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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 05 Dec 2012 10:44:29 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/05/t1354722284rvzafyh6tts9n3l.htm/, Retrieved Thu, 31 Oct 2024 23:34:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=196884, Retrieved Thu, 31 Oct 2024 23:34:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Structural Time Series Models] [HPC Retail Sales] [2008-03-06 16:52:55] [74be16979710d4c4e7c6647856088456]
- R  D    [Structural Time Series Models] [HPC Retail Sales] [2008-03-08 11:33:35] [74be16979710d4c4e7c6647856088456]
- RM D      [Structural Time Series Models] [Workshop 8 - OLO ...] [2012-11-22 14:39:38] [9f87ad58f325f963ff5b3a15384d509e]
- RMPD          [Exponential Smoothing] [Paper stat - wiss...] [2012-12-05 15:44:29] [3353489d44052879174bf0d9e8b7362f] [Current]
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Dataseries X:
1.0137
0.9834
0.9643
0.9470
0.9060
0.9492
0.9397
0.9041
0.8721
0.8552
0.8564
0.8973
0.9383
0.9217
0.9095
0.8920
0.8742
0.8532
0.8607
0.9005
0.9111
0.9059
0.8883
0.8924
0.8833
0.8700
0.8758
0.8858
0.9170
0.9554
0.9922
0.9778
0.9808
0.9811
1.0014
1.0183
1.0622
1.0773
1.0807
1.0848
1.1582
1.1663
1.1372
1.1139
1.1222
1.1692
1.1702
1.2286
1.2613
1.2646
1.2262
1.1985
1.2007
1.2138
1.2266
1.2176
1.2218
1.2490
1.2991
1.3408
1.3119
1.3014
1.3201
1.2938
1.2694
1.2165
1.2037
1.2292
1.2256
1.2015
1.1786
1.1856
1.2103
1.1938
1.2020
1.2271
1.2770
1.2650
1.2684
1.2811
1.2727
1.2611
1.2881
1.3213
1.2999
1.3074
1.3242
1.3516
1.3511
1.3419
1.3716
1.3622
1.3896
1.4227
1.4684
1.4570
1.4718
1.4748
1.5527
1.5750
1.5557
1.5553
1.5770
1.4975
1.4369
1.3322
1.2732
1.3449
1.3239
1.2785
1.3050
1.3190
1.3650
1.4016
1.4088
1.4268
1.4562
1.4816
1.4914
1.4614
1.4272
1.3686
1.3569
1.3406
1.2565
1.2208
1.2770
1.2894
1.3067
1.3898
1.3661
1.3220
1.3360
1.3649
1.3999
1.4442
1.4349
1.4388
1.4264
1.4343
1.3770
1.3706
1.3556
1.3179
1.2905
1.3224
1.3201
1.3162
1.2789
1.2526
1.2288
1.2400
1.2856
1.2974
1.2828




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196884&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196884&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196884&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.854978825109735
beta0.00715218941994085
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.854978825109735 \tabularnewline
beta & 0.00715218941994085 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196884&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]0.854978825109735[/C][/ROW]
[ROW][C]beta[/C][C]0.00715218941994085[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196884&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196884&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
alpha0.854978825109735
beta0.00715218941994085
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
130.93830.969540224358974-0.031240224358974
140.92170.92689654140936-0.00519654140936021
150.90950.9059712125454130.00352878745458673
160.8920.8849649335334710.00703506646652929
170.87420.8669953013889580.00720469861104178
180.85320.8483314243222490.00486857567775145
190.86070.911287482811404-0.0505874828114041
200.90050.8351704446028580.0653295553971417
210.91110.8613011745032250.0497988254967746
220.90590.889278810882820.0166211891171798
230.88830.906133575438585-0.0178335754385847
240.89240.934829527420517-0.0424295274205168
250.88330.939773178591962-0.0564731785919621
260.870.879221853103251-0.00922185310325141
270.87580.8559848242826730.0198151757173275
280.88580.8493756367215480.036424363278452
290.9170.8567016356190780.0602983643809224
300.95540.8835614017709860.0718385982290144
310.99220.996611098944871-0.00441109894487113
320.97780.977944673701786-0.000144673701785947
330.98080.9466040239238420.0341959760761582
340.98110.9570946681542570.0240053318457425
351.00140.9759757752877670.0254242247122327
361.01831.03906354407732-0.0207635440773228
371.06221.061601259800710.000598740199289072
381.07731.058153386585560.0191466134144391
391.08071.065010979770580.0156890202294215
401.08481.058886669010410.0259133309895918
411.15821.062227887385820.0959721126141804
421.16631.123019368904640.0432806310953635
431.13721.20217799483914-0.0649779948391371
441.11391.13355971994031-0.0196597199403052
451.12221.091607748137630.0305922518623707
461.16921.09861089651020.0705891034897985
471.17021.158882241129050.0113177588709492
481.22861.204481144834560.0241188551654445
491.26131.27003486864523-0.00873486864522954
501.26461.262784240679190.00181575932080991
511.22621.25570436751311-0.0295043675131115
521.19851.21352852366982-0.0150285236698247
531.20071.192880086752380.00781991324762066
541.21381.170977632449180.0428223675508188
551.22661.2343575659435-0.00775756594350319
561.21761.22189646313082-0.00429646313082488
571.22181.20112410398550.0206758960144997
581.2491.206145483686410.0428545163135923
591.29911.234635262515470.0644647374845257
601.34081.328381648788410.0124183512115874
611.31191.37994716682204-0.0680471668220393
621.30141.32393311432879-0.0225331143287881
631.32011.29176176556070.0283382344392977
641.29381.3017615086375-0.00796150863749667
651.26941.29113402486393-0.0217340248639337
661.21651.24952425263226-0.0330242526322571
671.20371.24074254699561-0.0370425469956095
681.22921.203587038353430.0256129616465679
691.22561.212032719844910.0135672801550899
701.20151.21417387902496-0.0126738790249576
711.17861.19796356675284-0.0193635667528353
721.18561.21161966370554-0.0260196637055439
731.21031.21754620544847-0.00724620544847099
741.19381.21938190143422-0.025581901434224
751.2021.191228396363790.0107716036362091
761.22711.180084460605410.0470155393945917
771.2771.213939715228450.0630602847715451
781.2651.243184307778260.0218156922217427
791.26841.28103654828682-0.012636548286824
801.28111.274312961479740.00678703852025953
811.27271.265279812744930.00742018725506499
821.26111.258686038925020.00241396107498093
831.28811.254823850778580.0332761492214175
841.32131.313260892257040.00803910774296401
851.29991.35197815676204-0.0520781567620368
861.30741.31349891884315-0.00609891884314573
871.32421.308068616549790.0161313834502139
881.35161.307589729276470.044010270723529
891.35111.34201040560860.00908959439140111
901.34191.319607867218680.0222921327813228
911.37161.353352069122220.0182479308777797
921.36221.37652066628525-0.0143206662852506
931.38961.35007340075660.0395265992434035
941.42271.370940954185090.0517590458149135
951.46841.414782216787610.0536177832123912
961.4571.48811418507083-0.031114185070831
971.47181.48556168160651-0.0137616816065087
981.47481.48766823046701-0.0128682304670074
991.55271.480790829255510.0719091707444945
1001.5751.533501532165630.0414984678343737
1011.55571.56215280725278-0.00645280725278408
1021.55531.529723825414660.0255761745853369
1031.5771.567056733648730.00994326635126663
1041.49751.57971851452706-0.082218514527058
1051.43691.50393045911345-0.0670304591134485
1061.33221.43571779340595-0.103517793405953
1071.27321.34637053508509-0.0731705350850915
1081.34491.297538271893680.0473617281063223
1091.32391.36360239634344-0.0397023963434424
1101.27851.34250602945084-0.0640060294508435
1111.3051.302734981861920.00226501813807656
1121.3191.289598911785040.0294010882149625
1131.3651.298986956737530.0660130432624728
1141.40161.331636473278770.0699635267212284
1151.40881.403400802390420.00539919760958307
1161.42681.397532581543220.029267418456778
1171.45621.418667451532360.0375325484676414
1181.48161.434604130579860.0469958694201416
1191.49141.479305872001610.0120941279983922
1201.46141.52233622167716-0.0609362216771572
1211.42721.4840029128521-0.0568029128521015
1221.36861.44547801807606-0.0768780180760624
1231.35691.40495027918451-0.0480502791845083
1241.34061.3530612047494-0.0124612047494042
1251.25651.33204160236324-0.0755416023632358
1261.22081.24344641354839-0.0226464135483944
1271.2771.225310318314870.0516896816851276
1281.28941.261406251974840.0279937480251553
1291.30671.281568364511140.0251316354888567
1301.38981.287116661187090.102683338812907
1311.36611.37355079916431-0.00745079916430735
1321.3221.38834246715908-0.0663424671590782
1331.3361.34501605548819-0.00901605548818862
1341.36491.343758517017180.0211414829828172
1351.39991.391137315386360.00876268461364416
1361.44421.393252007820370.0509479921796314
1371.43491.417954394562480.0169456054375219
1381.43881.417326750798020.0214732492019813
1391.42641.44918414965032-0.0227841496503174
1401.43431.419206525867770.0150934741322299
1411.3771.428881629184-0.0518816291839994
1421.37061.38031843931992-0.009718439319921
1431.35561.35447890632270.00112109367729807
1441.31791.36791049049502-0.0500104904950223
1451.29051.34681265436318-0.0563126543631842
1461.32241.309153327454340.0132466725456588
1471.32011.34760108609441-0.0275010860944069
1481.31621.32422107733851-0.00802107733851343
1491.27891.29260679012862-0.0137067901286152
1501.25261.26527286083641-0.0126728608364084
1511.22881.26015325561303-0.0313532556130289
1521.241.226925342301160.0130746576988374
1531.28561.223732304256720.061867695743284
1541.29741.277803219787320.0195967802126766
1551.28281.278045088137410.00475491186258648

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.9383 & 0.969540224358974 & -0.031240224358974 \tabularnewline
14 & 0.9217 & 0.92689654140936 & -0.00519654140936021 \tabularnewline
15 & 0.9095 & 0.905971212545413 & 0.00352878745458673 \tabularnewline
16 & 0.892 & 0.884964933533471 & 0.00703506646652929 \tabularnewline
17 & 0.8742 & 0.866995301388958 & 0.00720469861104178 \tabularnewline
18 & 0.8532 & 0.848331424322249 & 0.00486857567775145 \tabularnewline
19 & 0.8607 & 0.911287482811404 & -0.0505874828114041 \tabularnewline
20 & 0.9005 & 0.835170444602858 & 0.0653295553971417 \tabularnewline
21 & 0.9111 & 0.861301174503225 & 0.0497988254967746 \tabularnewline
22 & 0.9059 & 0.88927881088282 & 0.0166211891171798 \tabularnewline
23 & 0.8883 & 0.906133575438585 & -0.0178335754385847 \tabularnewline
24 & 0.8924 & 0.934829527420517 & -0.0424295274205168 \tabularnewline
25 & 0.8833 & 0.939773178591962 & -0.0564731785919621 \tabularnewline
26 & 0.87 & 0.879221853103251 & -0.00922185310325141 \tabularnewline
27 & 0.8758 & 0.855984824282673 & 0.0198151757173275 \tabularnewline
28 & 0.8858 & 0.849375636721548 & 0.036424363278452 \tabularnewline
29 & 0.917 & 0.856701635619078 & 0.0602983643809224 \tabularnewline
30 & 0.9554 & 0.883561401770986 & 0.0718385982290144 \tabularnewline
31 & 0.9922 & 0.996611098944871 & -0.00441109894487113 \tabularnewline
32 & 0.9778 & 0.977944673701786 & -0.000144673701785947 \tabularnewline
33 & 0.9808 & 0.946604023923842 & 0.0341959760761582 \tabularnewline
34 & 0.9811 & 0.957094668154257 & 0.0240053318457425 \tabularnewline
35 & 1.0014 & 0.975975775287767 & 0.0254242247122327 \tabularnewline
36 & 1.0183 & 1.03906354407732 & -0.0207635440773228 \tabularnewline
37 & 1.0622 & 1.06160125980071 & 0.000598740199289072 \tabularnewline
38 & 1.0773 & 1.05815338658556 & 0.0191466134144391 \tabularnewline
39 & 1.0807 & 1.06501097977058 & 0.0156890202294215 \tabularnewline
40 & 1.0848 & 1.05888666901041 & 0.0259133309895918 \tabularnewline
41 & 1.1582 & 1.06222788738582 & 0.0959721126141804 \tabularnewline
42 & 1.1663 & 1.12301936890464 & 0.0432806310953635 \tabularnewline
43 & 1.1372 & 1.20217799483914 & -0.0649779948391371 \tabularnewline
44 & 1.1139 & 1.13355971994031 & -0.0196597199403052 \tabularnewline
45 & 1.1222 & 1.09160774813763 & 0.0305922518623707 \tabularnewline
46 & 1.1692 & 1.0986108965102 & 0.0705891034897985 \tabularnewline
47 & 1.1702 & 1.15888224112905 & 0.0113177588709492 \tabularnewline
48 & 1.2286 & 1.20448114483456 & 0.0241188551654445 \tabularnewline
49 & 1.2613 & 1.27003486864523 & -0.00873486864522954 \tabularnewline
50 & 1.2646 & 1.26278424067919 & 0.00181575932080991 \tabularnewline
51 & 1.2262 & 1.25570436751311 & -0.0295043675131115 \tabularnewline
52 & 1.1985 & 1.21352852366982 & -0.0150285236698247 \tabularnewline
53 & 1.2007 & 1.19288008675238 & 0.00781991324762066 \tabularnewline
54 & 1.2138 & 1.17097763244918 & 0.0428223675508188 \tabularnewline
55 & 1.2266 & 1.2343575659435 & -0.00775756594350319 \tabularnewline
56 & 1.2176 & 1.22189646313082 & -0.00429646313082488 \tabularnewline
57 & 1.2218 & 1.2011241039855 & 0.0206758960144997 \tabularnewline
58 & 1.249 & 1.20614548368641 & 0.0428545163135923 \tabularnewline
59 & 1.2991 & 1.23463526251547 & 0.0644647374845257 \tabularnewline
60 & 1.3408 & 1.32838164878841 & 0.0124183512115874 \tabularnewline
61 & 1.3119 & 1.37994716682204 & -0.0680471668220393 \tabularnewline
62 & 1.3014 & 1.32393311432879 & -0.0225331143287881 \tabularnewline
63 & 1.3201 & 1.2917617655607 & 0.0283382344392977 \tabularnewline
64 & 1.2938 & 1.3017615086375 & -0.00796150863749667 \tabularnewline
65 & 1.2694 & 1.29113402486393 & -0.0217340248639337 \tabularnewline
66 & 1.2165 & 1.24952425263226 & -0.0330242526322571 \tabularnewline
67 & 1.2037 & 1.24074254699561 & -0.0370425469956095 \tabularnewline
68 & 1.2292 & 1.20358703835343 & 0.0256129616465679 \tabularnewline
69 & 1.2256 & 1.21203271984491 & 0.0135672801550899 \tabularnewline
70 & 1.2015 & 1.21417387902496 & -0.0126738790249576 \tabularnewline
71 & 1.1786 & 1.19796356675284 & -0.0193635667528353 \tabularnewline
72 & 1.1856 & 1.21161966370554 & -0.0260196637055439 \tabularnewline
73 & 1.2103 & 1.21754620544847 & -0.00724620544847099 \tabularnewline
74 & 1.1938 & 1.21938190143422 & -0.025581901434224 \tabularnewline
75 & 1.202 & 1.19122839636379 & 0.0107716036362091 \tabularnewline
76 & 1.2271 & 1.18008446060541 & 0.0470155393945917 \tabularnewline
77 & 1.277 & 1.21393971522845 & 0.0630602847715451 \tabularnewline
78 & 1.265 & 1.24318430777826 & 0.0218156922217427 \tabularnewline
79 & 1.2684 & 1.28103654828682 & -0.012636548286824 \tabularnewline
80 & 1.2811 & 1.27431296147974 & 0.00678703852025953 \tabularnewline
81 & 1.2727 & 1.26527981274493 & 0.00742018725506499 \tabularnewline
82 & 1.2611 & 1.25868603892502 & 0.00241396107498093 \tabularnewline
83 & 1.2881 & 1.25482385077858 & 0.0332761492214175 \tabularnewline
84 & 1.3213 & 1.31326089225704 & 0.00803910774296401 \tabularnewline
85 & 1.2999 & 1.35197815676204 & -0.0520781567620368 \tabularnewline
86 & 1.3074 & 1.31349891884315 & -0.00609891884314573 \tabularnewline
87 & 1.3242 & 1.30806861654979 & 0.0161313834502139 \tabularnewline
88 & 1.3516 & 1.30758972927647 & 0.044010270723529 \tabularnewline
89 & 1.3511 & 1.3420104056086 & 0.00908959439140111 \tabularnewline
90 & 1.3419 & 1.31960786721868 & 0.0222921327813228 \tabularnewline
91 & 1.3716 & 1.35335206912222 & 0.0182479308777797 \tabularnewline
92 & 1.3622 & 1.37652066628525 & -0.0143206662852506 \tabularnewline
93 & 1.3896 & 1.3500734007566 & 0.0395265992434035 \tabularnewline
94 & 1.4227 & 1.37094095418509 & 0.0517590458149135 \tabularnewline
95 & 1.4684 & 1.41478221678761 & 0.0536177832123912 \tabularnewline
96 & 1.457 & 1.48811418507083 & -0.031114185070831 \tabularnewline
97 & 1.4718 & 1.48556168160651 & -0.0137616816065087 \tabularnewline
98 & 1.4748 & 1.48766823046701 & -0.0128682304670074 \tabularnewline
99 & 1.5527 & 1.48079082925551 & 0.0719091707444945 \tabularnewline
100 & 1.575 & 1.53350153216563 & 0.0414984678343737 \tabularnewline
101 & 1.5557 & 1.56215280725278 & -0.00645280725278408 \tabularnewline
102 & 1.5553 & 1.52972382541466 & 0.0255761745853369 \tabularnewline
103 & 1.577 & 1.56705673364873 & 0.00994326635126663 \tabularnewline
104 & 1.4975 & 1.57971851452706 & -0.082218514527058 \tabularnewline
105 & 1.4369 & 1.50393045911345 & -0.0670304591134485 \tabularnewline
106 & 1.3322 & 1.43571779340595 & -0.103517793405953 \tabularnewline
107 & 1.2732 & 1.34637053508509 & -0.0731705350850915 \tabularnewline
108 & 1.3449 & 1.29753827189368 & 0.0473617281063223 \tabularnewline
109 & 1.3239 & 1.36360239634344 & -0.0397023963434424 \tabularnewline
110 & 1.2785 & 1.34250602945084 & -0.0640060294508435 \tabularnewline
111 & 1.305 & 1.30273498186192 & 0.00226501813807656 \tabularnewline
112 & 1.319 & 1.28959891178504 & 0.0294010882149625 \tabularnewline
113 & 1.365 & 1.29898695673753 & 0.0660130432624728 \tabularnewline
114 & 1.4016 & 1.33163647327877 & 0.0699635267212284 \tabularnewline
115 & 1.4088 & 1.40340080239042 & 0.00539919760958307 \tabularnewline
116 & 1.4268 & 1.39753258154322 & 0.029267418456778 \tabularnewline
117 & 1.4562 & 1.41866745153236 & 0.0375325484676414 \tabularnewline
118 & 1.4816 & 1.43460413057986 & 0.0469958694201416 \tabularnewline
119 & 1.4914 & 1.47930587200161 & 0.0120941279983922 \tabularnewline
120 & 1.4614 & 1.52233622167716 & -0.0609362216771572 \tabularnewline
121 & 1.4272 & 1.4840029128521 & -0.0568029128521015 \tabularnewline
122 & 1.3686 & 1.44547801807606 & -0.0768780180760624 \tabularnewline
123 & 1.3569 & 1.40495027918451 & -0.0480502791845083 \tabularnewline
124 & 1.3406 & 1.3530612047494 & -0.0124612047494042 \tabularnewline
125 & 1.2565 & 1.33204160236324 & -0.0755416023632358 \tabularnewline
126 & 1.2208 & 1.24344641354839 & -0.0226464135483944 \tabularnewline
127 & 1.277 & 1.22531031831487 & 0.0516896816851276 \tabularnewline
128 & 1.2894 & 1.26140625197484 & 0.0279937480251553 \tabularnewline
129 & 1.3067 & 1.28156836451114 & 0.0251316354888567 \tabularnewline
130 & 1.3898 & 1.28711666118709 & 0.102683338812907 \tabularnewline
131 & 1.3661 & 1.37355079916431 & -0.00745079916430735 \tabularnewline
132 & 1.322 & 1.38834246715908 & -0.0663424671590782 \tabularnewline
133 & 1.336 & 1.34501605548819 & -0.00901605548818862 \tabularnewline
134 & 1.3649 & 1.34375851701718 & 0.0211414829828172 \tabularnewline
135 & 1.3999 & 1.39113731538636 & 0.00876268461364416 \tabularnewline
136 & 1.4442 & 1.39325200782037 & 0.0509479921796314 \tabularnewline
137 & 1.4349 & 1.41795439456248 & 0.0169456054375219 \tabularnewline
138 & 1.4388 & 1.41732675079802 & 0.0214732492019813 \tabularnewline
139 & 1.4264 & 1.44918414965032 & -0.0227841496503174 \tabularnewline
140 & 1.4343 & 1.41920652586777 & 0.0150934741322299 \tabularnewline
141 & 1.377 & 1.428881629184 & -0.0518816291839994 \tabularnewline
142 & 1.3706 & 1.38031843931992 & -0.009718439319921 \tabularnewline
143 & 1.3556 & 1.3544789063227 & 0.00112109367729807 \tabularnewline
144 & 1.3179 & 1.36791049049502 & -0.0500104904950223 \tabularnewline
145 & 1.2905 & 1.34681265436318 & -0.0563126543631842 \tabularnewline
146 & 1.3224 & 1.30915332745434 & 0.0132466725456588 \tabularnewline
147 & 1.3201 & 1.34760108609441 & -0.0275010860944069 \tabularnewline
148 & 1.3162 & 1.32422107733851 & -0.00802107733851343 \tabularnewline
149 & 1.2789 & 1.29260679012862 & -0.0137067901286152 \tabularnewline
150 & 1.2526 & 1.26527286083641 & -0.0126728608364084 \tabularnewline
151 & 1.2288 & 1.26015325561303 & -0.0313532556130289 \tabularnewline
152 & 1.24 & 1.22692534230116 & 0.0130746576988374 \tabularnewline
153 & 1.2856 & 1.22373230425672 & 0.061867695743284 \tabularnewline
154 & 1.2974 & 1.27780321978732 & 0.0195967802126766 \tabularnewline
155 & 1.2828 & 1.27804508813741 & 0.00475491186258648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196884&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]0.9383[/C][C]0.969540224358974[/C][C]-0.031240224358974[/C][/ROW]
[ROW][C]14[/C][C]0.9217[/C][C]0.92689654140936[/C][C]-0.00519654140936021[/C][/ROW]
[ROW][C]15[/C][C]0.9095[/C][C]0.905971212545413[/C][C]0.00352878745458673[/C][/ROW]
[ROW][C]16[/C][C]0.892[/C][C]0.884964933533471[/C][C]0.00703506646652929[/C][/ROW]
[ROW][C]17[/C][C]0.8742[/C][C]0.866995301388958[/C][C]0.00720469861104178[/C][/ROW]
[ROW][C]18[/C][C]0.8532[/C][C]0.848331424322249[/C][C]0.00486857567775145[/C][/ROW]
[ROW][C]19[/C][C]0.8607[/C][C]0.911287482811404[/C][C]-0.0505874828114041[/C][/ROW]
[ROW][C]20[/C][C]0.9005[/C][C]0.835170444602858[/C][C]0.0653295553971417[/C][/ROW]
[ROW][C]21[/C][C]0.9111[/C][C]0.861301174503225[/C][C]0.0497988254967746[/C][/ROW]
[ROW][C]22[/C][C]0.9059[/C][C]0.88927881088282[/C][C]0.0166211891171798[/C][/ROW]
[ROW][C]23[/C][C]0.8883[/C][C]0.906133575438585[/C][C]-0.0178335754385847[/C][/ROW]
[ROW][C]24[/C][C]0.8924[/C][C]0.934829527420517[/C][C]-0.0424295274205168[/C][/ROW]
[ROW][C]25[/C][C]0.8833[/C][C]0.939773178591962[/C][C]-0.0564731785919621[/C][/ROW]
[ROW][C]26[/C][C]0.87[/C][C]0.879221853103251[/C][C]-0.00922185310325141[/C][/ROW]
[ROW][C]27[/C][C]0.8758[/C][C]0.855984824282673[/C][C]0.0198151757173275[/C][/ROW]
[ROW][C]28[/C][C]0.8858[/C][C]0.849375636721548[/C][C]0.036424363278452[/C][/ROW]
[ROW][C]29[/C][C]0.917[/C][C]0.856701635619078[/C][C]0.0602983643809224[/C][/ROW]
[ROW][C]30[/C][C]0.9554[/C][C]0.883561401770986[/C][C]0.0718385982290144[/C][/ROW]
[ROW][C]31[/C][C]0.9922[/C][C]0.996611098944871[/C][C]-0.00441109894487113[/C][/ROW]
[ROW][C]32[/C][C]0.9778[/C][C]0.977944673701786[/C][C]-0.000144673701785947[/C][/ROW]
[ROW][C]33[/C][C]0.9808[/C][C]0.946604023923842[/C][C]0.0341959760761582[/C][/ROW]
[ROW][C]34[/C][C]0.9811[/C][C]0.957094668154257[/C][C]0.0240053318457425[/C][/ROW]
[ROW][C]35[/C][C]1.0014[/C][C]0.975975775287767[/C][C]0.0254242247122327[/C][/ROW]
[ROW][C]36[/C][C]1.0183[/C][C]1.03906354407732[/C][C]-0.0207635440773228[/C][/ROW]
[ROW][C]37[/C][C]1.0622[/C][C]1.06160125980071[/C][C]0.000598740199289072[/C][/ROW]
[ROW][C]38[/C][C]1.0773[/C][C]1.05815338658556[/C][C]0.0191466134144391[/C][/ROW]
[ROW][C]39[/C][C]1.0807[/C][C]1.06501097977058[/C][C]0.0156890202294215[/C][/ROW]
[ROW][C]40[/C][C]1.0848[/C][C]1.05888666901041[/C][C]0.0259133309895918[/C][/ROW]
[ROW][C]41[/C][C]1.1582[/C][C]1.06222788738582[/C][C]0.0959721126141804[/C][/ROW]
[ROW][C]42[/C][C]1.1663[/C][C]1.12301936890464[/C][C]0.0432806310953635[/C][/ROW]
[ROW][C]43[/C][C]1.1372[/C][C]1.20217799483914[/C][C]-0.0649779948391371[/C][/ROW]
[ROW][C]44[/C][C]1.1139[/C][C]1.13355971994031[/C][C]-0.0196597199403052[/C][/ROW]
[ROW][C]45[/C][C]1.1222[/C][C]1.09160774813763[/C][C]0.0305922518623707[/C][/ROW]
[ROW][C]46[/C][C]1.1692[/C][C]1.0986108965102[/C][C]0.0705891034897985[/C][/ROW]
[ROW][C]47[/C][C]1.1702[/C][C]1.15888224112905[/C][C]0.0113177588709492[/C][/ROW]
[ROW][C]48[/C][C]1.2286[/C][C]1.20448114483456[/C][C]0.0241188551654445[/C][/ROW]
[ROW][C]49[/C][C]1.2613[/C][C]1.27003486864523[/C][C]-0.00873486864522954[/C][/ROW]
[ROW][C]50[/C][C]1.2646[/C][C]1.26278424067919[/C][C]0.00181575932080991[/C][/ROW]
[ROW][C]51[/C][C]1.2262[/C][C]1.25570436751311[/C][C]-0.0295043675131115[/C][/ROW]
[ROW][C]52[/C][C]1.1985[/C][C]1.21352852366982[/C][C]-0.0150285236698247[/C][/ROW]
[ROW][C]53[/C][C]1.2007[/C][C]1.19288008675238[/C][C]0.00781991324762066[/C][/ROW]
[ROW][C]54[/C][C]1.2138[/C][C]1.17097763244918[/C][C]0.0428223675508188[/C][/ROW]
[ROW][C]55[/C][C]1.2266[/C][C]1.2343575659435[/C][C]-0.00775756594350319[/C][/ROW]
[ROW][C]56[/C][C]1.2176[/C][C]1.22189646313082[/C][C]-0.00429646313082488[/C][/ROW]
[ROW][C]57[/C][C]1.2218[/C][C]1.2011241039855[/C][C]0.0206758960144997[/C][/ROW]
[ROW][C]58[/C][C]1.249[/C][C]1.20614548368641[/C][C]0.0428545163135923[/C][/ROW]
[ROW][C]59[/C][C]1.2991[/C][C]1.23463526251547[/C][C]0.0644647374845257[/C][/ROW]
[ROW][C]60[/C][C]1.3408[/C][C]1.32838164878841[/C][C]0.0124183512115874[/C][/ROW]
[ROW][C]61[/C][C]1.3119[/C][C]1.37994716682204[/C][C]-0.0680471668220393[/C][/ROW]
[ROW][C]62[/C][C]1.3014[/C][C]1.32393311432879[/C][C]-0.0225331143287881[/C][/ROW]
[ROW][C]63[/C][C]1.3201[/C][C]1.2917617655607[/C][C]0.0283382344392977[/C][/ROW]
[ROW][C]64[/C][C]1.2938[/C][C]1.3017615086375[/C][C]-0.00796150863749667[/C][/ROW]
[ROW][C]65[/C][C]1.2694[/C][C]1.29113402486393[/C][C]-0.0217340248639337[/C][/ROW]
[ROW][C]66[/C][C]1.2165[/C][C]1.24952425263226[/C][C]-0.0330242526322571[/C][/ROW]
[ROW][C]67[/C][C]1.2037[/C][C]1.24074254699561[/C][C]-0.0370425469956095[/C][/ROW]
[ROW][C]68[/C][C]1.2292[/C][C]1.20358703835343[/C][C]0.0256129616465679[/C][/ROW]
[ROW][C]69[/C][C]1.2256[/C][C]1.21203271984491[/C][C]0.0135672801550899[/C][/ROW]
[ROW][C]70[/C][C]1.2015[/C][C]1.21417387902496[/C][C]-0.0126738790249576[/C][/ROW]
[ROW][C]71[/C][C]1.1786[/C][C]1.19796356675284[/C][C]-0.0193635667528353[/C][/ROW]
[ROW][C]72[/C][C]1.1856[/C][C]1.21161966370554[/C][C]-0.0260196637055439[/C][/ROW]
[ROW][C]73[/C][C]1.2103[/C][C]1.21754620544847[/C][C]-0.00724620544847099[/C][/ROW]
[ROW][C]74[/C][C]1.1938[/C][C]1.21938190143422[/C][C]-0.025581901434224[/C][/ROW]
[ROW][C]75[/C][C]1.202[/C][C]1.19122839636379[/C][C]0.0107716036362091[/C][/ROW]
[ROW][C]76[/C][C]1.2271[/C][C]1.18008446060541[/C][C]0.0470155393945917[/C][/ROW]
[ROW][C]77[/C][C]1.277[/C][C]1.21393971522845[/C][C]0.0630602847715451[/C][/ROW]
[ROW][C]78[/C][C]1.265[/C][C]1.24318430777826[/C][C]0.0218156922217427[/C][/ROW]
[ROW][C]79[/C][C]1.2684[/C][C]1.28103654828682[/C][C]-0.012636548286824[/C][/ROW]
[ROW][C]80[/C][C]1.2811[/C][C]1.27431296147974[/C][C]0.00678703852025953[/C][/ROW]
[ROW][C]81[/C][C]1.2727[/C][C]1.26527981274493[/C][C]0.00742018725506499[/C][/ROW]
[ROW][C]82[/C][C]1.2611[/C][C]1.25868603892502[/C][C]0.00241396107498093[/C][/ROW]
[ROW][C]83[/C][C]1.2881[/C][C]1.25482385077858[/C][C]0.0332761492214175[/C][/ROW]
[ROW][C]84[/C][C]1.3213[/C][C]1.31326089225704[/C][C]0.00803910774296401[/C][/ROW]
[ROW][C]85[/C][C]1.2999[/C][C]1.35197815676204[/C][C]-0.0520781567620368[/C][/ROW]
[ROW][C]86[/C][C]1.3074[/C][C]1.31349891884315[/C][C]-0.00609891884314573[/C][/ROW]
[ROW][C]87[/C][C]1.3242[/C][C]1.30806861654979[/C][C]0.0161313834502139[/C][/ROW]
[ROW][C]88[/C][C]1.3516[/C][C]1.30758972927647[/C][C]0.044010270723529[/C][/ROW]
[ROW][C]89[/C][C]1.3511[/C][C]1.3420104056086[/C][C]0.00908959439140111[/C][/ROW]
[ROW][C]90[/C][C]1.3419[/C][C]1.31960786721868[/C][C]0.0222921327813228[/C][/ROW]
[ROW][C]91[/C][C]1.3716[/C][C]1.35335206912222[/C][C]0.0182479308777797[/C][/ROW]
[ROW][C]92[/C][C]1.3622[/C][C]1.37652066628525[/C][C]-0.0143206662852506[/C][/ROW]
[ROW][C]93[/C][C]1.3896[/C][C]1.3500734007566[/C][C]0.0395265992434035[/C][/ROW]
[ROW][C]94[/C][C]1.4227[/C][C]1.37094095418509[/C][C]0.0517590458149135[/C][/ROW]
[ROW][C]95[/C][C]1.4684[/C][C]1.41478221678761[/C][C]0.0536177832123912[/C][/ROW]
[ROW][C]96[/C][C]1.457[/C][C]1.48811418507083[/C][C]-0.031114185070831[/C][/ROW]
[ROW][C]97[/C][C]1.4718[/C][C]1.48556168160651[/C][C]-0.0137616816065087[/C][/ROW]
[ROW][C]98[/C][C]1.4748[/C][C]1.48766823046701[/C][C]-0.0128682304670074[/C][/ROW]
[ROW][C]99[/C][C]1.5527[/C][C]1.48079082925551[/C][C]0.0719091707444945[/C][/ROW]
[ROW][C]100[/C][C]1.575[/C][C]1.53350153216563[/C][C]0.0414984678343737[/C][/ROW]
[ROW][C]101[/C][C]1.5557[/C][C]1.56215280725278[/C][C]-0.00645280725278408[/C][/ROW]
[ROW][C]102[/C][C]1.5553[/C][C]1.52972382541466[/C][C]0.0255761745853369[/C][/ROW]
[ROW][C]103[/C][C]1.577[/C][C]1.56705673364873[/C][C]0.00994326635126663[/C][/ROW]
[ROW][C]104[/C][C]1.4975[/C][C]1.57971851452706[/C][C]-0.082218514527058[/C][/ROW]
[ROW][C]105[/C][C]1.4369[/C][C]1.50393045911345[/C][C]-0.0670304591134485[/C][/ROW]
[ROW][C]106[/C][C]1.3322[/C][C]1.43571779340595[/C][C]-0.103517793405953[/C][/ROW]
[ROW][C]107[/C][C]1.2732[/C][C]1.34637053508509[/C][C]-0.0731705350850915[/C][/ROW]
[ROW][C]108[/C][C]1.3449[/C][C]1.29753827189368[/C][C]0.0473617281063223[/C][/ROW]
[ROW][C]109[/C][C]1.3239[/C][C]1.36360239634344[/C][C]-0.0397023963434424[/C][/ROW]
[ROW][C]110[/C][C]1.2785[/C][C]1.34250602945084[/C][C]-0.0640060294508435[/C][/ROW]
[ROW][C]111[/C][C]1.305[/C][C]1.30273498186192[/C][C]0.00226501813807656[/C][/ROW]
[ROW][C]112[/C][C]1.319[/C][C]1.28959891178504[/C][C]0.0294010882149625[/C][/ROW]
[ROW][C]113[/C][C]1.365[/C][C]1.29898695673753[/C][C]0.0660130432624728[/C][/ROW]
[ROW][C]114[/C][C]1.4016[/C][C]1.33163647327877[/C][C]0.0699635267212284[/C][/ROW]
[ROW][C]115[/C][C]1.4088[/C][C]1.40340080239042[/C][C]0.00539919760958307[/C][/ROW]
[ROW][C]116[/C][C]1.4268[/C][C]1.39753258154322[/C][C]0.029267418456778[/C][/ROW]
[ROW][C]117[/C][C]1.4562[/C][C]1.41866745153236[/C][C]0.0375325484676414[/C][/ROW]
[ROW][C]118[/C][C]1.4816[/C][C]1.43460413057986[/C][C]0.0469958694201416[/C][/ROW]
[ROW][C]119[/C][C]1.4914[/C][C]1.47930587200161[/C][C]0.0120941279983922[/C][/ROW]
[ROW][C]120[/C][C]1.4614[/C][C]1.52233622167716[/C][C]-0.0609362216771572[/C][/ROW]
[ROW][C]121[/C][C]1.4272[/C][C]1.4840029128521[/C][C]-0.0568029128521015[/C][/ROW]
[ROW][C]122[/C][C]1.3686[/C][C]1.44547801807606[/C][C]-0.0768780180760624[/C][/ROW]
[ROW][C]123[/C][C]1.3569[/C][C]1.40495027918451[/C][C]-0.0480502791845083[/C][/ROW]
[ROW][C]124[/C][C]1.3406[/C][C]1.3530612047494[/C][C]-0.0124612047494042[/C][/ROW]
[ROW][C]125[/C][C]1.2565[/C][C]1.33204160236324[/C][C]-0.0755416023632358[/C][/ROW]
[ROW][C]126[/C][C]1.2208[/C][C]1.24344641354839[/C][C]-0.0226464135483944[/C][/ROW]
[ROW][C]127[/C][C]1.277[/C][C]1.22531031831487[/C][C]0.0516896816851276[/C][/ROW]
[ROW][C]128[/C][C]1.2894[/C][C]1.26140625197484[/C][C]0.0279937480251553[/C][/ROW]
[ROW][C]129[/C][C]1.3067[/C][C]1.28156836451114[/C][C]0.0251316354888567[/C][/ROW]
[ROW][C]130[/C][C]1.3898[/C][C]1.28711666118709[/C][C]0.102683338812907[/C][/ROW]
[ROW][C]131[/C][C]1.3661[/C][C]1.37355079916431[/C][C]-0.00745079916430735[/C][/ROW]
[ROW][C]132[/C][C]1.322[/C][C]1.38834246715908[/C][C]-0.0663424671590782[/C][/ROW]
[ROW][C]133[/C][C]1.336[/C][C]1.34501605548819[/C][C]-0.00901605548818862[/C][/ROW]
[ROW][C]134[/C][C]1.3649[/C][C]1.34375851701718[/C][C]0.0211414829828172[/C][/ROW]
[ROW][C]135[/C][C]1.3999[/C][C]1.39113731538636[/C][C]0.00876268461364416[/C][/ROW]
[ROW][C]136[/C][C]1.4442[/C][C]1.39325200782037[/C][C]0.0509479921796314[/C][/ROW]
[ROW][C]137[/C][C]1.4349[/C][C]1.41795439456248[/C][C]0.0169456054375219[/C][/ROW]
[ROW][C]138[/C][C]1.4388[/C][C]1.41732675079802[/C][C]0.0214732492019813[/C][/ROW]
[ROW][C]139[/C][C]1.4264[/C][C]1.44918414965032[/C][C]-0.0227841496503174[/C][/ROW]
[ROW][C]140[/C][C]1.4343[/C][C]1.41920652586777[/C][C]0.0150934741322299[/C][/ROW]
[ROW][C]141[/C][C]1.377[/C][C]1.428881629184[/C][C]-0.0518816291839994[/C][/ROW]
[ROW][C]142[/C][C]1.3706[/C][C]1.38031843931992[/C][C]-0.009718439319921[/C][/ROW]
[ROW][C]143[/C][C]1.3556[/C][C]1.3544789063227[/C][C]0.00112109367729807[/C][/ROW]
[ROW][C]144[/C][C]1.3179[/C][C]1.36791049049502[/C][C]-0.0500104904950223[/C][/ROW]
[ROW][C]145[/C][C]1.2905[/C][C]1.34681265436318[/C][C]-0.0563126543631842[/C][/ROW]
[ROW][C]146[/C][C]1.3224[/C][C]1.30915332745434[/C][C]0.0132466725456588[/C][/ROW]
[ROW][C]147[/C][C]1.3201[/C][C]1.34760108609441[/C][C]-0.0275010860944069[/C][/ROW]
[ROW][C]148[/C][C]1.3162[/C][C]1.32422107733851[/C][C]-0.00802107733851343[/C][/ROW]
[ROW][C]149[/C][C]1.2789[/C][C]1.29260679012862[/C][C]-0.0137067901286152[/C][/ROW]
[ROW][C]150[/C][C]1.2526[/C][C]1.26527286083641[/C][C]-0.0126728608364084[/C][/ROW]
[ROW][C]151[/C][C]1.2288[/C][C]1.26015325561303[/C][C]-0.0313532556130289[/C][/ROW]
[ROW][C]152[/C][C]1.24[/C][C]1.22692534230116[/C][C]0.0130746576988374[/C][/ROW]
[ROW][C]153[/C][C]1.2856[/C][C]1.22373230425672[/C][C]0.061867695743284[/C][/ROW]
[ROW][C]154[/C][C]1.2974[/C][C]1.27780321978732[/C][C]0.0195967802126766[/C][/ROW]
[ROW][C]155[/C][C]1.2828[/C][C]1.27804508813741[/C][C]0.00475491186258648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196884&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196884&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
130.93830.969540224358974-0.031240224358974
140.92170.92689654140936-0.00519654140936021
150.90950.9059712125454130.00352878745458673
160.8920.8849649335334710.00703506646652929
170.87420.8669953013889580.00720469861104178
180.85320.8483314243222490.00486857567775145
190.86070.911287482811404-0.0505874828114041
200.90050.8351704446028580.0653295553971417
210.91110.8613011745032250.0497988254967746
220.90590.889278810882820.0166211891171798
230.88830.906133575438585-0.0178335754385847
240.89240.934829527420517-0.0424295274205168
250.88330.939773178591962-0.0564731785919621
260.870.879221853103251-0.00922185310325141
270.87580.8559848242826730.0198151757173275
280.88580.8493756367215480.036424363278452
290.9170.8567016356190780.0602983643809224
300.95540.8835614017709860.0718385982290144
310.99220.996611098944871-0.00441109894487113
320.97780.977944673701786-0.000144673701785947
330.98080.9466040239238420.0341959760761582
340.98110.9570946681542570.0240053318457425
351.00140.9759757752877670.0254242247122327
361.01831.03906354407732-0.0207635440773228
371.06221.061601259800710.000598740199289072
381.07731.058153386585560.0191466134144391
391.08071.065010979770580.0156890202294215
401.08481.058886669010410.0259133309895918
411.15821.062227887385820.0959721126141804
421.16631.123019368904640.0432806310953635
431.13721.20217799483914-0.0649779948391371
441.11391.13355971994031-0.0196597199403052
451.12221.091607748137630.0305922518623707
461.16921.09861089651020.0705891034897985
471.17021.158882241129050.0113177588709492
481.22861.204481144834560.0241188551654445
491.26131.27003486864523-0.00873486864522954
501.26461.262784240679190.00181575932080991
511.22621.25570436751311-0.0295043675131115
521.19851.21352852366982-0.0150285236698247
531.20071.192880086752380.00781991324762066
541.21381.170977632449180.0428223675508188
551.22661.2343575659435-0.00775756594350319
561.21761.22189646313082-0.00429646313082488
571.22181.20112410398550.0206758960144997
581.2491.206145483686410.0428545163135923
591.29911.234635262515470.0644647374845257
601.34081.328381648788410.0124183512115874
611.31191.37994716682204-0.0680471668220393
621.30141.32393311432879-0.0225331143287881
631.32011.29176176556070.0283382344392977
641.29381.3017615086375-0.00796150863749667
651.26941.29113402486393-0.0217340248639337
661.21651.24952425263226-0.0330242526322571
671.20371.24074254699561-0.0370425469956095
681.22921.203587038353430.0256129616465679
691.22561.212032719844910.0135672801550899
701.20151.21417387902496-0.0126738790249576
711.17861.19796356675284-0.0193635667528353
721.18561.21161966370554-0.0260196637055439
731.21031.21754620544847-0.00724620544847099
741.19381.21938190143422-0.025581901434224
751.2021.191228396363790.0107716036362091
761.22711.180084460605410.0470155393945917
771.2771.213939715228450.0630602847715451
781.2651.243184307778260.0218156922217427
791.26841.28103654828682-0.012636548286824
801.28111.274312961479740.00678703852025953
811.27271.265279812744930.00742018725506499
821.26111.258686038925020.00241396107498093
831.28811.254823850778580.0332761492214175
841.32131.313260892257040.00803910774296401
851.29991.35197815676204-0.0520781567620368
861.30741.31349891884315-0.00609891884314573
871.32421.308068616549790.0161313834502139
881.35161.307589729276470.044010270723529
891.35111.34201040560860.00908959439140111
901.34191.319607867218680.0222921327813228
911.37161.353352069122220.0182479308777797
921.36221.37652066628525-0.0143206662852506
931.38961.35007340075660.0395265992434035
941.42271.370940954185090.0517590458149135
951.46841.414782216787610.0536177832123912
961.4571.48811418507083-0.031114185070831
971.47181.48556168160651-0.0137616816065087
981.47481.48766823046701-0.0128682304670074
991.55271.480790829255510.0719091707444945
1001.5751.533501532165630.0414984678343737
1011.55571.56215280725278-0.00645280725278408
1021.55531.529723825414660.0255761745853369
1031.5771.567056733648730.00994326635126663
1041.49751.57971851452706-0.082218514527058
1051.43691.50393045911345-0.0670304591134485
1061.33221.43571779340595-0.103517793405953
1071.27321.34637053508509-0.0731705350850915
1081.34491.297538271893680.0473617281063223
1091.32391.36360239634344-0.0397023963434424
1101.27851.34250602945084-0.0640060294508435
1111.3051.302734981861920.00226501813807656
1121.3191.289598911785040.0294010882149625
1131.3651.298986956737530.0660130432624728
1141.40161.331636473278770.0699635267212284
1151.40881.403400802390420.00539919760958307
1161.42681.397532581543220.029267418456778
1171.45621.418667451532360.0375325484676414
1181.48161.434604130579860.0469958694201416
1191.49141.479305872001610.0120941279983922
1201.46141.52233622167716-0.0609362216771572
1211.42721.4840029128521-0.0568029128521015
1221.36861.44547801807606-0.0768780180760624
1231.35691.40495027918451-0.0480502791845083
1241.34061.3530612047494-0.0124612047494042
1251.25651.33204160236324-0.0755416023632358
1261.22081.24344641354839-0.0226464135483944
1271.2771.225310318314870.0516896816851276
1281.28941.261406251974840.0279937480251553
1291.30671.281568364511140.0251316354888567
1301.38981.287116661187090.102683338812907
1311.36611.37355079916431-0.00745079916430735
1321.3221.38834246715908-0.0663424671590782
1331.3361.34501605548819-0.00901605548818862
1341.36491.343758517017180.0211414829828172
1351.39991.391137315386360.00876268461364416
1361.44421.393252007820370.0509479921796314
1371.43491.417954394562480.0169456054375219
1381.43881.417326750798020.0214732492019813
1391.42641.44918414965032-0.0227841496503174
1401.43431.419206525867770.0150934741322299
1411.3771.428881629184-0.0518816291839994
1421.37061.38031843931992-0.009718439319921
1431.35561.35447890632270.00112109367729807
1441.31791.36791049049502-0.0500104904950223
1451.29051.34681265436318-0.0563126543631842
1461.32241.309153327454340.0132466725456588
1471.32011.34760108609441-0.0275010860944069
1481.31621.32422107733851-0.00802107733851343
1491.27891.29260679012862-0.0137067901286152
1501.25261.26527286083641-0.0126728608364084
1511.22881.26015325561303-0.0313532556130289
1521.241.226925342301160.0130746576988374
1531.28561.223732304256720.061867695743284
1541.29741.277803219787320.0195967802126766
1551.28281.278045088137410.00475491186258648







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1561.286636115775791.210559191995271.36271303955631
1571.307155823790471.206760726778121.40755092080282
1581.327848130429821.207715619937311.44798064092234
1591.349097904865181.211816934266611.48637887546375
1601.352260852631671.199544308750161.50497739651319
1611.326934013090721.160017607143451.49385041903799
1621.311807002515661.131632839208481.49198116582284
1631.315228828089561.122543324588081.50791433159103
1641.315857452771371.111268983350171.52044592219258
1651.30908911196621.093104442042221.52507378189017
1661.304283189722871.07733177738311.53123460206264
1671.28564691691091.048097822153841.52319601166796

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
156 & 1.28663611577579 & 1.21055919199527 & 1.36271303955631 \tabularnewline
157 & 1.30715582379047 & 1.20676072677812 & 1.40755092080282 \tabularnewline
158 & 1.32784813042982 & 1.20771561993731 & 1.44798064092234 \tabularnewline
159 & 1.34909790486518 & 1.21181693426661 & 1.48637887546375 \tabularnewline
160 & 1.35226085263167 & 1.19954430875016 & 1.50497739651319 \tabularnewline
161 & 1.32693401309072 & 1.16001760714345 & 1.49385041903799 \tabularnewline
162 & 1.31180700251566 & 1.13163283920848 & 1.49198116582284 \tabularnewline
163 & 1.31522882808956 & 1.12254332458808 & 1.50791433159103 \tabularnewline
164 & 1.31585745277137 & 1.11126898335017 & 1.52044592219258 \tabularnewline
165 & 1.3090891119662 & 1.09310444204222 & 1.52507378189017 \tabularnewline
166 & 1.30428318972287 & 1.0773317773831 & 1.53123460206264 \tabularnewline
167 & 1.2856469169109 & 1.04809782215384 & 1.52319601166796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196884&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]156[/C][C]1.28663611577579[/C][C]1.21055919199527[/C][C]1.36271303955631[/C][/ROW]
[ROW][C]157[/C][C]1.30715582379047[/C][C]1.20676072677812[/C][C]1.40755092080282[/C][/ROW]
[ROW][C]158[/C][C]1.32784813042982[/C][C]1.20771561993731[/C][C]1.44798064092234[/C][/ROW]
[ROW][C]159[/C][C]1.34909790486518[/C][C]1.21181693426661[/C][C]1.48637887546375[/C][/ROW]
[ROW][C]160[/C][C]1.35226085263167[/C][C]1.19954430875016[/C][C]1.50497739651319[/C][/ROW]
[ROW][C]161[/C][C]1.32693401309072[/C][C]1.16001760714345[/C][C]1.49385041903799[/C][/ROW]
[ROW][C]162[/C][C]1.31180700251566[/C][C]1.13163283920848[/C][C]1.49198116582284[/C][/ROW]
[ROW][C]163[/C][C]1.31522882808956[/C][C]1.12254332458808[/C][C]1.50791433159103[/C][/ROW]
[ROW][C]164[/C][C]1.31585745277137[/C][C]1.11126898335017[/C][C]1.52044592219258[/C][/ROW]
[ROW][C]165[/C][C]1.3090891119662[/C][C]1.09310444204222[/C][C]1.52507378189017[/C][/ROW]
[ROW][C]166[/C][C]1.30428318972287[/C][C]1.0773317773831[/C][C]1.53123460206264[/C][/ROW]
[ROW][C]167[/C][C]1.2856469169109[/C][C]1.04809782215384[/C][C]1.52319601166796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196884&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196884&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
1561.286636115775791.210559191995271.36271303955631
1571.307155823790471.206760726778121.40755092080282
1581.327848130429821.207715619937311.44798064092234
1591.349097904865181.211816934266611.48637887546375
1601.352260852631671.199544308750161.50497739651319
1611.326934013090721.160017607143451.49385041903799
1621.311807002515661.131632839208481.49198116582284
1631.315228828089561.122543324588081.50791433159103
1641.315857452771371.111268983350171.52044592219258
1651.30908911196621.093104442042221.52507378189017
1661.304283189722871.07733177738311.53123460206264
1671.28564691691091.048097822153841.52319601166796



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')