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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 28 Apr 2016 14:27:59 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/28/t1461850089rtzghdpvw5hn00o.htm/, Retrieved Sat, 04 May 2024 17:28:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295034, Retrieved Sat, 04 May 2024 17:28:19 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-28 13:27:59] [e2ca982fef5d38be90899c2ec1ea6fcf] [Current]
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Dataseries X:
250785
250140
255755
254671
253919
253741
252729
253810
256653
255231
258405
251061
254811
254895
258325
257608
258759
258621
257852
260560
262358
260812
261165
257164
260720
259581
264743
261845
262262
261631
258953
259966
262850
262204
263418
262752
266433
267722
266003
262971
265521
264676
270223
269508
268457
265814
266680
263018
269285
269829
270911
266844
271244
269907
271296
270157
271322
267179
264101
265518
269419
268714
272482
268351
268175
270674
272764
272599
270333
270846
270491
269160
274027
273784
276663
274525
271344
271115
270798
273911
273985
271917
273338
270601
273547
275363
281229
277793
279913
282500
280041
282166
290304
283519
287816
285226
287595
289741
289148
288301
290155
289648
288225
289351
294735
305333
309030
310215
321935
325734
320846
323023
319753
321753
320757
324479
324641
322767
324181
321389
327897
334287
332653
334819
335264
339622
342440
346585
335378
337010
339130
341193
343507
348915
346431
348322
348288
346597
351076
355215
350562
355266
361565
363462
366183
365423
369208
366713
369354
371970
371824
373187
367270
368140
373742
364815
368558
371503
372611
370197
375441
375888
375132
381142
372024
376070
376864
371401
375687
384304
380738
379908
384007
384499
385106
387935
380435
379281
384153
380599




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295034&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295034&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295034&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.785955903365853
beta0.0130978913377891
gamma0.933597389032669

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.785955903365853 \tabularnewline
beta & 0.0130978913377891 \tabularnewline
gamma & 0.933597389032669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295034&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]0.785955903365853[/C][/ROW]
[ROW][C]beta[/C][C]0.0130978913377891[/C][/ROW]
[ROW][C]gamma[/C][C]0.933597389032669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295034&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295034&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
ParameterValue
alpha0.785955903365853
beta0.0130978913377891
gamma0.933597389032669







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13254811252764.6704059832046.32959401695
14254895254380.220568082514.779431918258
15258325258119.089166354205.910833645787
16257608257519.02872106688.9712789337209
17258759258818.68317857-59.683178570267
18258621258690.137387212-69.1373872116965
19257852257415.865945926436.134054073947
20260560258903.2052998711656.79470012937
21262358263189.652410659-831.652410659473
22260812261322.478491026-510.478491026297
23261165264203.894724282-3038.8947242818
24257164254467.8454679662696.15453203395
25260720260758.175672043-38.1756720430858
26259581260440.161925056-859.161925056396
27264743263034.1243509741708.87564902613
28261845263604.104565919-1759.10456591874
29262262263414.667105948-1152.66710594838
30261631262407.063298019-776.063298018824
31258953260652.739210333-1699.73921033289
32259966260657.905797857-691.905797856569
33262850262529.534193008320.465806991677
34262204261572.340426923631.659573076759
35263418264798.213961622-1380.21396162163
36262752257480.9735081015271.0264918989
37266433265244.2604172861188.73958271352
38267722265734.7446127771987.25538722344
39266003271116.596296056-5113.59629605623
40262971265598.728631334-2627.72863133362
41265521264806.158245413714.84175458661
42264676265319.198264201-643.198264200531
43270223263463.6959990826759.30400091829
44269508270384.749237451-876.749237451353
45268457272377.554567917-3920.55456791702
46265814268169.785842411-2355.78584241075
47266680268635.364319331-1955.36431933095
48263018262179.024357523838.975642476755
49269285265581.3412879123703.65871208755
50269829268172.0928001521656.90719984833
51270911271836.017849589-925.017849588767
52266844270110.74317876-3266.74317876005
53271244269481.1080949691762.89190503105
54269907270554.503161704-647.503161703527
55271296270182.8349765731113.16502342653
56270157271090.196346848-933.196346847981
57271322272379.65358028-1057.65358027961
58267179270713.4233835-3534.42338349967
59264101270299.263321574-6198.26332157373
60265518260989.5116238874528.48837611321
61269419267824.9805752221594.01942477789
62268714268287.832014308426.167985691573
63272482270395.019744512086.98025548994
64268351270526.618157502-2175.61815750215
65268175271728.39345153-3553.39345153014
66270674268055.7803647552618.21963524504
67272764270550.3103209952213.6896790046
68272599271872.686213764726.313786235522
69270333274417.635553012-4084.63555301249
70270846269822.2954719921023.70452800824
71270491272450.128035602-1959.1280356021
72269160268651.149480076508.850519924366
73274027271735.044931812291.95506818977
74273784272514.3373784671269.6626215335
75276663275626.3070325041036.69296749582
76274525274079.76510795445.23489204963
77271344277092.211619592-5748.21161959181
78271115272931.372172079-1816.37217207882
79270798271817.543842245-1019.5438422446
80273911270226.1058029733684.89419702732
81273985274090.037591489-105.037591489323
82271917273639.303786127-1722.30378612719
83273338273480.577057715-142.577057715331
84270601271588.950948953-987.950948953046
85273547273823.782246879-276.782246878603
86275363272324.4673995643038.53260043578
87281229276742.9383827154486.06161728455
88277793277787.5675949865.43240501423134
89279913279210.489736083702.51026391692
90282500280965.5264273251534.47357267537
91280041282739.230677265-2698.23067726492
92282166280845.9149744581320.08502554154
93290304282146.924489938157.07551006973
94283519288004.779874211-4485.779874211
95287816286099.4255161791716.57448382111
96285226285628.881731369-402.881731368543
97287595288600.491223598-1005.49122359796
98289741287318.2704006162422.7295993836
99289148291662.99369682-2514.99369682011
100288301286358.6472083851942.35279161501
101290155289512.054212609642.945787390927
102289648291454.767820005-1806.76782000484
103288225289790.422050066-1565.42205006647
104289351289635.933546634-284.933546633692
105294735291070.6947924963664.30520750378
106305333290853.72889992714479.2711000728
107309030305271.4568268723758.54317312763
108310215306181.2638632194033.73613678146
109321935312764.0980112839170.90198871703
110325734320514.5565582185219.44344178151
111320846326448.871990857-5602.87199085701
112323023319954.7262458223068.27375417849
113319753324091.407172788-4338.40717278805
114321753321936.199914176-183.199914175784
115320757321919.580537472-1162.58053747244
116324479322665.1812514071813.81874859333
117324641326887.847185423-2246.84718542261
118322767324474.48773232-1707.48773232027
119324181324149.51671134231.4832886579679
120321389322268.35700191-879.35700190952
121327897326049.0503439811847.94965601887
122334287327211.7508898727075.24911012792
123332653332418.501429552234.49857044837
124334819332281.6152778832537.38472211664
125335264334552.071072623711.928927376517
126339622337279.6493165582342.35068344203
127342440339161.3944305473278.60556945315
128346585344147.171356972437.82864303043
129335378348210.081262065-12832.0812620653
130337010337637.253763321-627.253763321089
131339130338572.198086404557.801913595642
132341193336991.5043323974201.49566760322
133343507345431.64527965-1924.64527965017
134348915344756.1136357974158.88636420271
135346431346356.00001124274.9999887577142
136348322346604.5635762471717.43642375304
137348288347907.973147118380.026852881711
138346597350739.262757413-4142.26275741257
139351076347683.4883733183392.51162668184
140355215352563.9576837352651.04231626453
141350562353718.418066229-3156.41806622909
142355266353264.1184343852001.88156561542
143361565356604.3035974744960.69640252588
144363462359359.5842989954102.41570100514
145366183366644.010402812-461.010402812331
146365423368495.92726634-3072.92726634024
147369208363682.8107237155525.18927628529
148366713368686.269537952-1973.26953795168
149369354366926.7746642582427.22533574194
150371970370589.5365153621380.46348463756
151371824373563.074164244-1739.07416424406
152373187374392.359517305-1205.35951730516
153367270371445.832982126-4175.83298212575
154368140371301.097715477-3161.09771547699
155373742371201.5135091442540.48649085616
156364815371885.032038681-7070.03203868051
157368558369363.406779708-805.406779707642
158371503370306.0698909981196.93010900164
159372611370494.3673376782116.63266232202
160370197371212.661504701-1015.66150470084
161375441370987.252760474453.7472395295
162375888375956.550852258-68.5508522579912
163375132377075.884952928-1943.88495292811
164381142377756.780579633385.21942036977
165372024377777.840828949-5753.84082894865
166376070376532.578844216-462.578844215546
167376864379657.986634237-2793.98663423723
168371401374138.171714183-2737.17171418271
169375687376228.260859157-541.260859157366
170384304377735.7900951296568.20990487112
171380738382341.885687475-1603.88568747503
172379908379484.210605264423.789394736232
173384007381472.0461157792534.95388422121
174384499383998.750939933500.249060066941
175385106385165.431307891-59.4313078908599
176387935388386.788488548-451.788488548133
177380435383520.80630177-3085.80630177015
178379281385412.269969669-6131.26996966865
179384153383540.50329715612.496702850447
180380599380668.509396041-69.5093960405211

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 254811 & 252764.670405983 & 2046.32959401695 \tabularnewline
14 & 254895 & 254380.220568082 & 514.779431918258 \tabularnewline
15 & 258325 & 258119.089166354 & 205.910833645787 \tabularnewline
16 & 257608 & 257519.028721066 & 88.9712789337209 \tabularnewline
17 & 258759 & 258818.68317857 & -59.683178570267 \tabularnewline
18 & 258621 & 258690.137387212 & -69.1373872116965 \tabularnewline
19 & 257852 & 257415.865945926 & 436.134054073947 \tabularnewline
20 & 260560 & 258903.205299871 & 1656.79470012937 \tabularnewline
21 & 262358 & 263189.652410659 & -831.652410659473 \tabularnewline
22 & 260812 & 261322.478491026 & -510.478491026297 \tabularnewline
23 & 261165 & 264203.894724282 & -3038.8947242818 \tabularnewline
24 & 257164 & 254467.845467966 & 2696.15453203395 \tabularnewline
25 & 260720 & 260758.175672043 & -38.1756720430858 \tabularnewline
26 & 259581 & 260440.161925056 & -859.161925056396 \tabularnewline
27 & 264743 & 263034.124350974 & 1708.87564902613 \tabularnewline
28 & 261845 & 263604.104565919 & -1759.10456591874 \tabularnewline
29 & 262262 & 263414.667105948 & -1152.66710594838 \tabularnewline
30 & 261631 & 262407.063298019 & -776.063298018824 \tabularnewline
31 & 258953 & 260652.739210333 & -1699.73921033289 \tabularnewline
32 & 259966 & 260657.905797857 & -691.905797856569 \tabularnewline
33 & 262850 & 262529.534193008 & 320.465806991677 \tabularnewline
34 & 262204 & 261572.340426923 & 631.659573076759 \tabularnewline
35 & 263418 & 264798.213961622 & -1380.21396162163 \tabularnewline
36 & 262752 & 257480.973508101 & 5271.0264918989 \tabularnewline
37 & 266433 & 265244.260417286 & 1188.73958271352 \tabularnewline
38 & 267722 & 265734.744612777 & 1987.25538722344 \tabularnewline
39 & 266003 & 271116.596296056 & -5113.59629605623 \tabularnewline
40 & 262971 & 265598.728631334 & -2627.72863133362 \tabularnewline
41 & 265521 & 264806.158245413 & 714.84175458661 \tabularnewline
42 & 264676 & 265319.198264201 & -643.198264200531 \tabularnewline
43 & 270223 & 263463.695999082 & 6759.30400091829 \tabularnewline
44 & 269508 & 270384.749237451 & -876.749237451353 \tabularnewline
45 & 268457 & 272377.554567917 & -3920.55456791702 \tabularnewline
46 & 265814 & 268169.785842411 & -2355.78584241075 \tabularnewline
47 & 266680 & 268635.364319331 & -1955.36431933095 \tabularnewline
48 & 263018 & 262179.024357523 & 838.975642476755 \tabularnewline
49 & 269285 & 265581.341287912 & 3703.65871208755 \tabularnewline
50 & 269829 & 268172.092800152 & 1656.90719984833 \tabularnewline
51 & 270911 & 271836.017849589 & -925.017849588767 \tabularnewline
52 & 266844 & 270110.74317876 & -3266.74317876005 \tabularnewline
53 & 271244 & 269481.108094969 & 1762.89190503105 \tabularnewline
54 & 269907 & 270554.503161704 & -647.503161703527 \tabularnewline
55 & 271296 & 270182.834976573 & 1113.16502342653 \tabularnewline
56 & 270157 & 271090.196346848 & -933.196346847981 \tabularnewline
57 & 271322 & 272379.65358028 & -1057.65358027961 \tabularnewline
58 & 267179 & 270713.4233835 & -3534.42338349967 \tabularnewline
59 & 264101 & 270299.263321574 & -6198.26332157373 \tabularnewline
60 & 265518 & 260989.511623887 & 4528.48837611321 \tabularnewline
61 & 269419 & 267824.980575222 & 1594.01942477789 \tabularnewline
62 & 268714 & 268287.832014308 & 426.167985691573 \tabularnewline
63 & 272482 & 270395.01974451 & 2086.98025548994 \tabularnewline
64 & 268351 & 270526.618157502 & -2175.61815750215 \tabularnewline
65 & 268175 & 271728.39345153 & -3553.39345153014 \tabularnewline
66 & 270674 & 268055.780364755 & 2618.21963524504 \tabularnewline
67 & 272764 & 270550.310320995 & 2213.6896790046 \tabularnewline
68 & 272599 & 271872.686213764 & 726.313786235522 \tabularnewline
69 & 270333 & 274417.635553012 & -4084.63555301249 \tabularnewline
70 & 270846 & 269822.295471992 & 1023.70452800824 \tabularnewline
71 & 270491 & 272450.128035602 & -1959.1280356021 \tabularnewline
72 & 269160 & 268651.149480076 & 508.850519924366 \tabularnewline
73 & 274027 & 271735.04493181 & 2291.95506818977 \tabularnewline
74 & 273784 & 272514.337378467 & 1269.6626215335 \tabularnewline
75 & 276663 & 275626.307032504 & 1036.69296749582 \tabularnewline
76 & 274525 & 274079.76510795 & 445.23489204963 \tabularnewline
77 & 271344 & 277092.211619592 & -5748.21161959181 \tabularnewline
78 & 271115 & 272931.372172079 & -1816.37217207882 \tabularnewline
79 & 270798 & 271817.543842245 & -1019.5438422446 \tabularnewline
80 & 273911 & 270226.105802973 & 3684.89419702732 \tabularnewline
81 & 273985 & 274090.037591489 & -105.037591489323 \tabularnewline
82 & 271917 & 273639.303786127 & -1722.30378612719 \tabularnewline
83 & 273338 & 273480.577057715 & -142.577057715331 \tabularnewline
84 & 270601 & 271588.950948953 & -987.950948953046 \tabularnewline
85 & 273547 & 273823.782246879 & -276.782246878603 \tabularnewline
86 & 275363 & 272324.467399564 & 3038.53260043578 \tabularnewline
87 & 281229 & 276742.938382715 & 4486.06161728455 \tabularnewline
88 & 277793 & 277787.567594986 & 5.43240501423134 \tabularnewline
89 & 279913 & 279210.489736083 & 702.51026391692 \tabularnewline
90 & 282500 & 280965.526427325 & 1534.47357267537 \tabularnewline
91 & 280041 & 282739.230677265 & -2698.23067726492 \tabularnewline
92 & 282166 & 280845.914974458 & 1320.08502554154 \tabularnewline
93 & 290304 & 282146.92448993 & 8157.07551006973 \tabularnewline
94 & 283519 & 288004.779874211 & -4485.779874211 \tabularnewline
95 & 287816 & 286099.425516179 & 1716.57448382111 \tabularnewline
96 & 285226 & 285628.881731369 & -402.881731368543 \tabularnewline
97 & 287595 & 288600.491223598 & -1005.49122359796 \tabularnewline
98 & 289741 & 287318.270400616 & 2422.7295993836 \tabularnewline
99 & 289148 & 291662.99369682 & -2514.99369682011 \tabularnewline
100 & 288301 & 286358.647208385 & 1942.35279161501 \tabularnewline
101 & 290155 & 289512.054212609 & 642.945787390927 \tabularnewline
102 & 289648 & 291454.767820005 & -1806.76782000484 \tabularnewline
103 & 288225 & 289790.422050066 & -1565.42205006647 \tabularnewline
104 & 289351 & 289635.933546634 & -284.933546633692 \tabularnewline
105 & 294735 & 291070.694792496 & 3664.30520750378 \tabularnewline
106 & 305333 & 290853.728899927 & 14479.2711000728 \tabularnewline
107 & 309030 & 305271.456826872 & 3758.54317312763 \tabularnewline
108 & 310215 & 306181.263863219 & 4033.73613678146 \tabularnewline
109 & 321935 & 312764.098011283 & 9170.90198871703 \tabularnewline
110 & 325734 & 320514.556558218 & 5219.44344178151 \tabularnewline
111 & 320846 & 326448.871990857 & -5602.87199085701 \tabularnewline
112 & 323023 & 319954.726245822 & 3068.27375417849 \tabularnewline
113 & 319753 & 324091.407172788 & -4338.40717278805 \tabularnewline
114 & 321753 & 321936.199914176 & -183.199914175784 \tabularnewline
115 & 320757 & 321919.580537472 & -1162.58053747244 \tabularnewline
116 & 324479 & 322665.181251407 & 1813.81874859333 \tabularnewline
117 & 324641 & 326887.847185423 & -2246.84718542261 \tabularnewline
118 & 322767 & 324474.48773232 & -1707.48773232027 \tabularnewline
119 & 324181 & 324149.516711342 & 31.4832886579679 \tabularnewline
120 & 321389 & 322268.35700191 & -879.35700190952 \tabularnewline
121 & 327897 & 326049.050343981 & 1847.94965601887 \tabularnewline
122 & 334287 & 327211.750889872 & 7075.24911012792 \tabularnewline
123 & 332653 & 332418.501429552 & 234.49857044837 \tabularnewline
124 & 334819 & 332281.615277883 & 2537.38472211664 \tabularnewline
125 & 335264 & 334552.071072623 & 711.928927376517 \tabularnewline
126 & 339622 & 337279.649316558 & 2342.35068344203 \tabularnewline
127 & 342440 & 339161.394430547 & 3278.60556945315 \tabularnewline
128 & 346585 & 344147.17135697 & 2437.82864303043 \tabularnewline
129 & 335378 & 348210.081262065 & -12832.0812620653 \tabularnewline
130 & 337010 & 337637.253763321 & -627.253763321089 \tabularnewline
131 & 339130 & 338572.198086404 & 557.801913595642 \tabularnewline
132 & 341193 & 336991.504332397 & 4201.49566760322 \tabularnewline
133 & 343507 & 345431.64527965 & -1924.64527965017 \tabularnewline
134 & 348915 & 344756.113635797 & 4158.88636420271 \tabularnewline
135 & 346431 & 346356.000011242 & 74.9999887577142 \tabularnewline
136 & 348322 & 346604.563576247 & 1717.43642375304 \tabularnewline
137 & 348288 & 347907.973147118 & 380.026852881711 \tabularnewline
138 & 346597 & 350739.262757413 & -4142.26275741257 \tabularnewline
139 & 351076 & 347683.488373318 & 3392.51162668184 \tabularnewline
140 & 355215 & 352563.957683735 & 2651.04231626453 \tabularnewline
141 & 350562 & 353718.418066229 & -3156.41806622909 \tabularnewline
142 & 355266 & 353264.118434385 & 2001.88156561542 \tabularnewline
143 & 361565 & 356604.303597474 & 4960.69640252588 \tabularnewline
144 & 363462 & 359359.584298995 & 4102.41570100514 \tabularnewline
145 & 366183 & 366644.010402812 & -461.010402812331 \tabularnewline
146 & 365423 & 368495.92726634 & -3072.92726634024 \tabularnewline
147 & 369208 & 363682.810723715 & 5525.18927628529 \tabularnewline
148 & 366713 & 368686.269537952 & -1973.26953795168 \tabularnewline
149 & 369354 & 366926.774664258 & 2427.22533574194 \tabularnewline
150 & 371970 & 370589.536515362 & 1380.46348463756 \tabularnewline
151 & 371824 & 373563.074164244 & -1739.07416424406 \tabularnewline
152 & 373187 & 374392.359517305 & -1205.35951730516 \tabularnewline
153 & 367270 & 371445.832982126 & -4175.83298212575 \tabularnewline
154 & 368140 & 371301.097715477 & -3161.09771547699 \tabularnewline
155 & 373742 & 371201.513509144 & 2540.48649085616 \tabularnewline
156 & 364815 & 371885.032038681 & -7070.03203868051 \tabularnewline
157 & 368558 & 369363.406779708 & -805.406779707642 \tabularnewline
158 & 371503 & 370306.069890998 & 1196.93010900164 \tabularnewline
159 & 372611 & 370494.367337678 & 2116.63266232202 \tabularnewline
160 & 370197 & 371212.661504701 & -1015.66150470084 \tabularnewline
161 & 375441 & 370987.25276047 & 4453.7472395295 \tabularnewline
162 & 375888 & 375956.550852258 & -68.5508522579912 \tabularnewline
163 & 375132 & 377075.884952928 & -1943.88495292811 \tabularnewline
164 & 381142 & 377756.78057963 & 3385.21942036977 \tabularnewline
165 & 372024 & 377777.840828949 & -5753.84082894865 \tabularnewline
166 & 376070 & 376532.578844216 & -462.578844215546 \tabularnewline
167 & 376864 & 379657.986634237 & -2793.98663423723 \tabularnewline
168 & 371401 & 374138.171714183 & -2737.17171418271 \tabularnewline
169 & 375687 & 376228.260859157 & -541.260859157366 \tabularnewline
170 & 384304 & 377735.790095129 & 6568.20990487112 \tabularnewline
171 & 380738 & 382341.885687475 & -1603.88568747503 \tabularnewline
172 & 379908 & 379484.210605264 & 423.789394736232 \tabularnewline
173 & 384007 & 381472.046115779 & 2534.95388422121 \tabularnewline
174 & 384499 & 383998.750939933 & 500.249060066941 \tabularnewline
175 & 385106 & 385165.431307891 & -59.4313078908599 \tabularnewline
176 & 387935 & 388386.788488548 & -451.788488548133 \tabularnewline
177 & 380435 & 383520.80630177 & -3085.80630177015 \tabularnewline
178 & 379281 & 385412.269969669 & -6131.26996966865 \tabularnewline
179 & 384153 & 383540.50329715 & 612.496702850447 \tabularnewline
180 & 380599 & 380668.509396041 & -69.5093960405211 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295034&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]254811[/C][C]252764.670405983[/C][C]2046.32959401695[/C][/ROW]
[ROW][C]14[/C][C]254895[/C][C]254380.220568082[/C][C]514.779431918258[/C][/ROW]
[ROW][C]15[/C][C]258325[/C][C]258119.089166354[/C][C]205.910833645787[/C][/ROW]
[ROW][C]16[/C][C]257608[/C][C]257519.028721066[/C][C]88.9712789337209[/C][/ROW]
[ROW][C]17[/C][C]258759[/C][C]258818.68317857[/C][C]-59.683178570267[/C][/ROW]
[ROW][C]18[/C][C]258621[/C][C]258690.137387212[/C][C]-69.1373872116965[/C][/ROW]
[ROW][C]19[/C][C]257852[/C][C]257415.865945926[/C][C]436.134054073947[/C][/ROW]
[ROW][C]20[/C][C]260560[/C][C]258903.205299871[/C][C]1656.79470012937[/C][/ROW]
[ROW][C]21[/C][C]262358[/C][C]263189.652410659[/C][C]-831.652410659473[/C][/ROW]
[ROW][C]22[/C][C]260812[/C][C]261322.478491026[/C][C]-510.478491026297[/C][/ROW]
[ROW][C]23[/C][C]261165[/C][C]264203.894724282[/C][C]-3038.8947242818[/C][/ROW]
[ROW][C]24[/C][C]257164[/C][C]254467.845467966[/C][C]2696.15453203395[/C][/ROW]
[ROW][C]25[/C][C]260720[/C][C]260758.175672043[/C][C]-38.1756720430858[/C][/ROW]
[ROW][C]26[/C][C]259581[/C][C]260440.161925056[/C][C]-859.161925056396[/C][/ROW]
[ROW][C]27[/C][C]264743[/C][C]263034.124350974[/C][C]1708.87564902613[/C][/ROW]
[ROW][C]28[/C][C]261845[/C][C]263604.104565919[/C][C]-1759.10456591874[/C][/ROW]
[ROW][C]29[/C][C]262262[/C][C]263414.667105948[/C][C]-1152.66710594838[/C][/ROW]
[ROW][C]30[/C][C]261631[/C][C]262407.063298019[/C][C]-776.063298018824[/C][/ROW]
[ROW][C]31[/C][C]258953[/C][C]260652.739210333[/C][C]-1699.73921033289[/C][/ROW]
[ROW][C]32[/C][C]259966[/C][C]260657.905797857[/C][C]-691.905797856569[/C][/ROW]
[ROW][C]33[/C][C]262850[/C][C]262529.534193008[/C][C]320.465806991677[/C][/ROW]
[ROW][C]34[/C][C]262204[/C][C]261572.340426923[/C][C]631.659573076759[/C][/ROW]
[ROW][C]35[/C][C]263418[/C][C]264798.213961622[/C][C]-1380.21396162163[/C][/ROW]
[ROW][C]36[/C][C]262752[/C][C]257480.973508101[/C][C]5271.0264918989[/C][/ROW]
[ROW][C]37[/C][C]266433[/C][C]265244.260417286[/C][C]1188.73958271352[/C][/ROW]
[ROW][C]38[/C][C]267722[/C][C]265734.744612777[/C][C]1987.25538722344[/C][/ROW]
[ROW][C]39[/C][C]266003[/C][C]271116.596296056[/C][C]-5113.59629605623[/C][/ROW]
[ROW][C]40[/C][C]262971[/C][C]265598.728631334[/C][C]-2627.72863133362[/C][/ROW]
[ROW][C]41[/C][C]265521[/C][C]264806.158245413[/C][C]714.84175458661[/C][/ROW]
[ROW][C]42[/C][C]264676[/C][C]265319.198264201[/C][C]-643.198264200531[/C][/ROW]
[ROW][C]43[/C][C]270223[/C][C]263463.695999082[/C][C]6759.30400091829[/C][/ROW]
[ROW][C]44[/C][C]269508[/C][C]270384.749237451[/C][C]-876.749237451353[/C][/ROW]
[ROW][C]45[/C][C]268457[/C][C]272377.554567917[/C][C]-3920.55456791702[/C][/ROW]
[ROW][C]46[/C][C]265814[/C][C]268169.785842411[/C][C]-2355.78584241075[/C][/ROW]
[ROW][C]47[/C][C]266680[/C][C]268635.364319331[/C][C]-1955.36431933095[/C][/ROW]
[ROW][C]48[/C][C]263018[/C][C]262179.024357523[/C][C]838.975642476755[/C][/ROW]
[ROW][C]49[/C][C]269285[/C][C]265581.341287912[/C][C]3703.65871208755[/C][/ROW]
[ROW][C]50[/C][C]269829[/C][C]268172.092800152[/C][C]1656.90719984833[/C][/ROW]
[ROW][C]51[/C][C]270911[/C][C]271836.017849589[/C][C]-925.017849588767[/C][/ROW]
[ROW][C]52[/C][C]266844[/C][C]270110.74317876[/C][C]-3266.74317876005[/C][/ROW]
[ROW][C]53[/C][C]271244[/C][C]269481.108094969[/C][C]1762.89190503105[/C][/ROW]
[ROW][C]54[/C][C]269907[/C][C]270554.503161704[/C][C]-647.503161703527[/C][/ROW]
[ROW][C]55[/C][C]271296[/C][C]270182.834976573[/C][C]1113.16502342653[/C][/ROW]
[ROW][C]56[/C][C]270157[/C][C]271090.196346848[/C][C]-933.196346847981[/C][/ROW]
[ROW][C]57[/C][C]271322[/C][C]272379.65358028[/C][C]-1057.65358027961[/C][/ROW]
[ROW][C]58[/C][C]267179[/C][C]270713.4233835[/C][C]-3534.42338349967[/C][/ROW]
[ROW][C]59[/C][C]264101[/C][C]270299.263321574[/C][C]-6198.26332157373[/C][/ROW]
[ROW][C]60[/C][C]265518[/C][C]260989.511623887[/C][C]4528.48837611321[/C][/ROW]
[ROW][C]61[/C][C]269419[/C][C]267824.980575222[/C][C]1594.01942477789[/C][/ROW]
[ROW][C]62[/C][C]268714[/C][C]268287.832014308[/C][C]426.167985691573[/C][/ROW]
[ROW][C]63[/C][C]272482[/C][C]270395.01974451[/C][C]2086.98025548994[/C][/ROW]
[ROW][C]64[/C][C]268351[/C][C]270526.618157502[/C][C]-2175.61815750215[/C][/ROW]
[ROW][C]65[/C][C]268175[/C][C]271728.39345153[/C][C]-3553.39345153014[/C][/ROW]
[ROW][C]66[/C][C]270674[/C][C]268055.780364755[/C][C]2618.21963524504[/C][/ROW]
[ROW][C]67[/C][C]272764[/C][C]270550.310320995[/C][C]2213.6896790046[/C][/ROW]
[ROW][C]68[/C][C]272599[/C][C]271872.686213764[/C][C]726.313786235522[/C][/ROW]
[ROW][C]69[/C][C]270333[/C][C]274417.635553012[/C][C]-4084.63555301249[/C][/ROW]
[ROW][C]70[/C][C]270846[/C][C]269822.295471992[/C][C]1023.70452800824[/C][/ROW]
[ROW][C]71[/C][C]270491[/C][C]272450.128035602[/C][C]-1959.1280356021[/C][/ROW]
[ROW][C]72[/C][C]269160[/C][C]268651.149480076[/C][C]508.850519924366[/C][/ROW]
[ROW][C]73[/C][C]274027[/C][C]271735.04493181[/C][C]2291.95506818977[/C][/ROW]
[ROW][C]74[/C][C]273784[/C][C]272514.337378467[/C][C]1269.6626215335[/C][/ROW]
[ROW][C]75[/C][C]276663[/C][C]275626.307032504[/C][C]1036.69296749582[/C][/ROW]
[ROW][C]76[/C][C]274525[/C][C]274079.76510795[/C][C]445.23489204963[/C][/ROW]
[ROW][C]77[/C][C]271344[/C][C]277092.211619592[/C][C]-5748.21161959181[/C][/ROW]
[ROW][C]78[/C][C]271115[/C][C]272931.372172079[/C][C]-1816.37217207882[/C][/ROW]
[ROW][C]79[/C][C]270798[/C][C]271817.543842245[/C][C]-1019.5438422446[/C][/ROW]
[ROW][C]80[/C][C]273911[/C][C]270226.105802973[/C][C]3684.89419702732[/C][/ROW]
[ROW][C]81[/C][C]273985[/C][C]274090.037591489[/C][C]-105.037591489323[/C][/ROW]
[ROW][C]82[/C][C]271917[/C][C]273639.303786127[/C][C]-1722.30378612719[/C][/ROW]
[ROW][C]83[/C][C]273338[/C][C]273480.577057715[/C][C]-142.577057715331[/C][/ROW]
[ROW][C]84[/C][C]270601[/C][C]271588.950948953[/C][C]-987.950948953046[/C][/ROW]
[ROW][C]85[/C][C]273547[/C][C]273823.782246879[/C][C]-276.782246878603[/C][/ROW]
[ROW][C]86[/C][C]275363[/C][C]272324.467399564[/C][C]3038.53260043578[/C][/ROW]
[ROW][C]87[/C][C]281229[/C][C]276742.938382715[/C][C]4486.06161728455[/C][/ROW]
[ROW][C]88[/C][C]277793[/C][C]277787.567594986[/C][C]5.43240501423134[/C][/ROW]
[ROW][C]89[/C][C]279913[/C][C]279210.489736083[/C][C]702.51026391692[/C][/ROW]
[ROW][C]90[/C][C]282500[/C][C]280965.526427325[/C][C]1534.47357267537[/C][/ROW]
[ROW][C]91[/C][C]280041[/C][C]282739.230677265[/C][C]-2698.23067726492[/C][/ROW]
[ROW][C]92[/C][C]282166[/C][C]280845.914974458[/C][C]1320.08502554154[/C][/ROW]
[ROW][C]93[/C][C]290304[/C][C]282146.92448993[/C][C]8157.07551006973[/C][/ROW]
[ROW][C]94[/C][C]283519[/C][C]288004.779874211[/C][C]-4485.779874211[/C][/ROW]
[ROW][C]95[/C][C]287816[/C][C]286099.425516179[/C][C]1716.57448382111[/C][/ROW]
[ROW][C]96[/C][C]285226[/C][C]285628.881731369[/C][C]-402.881731368543[/C][/ROW]
[ROW][C]97[/C][C]287595[/C][C]288600.491223598[/C][C]-1005.49122359796[/C][/ROW]
[ROW][C]98[/C][C]289741[/C][C]287318.270400616[/C][C]2422.7295993836[/C][/ROW]
[ROW][C]99[/C][C]289148[/C][C]291662.99369682[/C][C]-2514.99369682011[/C][/ROW]
[ROW][C]100[/C][C]288301[/C][C]286358.647208385[/C][C]1942.35279161501[/C][/ROW]
[ROW][C]101[/C][C]290155[/C][C]289512.054212609[/C][C]642.945787390927[/C][/ROW]
[ROW][C]102[/C][C]289648[/C][C]291454.767820005[/C][C]-1806.76782000484[/C][/ROW]
[ROW][C]103[/C][C]288225[/C][C]289790.422050066[/C][C]-1565.42205006647[/C][/ROW]
[ROW][C]104[/C][C]289351[/C][C]289635.933546634[/C][C]-284.933546633692[/C][/ROW]
[ROW][C]105[/C][C]294735[/C][C]291070.694792496[/C][C]3664.30520750378[/C][/ROW]
[ROW][C]106[/C][C]305333[/C][C]290853.728899927[/C][C]14479.2711000728[/C][/ROW]
[ROW][C]107[/C][C]309030[/C][C]305271.456826872[/C][C]3758.54317312763[/C][/ROW]
[ROW][C]108[/C][C]310215[/C][C]306181.263863219[/C][C]4033.73613678146[/C][/ROW]
[ROW][C]109[/C][C]321935[/C][C]312764.098011283[/C][C]9170.90198871703[/C][/ROW]
[ROW][C]110[/C][C]325734[/C][C]320514.556558218[/C][C]5219.44344178151[/C][/ROW]
[ROW][C]111[/C][C]320846[/C][C]326448.871990857[/C][C]-5602.87199085701[/C][/ROW]
[ROW][C]112[/C][C]323023[/C][C]319954.726245822[/C][C]3068.27375417849[/C][/ROW]
[ROW][C]113[/C][C]319753[/C][C]324091.407172788[/C][C]-4338.40717278805[/C][/ROW]
[ROW][C]114[/C][C]321753[/C][C]321936.199914176[/C][C]-183.199914175784[/C][/ROW]
[ROW][C]115[/C][C]320757[/C][C]321919.580537472[/C][C]-1162.58053747244[/C][/ROW]
[ROW][C]116[/C][C]324479[/C][C]322665.181251407[/C][C]1813.81874859333[/C][/ROW]
[ROW][C]117[/C][C]324641[/C][C]326887.847185423[/C][C]-2246.84718542261[/C][/ROW]
[ROW][C]118[/C][C]322767[/C][C]324474.48773232[/C][C]-1707.48773232027[/C][/ROW]
[ROW][C]119[/C][C]324181[/C][C]324149.516711342[/C][C]31.4832886579679[/C][/ROW]
[ROW][C]120[/C][C]321389[/C][C]322268.35700191[/C][C]-879.35700190952[/C][/ROW]
[ROW][C]121[/C][C]327897[/C][C]326049.050343981[/C][C]1847.94965601887[/C][/ROW]
[ROW][C]122[/C][C]334287[/C][C]327211.750889872[/C][C]7075.24911012792[/C][/ROW]
[ROW][C]123[/C][C]332653[/C][C]332418.501429552[/C][C]234.49857044837[/C][/ROW]
[ROW][C]124[/C][C]334819[/C][C]332281.615277883[/C][C]2537.38472211664[/C][/ROW]
[ROW][C]125[/C][C]335264[/C][C]334552.071072623[/C][C]711.928927376517[/C][/ROW]
[ROW][C]126[/C][C]339622[/C][C]337279.649316558[/C][C]2342.35068344203[/C][/ROW]
[ROW][C]127[/C][C]342440[/C][C]339161.394430547[/C][C]3278.60556945315[/C][/ROW]
[ROW][C]128[/C][C]346585[/C][C]344147.17135697[/C][C]2437.82864303043[/C][/ROW]
[ROW][C]129[/C][C]335378[/C][C]348210.081262065[/C][C]-12832.0812620653[/C][/ROW]
[ROW][C]130[/C][C]337010[/C][C]337637.253763321[/C][C]-627.253763321089[/C][/ROW]
[ROW][C]131[/C][C]339130[/C][C]338572.198086404[/C][C]557.801913595642[/C][/ROW]
[ROW][C]132[/C][C]341193[/C][C]336991.504332397[/C][C]4201.49566760322[/C][/ROW]
[ROW][C]133[/C][C]343507[/C][C]345431.64527965[/C][C]-1924.64527965017[/C][/ROW]
[ROW][C]134[/C][C]348915[/C][C]344756.113635797[/C][C]4158.88636420271[/C][/ROW]
[ROW][C]135[/C][C]346431[/C][C]346356.000011242[/C][C]74.9999887577142[/C][/ROW]
[ROW][C]136[/C][C]348322[/C][C]346604.563576247[/C][C]1717.43642375304[/C][/ROW]
[ROW][C]137[/C][C]348288[/C][C]347907.973147118[/C][C]380.026852881711[/C][/ROW]
[ROW][C]138[/C][C]346597[/C][C]350739.262757413[/C][C]-4142.26275741257[/C][/ROW]
[ROW][C]139[/C][C]351076[/C][C]347683.488373318[/C][C]3392.51162668184[/C][/ROW]
[ROW][C]140[/C][C]355215[/C][C]352563.957683735[/C][C]2651.04231626453[/C][/ROW]
[ROW][C]141[/C][C]350562[/C][C]353718.418066229[/C][C]-3156.41806622909[/C][/ROW]
[ROW][C]142[/C][C]355266[/C][C]353264.118434385[/C][C]2001.88156561542[/C][/ROW]
[ROW][C]143[/C][C]361565[/C][C]356604.303597474[/C][C]4960.69640252588[/C][/ROW]
[ROW][C]144[/C][C]363462[/C][C]359359.584298995[/C][C]4102.41570100514[/C][/ROW]
[ROW][C]145[/C][C]366183[/C][C]366644.010402812[/C][C]-461.010402812331[/C][/ROW]
[ROW][C]146[/C][C]365423[/C][C]368495.92726634[/C][C]-3072.92726634024[/C][/ROW]
[ROW][C]147[/C][C]369208[/C][C]363682.810723715[/C][C]5525.18927628529[/C][/ROW]
[ROW][C]148[/C][C]366713[/C][C]368686.269537952[/C][C]-1973.26953795168[/C][/ROW]
[ROW][C]149[/C][C]369354[/C][C]366926.774664258[/C][C]2427.22533574194[/C][/ROW]
[ROW][C]150[/C][C]371970[/C][C]370589.536515362[/C][C]1380.46348463756[/C][/ROW]
[ROW][C]151[/C][C]371824[/C][C]373563.074164244[/C][C]-1739.07416424406[/C][/ROW]
[ROW][C]152[/C][C]373187[/C][C]374392.359517305[/C][C]-1205.35951730516[/C][/ROW]
[ROW][C]153[/C][C]367270[/C][C]371445.832982126[/C][C]-4175.83298212575[/C][/ROW]
[ROW][C]154[/C][C]368140[/C][C]371301.097715477[/C][C]-3161.09771547699[/C][/ROW]
[ROW][C]155[/C][C]373742[/C][C]371201.513509144[/C][C]2540.48649085616[/C][/ROW]
[ROW][C]156[/C][C]364815[/C][C]371885.032038681[/C][C]-7070.03203868051[/C][/ROW]
[ROW][C]157[/C][C]368558[/C][C]369363.406779708[/C][C]-805.406779707642[/C][/ROW]
[ROW][C]158[/C][C]371503[/C][C]370306.069890998[/C][C]1196.93010900164[/C][/ROW]
[ROW][C]159[/C][C]372611[/C][C]370494.367337678[/C][C]2116.63266232202[/C][/ROW]
[ROW][C]160[/C][C]370197[/C][C]371212.661504701[/C][C]-1015.66150470084[/C][/ROW]
[ROW][C]161[/C][C]375441[/C][C]370987.25276047[/C][C]4453.7472395295[/C][/ROW]
[ROW][C]162[/C][C]375888[/C][C]375956.550852258[/C][C]-68.5508522579912[/C][/ROW]
[ROW][C]163[/C][C]375132[/C][C]377075.884952928[/C][C]-1943.88495292811[/C][/ROW]
[ROW][C]164[/C][C]381142[/C][C]377756.78057963[/C][C]3385.21942036977[/C][/ROW]
[ROW][C]165[/C][C]372024[/C][C]377777.840828949[/C][C]-5753.84082894865[/C][/ROW]
[ROW][C]166[/C][C]376070[/C][C]376532.578844216[/C][C]-462.578844215546[/C][/ROW]
[ROW][C]167[/C][C]376864[/C][C]379657.986634237[/C][C]-2793.98663423723[/C][/ROW]
[ROW][C]168[/C][C]371401[/C][C]374138.171714183[/C][C]-2737.17171418271[/C][/ROW]
[ROW][C]169[/C][C]375687[/C][C]376228.260859157[/C][C]-541.260859157366[/C][/ROW]
[ROW][C]170[/C][C]384304[/C][C]377735.790095129[/C][C]6568.20990487112[/C][/ROW]
[ROW][C]171[/C][C]380738[/C][C]382341.885687475[/C][C]-1603.88568747503[/C][/ROW]
[ROW][C]172[/C][C]379908[/C][C]379484.210605264[/C][C]423.789394736232[/C][/ROW]
[ROW][C]173[/C][C]384007[/C][C]381472.046115779[/C][C]2534.95388422121[/C][/ROW]
[ROW][C]174[/C][C]384499[/C][C]383998.750939933[/C][C]500.249060066941[/C][/ROW]
[ROW][C]175[/C][C]385106[/C][C]385165.431307891[/C][C]-59.4313078908599[/C][/ROW]
[ROW][C]176[/C][C]387935[/C][C]388386.788488548[/C][C]-451.788488548133[/C][/ROW]
[ROW][C]177[/C][C]380435[/C][C]383520.80630177[/C][C]-3085.80630177015[/C][/ROW]
[ROW][C]178[/C][C]379281[/C][C]385412.269969669[/C][C]-6131.26996966865[/C][/ROW]
[ROW][C]179[/C][C]384153[/C][C]383540.50329715[/C][C]612.496702850447[/C][/ROW]
[ROW][C]180[/C][C]380599[/C][C]380668.509396041[/C][C]-69.5093960405211[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295034&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295034&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
tObservedFittedResiduals
13254811252764.6704059832046.32959401695
14254895254380.220568082514.779431918258
15258325258119.089166354205.910833645787
16257608257519.02872106688.9712789337209
17258759258818.68317857-59.683178570267
18258621258690.137387212-69.1373872116965
19257852257415.865945926436.134054073947
20260560258903.2052998711656.79470012937
21262358263189.652410659-831.652410659473
22260812261322.478491026-510.478491026297
23261165264203.894724282-3038.8947242818
24257164254467.8454679662696.15453203395
25260720260758.175672043-38.1756720430858
26259581260440.161925056-859.161925056396
27264743263034.1243509741708.87564902613
28261845263604.104565919-1759.10456591874
29262262263414.667105948-1152.66710594838
30261631262407.063298019-776.063298018824
31258953260652.739210333-1699.73921033289
32259966260657.905797857-691.905797856569
33262850262529.534193008320.465806991677
34262204261572.340426923631.659573076759
35263418264798.213961622-1380.21396162163
36262752257480.9735081015271.0264918989
37266433265244.2604172861188.73958271352
38267722265734.7446127771987.25538722344
39266003271116.596296056-5113.59629605623
40262971265598.728631334-2627.72863133362
41265521264806.158245413714.84175458661
42264676265319.198264201-643.198264200531
43270223263463.6959990826759.30400091829
44269508270384.749237451-876.749237451353
45268457272377.554567917-3920.55456791702
46265814268169.785842411-2355.78584241075
47266680268635.364319331-1955.36431933095
48263018262179.024357523838.975642476755
49269285265581.3412879123703.65871208755
50269829268172.0928001521656.90719984833
51270911271836.017849589-925.017849588767
52266844270110.74317876-3266.74317876005
53271244269481.1080949691762.89190503105
54269907270554.503161704-647.503161703527
55271296270182.8349765731113.16502342653
56270157271090.196346848-933.196346847981
57271322272379.65358028-1057.65358027961
58267179270713.4233835-3534.42338349967
59264101270299.263321574-6198.26332157373
60265518260989.5116238874528.48837611321
61269419267824.9805752221594.01942477789
62268714268287.832014308426.167985691573
63272482270395.019744512086.98025548994
64268351270526.618157502-2175.61815750215
65268175271728.39345153-3553.39345153014
66270674268055.7803647552618.21963524504
67272764270550.3103209952213.6896790046
68272599271872.686213764726.313786235522
69270333274417.635553012-4084.63555301249
70270846269822.2954719921023.70452800824
71270491272450.128035602-1959.1280356021
72269160268651.149480076508.850519924366
73274027271735.044931812291.95506818977
74273784272514.3373784671269.6626215335
75276663275626.3070325041036.69296749582
76274525274079.76510795445.23489204963
77271344277092.211619592-5748.21161959181
78271115272931.372172079-1816.37217207882
79270798271817.543842245-1019.5438422446
80273911270226.1058029733684.89419702732
81273985274090.037591489-105.037591489323
82271917273639.303786127-1722.30378612719
83273338273480.577057715-142.577057715331
84270601271588.950948953-987.950948953046
85273547273823.782246879-276.782246878603
86275363272324.4673995643038.53260043578
87281229276742.9383827154486.06161728455
88277793277787.5675949865.43240501423134
89279913279210.489736083702.51026391692
90282500280965.5264273251534.47357267537
91280041282739.230677265-2698.23067726492
92282166280845.9149744581320.08502554154
93290304282146.924489938157.07551006973
94283519288004.779874211-4485.779874211
95287816286099.4255161791716.57448382111
96285226285628.881731369-402.881731368543
97287595288600.491223598-1005.49122359796
98289741287318.2704006162422.7295993836
99289148291662.99369682-2514.99369682011
100288301286358.6472083851942.35279161501
101290155289512.054212609642.945787390927
102289648291454.767820005-1806.76782000484
103288225289790.422050066-1565.42205006647
104289351289635.933546634-284.933546633692
105294735291070.6947924963664.30520750378
106305333290853.72889992714479.2711000728
107309030305271.4568268723758.54317312763
108310215306181.2638632194033.73613678146
109321935312764.0980112839170.90198871703
110325734320514.5565582185219.44344178151
111320846326448.871990857-5602.87199085701
112323023319954.7262458223068.27375417849
113319753324091.407172788-4338.40717278805
114321753321936.199914176-183.199914175784
115320757321919.580537472-1162.58053747244
116324479322665.1812514071813.81874859333
117324641326887.847185423-2246.84718542261
118322767324474.48773232-1707.48773232027
119324181324149.51671134231.4832886579679
120321389322268.35700191-879.35700190952
121327897326049.0503439811847.94965601887
122334287327211.7508898727075.24911012792
123332653332418.501429552234.49857044837
124334819332281.6152778832537.38472211664
125335264334552.071072623711.928927376517
126339622337279.6493165582342.35068344203
127342440339161.3944305473278.60556945315
128346585344147.171356972437.82864303043
129335378348210.081262065-12832.0812620653
130337010337637.253763321-627.253763321089
131339130338572.198086404557.801913595642
132341193336991.5043323974201.49566760322
133343507345431.64527965-1924.64527965017
134348915344756.1136357974158.88636420271
135346431346356.00001124274.9999887577142
136348322346604.5635762471717.43642375304
137348288347907.973147118380.026852881711
138346597350739.262757413-4142.26275741257
139351076347683.4883733183392.51162668184
140355215352563.9576837352651.04231626453
141350562353718.418066229-3156.41806622909
142355266353264.1184343852001.88156561542
143361565356604.3035974744960.69640252588
144363462359359.5842989954102.41570100514
145366183366644.010402812-461.010402812331
146365423368495.92726634-3072.92726634024
147369208363682.8107237155525.18927628529
148366713368686.269537952-1973.26953795168
149369354366926.7746642582427.22533574194
150371970370589.5365153621380.46348463756
151371824373563.074164244-1739.07416424406
152373187374392.359517305-1205.35951730516
153367270371445.832982126-4175.83298212575
154368140371301.097715477-3161.09771547699
155373742371201.5135091442540.48649085616
156364815371885.032038681-7070.03203868051
157368558369363.406779708-805.406779707642
158371503370306.0698909981196.93010900164
159372611370494.3673376782116.63266232202
160370197371212.661504701-1015.66150470084
161375441370987.252760474453.7472395295
162375888375956.550852258-68.5508522579912
163375132377075.884952928-1943.88495292811
164381142377756.780579633385.21942036977
165372024377777.840828949-5753.84082894865
166376070376532.578844216-462.578844215546
167376864379657.986634237-2793.98663423723
168371401374138.171714183-2737.17171418271
169375687376228.260859157-541.260859157366
170384304377735.7900951296568.20990487112
171380738382341.885687475-1603.88568747503
172379908379484.210605264423.789394736232
173384007381472.0461157792534.95388422121
174384499383998.750939933500.249060066941
175385106385165.431307891-59.4313078908599
176387935388386.788488548-451.788488548133
177380435383520.80630177-3085.80630177015
178379281385412.269969669-6131.26996966865
179384153383540.50329715612.496702850447
180380599380668.509396041-69.5093960405211







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
181385280.658408888379023.093285725391538.223532051
182388626.443308082380627.486904959396625.399711205
183386361.717660937376903.622253029395819.813068844
184385110.869570794374359.952579282395861.786562307
185387124.190002245375192.235214839399056.144789652
186387162.528562374130.573425271400194.48369873
187387729.636813781373659.404252121401799.869375441
188390825.354136507375765.51969921405885.188573804
189385698.80510204369688.756358384401708.853845696
190389349.47054797372421.715643812406277.225452129
191393649.815116504375831.605652263411468.024580744
192390159.424293501371473.893332545408844.955254457

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
181 & 385280.658408888 & 379023.093285725 & 391538.223532051 \tabularnewline
182 & 388626.443308082 & 380627.486904959 & 396625.399711205 \tabularnewline
183 & 386361.717660937 & 376903.622253029 & 395819.813068844 \tabularnewline
184 & 385110.869570794 & 374359.952579282 & 395861.786562307 \tabularnewline
185 & 387124.190002245 & 375192.235214839 & 399056.144789652 \tabularnewline
186 & 387162.528562 & 374130.573425271 & 400194.48369873 \tabularnewline
187 & 387729.636813781 & 373659.404252121 & 401799.869375441 \tabularnewline
188 & 390825.354136507 & 375765.51969921 & 405885.188573804 \tabularnewline
189 & 385698.80510204 & 369688.756358384 & 401708.853845696 \tabularnewline
190 & 389349.47054797 & 372421.715643812 & 406277.225452129 \tabularnewline
191 & 393649.815116504 & 375831.605652263 & 411468.024580744 \tabularnewline
192 & 390159.424293501 & 371473.893332545 & 408844.955254457 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295034&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]181[/C][C]385280.658408888[/C][C]379023.093285725[/C][C]391538.223532051[/C][/ROW]
[ROW][C]182[/C][C]388626.443308082[/C][C]380627.486904959[/C][C]396625.399711205[/C][/ROW]
[ROW][C]183[/C][C]386361.717660937[/C][C]376903.622253029[/C][C]395819.813068844[/C][/ROW]
[ROW][C]184[/C][C]385110.869570794[/C][C]374359.952579282[/C][C]395861.786562307[/C][/ROW]
[ROW][C]185[/C][C]387124.190002245[/C][C]375192.235214839[/C][C]399056.144789652[/C][/ROW]
[ROW][C]186[/C][C]387162.528562[/C][C]374130.573425271[/C][C]400194.48369873[/C][/ROW]
[ROW][C]187[/C][C]387729.636813781[/C][C]373659.404252121[/C][C]401799.869375441[/C][/ROW]
[ROW][C]188[/C][C]390825.354136507[/C][C]375765.51969921[/C][C]405885.188573804[/C][/ROW]
[ROW][C]189[/C][C]385698.80510204[/C][C]369688.756358384[/C][C]401708.853845696[/C][/ROW]
[ROW][C]190[/C][C]389349.47054797[/C][C]372421.715643812[/C][C]406277.225452129[/C][/ROW]
[ROW][C]191[/C][C]393649.815116504[/C][C]375831.605652263[/C][C]411468.024580744[/C][/ROW]
[ROW][C]192[/C][C]390159.424293501[/C][C]371473.893332545[/C][C]408844.955254457[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295034&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295034&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
tForecast95% Lower Bound95% Upper Bound
181385280.658408888379023.093285725391538.223532051
182388626.443308082380627.486904959396625.399711205
183386361.717660937376903.622253029395819.813068844
184385110.869570794374359.952579282395861.786562307
185387124.190002245375192.235214839399056.144789652
186387162.528562374130.573425271400194.48369873
187387729.636813781373659.404252121401799.869375441
188390825.354136507375765.51969921405885.188573804
189385698.80510204369688.756358384401708.853845696
190389349.47054797372421.715643812406277.225452129
191393649.815116504375831.605652263411468.024580744
192390159.424293501371473.893332545408844.955254457



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')