270006981488961
40	7.28	7.79002094266204	-0.510020942662044
41	7.52	7.28003955896318	0.239960441036824
42	7.23	7.51998138785007	-0.289981387850072
43	7.13	7.2300224919451	-0.100022491945103
44	7.21	7.13000775808549	0.0799922419145087
45	6.99	7.20999379552899	-0.219993795528992
46	6.77	6.99001706346883	-0.220017063468828
47	6.69	6.77001706527357	-0.0800170652735668
48	6.39	6.69000620639639	-0.300006206396393
49	6.85	6.39002326950421	0.459976730495792
50	6.74	6.84996432263654	-0.10996432263654
51	6.56	6.74000852920778	-0.180008529207776
52	6.62	6.56001396207524	0.0599860379247552
53	6.71	6.61999534727838	0.0900046527216176
54	6.67	6.70999301893227	-0.0399930189322735
55	6.54	6.6700031019949	-0.1300031019949
56	6.14	6.54001008348382	-0.400010083483822
57	6.13	6.14003102614587	-0.0100310261458674
58	5.86	6.13000077804059	-0.270000778040587
59	5.88	5.86002094218088	0.0199790578191159
60	5.75	5.87999845035616	-0.129998450356159
61	5.53	5.75001008312303	-0.220010083123025
62	5.86	5.53001706473215	0.329982935267852
63	5.9	5.8599744053985	0.0400255946015013
64	5.95	5.89999689547842	0.0500031045215801
65	5.69	5.94999612158873	-0.259996121588733
66	5.53	5.69002016618562	-0.16002016618562
67	5.71	5.53001241170966	0.179987588290339
68	5.6	5.709986039549	-0.109986039549004
69	5.73	5.60000853089221	0.129991469107788
70	5.6	5.72998991741846	-0.129989917418465
71	5.41	5.60001008246118	-0.190010082461181
72	5.13	5.41001473782982	-0.280014737829815
73	5	5.13002171889775	-0.130021718897747
74	5.04	5.00001008492781	0.0399899150721872
75	5.1	5.03999689824585	0.0600031017541536
76	4.96	5.09999534595485	-0.139995345954853
77	4.9	4.96001085851633	-0.060010858516331
78	4.8	4.90000465464679	-0.100004654646788
79	4.48	4.80000775670197	-0.320007756701969
80	4.29	4.48002482089264	-0.190024820892643
81	4.27	4.29001473897298	-0.0200147389729786
82	4.18	4.27000155241139	-0.0900015524113931
83	4.02	4.18000698082726	-0.160006980827256
84	3.82	4.02001241068696	-0.20001241068696
85	4.13	3.82001551364449	0.309984486355506
86	4.16	4.12997595654638	0.0300240434536212
87	3.98	4.15999767123283	-0.179997671232826
88	4.26	3.98001396123306	0.279986038766936
89	4.7	4.25997828332825	0.44002171667175
90	4.96	4.69996587041545	0.260034129584552
91	5.13	4.95997983086635	0.170020169133649
92	5.35	5.12998681265602	0.220013187343984
93	5.41	5.34998293502708	0.0600170649729224
94	5.42	5.40999534487182	0.0100046551281805
95	5.51	5.41999922400484	0.0900007759951613
96	5.75	5.50999301923297	0.240006980767035
97	5.67	5.74998138424029	-0.079981384240293
98	5.46	5.67000620362885	-0.21000620362885
99	5.56	5.46001628879715	0.0999837112028521
100	5.56	5.55999224492247	7.75507752504012e-06
101	5.54	5.55999999939849	-0.0199999993984896
102	5.53	5.54000155126814	-0.0100015512681413
103	5.65	5.53000077575442	0.119999224245585
104	5.58	5.64999069245104	-0.0699906924510429
105	5.57	5.58000542871673	-0.0100054287167319
106	5.36	5.57000077605516	-0.210000776055164
107	5.23	5.36001628837617	-0.130016288376166
108	5.11	5.2300100845066	-0.120010084506603
109	5.07	5.11000930839132	-0.0400093083913164
110	5.04	5.07000310325837	-0.030003103258367
111	5.34	5.04000232714298	0.299997672857018
112	5.43	5.33997673115768	0.0900232688423168
113	5.31	5.42999301748834	-0.119993017488344
114	5.12	5.31000930706754	-0.190009307067539
115	4.97	5.12001473776967	-0.150014737769673
116	5	4.97001163565452	0.0299883643454795
117	4.64	4.99999767400022	-0.359997674000219
118	4.8	4.64002792264697	0.15997207735303
119	5.1	4.79998759202027	0.300012407979727
120	5.11	5.09997673001478	0.0100232699852238
121	5.12	5.10999922256101	0.010000777438993
122	5.36	5.11999922430561	0.240000775694395
123	5.26	5.35998138472158	-0.0999813847215805
124	5.27	5.26000775489707	0.00999224510292507
125	5.1	5.2699992249674	-0.169999224967402
126	4.94	5.10001318571948	-0.160013185719482
127	4.68	4.94001241116823	-0.260012411168233
128	4.41	4.68002016744909	-0.270020167449094
129	4.6	4.41002094368479	0.189979056315207
130	4.53	4.59998526457668	-0.0699852645766779
131	4.18	4.53000542829573	-0.350005428295728
132	4	4.18002714761433	-0.180027147614325
133	3.87	4.00001396351935	-0.130013963519352
134	4.09	3.87001008432628	0.21998991567372
135	4.13	4.08998293683211	0.040017063167892
136	3.74	4.12999689614015	-0.389996896140146
137	3.81	3.74003024948892	0.0699697505110821
138	4.11	3.8099945729076	0.300005427092404
139	4.14	4.10997673055624	0.0300232694437614
140	3.99	4.13999767129286	-0.14999767129286
141	4.28	3.99001163433079	0.289988365669213
142	4.37	4.27997750751367	0.0900224924863258
143	4.24	4.36999301754856	-0.129993017548561
144	4.19	4.24001008270164	-0.0500100827016388
145	4.01	4.19000387895252	-0.180003878952519
146	3.95	4.01001396171456	-0.0600139617145556
147	4.3	3.95000465488748	0.349995345112518
148	4.37	4.29997285316776	0.0700271468322393
149	4.4	4.36999456845574	0.0300054315442591
150	4.29	4.39999767267643	-0.109997672676429
151	4.12	4.29000853179452	-0.170008531794518
152	4.07	4.12001318644135	-0.050013186441352
153	3.93	4.07000387919326	-0.140003879193256
154	3.79	3.9300108591782	-0.140010859178199
155	3.67	3.79001085971959	-0.12001085971959
156	3.53	3.67000930845144	-0.140009308451444
157	3.69	3.53001085959931	0.15998914040069
158	3.69	3.6899875906968	1.24093031956818e-05
159	3.48	3.68999999903749	-0.209999999037492
160	3.31	3.4800162883159	-0.170016288315898
161	3.16	3.31001318704297	-0.150013187042974
162	3.25	3.16001163553424	0.0899883644657589
163	3.14	3.24999302019565	-0.109993020195646
164	3.19	3.14000853143366	0.0499914685663438
165	3.43	3.18999612249126	0.240003877508743
166	3.45	3.42998138448099	0.0200186155190076
167	3.31	3.44999844728793	-0.139998447287929
168	3.51	3.31001085875688	0.199989141243118
169	3.53	3.50998448816036	0.0200155118396368
170	3.83	3.52999844752866	0.300001552471339
171	4.02	3.82997673085677	0.190023269143233
172	3.99	4.01998526114738	-0.0299852611473801
173	4.11	3.99000232575909	0.119997674240914
174	3.96	4.10999069257127	-0.149990692571267
175	3.83	3.96001163378949	-0.130011633789493
176	3.71	3.83001008414558	-0.120010084145578
177	3.81	3.71000930839129	0.0999906916087121
178	3.73	3.80999224438105	-0.0799922443810512
179	3.99	3.7300062044712	0.259993795528801
180	4.17	3.9899798339948	0.180020166005202
181	4	4.16998603702216	-0.169986037022165
182	4.1	4.00001318469658	0.0999868153034189
183	4.24	4.09999224468171	0.14000775531829
184	4.45	4.23998914052116	0.210010859478844
185	4.62	4.44998371084173	0.170016289158271
186	4.49	4.61998681295696	-0.12998681295696
187	4.45	4.49001008222039	-0.0400100822203893
188	4.49	4.45000310331839	0.0399968966816129
189	4.36	4.48999689770433	-0.129996897704328
190	4.32	4.3600100830026	-0.0400100830025965
191	4.45	4.32000310331845	0.129996896681552
192	4.13	4.44998991699748	-0.319989916997483
193	4.14	4.13002481950893	0.00997518049106549
194	4.3	4.13999922629099	0.160000773709008
195	4.42	4.29998758979449	0.120012410205515
196	4.67	4.41999069142829	0.250009308571705
197	4.96	4.66998060842565	0.290019391574353
198	4.73	4.9599775051072	-0.229977505107199
199	4.52	4.73001783783938	-0.210017837839381
200	4.36	4.52001628969954	-0.160016289699536
201	4.15	4.36001241140899	-0.210012411408988
202	3.92	4.15001628927864	-0.230016289278645
203	3.88	3.92001784084761	-0.0400178408476126
204	4.2	3.88000310392017	0.319996896079827
205	3.95	4.19997517994974	-0.249975179949744
206	3.78	3.95001938892722	-0.170019388927221
207	3.69	3.78001318728347	-0.0900131872834682
208	3.77	3.6900069817297	0.0799930182703039
209	3.66	3.76999379546878	-0.109993795468775
210	3.53	3.66000853149379	-0.130008531493789
211	3.5	3.53001008390495	-0.0300100839049526
212	3.14	3.50000232768442	-0.360002327684424
213	3.42	3.14002792300793	0.279972076992075
214	3.3	3.41997828441117	-0.119978284411173
215	2.81	3.30000930592479	-0.490009305924792
216	3.15	2.8100380067924	0.339961993207597
217	3.37	3.14997363138874	0.220026368611258
218	4.05	3.36998293400469	0.680017065995306
219	4	4.04994725555791	-0.0499472555579148
220	4.2	4.00000387407943	0.19999612592057
221	4.21	4.19998448761861	0.0100155123813916
222	4.24	4.20999922316271	0.0300007768372872
223	4.24	4.23999767303746	2.3269625355482e-06
224	4.17	4.23999999981951	-0.0699999998195135
225	4.12	4.17000542943864	-0.0500054294386434
226	4.35	4.1200038785916	0.229996121408404
227	3.98	4.34998216071668	-0.369982160716675
228	3.62	3.9800286970778	-0.3600286970778
229	4.39	3.62002792505323	0.769972074946774
230	5.01	4.38994027834073	0.620059721659271
231	4.07	5.00995190605396	-0.93995190605396
232	3.7	4.0700729058745	-0.3700729058745
233	3.59	3.7000287041163	-0.110028704116305
234	3.44	3.59000853420142	-0.150008534201422
235	3.33	3.44001163517335	-0.110011635173351
236	2.98	3.3300085328775	-0.350008532877497
237	3.14	2.98002714785513	0.159972852144873
238	2.55	3.13998759196018	-0.589987591960178
239	2.49	2.55004576144913	-0.0600457614491323
240	2.53	2.49000465735398	0.039995342646022
241	2.43	2.52999689782486	-0.0999968978248642

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
242	2.43000775610032	1.99184462333704	2.86817088886361
243	2.43000775610032	1.8103755420741	3.04963997012655
244	2.43000775610032	1.67112619063365	3.188889321567
245	2.43000775610032	1.55373246821914	3.30628304398151
246	2.43000775610032	1.4503060005148	3.40970951168585
247	2.43000775610032	1.35680102874373	3.50321448345692
248	2.43000775610032	1.27081414440745	3.5892013677932
249	2.43000775610032	1.19077937556037	3.66923613664028
250	2.43000775610032	1.11560898522378	3.74440652697687
251	2.43000775610032	1.0445109936978	3.81550451850285
252	2.43000775610032	0.976887517312775	3.88312799488787
253	2.43000775610032	0.912274058075506	3.94774145412514

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
242 & 2.43000775610032 & 1.99184462333704 & 2.86817088886361 \tabularnewline
243 & 2.43000775610032 & 1.8103755420741 & 3.04963997012655 \tabularnewline
244 & 2.43000775610032 & 1.67112619063365 & 3.188889321567 \tabularnewline
245 & 2.43000775610032 & 1.55373246821914 & 3.30628304398151 \tabularnewline
246 & 2.43000775610032 & 1.4503060005148 & 3.40970951168585 \tabularnewline
247 & 2.43000775610032 & 1.35680102874373 & 3.50321448345692 \tabularnewline
248 & 2.43000775610032 & 1.27081414440745 & 3.5892013677932 \tabularnewline
249 & 2.43000775610032 & 1.19077937556037 & 3.66923613664028 \tabularnewline
250 & 2.43000775610032 & 1.11560898522378 & 3.74440652697687 \tabularnewline
251 & 2.43000775610032 & 1.0445109936978 & 3.81550451850285 \tabularnewline
252 & 2.43000775610032 & 0.976887517312775 & 3.88312799488787 \tabularnewline
253 & 2.43000775610032 & 0.912274058075506 & 3.94774145412514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191800&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]242[/C][C]2.43000775610032[/C][C]1.99184462333704[/C][C]2.86817088886361[/C][/ROW]
[ROW][C]243[/C][C]2.43000775610032[/C][C]1.8103755420741[/C][C]3.04963997012655[/C][/ROW]
[ROW][C]244[/C][C]2.43000775610032[/C][C]1.67112619063365[/C][C]3.188889321567[/C][/ROW]
[ROW][C]245[/C][C]2.43000775610032[/C][C]1.55373246821914[/C][C]3.30628304398151[/C][/ROW]
[ROW][C]246[/C][C]2.43000775610032[/C][C]1.4503060005148[/C][C]3.40970951168585[/C][/ROW]
[ROW][C]247[/C][C]2.43000775610032[/C][C]1.35680102874373[/C][C]3.50321448345692[/C][/ROW]
[ROW][C]248[/C][C]2.43000775610032[/C][C]1.27081414440745[/C][C]3.5892013677932[/C][/ROW]
[ROW][C]249[/C][C]2.43000775610032[/C][C]1.19077937556037[/C][C]3.66923613664028[/C][/ROW]
[ROW][C]250[/C][C]2.43000775610032[/C][C]1.11560898522378[/C][C]3.74440652697687[/C][/ROW]
[ROW][C]251[/C][C]2.43000775610032[/C][C]1.0445109936978[/C][C]3.81550451850285[/C][/ROW]
[ROW][C]252[/C][C]2.43000775610032[/C][C]0.976887517312775[/C][C]3.88312799488787[/C][/ROW]
[ROW][C]253[/C][C]2.43000775610032[/C][C]0.912274058075506[/C][C]3.94774145412514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191800&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191800&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
242	2.43000775610032	1.99184462333704	2.86817088886361
243	2.43000775610032	1.8103755420741	3.04963997012655
244	2.43000775610032	1.67112619063365	3.188889321567
245	2.43000775610032	1.55373246821914	3.30628304398151
246	2.43000775610032	1.4503060005148	3.40970951168585
247	2.43000775610032	1.35680102874373	3.50321448345692
248	2.43000775610032	1.27081414440745	3.5892013677932
249	2.43000775610032	1.19077937556037	3.66923613664028
250	2.43000775610032	1.11560898522378	3.74440652697687
251	2.43000775610032	1.0445109936978	3.81550451850285
252	2.43000775610032	0.976887517312775	3.88312799488787
253	2.43000775610032	0.912274058075506	3.94774145412514

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code