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*The author of this computation has been verified*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 26 Dec 2010 22:36:18 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/26/t1293402867f7qw1qksqv23ape.htm/, Retrieved Mon, 06 May 2024 16:27:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115826, Retrieved Mon, 06 May 2024 16:27:00 +0000

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107

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

-       [Exponential Smoothing] [paper ES triple] [2010-12-26 22:36:18] [4c854bb223ec27caaa7bcfc5e77b0dbd] [Current]

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Dataseries X:

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5.2
7.9
8.7
8.9
15.3
15.4
18.1
19.7
13
12.6
6.2
3.5
3.4
0
9.5
8.9
10.4
13.2
18.9
19
16.3
10.6
5.8
3.6
2.6
5
7.3
9.2
15.7
16.8
18.4
18.1
14.6
7.8
7.6
3.8
5.6
2.2
6.8
11.8
14.9
16.7
16.7
15.9
13.6
9.2
2.8
2.5
4.8
2.8
7.8
9
12.9
16.4
21.8
17.8
13.5
10
10.4
5.5
4
6.8
5.7
9.1
13.6
15
20.9
20.4
14
13.7
7.1
0.8
2.1
1.3
3.9
10.7
11.1
16.4
17.1
17.3
12.9
10.9
5.3
0.7
-0.2
6.5
8.6
8.5
13.3
16.2
17.5
21.2
14.8
10.3
7.3
5.1
4.4
6.2
7.7
9.3
15.6
16.3
16.6
17.4
15.3
9.7
3.7
4.6
5.4
3.1
7.9
10.1
15
15.6
19.7
18.1
17.7
10.7
6.2
4.2
4
5.9
7.1
10.5
15.1
16.8
15.3
18.4
16.1
11.3
7.9
5.6
3.4
4.8
6.5
8.5
15.1
15.7
18.7
19.2
12.9
14.4
6.2
3.3
4.6
7.2
7.8
9.9
13.6
17.1
17.8
18.6
14.7
10.5
8.6
4.4
2.3
2.8
8.8
10.7
13.9
19.3
19.5
20.4
15.3
7.9
8.3
4.5
3.2
5
6.6
11.1
12.8
16.3
17.4
18.9
15.8
11.7
6.4
2.9
4.7
2.4
7.2
10.7
13.4
18.5
18.3
16.8
16.6
14.1
6.1
3.5
1.7
2.3
4.5
9.3
14.2
17.3
23
16.3
18.4
14.2
9.1
5.9
7.2
6.8
8
14.3
14.6
17.5
17.2
17.2
14.1
10.5
6.8
4.1
6.5
6.1
6.3
9.3
16.4
16.1
18
17.6
14
10.5
6.9
2.8
0.7
3.6
6.7
12.5
14.4
16.5
18.7
19.4
15.8
11.3
9.7
2.9

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115826&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115826&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115826&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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.109108961234570
beta	0.0227447508615387
gamma	0.245515224436701

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.109108961234570 \tabularnewline
beta & 0.0227447508615387 \tabularnewline
gamma & 0.245515224436701 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115826&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]0.109108961234570[/C][/ROW]
[ROW][C]beta[/C][C]0.0227447508615387[/C][/ROW]
[ROW][C]gamma[/C][C]0.245515224436701[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115826&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115826&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	0.109108961234570
beta	0.0227447508615387
gamma	0.245515224436701

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	3.4	4.58159722222222	-1.18159722222222
14	0	0.9563708465851	-0.9563708465851
15	9.5	10.1491786365861	-0.649178636586125
16	8.9	9.32805947803669	-0.428059478036692
17	10.4	10.7841707714203	-0.384170771420342
18	13.2	13.4566173362391	-0.256617336239108
19	18.9	17.0590109545510	1.84098904544905
20	19	19.1698409280162	-0.169840928016178
21	16.3	12.6525165117421	3.64748348825789
22	10.6	12.5315815303507	-1.93158153035073
23	5.8	6.03462703895405	-0.234627038954051
24	3.6	3.51390989241083	0.0860901075891731
25	2.6	3.13245192076494	-0.532451920764941
26	5	-0.372605145762412	5.37260514576241
27	7.3	9.59372688888614	-2.29372688888614
28	9.2	8.6532412967104	0.546758703289598
29	15.7	10.2394365300667	5.46056346993327
30	16.8	13.6061228993839	3.19387710061615
31	18.4	18.0809906329937	0.319009367006259
32	18.1	19.6193489601023	-1.51934896010233
33	14.6	13.8197986361009	0.780201363899069
34	7.8	12.1886723679915	-4.38867236799146
35	7.6	5.81164867968252	1.78835132031748
36	3.8	3.6036776722818	0.196322327718201
37	5.6	3.12110001805014	2.47889998194986
38	2.2	1.26582386713320	0.934176132866802
39	6.8	9.08965082938107	-2.28965082938107
40	11.8	8.78951538508724	3.01048461491276
41	14.9	11.7440362599361	3.15596374006389
42	16.7	14.3824924545376	2.31750754546238
43	16.7	18.1497620004817	-1.44976200048166
44	15.9	19.1054765405788	-3.20547654057882
45	13.6	13.6331888605233	-0.033188860523266
46	9.2	10.7889818193017	-1.58898181930174
47	2.8	6.08170237718291	-3.28170237718291
48	2.5	2.97292984617687	-0.472929846176875
49	4.8	2.91553899948972	1.88446100051028
50	2.8	0.655001877556304	2.14499812244370
51	7.8	7.90627714916906	-0.106277149169064
52	9	9.00954589777025	-0.0095458977702485
53	12.9	11.6647741340474	1.23522586595262
54	16.4	13.9039002280447	2.49609977195529
55	21.8	16.8607271288579	4.93927287114213
56	17.8	18.1394513793061	-0.339451379306059
57	13.5	13.6907826543287	-0.190782654328711
58	10	10.5057391758765	-0.505739175876473
59	10.4	5.56574810113977	4.83425189886023
60	5.5	3.99633629548552	1.50366370451448
61	4	4.71462262518618	-0.714622625186177
62	6.8	2.26542608247820	4.5345739175218
63	5.7	9.3288775096819	-3.6288775096819
64	9.1	10.1040822905504	-1.00408229055044
65	13.6	12.9557207120591	0.64427928794092
66	15	15.4373477088581	-0.437347708858141
67	20.9	18.6324089904038	2.26759100959620
68	20.4	18.4823085395892	1.91769146041078
69	14	14.3353145929054	-0.335314592905434
70	13.7	11.0881354693262	2.61186453067384
71	7.1	7.68656529625276	-0.586565296252761
72	0.8	4.8140110442704	-4.01401104427041
73	2.1	4.44818472762206	-2.34818472762206
74	1.3	2.96795556133288	-1.66795556133288
75	3.9	7.55275408011954	-3.65275408011954
76	10.7	8.88307730430632	1.81692269569368
77	11.1	12.3936642981000	-1.29366429809998
78	16.4	14.4130635557960	1.98693644420403
79	17.1	18.4560968208236	-1.35609682082355
80	17.3	17.8169110987015	-0.516911098701453
81	12.9	12.8882685204609	0.0117314795390868
82	10.9	10.3012273396169	0.598772660383075
83	5.3	5.95307457364835	-0.653074573648346
84	0.7	2.29607024315198	-1.59607024315198
85	-0.2	2.53690782769973	-2.73690782769973
86	6.5	1.14056868601959	5.35943131398041
87	8.6	6.05294649750936	2.54705350249064
88	8.5	9.26643584146882	-0.766435841468818
89	13.3	11.8187177737818	1.48128222621821
90	16.2	14.8692648548251	1.33073514517488
91	17.5	18.1186788314571	-0.618678831457103
92	21.2	17.7545257145555	3.44547428544447
93	14.8	13.3946975944784	1.40530240552158
94	10.3	11.1124219279581	-0.812421927958102
95	7.3	6.35729240232238	0.942707597677617
96	5.1	2.69291387841357	2.40708612158643
97	4.4	3.15570439412523	1.24429560587477
98	6.2	4.00922574813211	2.19077425186789
99	7.7	7.9974523353418	-0.297452335341797
100	9.3	10.2054923938311	-0.905492393831103
101	15.6	13.2635566673641	2.33644333263594
102	16.3	16.4059202687909	-0.105920268790889
103	16.6	19.1000664380855	-2.50006643808548
104	17.4	19.4427836630769	-2.04278366307689
105	15.3	14.0474814332894	1.25251856671058
106	9.7	11.2726649667697	-1.57266496676967
107	3.7	6.82580038788644	-3.12580038788644
108	4.6	3.03503363562198	1.56496636437802
109	5.4	3.14674031374425	2.25325968625575
110	3.1	4.31500634357628	-1.21500634357628
111	7.9	7.37657357684682	0.523426423153176
112	10.1	9.53240597979732	0.567594020202675
113	15	13.4551748513742	1.54482514862581
114	15.6	15.9698674403621	-0.369867440362063
115	19.7	18.1038076765255	1.59619232347446
116	18.1	18.9959074063675	-0.895907406367478
117	17.7	14.4517821430725	3.24821785692748
118	10.7	11.2869920746194	-0.586992074619451
119	6.2	6.62062872992045	-0.420628729920449
120	4.2	4.17040118896349	0.0295988110365091
121	4	4.28070573554931	-0.280705735549313
122	5.9	4.42317216717721	1.47682783282279
123	7.1	8.17464881393191	-1.07464881393191
124	10.5	10.1777751286119	0.322224871388078
125	15.1	14.2989078255951	0.801092174404939
126	16.8	16.3231998861123	0.476800113887702
127	15.3	18.9911942169848	-3.69119421698484
128	18.4	18.7598250473786	-0.359825047378578
129	16.1	15.1804775625236	0.919522437476431
130	11.3	10.9168147743147	0.383185225685343
131	7.9	6.38917630382262	1.51082369617738
132	5.6	4.24943942127937	1.35056057872063
133	3.4	4.44055365736714	-1.04055365736714
134	4.8	4.88720178877641	-0.087201788776408
135	6.5	7.9087370942207	-1.40873709422071
136	8.5	10.1789026577129	-1.67890265771287
137	15.1	14.1794265026914	0.920573497308599
138	15.7	16.1391107620271	-0.439110762027131
139	18.7	17.7865310777461	0.913468922253859
140	19.2	18.7886748099040	0.41132519009604
141	12.9	15.5776501559411	-2.67765015594108
142	14.4	10.7996202512013	3.60037974879872
143	6.2	6.8730640827102	-0.673064082710194
144	3.3	4.45798410997156	-1.15798410997156
145	4.6	3.84415886072835	0.75584113927165
146	7.2	4.69155910200919	2.50844089799081
147	7.8	7.70991315728871	0.090086842711286
148	9.9	10.0909075607598	-0.190907560759751
149	13.6	14.8324404377178	-1.23244043771784
150	17.1	16.2645474549773	0.835452545022658
151	17.8	18.3547791543433	-0.554779154343333
152	18.6	19.0911466125117	-0.491146612511653
153	14.7	15.1080265924714	-0.408026592471405
154	10.5	11.9584576696969	-1.45845766969692
155	8.6	6.54031192102597	2.05968807897403
156	4.4	4.3192099979424	0.0807900020575989
157	2.3	4.26410172632599	-1.96410172632599
158	2.8	5.19627306668732	-2.39627306668732
159	8.8	7.13654678060156	1.66345321939844
160	10.7	9.61768094813946	1.08231905186054
161	13.9	14.2634148249320	-0.363414824931963
162	19.3	16.2378938778460	3.06210612215396
163	19.5	18.2677664574395	1.23223354256048
164	20.4	19.2182406065344	1.18175939346555
165	15.3	15.4451912361175	-0.14519123611748
166	7.9	12.1045553000659	-4.20455530006594
167	8.3	7.15949865034186	1.14050134965814
168	4.5	4.40618344426226	0.0938165557377433
169	3.2	3.90617242595118	-0.706172425951179
170	5	4.88513881074623	0.114861189253766
171	6.6	7.99767593134607	-1.39767593134607
172	11.1	10.0204100250225	1.07958997497754
173	12.8	14.3523243389097	-1.55232433890966
174	16.3	16.9460869291732	-0.646086929173233
175	17.4	18.1616660696579	-0.76166606965792
176	18.9	18.8691464208698	0.0308535791302482
177	15.8	14.6630250065956	1.1369749934044
178	11.7	10.5603154362884	1.13968456371161
179	6.4	7.36666002880971	-0.966660028809713
180	2.9	4.14845373224355	-1.24845373224355
181	4.7	3.31763615470415	1.38236384529585
182	2.4	4.69987266647393	-2.29987266647393
183	7.2	7.20792459172523	-0.00792459172523063
184	10.7	9.91740469949437	0.782595300505626
185	13.4	13.6337716204613	-0.233771620461345
186	18.5	16.5654201307873	1.93457986921272
187	18.3	18.0394982864143	0.260501713585700
188	16.8	19.0365941215135	-2.23659412151354
189	16.6	14.8241279089308	1.77587209106919
190	14.1	10.7924210170246	3.30757898297541
191	6.1	7.3806678152282	-1.28066781522820
192	3.5	4.07186580745141	-0.571865807451407
193	1.7	3.89728208659807	-2.19728208659807
194	2.3	4.08163839000467	-1.78163839000467
195	4.5	7.14692898291867	-2.64692898291867
196	9.3	9.73421227297943	-0.434212272979424
197	14.2	13.0853215975591	1.11467840244092
198	17.3	16.6315363940932	0.668463605906798
199	23	17.5913218461818	5.40867815381816
200	16.3	18.6067413494982	-2.30674134949819
201	18.4	15.2668778666604	3.13312213333958
202	14.2	11.7242739445940	2.47572605540603
203	9.1	7.22210756028859	1.87789243971141
204	5.9	4.42472992160946	1.47527007839054
205	7.2	4.13482720416418	3.06517279583582
206	6.8	5.01417979504679	1.78582020495321
207	8	8.31820528104268	-0.318205281042676
208	14.3	11.6880897459961	2.61191025400392
209	14.6	15.7624374296896	-1.16243742968956
210	17.5	19.0090424993913	-1.50904249939135
211	17.2	20.8090964733673	-3.60909647336733
212	17.2	19.1716835179484	-1.97168351794840
213	14.1	17.0777166125462	-2.97771661254622
214	10.5	12.7289019852212	-2.22890198522123
215	6.8	7.57530775326229	-0.775307753262285
216	4.1	4.38644513108627	-0.286445131086266
217	6.5	4.23377411650648	2.26622588349352
218	6.1	4.72583784270226	1.37416215729774
219	6.3	7.50343106928831	-1.20343106928831
220	9.3	11.3941201050319	-2.09412010503187
221	16.4	14.0942603654181	2.30573963458189
222	16.1	17.6168850483410	-1.51688504834097
223	18	18.9301471159034	-0.93014711590341
224	17.6	17.9232296592855	-0.323229659285516
225	14	15.7732190024372	-1.77321900243723
226	10.5	11.7067432949641	-1.20674329496408
227	6.9	6.97228436852123	-0.0722843685212275
228	2.8	3.95846803938906	-1.15846803938906
229	0.7	4.25823885681884	-3.55823885681884
230	3.6	3.89447673748547	-0.294476737485466
231	6.7	5.89686963250033	0.803130367499673
232	12.5	9.78730724419937	2.71269275580063
233	14.4	13.9618449809456	0.438155019054411
234	16.5	16.4275139352394	0.072486064760593
235	18.7	18.0293974336996	0.670602566300399
236	19.4	17.3207292352203	2.07927076477968
237	15.8	15.1125065089669	0.687493491033143
238	11.3	11.4413328157303	-0.141332815730257
239	9.7	7.07681337610198	2.62318662389802
240	2.9	4.13176478608773	-1.23176478608773

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.4 & 4.58159722222222 & -1.18159722222222 \tabularnewline
14 & 0 & 0.9563708465851 & -0.9563708465851 \tabularnewline
15 & 9.5 & 10.1491786365861 & -0.649178636586125 \tabularnewline
16 & 8.9 & 9.32805947803669 & -0.428059478036692 \tabularnewline
17 & 10.4 & 10.7841707714203 & -0.384170771420342 \tabularnewline
18 & 13.2 & 13.4566173362391 & -0.256617336239108 \tabularnewline
19 & 18.9 & 17.0590109545510 & 1.84098904544905 \tabularnewline
20 & 19 & 19.1698409280162 & -0.169840928016178 \tabularnewline
21 & 16.3 & 12.6525165117421 & 3.64748348825789 \tabularnewline
22 & 10.6 & 12.5315815303507 & -1.93158153035073 \tabularnewline
23 & 5.8 & 6.03462703895405 & -0.234627038954051 \tabularnewline
24 & 3.6 & 3.51390989241083 & 0.0860901075891731 \tabularnewline
25 & 2.6 & 3.13245192076494 & -0.532451920764941 \tabularnewline
26 & 5 & -0.372605145762412 & 5.37260514576241 \tabularnewline
27 & 7.3 & 9.59372688888614 & -2.29372688888614 \tabularnewline
28 & 9.2 & 8.6532412967104 & 0.546758703289598 \tabularnewline
29 & 15.7 & 10.2394365300667 & 5.46056346993327 \tabularnewline
30 & 16.8 & 13.6061228993839 & 3.19387710061615 \tabularnewline
31 & 18.4 & 18.0809906329937 & 0.319009367006259 \tabularnewline
32 & 18.1 & 19.6193489601023 & -1.51934896010233 \tabularnewline
33 & 14.6 & 13.8197986361009 & 0.780201363899069 \tabularnewline
34 & 7.8 & 12.1886723679915 & -4.38867236799146 \tabularnewline
35 & 7.6 & 5.81164867968252 & 1.78835132031748 \tabularnewline
36 & 3.8 & 3.6036776722818 & 0.196322327718201 \tabularnewline
37 & 5.6 & 3.12110001805014 & 2.47889998194986 \tabularnewline
38 & 2.2 & 1.26582386713320 & 0.934176132866802 \tabularnewline
39 & 6.8 & 9.08965082938107 & -2.28965082938107 \tabularnewline
40 & 11.8 & 8.78951538508724 & 3.01048461491276 \tabularnewline
41 & 14.9 & 11.7440362599361 & 3.15596374006389 \tabularnewline
42 & 16.7 & 14.3824924545376 & 2.31750754546238 \tabularnewline
43 & 16.7 & 18.1497620004817 & -1.44976200048166 \tabularnewline
44 & 15.9 & 19.1054765405788 & -3.20547654057882 \tabularnewline
45 & 13.6 & 13.6331888605233 & -0.033188860523266 \tabularnewline
46 & 9.2 & 10.7889818193017 & -1.58898181930174 \tabularnewline
47 & 2.8 & 6.08170237718291 & -3.28170237718291 \tabularnewline
48 & 2.5 & 2.97292984617687 & -0.472929846176875 \tabularnewline
49 & 4.8 & 2.91553899948972 & 1.88446100051028 \tabularnewline
50 & 2.8 & 0.655001877556304 & 2.14499812244370 \tabularnewline
51 & 7.8 & 7.90627714916906 & -0.106277149169064 \tabularnewline
52 & 9 & 9.00954589777025 & -0.0095458977702485 \tabularnewline
53 & 12.9 & 11.6647741340474 & 1.23522586595262 \tabularnewline
54 & 16.4 & 13.9039002280447 & 2.49609977195529 \tabularnewline
55 & 21.8 & 16.8607271288579 & 4.93927287114213 \tabularnewline
56 & 17.8 & 18.1394513793061 & -0.339451379306059 \tabularnewline
57 & 13.5 & 13.6907826543287 & -0.190782654328711 \tabularnewline
58 & 10 & 10.5057391758765 & -0.505739175876473 \tabularnewline
59 & 10.4 & 5.56574810113977 & 4.83425189886023 \tabularnewline
60 & 5.5 & 3.99633629548552 & 1.50366370451448 \tabularnewline
61 & 4 & 4.71462262518618 & -0.714622625186177 \tabularnewline
62 & 6.8 & 2.26542608247820 & 4.5345739175218 \tabularnewline
63 & 5.7 & 9.3288775096819 & -3.6288775096819 \tabularnewline
64 & 9.1 & 10.1040822905504 & -1.00408229055044 \tabularnewline
65 & 13.6 & 12.9557207120591 & 0.64427928794092 \tabularnewline
66 & 15 & 15.4373477088581 & -0.437347708858141 \tabularnewline
67 & 20.9 & 18.6324089904038 & 2.26759100959620 \tabularnewline
68 & 20.4 & 18.4823085395892 & 1.91769146041078 \tabularnewline
69 & 14 & 14.3353145929054 & -0.335314592905434 \tabularnewline
70 & 13.7 & 11.0881354693262 & 2.61186453067384 \tabularnewline
71 & 7.1 & 7.68656529625276 & -0.586565296252761 \tabularnewline
72 & 0.8 & 4.8140110442704 & -4.01401104427041 \tabularnewline
73 & 2.1 & 4.44818472762206 & -2.34818472762206 \tabularnewline
74 & 1.3 & 2.96795556133288 & -1.66795556133288 \tabularnewline
75 & 3.9 & 7.55275408011954 & -3.65275408011954 \tabularnewline
76 & 10.7 & 8.88307730430632 & 1.81692269569368 \tabularnewline
77 & 11.1 & 12.3936642981000 & -1.29366429809998 \tabularnewline
78 & 16.4 & 14.4130635557960 & 1.98693644420403 \tabularnewline
79 & 17.1 & 18.4560968208236 & -1.35609682082355 \tabularnewline
80 & 17.3 & 17.8169110987015 & -0.516911098701453 \tabularnewline
81 & 12.9 & 12.8882685204609 & 0.0117314795390868 \tabularnewline
82 & 10.9 & 10.3012273396169 & 0.598772660383075 \tabularnewline
83 & 5.3 & 5.95307457364835 & -0.653074573648346 \tabularnewline
84 & 0.7 & 2.29607024315198 & -1.59607024315198 \tabularnewline
85 & -0.2 & 2.53690782769973 & -2.73690782769973 \tabularnewline
86 & 6.5 & 1.14056868601959 & 5.35943131398041 \tabularnewline
87 & 8.6 & 6.05294649750936 & 2.54705350249064 \tabularnewline
88 & 8.5 & 9.26643584146882 & -0.766435841468818 \tabularnewline
89 & 13.3 & 11.8187177737818 & 1.48128222621821 \tabularnewline
90 & 16.2 & 14.8692648548251 & 1.33073514517488 \tabularnewline
91 & 17.5 & 18.1186788314571 & -0.618678831457103 \tabularnewline
92 & 21.2 & 17.7545257145555 & 3.44547428544447 \tabularnewline
93 & 14.8 & 13.3946975944784 & 1.40530240552158 \tabularnewline
94 & 10.3 & 11.1124219279581 & -0.812421927958102 \tabularnewline
95 & 7.3 & 6.35729240232238 & 0.942707597677617 \tabularnewline
96 & 5.1 & 2.69291387841357 & 2.40708612158643 \tabularnewline
97 & 4.4 & 3.15570439412523 & 1.24429560587477 \tabularnewline
98 & 6.2 & 4.00922574813211 & 2.19077425186789 \tabularnewline
99 & 7.7 & 7.9974523353418 & -0.297452335341797 \tabularnewline
100 & 9.3 & 10.2054923938311 & -0.905492393831103 \tabularnewline
101 & 15.6 & 13.2635566673641 & 2.33644333263594 \tabularnewline
102 & 16.3 & 16.4059202687909 & -0.105920268790889 \tabularnewline
103 & 16.6 & 19.1000664380855 & -2.50006643808548 \tabularnewline
104 & 17.4 & 19.4427836630769 & -2.04278366307689 \tabularnewline
105 & 15.3 & 14.0474814332894 & 1.25251856671058 \tabularnewline
106 & 9.7 & 11.2726649667697 & -1.57266496676967 \tabularnewline
107 & 3.7 & 6.82580038788644 & -3.12580038788644 \tabularnewline
108 & 4.6 & 3.03503363562198 & 1.56496636437802 \tabularnewline
109 & 5.4 & 3.14674031374425 & 2.25325968625575 \tabularnewline
110 & 3.1 & 4.31500634357628 & -1.21500634357628 \tabularnewline
111 & 7.9 & 7.37657357684682 & 0.523426423153176 \tabularnewline
112 & 10.1 & 9.53240597979732 & 0.567594020202675 \tabularnewline
113 & 15 & 13.4551748513742 & 1.54482514862581 \tabularnewline
114 & 15.6 & 15.9698674403621 & -0.369867440362063 \tabularnewline
115 & 19.7 & 18.1038076765255 & 1.59619232347446 \tabularnewline
116 & 18.1 & 18.9959074063675 & -0.895907406367478 \tabularnewline
117 & 17.7 & 14.4517821430725 & 3.24821785692748 \tabularnewline
118 & 10.7 & 11.2869920746194 & -0.586992074619451 \tabularnewline
119 & 6.2 & 6.62062872992045 & -0.420628729920449 \tabularnewline
120 & 4.2 & 4.17040118896349 & 0.0295988110365091 \tabularnewline
121 & 4 & 4.28070573554931 & -0.280705735549313 \tabularnewline
122 & 5.9 & 4.42317216717721 & 1.47682783282279 \tabularnewline
123 & 7.1 & 8.17464881393191 & -1.07464881393191 \tabularnewline
124 & 10.5 & 10.1777751286119 & 0.322224871388078 \tabularnewline
125 & 15.1 & 14.2989078255951 & 0.801092174404939 \tabularnewline
126 & 16.8 & 16.3231998861123 & 0.476800113887702 \tabularnewline
127 & 15.3 & 18.9911942169848 & -3.69119421698484 \tabularnewline
128 & 18.4 & 18.7598250473786 & -0.359825047378578 \tabularnewline
129 & 16.1 & 15.1804775625236 & 0.919522437476431 \tabularnewline
130 & 11.3 & 10.9168147743147 & 0.383185225685343 \tabularnewline
131 & 7.9 & 6.38917630382262 & 1.51082369617738 \tabularnewline
132 & 5.6 & 4.24943942127937 & 1.35056057872063 \tabularnewline
133 & 3.4 & 4.44055365736714 & -1.04055365736714 \tabularnewline
134 & 4.8 & 4.88720178877641 & -0.087201788776408 \tabularnewline
135 & 6.5 & 7.9087370942207 & -1.40873709422071 \tabularnewline
136 & 8.5 & 10.1789026577129 & -1.67890265771287 \tabularnewline
137 & 15.1 & 14.1794265026914 & 0.920573497308599 \tabularnewline
138 & 15.7 & 16.1391107620271 & -0.439110762027131 \tabularnewline
139 & 18.7 & 17.7865310777461 & 0.913468922253859 \tabularnewline
140 & 19.2 & 18.7886748099040 & 0.41132519009604 \tabularnewline
141 & 12.9 & 15.5776501559411 & -2.67765015594108 \tabularnewline
142 & 14.4 & 10.7996202512013 & 3.60037974879872 \tabularnewline
143 & 6.2 & 6.8730640827102 & -0.673064082710194 \tabularnewline
144 & 3.3 & 4.45798410997156 & -1.15798410997156 \tabularnewline
145 & 4.6 & 3.84415886072835 & 0.75584113927165 \tabularnewline
146 & 7.2 & 4.69155910200919 & 2.50844089799081 \tabularnewline
147 & 7.8 & 7.70991315728871 & 0.090086842711286 \tabularnewline
148 & 9.9 & 10.0909075607598 & -0.190907560759751 \tabularnewline
149 & 13.6 & 14.8324404377178 & -1.23244043771784 \tabularnewline
150 & 17.1 & 16.2645474549773 & 0.835452545022658 \tabularnewline
151 & 17.8 & 18.3547791543433 & -0.554779154343333 \tabularnewline
152 & 18.6 & 19.0911466125117 & -0.491146612511653 \tabularnewline
153 & 14.7 & 15.1080265924714 & -0.408026592471405 \tabularnewline
154 & 10.5 & 11.9584576696969 & -1.45845766969692 \tabularnewline
155 & 8.6 & 6.54031192102597 & 2.05968807897403 \tabularnewline
156 & 4.4 & 4.3192099979424 & 0.0807900020575989 \tabularnewline
157 & 2.3 & 4.26410172632599 & -1.96410172632599 \tabularnewline
158 & 2.8 & 5.19627306668732 & -2.39627306668732 \tabularnewline
159 & 8.8 & 7.13654678060156 & 1.66345321939844 \tabularnewline
160 & 10.7 & 9.61768094813946 & 1.08231905186054 \tabularnewline
161 & 13.9 & 14.2634148249320 & -0.363414824931963 \tabularnewline
162 & 19.3 & 16.2378938778460 & 3.06210612215396 \tabularnewline
163 & 19.5 & 18.2677664574395 & 1.23223354256048 \tabularnewline
164 & 20.4 & 19.2182406065344 & 1.18175939346555 \tabularnewline
165 & 15.3 & 15.4451912361175 & -0.14519123611748 \tabularnewline
166 & 7.9 & 12.1045553000659 & -4.20455530006594 \tabularnewline
167 & 8.3 & 7.15949865034186 & 1.14050134965814 \tabularnewline
168 & 4.5 & 4.40618344426226 & 0.0938165557377433 \tabularnewline
169 & 3.2 & 3.90617242595118 & -0.706172425951179 \tabularnewline
170 & 5 & 4.88513881074623 & 0.114861189253766 \tabularnewline
171 & 6.6 & 7.99767593134607 & -1.39767593134607 \tabularnewline
172 & 11.1 & 10.0204100250225 & 1.07958997497754 \tabularnewline
173 & 12.8 & 14.3523243389097 & -1.55232433890966 \tabularnewline
174 & 16.3 & 16.9460869291732 & -0.646086929173233 \tabularnewline
175 & 17.4 & 18.1616660696579 & -0.76166606965792 \tabularnewline
176 & 18.9 & 18.8691464208698 & 0.0308535791302482 \tabularnewline
177 & 15.8 & 14.6630250065956 & 1.1369749934044 \tabularnewline
178 & 11.7 & 10.5603154362884 & 1.13968456371161 \tabularnewline
179 & 6.4 & 7.36666002880971 & -0.966660028809713 \tabularnewline
180 & 2.9 & 4.14845373224355 & -1.24845373224355 \tabularnewline
181 & 4.7 & 3.31763615470415 & 1.38236384529585 \tabularnewline
182 & 2.4 & 4.69987266647393 & -2.29987266647393 \tabularnewline
183 & 7.2 & 7.20792459172523 & -0.00792459172523063 \tabularnewline
184 & 10.7 & 9.91740469949437 & 0.782595300505626 \tabularnewline
185 & 13.4 & 13.6337716204613 & -0.233771620461345 \tabularnewline
186 & 18.5 & 16.5654201307873 & 1.93457986921272 \tabularnewline
187 & 18.3 & 18.0394982864143 & 0.260501713585700 \tabularnewline
188 & 16.8 & 19.0365941215135 & -2.23659412151354 \tabularnewline
189 & 16.6 & 14.8241279089308 & 1.77587209106919 \tabularnewline
190 & 14.1 & 10.7924210170246 & 3.30757898297541 \tabularnewline
191 & 6.1 & 7.3806678152282 & -1.28066781522820 \tabularnewline
192 & 3.5 & 4.07186580745141 & -0.571865807451407 \tabularnewline
193 & 1.7 & 3.89728208659807 & -2.19728208659807 \tabularnewline
194 & 2.3 & 4.08163839000467 & -1.78163839000467 \tabularnewline
195 & 4.5 & 7.14692898291867 & -2.64692898291867 \tabularnewline
196 & 9.3 & 9.73421227297943 & -0.434212272979424 \tabularnewline
197 & 14.2 & 13.0853215975591 & 1.11467840244092 \tabularnewline
198 & 17.3 & 16.6315363940932 & 0.668463605906798 \tabularnewline
199 & 23 & 17.5913218461818 & 5.40867815381816 \tabularnewline
200 & 16.3 & 18.6067413494982 & -2.30674134949819 \tabularnewline
201 & 18.4 & 15.2668778666604 & 3.13312213333958 \tabularnewline
202 & 14.2 & 11.7242739445940 & 2.47572605540603 \tabularnewline
203 & 9.1 & 7.22210756028859 & 1.87789243971141 \tabularnewline
204 & 5.9 & 4.42472992160946 & 1.47527007839054 \tabularnewline
205 & 7.2 & 4.13482720416418 & 3.06517279583582 \tabularnewline
206 & 6.8 & 5.01417979504679 & 1.78582020495321 \tabularnewline
207 & 8 & 8.31820528104268 & -0.318205281042676 \tabularnewline
208 & 14.3 & 11.6880897459961 & 2.61191025400392 \tabularnewline
209 & 14.6 & 15.7624374296896 & -1.16243742968956 \tabularnewline
210 & 17.5 & 19.0090424993913 & -1.50904249939135 \tabularnewline
211 & 17.2 & 20.8090964733673 & -3.60909647336733 \tabularnewline
212 & 17.2 & 19.1716835179484 & -1.97168351794840 \tabularnewline
213 & 14.1 & 17.0777166125462 & -2.97771661254622 \tabularnewline
214 & 10.5 & 12.7289019852212 & -2.22890198522123 \tabularnewline
215 & 6.8 & 7.57530775326229 & -0.775307753262285 \tabularnewline
216 & 4.1 & 4.38644513108627 & -0.286445131086266 \tabularnewline
217 & 6.5 & 4.23377411650648 & 2.26622588349352 \tabularnewline
218 & 6.1 & 4.72583784270226 & 1.37416215729774 \tabularnewline
219 & 6.3 & 7.50343106928831 & -1.20343106928831 \tabularnewline
220 & 9.3 & 11.3941201050319 & -2.09412010503187 \tabularnewline
221 & 16.4 & 14.0942603654181 & 2.30573963458189 \tabularnewline
222 & 16.1 & 17.6168850483410 & -1.51688504834097 \tabularnewline
223 & 18 & 18.9301471159034 & -0.93014711590341 \tabularnewline
224 & 17.6 & 17.9232296592855 & -0.323229659285516 \tabularnewline
225 & 14 & 15.7732190024372 & -1.77321900243723 \tabularnewline
226 & 10.5 & 11.7067432949641 & -1.20674329496408 \tabularnewline
227 & 6.9 & 6.97228436852123 & -0.0722843685212275 \tabularnewline
228 & 2.8 & 3.95846803938906 & -1.15846803938906 \tabularnewline
229 & 0.7 & 4.25823885681884 & -3.55823885681884 \tabularnewline
230 & 3.6 & 3.89447673748547 & -0.294476737485466 \tabularnewline
231 & 6.7 & 5.89686963250033 & 0.803130367499673 \tabularnewline
232 & 12.5 & 9.78730724419937 & 2.71269275580063 \tabularnewline
233 & 14.4 & 13.9618449809456 & 0.438155019054411 \tabularnewline
234 & 16.5 & 16.4275139352394 & 0.072486064760593 \tabularnewline
235 & 18.7 & 18.0293974336996 & 0.670602566300399 \tabularnewline
236 & 19.4 & 17.3207292352203 & 2.07927076477968 \tabularnewline
237 & 15.8 & 15.1125065089669 & 0.687493491033143 \tabularnewline
238 & 11.3 & 11.4413328157303 & -0.141332815730257 \tabularnewline
239 & 9.7 & 7.07681337610198 & 2.62318662389802 \tabularnewline
240 & 2.9 & 4.13176478608773 & -1.23176478608773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115826&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]13[/C][C]3.4[/C][C]4.58159722222222[/C][C]-1.18159722222222[/C][/ROW]
[ROW][C]14[/C][C]0[/C][C]0.9563708465851[/C][C]-0.9563708465851[/C][/ROW]
[ROW][C]15[/C][C]9.5[/C][C]10.1491786365861[/C][C]-0.649178636586125[/C][/ROW]
[ROW][C]16[/C][C]8.9[/C][C]9.32805947803669[/C][C]-0.428059478036692[/C][/ROW]
[ROW][C]17[/C][C]10.4[/C][C]10.7841707714203[/C][C]-0.384170771420342[/C][/ROW]
[ROW][C]18[/C][C]13.2[/C][C]13.4566173362391[/C][C]-0.256617336239108[/C][/ROW]
[ROW][C]19[/C][C]18.9[/C][C]17.0590109545510[/C][C]1.84098904544905[/C][/ROW]
[ROW][C]20[/C][C]19[/C][C]19.1698409280162[/C][C]-0.169840928016178[/C][/ROW]
[ROW][C]21[/C][C]16.3[/C][C]12.6525165117421[/C][C]3.64748348825789[/C][/ROW]
[ROW][C]22[/C][C]10.6[/C][C]12.5315815303507[/C][C]-1.93158153035073[/C][/ROW]
[ROW][C]23[/C][C]5.8[/C][C]6.03462703895405[/C][C]-0.234627038954051[/C][/ROW]
[ROW][C]24[/C][C]3.6[/C][C]3.51390989241083[/C][C]0.0860901075891731[/C][/ROW]
[ROW][C]25[/C][C]2.6[/C][C]3.13245192076494[/C][C]-0.532451920764941[/C][/ROW]
[ROW][C]26[/C][C]5[/C][C]-0.372605145762412[/C][C]5.37260514576241[/C][/ROW]
[ROW][C]27[/C][C]7.3[/C][C]9.59372688888614[/C][C]-2.29372688888614[/C][/ROW]
[ROW][C]28[/C][C]9.2[/C][C]8.6532412967104[/C][C]0.546758703289598[/C][/ROW]
[ROW][C]29[/C][C]15.7[/C][C]10.2394365300667[/C][C]5.46056346993327[/C][/ROW]
[ROW][C]30[/C][C]16.8[/C][C]13.6061228993839[/C][C]3.19387710061615[/C][/ROW]
[ROW][C]31[/C][C]18.4[/C][C]18.0809906329937[/C][C]0.319009367006259[/C][/ROW]
[ROW][C]32[/C][C]18.1[/C][C]19.6193489601023[/C][C]-1.51934896010233[/C][/ROW]
[ROW][C]33[/C][C]14.6[/C][C]13.8197986361009[/C][C]0.780201363899069[/C][/ROW]
[ROW][C]34[/C][C]7.8[/C][C]12.1886723679915[/C][C]-4.38867236799146[/C][/ROW]
[ROW][C]35[/C][C]7.6[/C][C]5.81164867968252[/C][C]1.78835132031748[/C][/ROW]
[ROW][C]36[/C][C]3.8[/C][C]3.6036776722818[/C][C]0.196322327718201[/C][/ROW]
[ROW][C]37[/C][C]5.6[/C][C]3.12110001805014[/C][C]2.47889998194986[/C][/ROW]
[ROW][C]38[/C][C]2.2[/C][C]1.26582386713320[/C][C]0.934176132866802[/C][/ROW]
[ROW][C]39[/C][C]6.8[/C][C]9.08965082938107[/C][C]-2.28965082938107[/C][/ROW]
[ROW][C]40[/C][C]11.8[/C][C]8.78951538508724[/C][C]3.01048461491276[/C][/ROW]
[ROW][C]41[/C][C]14.9[/C][C]11.7440362599361[/C][C]3.15596374006389[/C][/ROW]
[ROW][C]42[/C][C]16.7[/C][C]14.3824924545376[/C][C]2.31750754546238[/C][/ROW]
[ROW][C]43[/C][C]16.7[/C][C]18.1497620004817[/C][C]-1.44976200048166[/C][/ROW]
[ROW][C]44[/C][C]15.9[/C][C]19.1054765405788[/C][C]-3.20547654057882[/C][/ROW]
[ROW][C]45[/C][C]13.6[/C][C]13.6331888605233[/C][C]-0.033188860523266[/C][/ROW]
[ROW][C]46[/C][C]9.2[/C][C]10.7889818193017[/C][C]-1.58898181930174[/C][/ROW]
[ROW][C]47[/C][C]2.8[/C][C]6.08170237718291[/C][C]-3.28170237718291[/C][/ROW]
[ROW][C]48[/C][C]2.5[/C][C]2.97292984617687[/C][C]-0.472929846176875[/C][/ROW]
[ROW][C]49[/C][C]4.8[/C][C]2.91553899948972[/C][C]1.88446100051028[/C][/ROW]
[ROW][C]50[/C][C]2.8[/C][C]0.655001877556304[/C][C]2.14499812244370[/C][/ROW]
[ROW][C]51[/C][C]7.8[/C][C]7.90627714916906[/C][C]-0.106277149169064[/C][/ROW]
[ROW][C]52[/C][C]9[/C][C]9.00954589777025[/C][C]-0.0095458977702485[/C][/ROW]
[ROW][C]53[/C][C]12.9[/C][C]11.6647741340474[/C][C]1.23522586595262[/C][/ROW]
[ROW][C]54[/C][C]16.4[/C][C]13.9039002280447[/C][C]2.49609977195529[/C][/ROW]
[ROW][C]55[/C][C]21.8[/C][C]16.8607271288579[/C][C]4.93927287114213[/C][/ROW]
[ROW][C]56[/C][C]17.8[/C][C]18.1394513793061[/C][C]-0.339451379306059[/C][/ROW]
[ROW][C]57[/C][C]13.5[/C][C]13.6907826543287[/C][C]-0.190782654328711[/C][/ROW]
[ROW][C]58[/C][C]10[/C][C]10.5057391758765[/C][C]-0.505739175876473[/C][/ROW]
[ROW][C]59[/C][C]10.4[/C][C]5.56574810113977[/C][C]4.83425189886023[/C][/ROW]
[ROW][C]60[/C][C]5.5[/C][C]3.99633629548552[/C][C]1.50366370451448[/C][/ROW]
[ROW][C]61[/C][C]4[/C][C]4.71462262518618[/C][C]-0.714622625186177[/C][/ROW]
[ROW][C]62[/C][C]6.8[/C][C]2.26542608247820[/C][C]4.5345739175218[/C][/ROW]
[ROW][C]63[/C][C]5.7[/C][C]9.3288775096819[/C][C]-3.6288775096819[/C][/ROW]
[ROW][C]64[/C][C]9.1[/C][C]10.1040822905504[/C][C]-1.00408229055044[/C][/ROW]
[ROW][C]65[/C][C]13.6[/C][C]12.9557207120591[/C][C]0.64427928794092[/C][/ROW]
[ROW][C]66[/C][C]15[/C][C]15.4373477088581[/C][C]-0.437347708858141[/C][/ROW]
[ROW][C]67[/C][C]20.9[/C][C]18.6324089904038[/C][C]2.26759100959620[/C][/ROW]
[ROW][C]68[/C][C]20.4[/C][C]18.4823085395892[/C][C]1.91769146041078[/C][/ROW]
[ROW][C]69[/C][C]14[/C][C]14.3353145929054[/C][C]-0.335314592905434[/C][/ROW]
[ROW][C]70[/C][C]13.7[/C][C]11.0881354693262[/C][C]2.61186453067384[/C][/ROW]
[ROW][C]71[/C][C]7.1[/C][C]7.68656529625276[/C][C]-0.586565296252761[/C][/ROW]
[ROW][C]72[/C][C]0.8[/C][C]4.8140110442704[/C][C]-4.01401104427041[/C][/ROW]
[ROW][C]73[/C][C]2.1[/C][C]4.44818472762206[/C][C]-2.34818472762206[/C][/ROW]
[ROW][C]74[/C][C]1.3[/C][C]2.96795556133288[/C][C]-1.66795556133288[/C][/ROW]
[ROW][C]75[/C][C]3.9[/C][C]7.55275408011954[/C][C]-3.65275408011954[/C][/ROW]
[ROW][C]76[/C][C]10.7[/C][C]8.88307730430632[/C][C]1.81692269569368[/C][/ROW]
[ROW][C]77[/C][C]11.1[/C][C]12.3936642981000[/C][C]-1.29366429809998[/C][/ROW]
[ROW][C]78[/C][C]16.4[/C][C]14.4130635557960[/C][C]1.98693644420403[/C][/ROW]
[ROW][C]79[/C][C]17.1[/C][C]18.4560968208236[/C][C]-1.35609682082355[/C][/ROW]
[ROW][C]80[/C][C]17.3[/C][C]17.8169110987015[/C][C]-0.516911098701453[/C][/ROW]
[ROW][C]81[/C][C]12.9[/C][C]12.8882685204609[/C][C]0.0117314795390868[/C][/ROW]
[ROW][C]82[/C][C]10.9[/C][C]10.3012273396169[/C][C]0.598772660383075[/C][/ROW]
[ROW][C]83[/C][C]5.3[/C][C]5.95307457364835[/C][C]-0.653074573648346[/C][/ROW]
[ROW][C]84[/C][C]0.7[/C][C]2.29607024315198[/C][C]-1.59607024315198[/C][/ROW]
[ROW][C]85[/C][C]-0.2[/C][C]2.53690782769973[/C][C]-2.73690782769973[/C][/ROW]
[ROW][C]86[/C][C]6.5[/C][C]1.14056868601959[/C][C]5.35943131398041[/C][/ROW]
[ROW][C]87[/C][C]8.6[/C][C]6.05294649750936[/C][C]2.54705350249064[/C][/ROW]
[ROW][C]88[/C][C]8.5[/C][C]9.26643584146882[/C][C]-0.766435841468818[/C][/ROW]
[ROW][C]89[/C][C]13.3[/C][C]11.8187177737818[/C][C]1.48128222621821[/C][/ROW]
[ROW][C]90[/C][C]16.2[/C][C]14.8692648548251[/C][C]1.33073514517488[/C][/ROW]
[ROW][C]91[/C][C]17.5[/C][C]18.1186788314571[/C][C]-0.618678831457103[/C][/ROW]
[ROW][C]92[/C][C]21.2[/C][C]17.7545257145555[/C][C]3.44547428544447[/C][/ROW]
[ROW][C]93[/C][C]14.8[/C][C]13.3946975944784[/C][C]1.40530240552158[/C][/ROW]
[ROW][C]94[/C][C]10.3[/C][C]11.1124219279581[/C][C]-0.812421927958102[/C][/ROW]
[ROW][C]95[/C][C]7.3[/C][C]6.35729240232238[/C][C]0.942707597677617[/C][/ROW]
[ROW][C]96[/C][C]5.1[/C][C]2.69291387841357[/C][C]2.40708612158643[/C][/ROW]
[ROW][C]97[/C][C]4.4[/C][C]3.15570439412523[/C][C]1.24429560587477[/C][/ROW]
[ROW][C]98[/C][C]6.2[/C][C]4.00922574813211[/C][C]2.19077425186789[/C][/ROW]
[ROW][C]99[/C][C]7.7[/C][C]7.9974523353418[/C][C]-0.297452335341797[/C][/ROW]
[ROW][C]100[/C][C]9.3[/C][C]10.2054923938311[/C][C]-0.905492393831103[/C][/ROW]
[ROW][C]101[/C][C]15.6[/C][C]13.2635566673641[/C][C]2.33644333263594[/C][/ROW]
[ROW][C]102[/C][C]16.3[/C][C]16.4059202687909[/C][C]-0.105920268790889[/C][/ROW]
[ROW][C]103[/C][C]16.6[/C][C]19.1000664380855[/C][C]-2.50006643808548[/C][/ROW]
[ROW][C]104[/C][C]17.4[/C][C]19.4427836630769[/C][C]-2.04278366307689[/C][/ROW]
[ROW][C]105[/C][C]15.3[/C][C]14.0474814332894[/C][C]1.25251856671058[/C][/ROW]
[ROW][C]106[/C][C]9.7[/C][C]11.2726649667697[/C][C]-1.57266496676967[/C][/ROW]
[ROW][C]107[/C][C]3.7[/C][C]6.82580038788644[/C][C]-3.12580038788644[/C][/ROW]
[ROW][C]108[/C][C]4.6[/C][C]3.03503363562198[/C][C]1.56496636437802[/C][/ROW]
[ROW][C]109[/C][C]5.4[/C][C]3.14674031374425[/C][C]2.25325968625575[/C][/ROW]
[ROW][C]110[/C][C]3.1[/C][C]4.31500634357628[/C][C]-1.21500634357628[/C][/ROW]
[ROW][C]111[/C][C]7.9[/C][C]7.37657357684682[/C][C]0.523426423153176[/C][/ROW]
[ROW][C]112[/C][C]10.1[/C][C]9.53240597979732[/C][C]0.567594020202675[/C][/ROW]
[ROW][C]113[/C][C]15[/C][C]13.4551748513742[/C][C]1.54482514862581[/C][/ROW]
[ROW][C]114[/C][C]15.6[/C][C]15.9698674403621[/C][C]-0.369867440362063[/C][/ROW]
[ROW][C]115[/C][C]19.7[/C][C]18.1038076765255[/C][C]1.59619232347446[/C][/ROW]
[ROW][C]116[/C][C]18.1[/C][C]18.9959074063675[/C][C]-0.895907406367478[/C][/ROW]
[ROW][C]117[/C][C]17.7[/C][C]14.4517821430725[/C][C]3.24821785692748[/C][/ROW]
[ROW][C]118[/C][C]10.7[/C][C]11.2869920746194[/C][C]-0.586992074619451[/C][/ROW]
[ROW][C]119[/C][C]6.2[/C][C]6.62062872992045[/C][C]-0.420628729920449[/C][/ROW]
[ROW][C]120[/C][C]4.2[/C][C]4.17040118896349[/C][C]0.0295988110365091[/C][/ROW]
[ROW][C]121[/C][C]4[/C][C]4.28070573554931[/C][C]-0.280705735549313[/C][/ROW]
[ROW][C]122[/C][C]5.9[/C][C]4.42317216717721[/C][C]1.47682783282279[/C][/ROW]
[ROW][C]123[/C][C]7.1[/C][C]8.17464881393191[/C][C]-1.07464881393191[/C][/ROW]
[ROW][C]124[/C][C]10.5[/C][C]10.1777751286119[/C][C]0.322224871388078[/C][/ROW]
[ROW][C]125[/C][C]15.1[/C][C]14.2989078255951[/C][C]0.801092174404939[/C][/ROW]
[ROW][C]126[/C][C]16.8[/C][C]16.3231998861123[/C][C]0.476800113887702[/C][/ROW]
[ROW][C]127[/C][C]15.3[/C][C]18.9911942169848[/C][C]-3.69119421698484[/C][/ROW]
[ROW][C]128[/C][C]18.4[/C][C]18.7598250473786[/C][C]-0.359825047378578[/C][/ROW]
[ROW][C]129[/C][C]16.1[/C][C]15.1804775625236[/C][C]0.919522437476431[/C][/ROW]
[ROW][C]130[/C][C]11.3[/C][C]10.9168147743147[/C][C]0.383185225685343[/C][/ROW]
[ROW][C]131[/C][C]7.9[/C][C]6.38917630382262[/C][C]1.51082369617738[/C][/ROW]
[ROW][C]132[/C][C]5.6[/C][C]4.24943942127937[/C][C]1.35056057872063[/C][/ROW]
[ROW][C]133[/C][C]3.4[/C][C]4.44055365736714[/C][C]-1.04055365736714[/C][/ROW]
[ROW][C]134[/C][C]4.8[/C][C]4.88720178877641[/C][C]-0.087201788776408[/C][/ROW]
[ROW][C]135[/C][C]6.5[/C][C]7.9087370942207[/C][C]-1.40873709422071[/C][/ROW]
[ROW][C]136[/C][C]8.5[/C][C]10.1789026577129[/C][C]-1.67890265771287[/C][/ROW]
[ROW][C]137[/C][C]15.1[/C][C]14.1794265026914[/C][C]0.920573497308599[/C][/ROW]
[ROW][C]138[/C][C]15.7[/C][C]16.1391107620271[/C][C]-0.439110762027131[/C][/ROW]
[ROW][C]139[/C][C]18.7[/C][C]17.7865310777461[/C][C]0.913468922253859[/C][/ROW]
[ROW][C]140[/C][C]19.2[/C][C]18.7886748099040[/C][C]0.41132519009604[/C][/ROW]
[ROW][C]141[/C][C]12.9[/C][C]15.5776501559411[/C][C]-2.67765015594108[/C][/ROW]
[ROW][C]142[/C][C]14.4[/C][C]10.7996202512013[/C][C]3.60037974879872[/C][/ROW]
[ROW][C]143[/C][C]6.2[/C][C]6.8730640827102[/C][C]-0.673064082710194[/C][/ROW]
[ROW][C]144[/C][C]3.3[/C][C]4.45798410997156[/C][C]-1.15798410997156[/C][/ROW]
[ROW][C]145[/C][C]4.6[/C][C]3.84415886072835[/C][C]0.75584113927165[/C][/ROW]
[ROW][C]146[/C][C]7.2[/C][C]4.69155910200919[/C][C]2.50844089799081[/C][/ROW]
[ROW][C]147[/C][C]7.8[/C][C]7.70991315728871[/C][C]0.090086842711286[/C][/ROW]
[ROW][C]148[/C][C]9.9[/C][C]10.0909075607598[/C][C]-0.190907560759751[/C][/ROW]
[ROW][C]149[/C][C]13.6[/C][C]14.8324404377178[/C][C]-1.23244043771784[/C][/ROW]
[ROW][C]150[/C][C]17.1[/C][C]16.2645474549773[/C][C]0.835452545022658[/C][/ROW]
[ROW][C]151[/C][C]17.8[/C][C]18.3547791543433[/C][C]-0.554779154343333[/C][/ROW]
[ROW][C]152[/C][C]18.6[/C][C]19.0911466125117[/C][C]-0.491146612511653[/C][/ROW]
[ROW][C]153[/C][C]14.7[/C][C]15.1080265924714[/C][C]-0.408026592471405[/C][/ROW]
[ROW][C]154[/C][C]10.5[/C][C]11.9584576696969[/C][C]-1.45845766969692[/C][/ROW]
[ROW][C]155[/C][C]8.6[/C][C]6.54031192102597[/C][C]2.05968807897403[/C][/ROW]
[ROW][C]156[/C][C]4.4[/C][C]4.3192099979424[/C][C]0.0807900020575989[/C][/ROW]
[ROW][C]157[/C][C]2.3[/C][C]4.26410172632599[/C][C]-1.96410172632599[/C][/ROW]
[ROW][C]158[/C][C]2.8[/C][C]5.19627306668732[/C][C]-2.39627306668732[/C][/ROW]
[ROW][C]159[/C][C]8.8[/C][C]7.13654678060156[/C][C]1.66345321939844[/C][/ROW]
[ROW][C]160[/C][C]10.7[/C][C]9.61768094813946[/C][C]1.08231905186054[/C][/ROW]
[ROW][C]161[/C][C]13.9[/C][C]14.2634148249320[/C][C]-0.363414824931963[/C][/ROW]
[ROW][C]162[/C][C]19.3[/C][C]16.2378938778460[/C][C]3.06210612215396[/C][/ROW]
[ROW][C]163[/C][C]19.5[/C][C]18.2677664574395[/C][C]1.23223354256048[/C][/ROW]
[ROW][C]164[/C][C]20.4[/C][C]19.2182406065344[/C][C]1.18175939346555[/C][/ROW]
[ROW][C]165[/C][C]15.3[/C][C]15.4451912361175[/C][C]-0.14519123611748[/C][/ROW]
[ROW][C]166[/C][C]7.9[/C][C]12.1045553000659[/C][C]-4.20455530006594[/C][/ROW]
[ROW][C]167[/C][C]8.3[/C][C]7.15949865034186[/C][C]1.14050134965814[/C][/ROW]
[ROW][C]168[/C][C]4.5[/C][C]4.40618344426226[/C][C]0.0938165557377433[/C][/ROW]
[ROW][C]169[/C][C]3.2[/C][C]3.90617242595118[/C][C]-0.706172425951179[/C][/ROW]
[ROW][C]170[/C][C]5[/C][C]4.88513881074623[/C][C]0.114861189253766[/C][/ROW]
[ROW][C]171[/C][C]6.6[/C][C]7.99767593134607[/C][C]-1.39767593134607[/C][/ROW]
[ROW][C]172[/C][C]11.1[/C][C]10.0204100250225[/C][C]1.07958997497754[/C][/ROW]
[ROW][C]173[/C][C]12.8[/C][C]14.3523243389097[/C][C]-1.55232433890966[/C][/ROW]
[ROW][C]174[/C][C]16.3[/C][C]16.9460869291732[/C][C]-0.646086929173233[/C][/ROW]
[ROW][C]175[/C][C]17.4[/C][C]18.1616660696579[/C][C]-0.76166606965792[/C][/ROW]
[ROW][C]176[/C][C]18.9[/C][C]18.8691464208698[/C][C]0.0308535791302482[/C][/ROW]
[ROW][C]177[/C][C]15.8[/C][C]14.6630250065956[/C][C]1.1369749934044[/C][/ROW]
[ROW][C]178[/C][C]11.7[/C][C]10.5603154362884[/C][C]1.13968456371161[/C][/ROW]
[ROW][C]179[/C][C]6.4[/C][C]7.36666002880971[/C][C]-0.966660028809713[/C][/ROW]
[ROW][C]180[/C][C]2.9[/C][C]4.14845373224355[/C][C]-1.24845373224355[/C][/ROW]
[ROW][C]181[/C][C]4.7[/C][C]3.31763615470415[/C][C]1.38236384529585[/C][/ROW]
[ROW][C]182[/C][C]2.4[/C][C]4.69987266647393[/C][C]-2.29987266647393[/C][/ROW]
[ROW][C]183[/C][C]7.2[/C][C]7.20792459172523[/C][C]-0.00792459172523063[/C][/ROW]
[ROW][C]184[/C][C]10.7[/C][C]9.91740469949437[/C][C]0.782595300505626[/C][/ROW]
[ROW][C]185[/C][C]13.4[/C][C]13.6337716204613[/C][C]-0.233771620461345[/C][/ROW]
[ROW][C]186[/C][C]18.5[/C][C]16.5654201307873[/C][C]1.93457986921272[/C][/ROW]
[ROW][C]187[/C][C]18.3[/C][C]18.0394982864143[/C][C]0.260501713585700[/C][/ROW]
[ROW][C]188[/C][C]16.8[/C][C]19.0365941215135[/C][C]-2.23659412151354[/C][/ROW]
[ROW][C]189[/C][C]16.6[/C][C]14.8241279089308[/C][C]1.77587209106919[/C][/ROW]
[ROW][C]190[/C][C]14.1[/C][C]10.7924210170246[/C][C]3.30757898297541[/C][/ROW]
[ROW][C]191[/C][C]6.1[/C][C]7.3806678152282[/C][C]-1.28066781522820[/C][/ROW]
[ROW][C]192[/C][C]3.5[/C][C]4.07186580745141[/C][C]-0.571865807451407[/C][/ROW]
[ROW][C]193[/C][C]1.7[/C][C]3.89728208659807[/C][C]-2.19728208659807[/C][/ROW]
[ROW][C]194[/C][C]2.3[/C][C]4.08163839000467[/C][C]-1.78163839000467[/C][/ROW]
[ROW][C]195[/C][C]4.5[/C][C]7.14692898291867[/C][C]-2.64692898291867[/C][/ROW]
[ROW][C]196[/C][C]9.3[/C][C]9.73421227297943[/C][C]-0.434212272979424[/C][/ROW]
[ROW][C]197[/C][C]14.2[/C][C]13.0853215975591[/C][C]1.11467840244092[/C][/ROW]
[ROW][C]198[/C][C]17.3[/C][C]16.6315363940932[/C][C]0.668463605906798[/C][/ROW]
[ROW][C]199[/C][C]23[/C][C]17.5913218461818[/C][C]5.40867815381816[/C][/ROW]
[ROW][C]200[/C][C]16.3[/C][C]18.6067413494982[/C][C]-2.30674134949819[/C][/ROW]
[ROW][C]201[/C][C]18.4[/C][C]15.2668778666604[/C][C]3.13312213333958[/C][/ROW]
[ROW][C]202[/C][C]14.2[/C][C]11.7242739445940[/C][C]2.47572605540603[/C][/ROW]
[ROW][C]203[/C][C]9.1[/C][C]7.22210756028859[/C][C]1.87789243971141[/C][/ROW]
[ROW][C]204[/C][C]5.9[/C][C]4.42472992160946[/C][C]1.47527007839054[/C][/ROW]
[ROW][C]205[/C][C]7.2[/C][C]4.13482720416418[/C][C]3.06517279583582[/C][/ROW]
[ROW][C]206[/C][C]6.8[/C][C]5.01417979504679[/C][C]1.78582020495321[/C][/ROW]
[ROW][C]207[/C][C]8[/C][C]8.31820528104268[/C][C]-0.318205281042676[/C][/ROW]
[ROW][C]208[/C][C]14.3[/C][C]11.6880897459961[/C][C]2.61191025400392[/C][/ROW]
[ROW][C]209[/C][C]14.6[/C][C]15.7624374296896[/C][C]-1.16243742968956[/C][/ROW]
[ROW][C]210[/C][C]17.5[/C][C]19.0090424993913[/C][C]-1.50904249939135[/C][/ROW]
[ROW][C]211[/C][C]17.2[/C][C]20.8090964733673[/C][C]-3.60909647336733[/C][/ROW]
[ROW][C]212[/C][C]17.2[/C][C]19.1716835179484[/C][C]-1.97168351794840[/C][/ROW]
[ROW][C]213[/C][C]14.1[/C][C]17.0777166125462[/C][C]-2.97771661254622[/C][/ROW]
[ROW][C]214[/C][C]10.5[/C][C]12.7289019852212[/C][C]-2.22890198522123[/C][/ROW]
[ROW][C]215[/C][C]6.8[/C][C]7.57530775326229[/C][C]-0.775307753262285[/C][/ROW]
[ROW][C]216[/C][C]4.1[/C][C]4.38644513108627[/C][C]-0.286445131086266[/C][/ROW]
[ROW][C]217[/C][C]6.5[/C][C]4.23377411650648[/C][C]2.26622588349352[/C][/ROW]
[ROW][C]218[/C][C]6.1[/C][C]4.72583784270226[/C][C]1.37416215729774[/C][/ROW]
[ROW][C]219[/C][C]6.3[/C][C]7.50343106928831[/C][C]-1.20343106928831[/C][/ROW]
[ROW][C]220[/C][C]9.3[/C][C]11.3941201050319[/C][C]-2.09412010503187[/C][/ROW]
[ROW][C]221[/C][C]16.4[/C][C]14.0942603654181[/C][C]2.30573963458189[/C][/ROW]
[ROW][C]222[/C][C]16.1[/C][C]17.6168850483410[/C][C]-1.51688504834097[/C][/ROW]
[ROW][C]223[/C][C]18[/C][C]18.9301471159034[/C][C]-0.93014711590341[/C][/ROW]
[ROW][C]224[/C][C]17.6[/C][C]17.9232296592855[/C][C]-0.323229659285516[/C][/ROW]
[ROW][C]225[/C][C]14[/C][C]15.7732190024372[/C][C]-1.77321900243723[/C][/ROW]
[ROW][C]226[/C][C]10.5[/C][C]11.7067432949641[/C][C]-1.20674329496408[/C][/ROW]
[ROW][C]227[/C][C]6.9[/C][C]6.97228436852123[/C][C]-0.0722843685212275[/C][/ROW]
[ROW][C]228[/C][C]2.8[/C][C]3.95846803938906[/C][C]-1.15846803938906[/C][/ROW]
[ROW][C]229[/C][C]0.7[/C][C]4.25823885681884[/C][C]-3.55823885681884[/C][/ROW]
[ROW][C]230[/C][C]3.6[/C][C]3.89447673748547[/C][C]-0.294476737485466[/C][/ROW]
[ROW][C]231[/C][C]6.7[/C][C]5.89686963250033[/C][C]0.803130367499673[/C][/ROW]
[ROW][C]232[/C][C]12.5[/C][C]9.78730724419937[/C][C]2.71269275580063[/C][/ROW]
[ROW][C]233[/C][C]14.4[/C][C]13.9618449809456[/C][C]0.438155019054411[/C][/ROW]
[ROW][C]234[/C][C]16.5[/C][C]16.4275139352394[/C][C]0.072486064760593[/C][/ROW]
[ROW][C]235[/C][C]18.7[/C][C]18.0293974336996[/C][C]0.670602566300399[/C][/ROW]
[ROW][C]236[/C][C]19.4[/C][C]17.3207292352203[/C][C]2.07927076477968[/C][/ROW]
[ROW][C]237[/C][C]15.8[/C][C]15.1125065089669[/C][C]0.687493491033143[/C][/ROW]
[ROW][C]238[/C][C]11.3[/C][C]11.4413328157303[/C][C]-0.141332815730257[/C][/ROW]
[ROW][C]239[/C][C]9.7[/C][C]7.07681337610198[/C][C]2.62318662389802[/C][/ROW]
[ROW][C]240[/C][C]2.9[/C][C]4.13176478608773[/C][C]-1.23176478608773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115826&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115826&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
13	3.4	4.58159722222222	-1.18159722222222
14	0	0.9563708465851	-0.9563708465851
15	9.5	10.1491786365861	-0.649178636586125
16	8.9	9.32805947803669	-0.428059478036692
17	10.4	10.7841707714203	-0.384170771420342
18	13.2	13.4566173362391	-0.256617336239108
19	18.9	17.0590109545510	1.84098904544905
20	19	19.1698409280162	-0.169840928016178
21	16.3	12.6525165117421	3.64748348825789
22	10.6	12.5315815303507	-1.93158153035073
23	5.8	6.03462703895405	-0.234627038954051
24	3.6	3.51390989241083	0.0860901075891731
25	2.6	3.13245192076494	-0.532451920764941
26	5	-0.372605145762412	5.37260514576241
27	7.3	9.59372688888614	-2.29372688888614
28	9.2	8.6532412967104	0.546758703289598
29	15.7	10.2394365300667	5.46056346993327
30	16.8	13.6061228993839	3.19387710061615
31	18.4	18.0809906329937	0.319009367006259
32	18.1	19.6193489601023	-1.51934896010233
33	14.6	13.8197986361009	0.780201363899069
34	7.8	12.1886723679915	-4.38867236799146
35	7.6	5.81164867968252	1.78835132031748
36	3.8	3.6036776722818	0.196322327718201
37	5.6	3.12110001805014	2.47889998194986
38	2.2	1.26582386713320	0.934176132866802
39	6.8	9.08965082938107	-2.28965082938107
40	11.8	8.78951538508724	3.01048461491276
41	14.9	11.7440362599361	3.15596374006389
42	16.7	14.3824924545376	2.31750754546238
43	16.7	18.1497620004817	-1.44976200048166
44	15.9	19.1054765405788	-3.20547654057882
45	13.6	13.6331888605233	-0.033188860523266
46	9.2	10.7889818193017	-1.58898181930174
47	2.8	6.08170237718291	-3.28170237718291
48	2.5	2.97292984617687	-0.472929846176875
49	4.8	2.91553899948972	1.88446100051028
50	2.8	0.655001877556304	2.14499812244370
51	7.8	7.90627714916906	-0.106277149169064
52	9	9.00954589777025	-0.0095458977702485
53	12.9	11.6647741340474	1.23522586595262
54	16.4	13.9039002280447	2.49609977195529
55	21.8	16.8607271288579	4.93927287114213
56	17.8	18.1394513793061	-0.339451379306059
57	13.5	13.6907826543287	-0.190782654328711
58	10	10.5057391758765	-0.505739175876473
59	10.4	5.56574810113977	4.83425189886023
60	5.5	3.99633629548552	1.50366370451448
61	4	4.71462262518618	-0.714622625186177
62	6.8	2.26542608247820	4.5345739175218
63	5.7	9.3288775096819	-3.6288775096819
64	9.1	10.1040822905504	-1.00408229055044
65	13.6	12.9557207120591	0.64427928794092
66	15	15.4373477088581	-0.437347708858141
67	20.9	18.6324089904038	2.26759100959620
68	20.4	18.4823085395892	1.91769146041078
69	14	14.3353145929054	-0.335314592905434
70	13.7	11.0881354693262	2.61186453067384
71	7.1	7.68656529625276	-0.586565296252761
72	0.8	4.8140110442704	-4.01401104427041
73	2.1	4.44818472762206	-2.34818472762206
74	1.3	2.96795556133288	-1.66795556133288
75	3.9	7.55275408011954	-3.65275408011954
76	10.7	8.88307730430632	1.81692269569368
77	11.1	12.3936642981000	-1.29366429809998
78	16.4	14.4130635557960	1.98693644420403
79	17.1	18.4560968208236	-1.35609682082355
80	17.3	17.8169110987015	-0.516911098701453
81	12.9	12.8882685204609	0.0117314795390868
82	10.9	10.3012273396169	0.598772660383075
83	5.3	5.95307457364835	-0.653074573648346
84	0.7	2.29607024315198	-1.59607024315198
85	-0.2	2.53690782769973	-2.73690782769973
86	6.5	1.14056868601959	5.35943131398041
87	8.6	6.05294649750936	2.54705350249064
88	8.5	9.26643584146882	-0.766435841468818
89	13.3	11.8187177737818	1.48128222621821
90	16.2	14.8692648548251	1.33073514517488
91	17.5	18.1186788314571	-0.618678831457103
92	21.2	17.7545257145555	3.44547428544447
93	14.8	13.3946975944784	1.40530240552158
94	10.3	11.1124219279581	-0.812421927958102
95	7.3	6.35729240232238	0.942707597677617
96	5.1	2.69291387841357	2.40708612158643
97	4.4	3.15570439412523	1.24429560587477
98	6.2	4.00922574813211	2.19077425186789
99	7.7	7.9974523353418	-0.297452335341797
100	9.3	10.2054923938311	-0.905492393831103
101	15.6	13.2635566673641	2.33644333263594
102	16.3	16.4059202687909	-0.105920268790889
103	16.6	19.1000664380855	-2.50006643808548
104	17.4	19.4427836630769	-2.04278366307689
105	15.3	14.0474814332894	1.25251856671058
106	9.7	11.2726649667697	-1.57266496676967
107	3.7	6.82580038788644	-3.12580038788644
108	4.6	3.03503363562198	1.56496636437802
109	5.4	3.14674031374425	2.25325968625575
110	3.1	4.31500634357628	-1.21500634357628
111	7.9	7.37657357684682	0.523426423153176
112	10.1	9.53240597979732	0.567594020202675
113	15	13.4551748513742	1.54482514862581
114	15.6	15.9698674403621	-0.369867440362063
115	19.7	18.1038076765255	1.59619232347446
116	18.1	18.9959074063675	-0.895907406367478
117	17.7	14.4517821430725	3.24821785692748
118	10.7	11.2869920746194	-0.586992074619451
119	6.2	6.62062872992045	-0.420628729920449
120	4.2	4.17040118896349	0.0295988110365091
121	4	4.28070573554931	-0.280705735549313
122	5.9	4.42317216717721	1.47682783282279
123	7.1	8.17464881393191	-1.07464881393191
124	10.5	10.1777751286119	0.322224871388078
125	15.1	14.2989078255951	0.801092174404939
126	16.8	16.3231998861123	0.476800113887702
127	15.3	18.9911942169848	-3.69119421698484
128	18.4	18.7598250473786	-0.359825047378578
129	16.1	15.1804775625236	0.919522437476431
130	11.3	10.9168147743147	0.383185225685343
131	7.9	6.38917630382262	1.51082369617738
132	5.6	4.24943942127937	1.35056057872063
133	3.4	4.44055365736714	-1.04055365736714
134	4.8	4.88720178877641	-0.087201788776408
135	6.5	7.9087370942207	-1.40873709422071
136	8.5	10.1789026577129	-1.67890265771287
137	15.1	14.1794265026914	0.920573497308599
138	15.7	16.1391107620271	-0.439110762027131
139	18.7	17.7865310777461	0.913468922253859
140	19.2	18.7886748099040	0.41132519009604
141	12.9	15.5776501559411	-2.67765015594108
142	14.4	10.7996202512013	3.60037974879872
143	6.2	6.8730640827102	-0.673064082710194
144	3.3	4.45798410997156	-1.15798410997156
145	4.6	3.84415886072835	0.75584113927165
146	7.2	4.69155910200919	2.50844089799081
147	7.8	7.70991315728871	0.090086842711286
148	9.9	10.0909075607598	-0.190907560759751
149	13.6	14.8324404377178	-1.23244043771784
150	17.1	16.2645474549773	0.835452545022658
151	17.8	18.3547791543433	-0.554779154343333
152	18.6	19.0911466125117	-0.491146612511653
153	14.7	15.1080265924714	-0.408026592471405
154	10.5	11.9584576696969	-1.45845766969692
155	8.6	6.54031192102597	2.05968807897403
156	4.4	4.3192099979424	0.0807900020575989
157	2.3	4.26410172632599	-1.96410172632599
158	2.8	5.19627306668732	-2.39627306668732
159	8.8	7.13654678060156	1.66345321939844
160	10.7	9.61768094813946	1.08231905186054
161	13.9	14.2634148249320	-0.363414824931963
162	19.3	16.2378938778460	3.06210612215396
163	19.5	18.2677664574395	1.23223354256048
164	20.4	19.2182406065344	1.18175939346555
165	15.3	15.4451912361175	-0.14519123611748
166	7.9	12.1045553000659	-4.20455530006594
167	8.3	7.15949865034186	1.14050134965814
168	4.5	4.40618344426226	0.0938165557377433
169	3.2	3.90617242595118	-0.706172425951179
170	5	4.88513881074623	0.114861189253766
171	6.6	7.99767593134607	-1.39767593134607
172	11.1	10.0204100250225	1.07958997497754
173	12.8	14.3523243389097	-1.55232433890966
174	16.3	16.9460869291732	-0.646086929173233
175	17.4	18.1616660696579	-0.76166606965792
176	18.9	18.8691464208698	0.0308535791302482
177	15.8	14.6630250065956	1.1369749934044
178	11.7	10.5603154362884	1.13968456371161
179	6.4	7.36666002880971	-0.966660028809713
180	2.9	4.14845373224355	-1.24845373224355
181	4.7	3.31763615470415	1.38236384529585
182	2.4	4.69987266647393	-2.29987266647393
183	7.2	7.20792459172523	-0.00792459172523063
184	10.7	9.91740469949437	0.782595300505626
185	13.4	13.6337716204613	-0.233771620461345
186	18.5	16.5654201307873	1.93457986921272
187	18.3	18.0394982864143	0.260501713585700
188	16.8	19.0365941215135	-2.23659412151354
189	16.6	14.8241279089308	1.77587209106919
190	14.1	10.7924210170246	3.30757898297541
191	6.1	7.3806678152282	-1.28066781522820
192	3.5	4.07186580745141	-0.571865807451407
193	1.7	3.89728208659807	-2.19728208659807
194	2.3	4.08163839000467	-1.78163839000467
195	4.5	7.14692898291867	-2.64692898291867
196	9.3	9.73421227297943	-0.434212272979424
197	14.2	13.0853215975591	1.11467840244092
198	17.3	16.6315363940932	0.668463605906798
199	23	17.5913218461818	5.40867815381816
200	16.3	18.6067413494982	-2.30674134949819
201	18.4	15.2668778666604	3.13312213333958
202	14.2	11.7242739445940	2.47572605540603
203	9.1	7.22210756028859	1.87789243971141
204	5.9	4.42472992160946	1.47527007839054
205	7.2	4.13482720416418	3.06517279583582
206	6.8	5.01417979504679	1.78582020495321
207	8	8.31820528104268	-0.318205281042676
208	14.3	11.6880897459961	2.61191025400392
209	14.6	15.7624374296896	-1.16243742968956
210	17.5	19.0090424993913	-1.50904249939135
211	17.2	20.8090964733673	-3.60909647336733
212	17.2	19.1716835179484	-1.97168351794840
213	14.1	17.0777166125462	-2.97771661254622
214	10.5	12.7289019852212	-2.22890198522123
215	6.8	7.57530775326229	-0.775307753262285
216	4.1	4.38644513108627	-0.286445131086266
217	6.5	4.23377411650648	2.26622588349352
218	6.1	4.72583784270226	1.37416215729774
219	6.3	7.50343106928831	-1.20343106928831
220	9.3	11.3941201050319	-2.09412010503187
221	16.4	14.0942603654181	2.30573963458189
222	16.1	17.6168850483410	-1.51688504834097
223	18	18.9301471159034	-0.93014711590341
224	17.6	17.9232296592855	-0.323229659285516
225	14	15.7732190024372	-1.77321900243723
226	10.5	11.7067432949641	-1.20674329496408
227	6.9	6.97228436852123	-0.0722843685212275
228	2.8	3.95846803938906	-1.15846803938906
229	0.7	4.25823885681884	-3.55823885681884
230	3.6	3.89447673748547	-0.294476737485466
231	6.7	5.89686963250033	0.803130367499673
232	12.5	9.78730724419937	2.71269275580063
233	14.4	13.9618449809456	0.438155019054411
234	16.5	16.4275139352394	0.072486064760593
235	18.7	18.0293974336996	0.670602566300399
236	19.4	17.3207292352203	2.07927076477968
237	15.8	15.1125065089669	0.687493491033143
238	11.3	11.4413328157303	-0.141332815730257
239	9.7	7.07681337610198	2.62318662389802
240	2.9	4.13176478608773	-1.23176478608773

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
241	3.91070668600518	0.158000081670111	7.66341329034024
242	4.66994839507301	0.893948854527247	8.44594793561877
243	6.96617294738838	3.16598547526647	10.7663604195103
244	11.2062871495763	7.38101105514013	15.0315632440124
245	14.6002421585177	10.7489718333377	18.4515124836976
246	16.9499352249460	13.0717609068749	20.8281095430172
247	18.6863669131940	14.7803754345676	22.5923583918204
248	18.2226126243335	14.2878881424782	22.1573371061888
249	15.4879115345081	11.5235362427872	19.4522868262291
250	11.5635414804101	7.568596298205	15.5584866626152
251	7.8225716577233	3.79613689791498	11.8490064175316
252	3.74506991847836	-0.313774068834694	7.80391390579142

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
241 & 3.91070668600518 & 0.158000081670111 & 7.66341329034024 \tabularnewline
242 & 4.66994839507301 & 0.893948854527247 & 8.44594793561877 \tabularnewline
243 & 6.96617294738838 & 3.16598547526647 & 10.7663604195103 \tabularnewline
244 & 11.2062871495763 & 7.38101105514013 & 15.0315632440124 \tabularnewline
245 & 14.6002421585177 & 10.7489718333377 & 18.4515124836976 \tabularnewline
246 & 16.9499352249460 & 13.0717609068749 & 20.8281095430172 \tabularnewline
247 & 18.6863669131940 & 14.7803754345676 & 22.5923583918204 \tabularnewline
248 & 18.2226126243335 & 14.2878881424782 & 22.1573371061888 \tabularnewline
249 & 15.4879115345081 & 11.5235362427872 & 19.4522868262291 \tabularnewline
250 & 11.5635414804101 & 7.568596298205 & 15.5584866626152 \tabularnewline
251 & 7.8225716577233 & 3.79613689791498 & 11.8490064175316 \tabularnewline
252 & 3.74506991847836 & -0.313774068834694 & 7.80391390579142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115826&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]241[/C][C]3.91070668600518[/C][C]0.158000081670111[/C][C]7.66341329034024[/C][/ROW]
[ROW][C]242[/C][C]4.66994839507301[/C][C]0.893948854527247[/C][C]8.44594793561877[/C][/ROW]
[ROW][C]243[/C][C]6.96617294738838[/C][C]3.16598547526647[/C][C]10.7663604195103[/C][/ROW]
[ROW][C]244[/C][C]11.2062871495763[/C][C]7.38101105514013[/C][C]15.0315632440124[/C][/ROW]
[ROW][C]245[/C][C]14.6002421585177[/C][C]10.7489718333377[/C][C]18.4515124836976[/C][/ROW]
[ROW][C]246[/C][C]16.9499352249460[/C][C]13.0717609068749[/C][C]20.8281095430172[/C][/ROW]
[ROW][C]247[/C][C]18.6863669131940[/C][C]14.7803754345676[/C][C]22.5923583918204[/C][/ROW]
[ROW][C]248[/C][C]18.2226126243335[/C][C]14.2878881424782[/C][C]22.1573371061888[/C][/ROW]
[ROW][C]249[/C][C]15.4879115345081[/C][C]11.5235362427872[/C][C]19.4522868262291[/C][/ROW]
[ROW][C]250[/C][C]11.5635414804101[/C][C]7.568596298205[/C][C]15.5584866626152[/C][/ROW]
[ROW][C]251[/C][C]7.8225716577233[/C][C]3.79613689791498[/C][C]11.8490064175316[/C][/ROW]
[ROW][C]252[/C][C]3.74506991847836[/C][C]-0.313774068834694[/C][C]7.80391390579142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115826&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115826&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
241	3.91070668600518	0.158000081670111	7.66341329034024
242	4.66994839507301	0.893948854527247	8.44594793561877
243	6.96617294738838	3.16598547526647	10.7663604195103
244	11.2062871495763	7.38101105514013	15.0315632440124
245	14.6002421585177	10.7489718333377	18.4515124836976
246	16.9499352249460	13.0717609068749	20.8281095430172
247	18.6863669131940	14.7803754345676	22.5923583918204
248	18.2226126243335	14.2878881424782	22.1573371061888
249	15.4879115345081	11.5235362427872	19.4522868262291
250	11.5635414804101	7.568596298205	15.5584866626152
251	7.8225716577233	3.79613689791498	11.8490064175316
252	3.74506991847836	-0.313774068834694	7.80391390579142

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 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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