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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 26 Nov 2015 09:29:28 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/26/t1448530242tbxlm7aclk4avtf.htm/, Retrieved Tue, 14 May 2024 18:32:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284174, Retrieved Tue, 14 May 2024 18:32:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Addidtief model T...] [2015-11-26 09:29:28] [002d4cc575a6d7b5895f2103ed304b4f] [Current]
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Dataseries X:
24158
24359
24628
25021
25315
25481
26043
26207
26466
26276
26236
26211
26265
25996
25794
25752
25491
25092
25759
25624
25138
25042
25014
25244
25493
25269
25170
25332
24966
24851
25518
25403
25028
24895
24905
25317
25718
25822
25967
25907
25940
26247
26900
26980
26677
26701
26808
27469
27586
27567
27508
27444
27380
27500
28217
28355
27627
27565
27496
27453
27705
27462
27152
27016
26836
26722
27391
27139
26644
26455
26294
26437
26954
26620
26307
26003
25798
25603
26242
26051
25658
25489
25425
25183
24774
24977
24980
25081
25240
25419
26309
26600
26690
26889
27109
27646
28330
28332
28202
28163
28077
28351
28950
28972
28812
28979
29112
29139




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284174&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]1 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=284174&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284174&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.870921819347305
beta0.166111620762831
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.870921819347305 \tabularnewline
beta & 0.166111620762831 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284174&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]0.870921819347305[/C][/ROW]
[ROW][C]beta[/C][C]0.166111620762831[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284174&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284174&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
alpha0.870921819347305
beta0.166111620762831
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132626526043.6490384615221.350961538465
142599626022.7461880103-26.7461880102601
152579425892.4007393951-98.4007393951433
162575225872.5391204339-120.539120433928
172549125592.5416128381-101.541612838137
182509225165.2744001323-73.2744001322717
192575925947.483428393-188.483428393021
202562425722.4197916155-98.4197916155426
212513825695.764460192-557.764460192
222504224777.1139187908264.886081209239
232501424804.4988152024209.501184797577
242524424875.6230491646368.376950835402
252549325265.1470804371227.852919562891
262526925189.737027386879.2629726132436
272517025129.658629835340.3413701647478
282533225235.035212149396.9647878507094
292496625185.647362052-219.647362051983
302485124680.8101635263170.189836473724
312551825717.0507720044-199.050772004375
322540325549.7445114873-146.744511487286
332502825470.0550604284-442.055060428411
342489524823.44860866171.5513913389586
352490524712.4193620313192.580637968655
362531724823.9808563772493.019143622798
372571825356.6182609649361.381739035107
382582225450.3376502773371.662349722734
392596725754.2098071614212.790192838569
402590726156.3503778761-249.350377876119
412594025853.645575171386.3544248287144
422624725799.0650382216447.934961778374
432690027203.1540354049-303.154035404852
442698027110.4879295195-130.487929519481
452667727167.7447468007-490.744746800749
462670126698.89102757332.1089724266858
472680826686.8211034377121.178896562331
482746926908.463617607560.536382392991
492758627626.1657753749-40.1657753748914
502756727456.6577355885110.342264411462
512750827559.7904214123-51.7904214122645
522744427680.9295805317-236.929580531723
532738027443.2512884934-63.2512884934295
542750027294.2813377584205.718662241605
552821728344.6614928184-127.661492818403
562835528406.7034649933-51.7034649933375
572762728477.0522306895-850.052230689529
582756527697.8834809498-132.883480949789
592749627503.0826586056-7.08265860556639
602745327570.6428671056-117.642867105573
612770527422.966042424282.033957576001
622746227402.90846028159.0915397189565
632715227282.475901298-130.475901297988
642701627141.8032081244-125.803208124438
652683626870.0165297152-34.0165297151907
662672226632.146472835889.853527164214
672739127372.743366119218.256633880821
682713927426.941468733-287.941468733028
692664427009.5877147218-365.587714721783
702645526636.0998339456-181.099833945598
712629426299.7483217538-5.7483217538429
722643726238.5966043455198.403395654463
732695426347.8802918775606.119708122547
742662026558.303989893261.696010106778
752630726393.0524202998-86.0524202997804
762600326275.4807238852-272.480723885161
772579825850.3856585123-52.3856585122521
782560325572.43758642430.5624135760336
792624226203.508437413738.4915625862559
802605126190.0869577849-139.086957784933
812565825868.1670970146-210.16709701459
822548925652.1522085766-163.152208576572
832542525354.962641469370.0373585306588
842518325398.0267034259-215.026703425916
852477425151.922191703-377.922191703041
862497724244.7373496705732.262650329532
872498024551.1250752918428.874924708176
882508124839.1449482783241.855051721679
892524024946.0086159756293.991384024368
902541925086.1481153334332.851884666576
912630926130.9586925409178.041307459109
922660026385.787062612214.212937388005
932669026583.1353174562106.864682543757
942688926915.9104047544-26.9104047544388
952710927053.798101373355.2018986266849
962764627331.3214566432314.678543356757
972833027886.33050095443.669499049971
982833228317.656243583914.3437564160922
992820228335.4383242447-133.438324244747
1002816328404.0434645325-241.043464532544
1012807728321.6652290737-244.665229073704
1022835128144.3606831466206.639316853405
1032895029187.6758211521-237.67582115213
1042897229153.3826543789-181.382654378875
1052881229003.3774650275-191.377465027508
1062897929027.0284578481-48.0284578481478
1072911229121.9566784484-9.95667844841591
1082913929331.6320642671-192.632064267102

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 26265 & 26043.6490384615 & 221.350961538465 \tabularnewline
14 & 25996 & 26022.7461880103 & -26.7461880102601 \tabularnewline
15 & 25794 & 25892.4007393951 & -98.4007393951433 \tabularnewline
16 & 25752 & 25872.5391204339 & -120.539120433928 \tabularnewline
17 & 25491 & 25592.5416128381 & -101.541612838137 \tabularnewline
18 & 25092 & 25165.2744001323 & -73.2744001322717 \tabularnewline
19 & 25759 & 25947.483428393 & -188.483428393021 \tabularnewline
20 & 25624 & 25722.4197916155 & -98.4197916155426 \tabularnewline
21 & 25138 & 25695.764460192 & -557.764460192 \tabularnewline
22 & 25042 & 24777.1139187908 & 264.886081209239 \tabularnewline
23 & 25014 & 24804.4988152024 & 209.501184797577 \tabularnewline
24 & 25244 & 24875.6230491646 & 368.376950835402 \tabularnewline
25 & 25493 & 25265.1470804371 & 227.852919562891 \tabularnewline
26 & 25269 & 25189.7370273868 & 79.2629726132436 \tabularnewline
27 & 25170 & 25129.6586298353 & 40.3413701647478 \tabularnewline
28 & 25332 & 25235.0352121493 & 96.9647878507094 \tabularnewline
29 & 24966 & 25185.647362052 & -219.647362051983 \tabularnewline
30 & 24851 & 24680.8101635263 & 170.189836473724 \tabularnewline
31 & 25518 & 25717.0507720044 & -199.050772004375 \tabularnewline
32 & 25403 & 25549.7445114873 & -146.744511487286 \tabularnewline
33 & 25028 & 25470.0550604284 & -442.055060428411 \tabularnewline
34 & 24895 & 24823.448608661 & 71.5513913389586 \tabularnewline
35 & 24905 & 24712.4193620313 & 192.580637968655 \tabularnewline
36 & 25317 & 24823.9808563772 & 493.019143622798 \tabularnewline
37 & 25718 & 25356.6182609649 & 361.381739035107 \tabularnewline
38 & 25822 & 25450.3376502773 & 371.662349722734 \tabularnewline
39 & 25967 & 25754.2098071614 & 212.790192838569 \tabularnewline
40 & 25907 & 26156.3503778761 & -249.350377876119 \tabularnewline
41 & 25940 & 25853.6455751713 & 86.3544248287144 \tabularnewline
42 & 26247 & 25799.0650382216 & 447.934961778374 \tabularnewline
43 & 26900 & 27203.1540354049 & -303.154035404852 \tabularnewline
44 & 26980 & 27110.4879295195 & -130.487929519481 \tabularnewline
45 & 26677 & 27167.7447468007 & -490.744746800749 \tabularnewline
46 & 26701 & 26698.8910275733 & 2.1089724266858 \tabularnewline
47 & 26808 & 26686.8211034377 & 121.178896562331 \tabularnewline
48 & 27469 & 26908.463617607 & 560.536382392991 \tabularnewline
49 & 27586 & 27626.1657753749 & -40.1657753748914 \tabularnewline
50 & 27567 & 27456.6577355885 & 110.342264411462 \tabularnewline
51 & 27508 & 27559.7904214123 & -51.7904214122645 \tabularnewline
52 & 27444 & 27680.9295805317 & -236.929580531723 \tabularnewline
53 & 27380 & 27443.2512884934 & -63.2512884934295 \tabularnewline
54 & 27500 & 27294.2813377584 & 205.718662241605 \tabularnewline
55 & 28217 & 28344.6614928184 & -127.661492818403 \tabularnewline
56 & 28355 & 28406.7034649933 & -51.7034649933375 \tabularnewline
57 & 27627 & 28477.0522306895 & -850.052230689529 \tabularnewline
58 & 27565 & 27697.8834809498 & -132.883480949789 \tabularnewline
59 & 27496 & 27503.0826586056 & -7.08265860556639 \tabularnewline
60 & 27453 & 27570.6428671056 & -117.642867105573 \tabularnewline
61 & 27705 & 27422.966042424 & 282.033957576001 \tabularnewline
62 & 27462 & 27402.908460281 & 59.0915397189565 \tabularnewline
63 & 27152 & 27282.475901298 & -130.475901297988 \tabularnewline
64 & 27016 & 27141.8032081244 & -125.803208124438 \tabularnewline
65 & 26836 & 26870.0165297152 & -34.0165297151907 \tabularnewline
66 & 26722 & 26632.1464728358 & 89.853527164214 \tabularnewline
67 & 27391 & 27372.7433661192 & 18.256633880821 \tabularnewline
68 & 27139 & 27426.941468733 & -287.941468733028 \tabularnewline
69 & 26644 & 27009.5877147218 & -365.587714721783 \tabularnewline
70 & 26455 & 26636.0998339456 & -181.099833945598 \tabularnewline
71 & 26294 & 26299.7483217538 & -5.7483217538429 \tabularnewline
72 & 26437 & 26238.5966043455 & 198.403395654463 \tabularnewline
73 & 26954 & 26347.8802918775 & 606.119708122547 \tabularnewline
74 & 26620 & 26558.3039898932 & 61.696010106778 \tabularnewline
75 & 26307 & 26393.0524202998 & -86.0524202997804 \tabularnewline
76 & 26003 & 26275.4807238852 & -272.480723885161 \tabularnewline
77 & 25798 & 25850.3856585123 & -52.3856585122521 \tabularnewline
78 & 25603 & 25572.437586424 & 30.5624135760336 \tabularnewline
79 & 26242 & 26203.5084374137 & 38.4915625862559 \tabularnewline
80 & 26051 & 26190.0869577849 & -139.086957784933 \tabularnewline
81 & 25658 & 25868.1670970146 & -210.16709701459 \tabularnewline
82 & 25489 & 25652.1522085766 & -163.152208576572 \tabularnewline
83 & 25425 & 25354.9626414693 & 70.0373585306588 \tabularnewline
84 & 25183 & 25398.0267034259 & -215.026703425916 \tabularnewline
85 & 24774 & 25151.922191703 & -377.922191703041 \tabularnewline
86 & 24977 & 24244.7373496705 & 732.262650329532 \tabularnewline
87 & 24980 & 24551.1250752918 & 428.874924708176 \tabularnewline
88 & 25081 & 24839.1449482783 & 241.855051721679 \tabularnewline
89 & 25240 & 24946.0086159756 & 293.991384024368 \tabularnewline
90 & 25419 & 25086.1481153334 & 332.851884666576 \tabularnewline
91 & 26309 & 26130.9586925409 & 178.041307459109 \tabularnewline
92 & 26600 & 26385.787062612 & 214.212937388005 \tabularnewline
93 & 26690 & 26583.1353174562 & 106.864682543757 \tabularnewline
94 & 26889 & 26915.9104047544 & -26.9104047544388 \tabularnewline
95 & 27109 & 27053.7981013733 & 55.2018986266849 \tabularnewline
96 & 27646 & 27331.3214566432 & 314.678543356757 \tabularnewline
97 & 28330 & 27886.33050095 & 443.669499049971 \tabularnewline
98 & 28332 & 28317.6562435839 & 14.3437564160922 \tabularnewline
99 & 28202 & 28335.4383242447 & -133.438324244747 \tabularnewline
100 & 28163 & 28404.0434645325 & -241.043464532544 \tabularnewline
101 & 28077 & 28321.6652290737 & -244.665229073704 \tabularnewline
102 & 28351 & 28144.3606831466 & 206.639316853405 \tabularnewline
103 & 28950 & 29187.6758211521 & -237.67582115213 \tabularnewline
104 & 28972 & 29153.3826543789 & -181.382654378875 \tabularnewline
105 & 28812 & 29003.3774650275 & -191.377465027508 \tabularnewline
106 & 28979 & 29027.0284578481 & -48.0284578481478 \tabularnewline
107 & 29112 & 29121.9566784484 & -9.95667844841591 \tabularnewline
108 & 29139 & 29331.6320642671 & -192.632064267102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284174&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]26265[/C][C]26043.6490384615[/C][C]221.350961538465[/C][/ROW]
[ROW][C]14[/C][C]25996[/C][C]26022.7461880103[/C][C]-26.7461880102601[/C][/ROW]
[ROW][C]15[/C][C]25794[/C][C]25892.4007393951[/C][C]-98.4007393951433[/C][/ROW]
[ROW][C]16[/C][C]25752[/C][C]25872.5391204339[/C][C]-120.539120433928[/C][/ROW]
[ROW][C]17[/C][C]25491[/C][C]25592.5416128381[/C][C]-101.541612838137[/C][/ROW]
[ROW][C]18[/C][C]25092[/C][C]25165.2744001323[/C][C]-73.2744001322717[/C][/ROW]
[ROW][C]19[/C][C]25759[/C][C]25947.483428393[/C][C]-188.483428393021[/C][/ROW]
[ROW][C]20[/C][C]25624[/C][C]25722.4197916155[/C][C]-98.4197916155426[/C][/ROW]
[ROW][C]21[/C][C]25138[/C][C]25695.764460192[/C][C]-557.764460192[/C][/ROW]
[ROW][C]22[/C][C]25042[/C][C]24777.1139187908[/C][C]264.886081209239[/C][/ROW]
[ROW][C]23[/C][C]25014[/C][C]24804.4988152024[/C][C]209.501184797577[/C][/ROW]
[ROW][C]24[/C][C]25244[/C][C]24875.6230491646[/C][C]368.376950835402[/C][/ROW]
[ROW][C]25[/C][C]25493[/C][C]25265.1470804371[/C][C]227.852919562891[/C][/ROW]
[ROW][C]26[/C][C]25269[/C][C]25189.7370273868[/C][C]79.2629726132436[/C][/ROW]
[ROW][C]27[/C][C]25170[/C][C]25129.6586298353[/C][C]40.3413701647478[/C][/ROW]
[ROW][C]28[/C][C]25332[/C][C]25235.0352121493[/C][C]96.9647878507094[/C][/ROW]
[ROW][C]29[/C][C]24966[/C][C]25185.647362052[/C][C]-219.647362051983[/C][/ROW]
[ROW][C]30[/C][C]24851[/C][C]24680.8101635263[/C][C]170.189836473724[/C][/ROW]
[ROW][C]31[/C][C]25518[/C][C]25717.0507720044[/C][C]-199.050772004375[/C][/ROW]
[ROW][C]32[/C][C]25403[/C][C]25549.7445114873[/C][C]-146.744511487286[/C][/ROW]
[ROW][C]33[/C][C]25028[/C][C]25470.0550604284[/C][C]-442.055060428411[/C][/ROW]
[ROW][C]34[/C][C]24895[/C][C]24823.448608661[/C][C]71.5513913389586[/C][/ROW]
[ROW][C]35[/C][C]24905[/C][C]24712.4193620313[/C][C]192.580637968655[/C][/ROW]
[ROW][C]36[/C][C]25317[/C][C]24823.9808563772[/C][C]493.019143622798[/C][/ROW]
[ROW][C]37[/C][C]25718[/C][C]25356.6182609649[/C][C]361.381739035107[/C][/ROW]
[ROW][C]38[/C][C]25822[/C][C]25450.3376502773[/C][C]371.662349722734[/C][/ROW]
[ROW][C]39[/C][C]25967[/C][C]25754.2098071614[/C][C]212.790192838569[/C][/ROW]
[ROW][C]40[/C][C]25907[/C][C]26156.3503778761[/C][C]-249.350377876119[/C][/ROW]
[ROW][C]41[/C][C]25940[/C][C]25853.6455751713[/C][C]86.3544248287144[/C][/ROW]
[ROW][C]42[/C][C]26247[/C][C]25799.0650382216[/C][C]447.934961778374[/C][/ROW]
[ROW][C]43[/C][C]26900[/C][C]27203.1540354049[/C][C]-303.154035404852[/C][/ROW]
[ROW][C]44[/C][C]26980[/C][C]27110.4879295195[/C][C]-130.487929519481[/C][/ROW]
[ROW][C]45[/C][C]26677[/C][C]27167.7447468007[/C][C]-490.744746800749[/C][/ROW]
[ROW][C]46[/C][C]26701[/C][C]26698.8910275733[/C][C]2.1089724266858[/C][/ROW]
[ROW][C]47[/C][C]26808[/C][C]26686.8211034377[/C][C]121.178896562331[/C][/ROW]
[ROW][C]48[/C][C]27469[/C][C]26908.463617607[/C][C]560.536382392991[/C][/ROW]
[ROW][C]49[/C][C]27586[/C][C]27626.1657753749[/C][C]-40.1657753748914[/C][/ROW]
[ROW][C]50[/C][C]27567[/C][C]27456.6577355885[/C][C]110.342264411462[/C][/ROW]
[ROW][C]51[/C][C]27508[/C][C]27559.7904214123[/C][C]-51.7904214122645[/C][/ROW]
[ROW][C]52[/C][C]27444[/C][C]27680.9295805317[/C][C]-236.929580531723[/C][/ROW]
[ROW][C]53[/C][C]27380[/C][C]27443.2512884934[/C][C]-63.2512884934295[/C][/ROW]
[ROW][C]54[/C][C]27500[/C][C]27294.2813377584[/C][C]205.718662241605[/C][/ROW]
[ROW][C]55[/C][C]28217[/C][C]28344.6614928184[/C][C]-127.661492818403[/C][/ROW]
[ROW][C]56[/C][C]28355[/C][C]28406.7034649933[/C][C]-51.7034649933375[/C][/ROW]
[ROW][C]57[/C][C]27627[/C][C]28477.0522306895[/C][C]-850.052230689529[/C][/ROW]
[ROW][C]58[/C][C]27565[/C][C]27697.8834809498[/C][C]-132.883480949789[/C][/ROW]
[ROW][C]59[/C][C]27496[/C][C]27503.0826586056[/C][C]-7.08265860556639[/C][/ROW]
[ROW][C]60[/C][C]27453[/C][C]27570.6428671056[/C][C]-117.642867105573[/C][/ROW]
[ROW][C]61[/C][C]27705[/C][C]27422.966042424[/C][C]282.033957576001[/C][/ROW]
[ROW][C]62[/C][C]27462[/C][C]27402.908460281[/C][C]59.0915397189565[/C][/ROW]
[ROW][C]63[/C][C]27152[/C][C]27282.475901298[/C][C]-130.475901297988[/C][/ROW]
[ROW][C]64[/C][C]27016[/C][C]27141.8032081244[/C][C]-125.803208124438[/C][/ROW]
[ROW][C]65[/C][C]26836[/C][C]26870.0165297152[/C][C]-34.0165297151907[/C][/ROW]
[ROW][C]66[/C][C]26722[/C][C]26632.1464728358[/C][C]89.853527164214[/C][/ROW]
[ROW][C]67[/C][C]27391[/C][C]27372.7433661192[/C][C]18.256633880821[/C][/ROW]
[ROW][C]68[/C][C]27139[/C][C]27426.941468733[/C][C]-287.941468733028[/C][/ROW]
[ROW][C]69[/C][C]26644[/C][C]27009.5877147218[/C][C]-365.587714721783[/C][/ROW]
[ROW][C]70[/C][C]26455[/C][C]26636.0998339456[/C][C]-181.099833945598[/C][/ROW]
[ROW][C]71[/C][C]26294[/C][C]26299.7483217538[/C][C]-5.7483217538429[/C][/ROW]
[ROW][C]72[/C][C]26437[/C][C]26238.5966043455[/C][C]198.403395654463[/C][/ROW]
[ROW][C]73[/C][C]26954[/C][C]26347.8802918775[/C][C]606.119708122547[/C][/ROW]
[ROW][C]74[/C][C]26620[/C][C]26558.3039898932[/C][C]61.696010106778[/C][/ROW]
[ROW][C]75[/C][C]26307[/C][C]26393.0524202998[/C][C]-86.0524202997804[/C][/ROW]
[ROW][C]76[/C][C]26003[/C][C]26275.4807238852[/C][C]-272.480723885161[/C][/ROW]
[ROW][C]77[/C][C]25798[/C][C]25850.3856585123[/C][C]-52.3856585122521[/C][/ROW]
[ROW][C]78[/C][C]25603[/C][C]25572.437586424[/C][C]30.5624135760336[/C][/ROW]
[ROW][C]79[/C][C]26242[/C][C]26203.5084374137[/C][C]38.4915625862559[/C][/ROW]
[ROW][C]80[/C][C]26051[/C][C]26190.0869577849[/C][C]-139.086957784933[/C][/ROW]
[ROW][C]81[/C][C]25658[/C][C]25868.1670970146[/C][C]-210.16709701459[/C][/ROW]
[ROW][C]82[/C][C]25489[/C][C]25652.1522085766[/C][C]-163.152208576572[/C][/ROW]
[ROW][C]83[/C][C]25425[/C][C]25354.9626414693[/C][C]70.0373585306588[/C][/ROW]
[ROW][C]84[/C][C]25183[/C][C]25398.0267034259[/C][C]-215.026703425916[/C][/ROW]
[ROW][C]85[/C][C]24774[/C][C]25151.922191703[/C][C]-377.922191703041[/C][/ROW]
[ROW][C]86[/C][C]24977[/C][C]24244.7373496705[/C][C]732.262650329532[/C][/ROW]
[ROW][C]87[/C][C]24980[/C][C]24551.1250752918[/C][C]428.874924708176[/C][/ROW]
[ROW][C]88[/C][C]25081[/C][C]24839.1449482783[/C][C]241.855051721679[/C][/ROW]
[ROW][C]89[/C][C]25240[/C][C]24946.0086159756[/C][C]293.991384024368[/C][/ROW]
[ROW][C]90[/C][C]25419[/C][C]25086.1481153334[/C][C]332.851884666576[/C][/ROW]
[ROW][C]91[/C][C]26309[/C][C]26130.9586925409[/C][C]178.041307459109[/C][/ROW]
[ROW][C]92[/C][C]26600[/C][C]26385.787062612[/C][C]214.212937388005[/C][/ROW]
[ROW][C]93[/C][C]26690[/C][C]26583.1353174562[/C][C]106.864682543757[/C][/ROW]
[ROW][C]94[/C][C]26889[/C][C]26915.9104047544[/C][C]-26.9104047544388[/C][/ROW]
[ROW][C]95[/C][C]27109[/C][C]27053.7981013733[/C][C]55.2018986266849[/C][/ROW]
[ROW][C]96[/C][C]27646[/C][C]27331.3214566432[/C][C]314.678543356757[/C][/ROW]
[ROW][C]97[/C][C]28330[/C][C]27886.33050095[/C][C]443.669499049971[/C][/ROW]
[ROW][C]98[/C][C]28332[/C][C]28317.6562435839[/C][C]14.3437564160922[/C][/ROW]
[ROW][C]99[/C][C]28202[/C][C]28335.4383242447[/C][C]-133.438324244747[/C][/ROW]
[ROW][C]100[/C][C]28163[/C][C]28404.0434645325[/C][C]-241.043464532544[/C][/ROW]
[ROW][C]101[/C][C]28077[/C][C]28321.6652290737[/C][C]-244.665229073704[/C][/ROW]
[ROW][C]102[/C][C]28351[/C][C]28144.3606831466[/C][C]206.639316853405[/C][/ROW]
[ROW][C]103[/C][C]28950[/C][C]29187.6758211521[/C][C]-237.67582115213[/C][/ROW]
[ROW][C]104[/C][C]28972[/C][C]29153.3826543789[/C][C]-181.382654378875[/C][/ROW]
[ROW][C]105[/C][C]28812[/C][C]29003.3774650275[/C][C]-191.377465027508[/C][/ROW]
[ROW][C]106[/C][C]28979[/C][C]29027.0284578481[/C][C]-48.0284578481478[/C][/ROW]
[ROW][C]107[/C][C]29112[/C][C]29121.9566784484[/C][C]-9.95667844841591[/C][/ROW]
[ROW][C]108[/C][C]29139[/C][C]29331.6320642671[/C][C]-192.632064267102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284174&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284174&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
132626526043.6490384615221.350961538465
142599626022.7461880103-26.7461880102601
152579425892.4007393951-98.4007393951433
162575225872.5391204339-120.539120433928
172549125592.5416128381-101.541612838137
182509225165.2744001323-73.2744001322717
192575925947.483428393-188.483428393021
202562425722.4197916155-98.4197916155426
212513825695.764460192-557.764460192
222504224777.1139187908264.886081209239
232501424804.4988152024209.501184797577
242524424875.6230491646368.376950835402
252549325265.1470804371227.852919562891
262526925189.737027386879.2629726132436
272517025129.658629835340.3413701647478
282533225235.035212149396.9647878507094
292496625185.647362052-219.647362051983
302485124680.8101635263170.189836473724
312551825717.0507720044-199.050772004375
322540325549.7445114873-146.744511487286
332502825470.0550604284-442.055060428411
342489524823.44860866171.5513913389586
352490524712.4193620313192.580637968655
362531724823.9808563772493.019143622798
372571825356.6182609649361.381739035107
382582225450.3376502773371.662349722734
392596725754.2098071614212.790192838569
402590726156.3503778761-249.350377876119
412594025853.645575171386.3544248287144
422624725799.0650382216447.934961778374
432690027203.1540354049-303.154035404852
442698027110.4879295195-130.487929519481
452667727167.7447468007-490.744746800749
462670126698.89102757332.1089724266858
472680826686.8211034377121.178896562331
482746926908.463617607560.536382392991
492758627626.1657753749-40.1657753748914
502756727456.6577355885110.342264411462
512750827559.7904214123-51.7904214122645
522744427680.9295805317-236.929580531723
532738027443.2512884934-63.2512884934295
542750027294.2813377584205.718662241605
552821728344.6614928184-127.661492818403
562835528406.7034649933-51.7034649933375
572762728477.0522306895-850.052230689529
582756527697.8834809498-132.883480949789
592749627503.0826586056-7.08265860556639
602745327570.6428671056-117.642867105573
612770527422.966042424282.033957576001
622746227402.90846028159.0915397189565
632715227282.475901298-130.475901297988
642701627141.8032081244-125.803208124438
652683626870.0165297152-34.0165297151907
662672226632.146472835889.853527164214
672739127372.743366119218.256633880821
682713927426.941468733-287.941468733028
692664427009.5877147218-365.587714721783
702645526636.0998339456-181.099833945598
712629426299.7483217538-5.7483217538429
722643726238.5966043455198.403395654463
732695426347.8802918775606.119708122547
742662026558.303989893261.696010106778
752630726393.0524202998-86.0524202997804
762600326275.4807238852-272.480723885161
772579825850.3856585123-52.3856585122521
782560325572.43758642430.5624135760336
792624226203.508437413738.4915625862559
802605126190.0869577849-139.086957784933
812565825868.1670970146-210.16709701459
822548925652.1522085766-163.152208576572
832542525354.962641469370.0373585306588
842518325398.0267034259-215.026703425916
852477425151.922191703-377.922191703041
862497724244.7373496705732.262650329532
872498024551.1250752918428.874924708176
882508124839.1449482783241.855051721679
892524024946.0086159756293.991384024368
902541925086.1481153334332.851884666576
912630926130.9586925409178.041307459109
922660026385.787062612214.212937388005
932669026583.1353174562106.864682543757
942688926915.9104047544-26.9104047544388
952710927053.798101373355.2018986266849
962764627331.3214566432314.678543356757
972833027886.33050095443.669499049971
982833228317.656243583914.3437564160922
992820228335.4383242447-133.438324244747
1002816328404.0434645325-241.043464532544
1012807728321.6652290737-244.665229073704
1022835128144.3606831466206.639316853405
1032895029187.6758211521-237.67582115213
1042897229153.3826543789-181.382654378875
1052881229003.3774650275-191.377465027508
1062897929027.0284578481-48.0284578481478
1072911229121.9566784484-9.95667844841591
1082913929331.6320642671-192.632064267102







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10929343.477688099528834.781392833429852.1739833656
11029150.814165998928425.778771052529875.8495609453
11128952.782167843428017.882545436229887.6817902506
11228958.770387960927812.172471145930105.3683047759
11328955.784696493627592.532451896730319.0369410905
11428955.143804986727368.897000573930541.3906093995
11529636.57210331227820.343750089331452.8004565347
11629726.35807130727672.871250338931779.8448922751
11729669.089409204527370.96432015931967.2144982499
11829841.661591801127291.51850641332391.8046771891
11929954.024519299227144.541908760832763.5071298375
12030120.923861175127044.871326567533196.9763957828

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 29343.4776880995 & 28834.7813928334 & 29852.1739833656 \tabularnewline
110 & 29150.8141659989 & 28425.7787710525 & 29875.8495609453 \tabularnewline
111 & 28952.7821678434 & 28017.8825454362 & 29887.6817902506 \tabularnewline
112 & 28958.7703879609 & 27812.1724711459 & 30105.3683047759 \tabularnewline
113 & 28955.7846964936 & 27592.5324518967 & 30319.0369410905 \tabularnewline
114 & 28955.1438049867 & 27368.8970005739 & 30541.3906093995 \tabularnewline
115 & 29636.572103312 & 27820.3437500893 & 31452.8004565347 \tabularnewline
116 & 29726.358071307 & 27672.8712503389 & 31779.8448922751 \tabularnewline
117 & 29669.0894092045 & 27370.964320159 & 31967.2144982499 \tabularnewline
118 & 29841.6615918011 & 27291.518506413 & 32391.8046771891 \tabularnewline
119 & 29954.0245192992 & 27144.5419087608 & 32763.5071298375 \tabularnewline
120 & 30120.9238611751 & 27044.8713265675 & 33196.9763957828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284174&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]109[/C][C]29343.4776880995[/C][C]28834.7813928334[/C][C]29852.1739833656[/C][/ROW]
[ROW][C]110[/C][C]29150.8141659989[/C][C]28425.7787710525[/C][C]29875.8495609453[/C][/ROW]
[ROW][C]111[/C][C]28952.7821678434[/C][C]28017.8825454362[/C][C]29887.6817902506[/C][/ROW]
[ROW][C]112[/C][C]28958.7703879609[/C][C]27812.1724711459[/C][C]30105.3683047759[/C][/ROW]
[ROW][C]113[/C][C]28955.7846964936[/C][C]27592.5324518967[/C][C]30319.0369410905[/C][/ROW]
[ROW][C]114[/C][C]28955.1438049867[/C][C]27368.8970005739[/C][C]30541.3906093995[/C][/ROW]
[ROW][C]115[/C][C]29636.572103312[/C][C]27820.3437500893[/C][C]31452.8004565347[/C][/ROW]
[ROW][C]116[/C][C]29726.358071307[/C][C]27672.8712503389[/C][C]31779.8448922751[/C][/ROW]
[ROW][C]117[/C][C]29669.0894092045[/C][C]27370.964320159[/C][C]31967.2144982499[/C][/ROW]
[ROW][C]118[/C][C]29841.6615918011[/C][C]27291.518506413[/C][C]32391.8046771891[/C][/ROW]
[ROW][C]119[/C][C]29954.0245192992[/C][C]27144.5419087608[/C][C]32763.5071298375[/C][/ROW]
[ROW][C]120[/C][C]30120.9238611751[/C][C]27044.8713265675[/C][C]33196.9763957828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284174&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284174&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
10929343.477688099528834.781392833429852.1739833656
11029150.814165998928425.778771052529875.8495609453
11128952.782167843428017.882545436229887.6817902506
11228958.770387960927812.172471145930105.3683047759
11328955.784696493627592.532451896730319.0369410905
11428955.143804986727368.897000573930541.3906093995
11529636.57210331227820.343750089331452.8004565347
11629726.35807130727672.871250338931779.8448922751
11729669.089409204527370.96432015931967.2144982499
11829841.661591801127291.51850641332391.8046771891
11929954.024519299227144.541908760832763.5071298375
12030120.923861175127044.871326567533196.9763957828



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')