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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 computationTue, 29 Nov 2011 05:45:34 -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/2011/Nov/29/t13225635537z3f57c3usjnt4s.htm/, Retrieved Thu, 28 Mar 2024 10:19:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148184, Retrieved Thu, 28 Mar 2024 10:19:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Single] [2011-11-29 10:45:34] [5988e21ec0676b551e455a86717edc1d] [Current]
- R P     [Exponential Smoothing] [Double] [2011-11-29 10:57:03] [f2faabc3a2466a29562900bc59f67898]
-   P       [Exponential Smoothing] [Triple] [2011-11-29 11:02:24] [f2faabc3a2466a29562900bc59f67898]
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Dataseries X:
16111
15554
15220
14807
14291
14653
17006
18032
16558
16102
15055
15484
14596
14609
13923
14226
14056
14278
16142
16509
15680
14086
13129
13086
13096
12280
11534
11135
10903
10926
13220
13581
11788
11088
10434
11061
10828
10270
10360
9899
9395
9944
12117
12474
11106
10643
10227
11273
11516
11583
11605
11414
11181
12000
14007
14582
13251
12806
12645
13869
13342
13079
12513
12331
11882
12388
14394
14635
13218
12554
12031
12429




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148184&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148184&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148184&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148184&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148184&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148184&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21555416111-557
31522015554.0368215775-334.036821577472
41480715220.0220821593-413.022082159254
51429114807.0273036348-516.027303634823
61465314291.034112997361.965887002982
71700614652.97607153512353.0239284649
81803217005.84444873811026.1555512619
91655818031.9321639746-1473.93216397463
101610216558.0974371766-456.097437176599
111505516102.0301512157-1047.03015121565
121548415055.0692159817428.930784018259
131459615483.9716446892-887.971644689238
141460914596.058701107212.9412988928034
151392314608.9991444901-685.999144490053
161422613923.0453493189302.954650681068
171405614225.9799725886-169.979972588617
181427814056.0112368595221.988763140522
191614214277.98532499741864.01467500259
201650916141.8767756539367.12322434608
211568016508.9757305992-828.975730599195
221408615680.0548010666-1594.05480106658
231312914086.1053781191-957.105378119128
241308613129.0632713282-43.0632713282412
251309613086.0028467829.99715321798612
261228013095.9993391186-815.999339118578
271153412280.0539432368-746.053943236775
281113511534.0493193592-399.049319359192
291090311135.0263799379-232.026379937932
301092610903.015338558922.984661441069
311322010925.99848055392294.00151944612
321358113219.8483505302361.151649469788
331178813580.9761253619-1792.97612536187
341108811788.1185282034-700.118528203424
351043411088.0462827085-654.046282708485
361106110434.0432370123626.956762987667
371082811060.9585537935-232.9585537935
381027010828.0154001821-558.015400182112
391036010270.036888702589.9631112975057
40989910359.9940528121-460.994052812079
4193959899.03047491603-504.030474916033
4299449395.03331992313548.966680076874
43121179943.96370948092173.0362905191
441247412116.8563471739357.143652826073
451110612473.9763903183-1367.97639031834
461064311106.0904327624-463.090432762365
471022710643.0306135013-416.030613501342
481127310227.02750251971045.97249748031
491151611272.9308539365243.069146063466
501158311515.983931437467.0160685626452
511160511582.995569771322.0044302286551
521141411604.998545354-190.998545353981
531118111414.0126263335-233.012626333457
541200011181.0154037567818.984596243317
551400711999.94585941692007.05414058305
561458214006.8673197495575.132680250503
571325114581.9619797261-1330.96197972613
581280613251.0879858522-445.087985852155
591264512806.0294234143-161.029423414278
601386912645.01064516591223.98935483413
611334213868.919085783-526.919085783025
621307913342.0348330196-263.034833019639
631251313079.0173884335-566.01738843354
641233112513.0374176896-182.037417689622
651188212331.0120339405-449.012033940537
661238811882.0296828212505.970317178826
671439412387.96655183982006.0334481602
681463514393.8673872244241.132612775627
691321814634.9840594557-1416.98405945569
701255413218.0936725105-664.093672510455
711203112554.0439012147-523.043901214744
721242912031.034576843397.965423157037

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 15554 & 16111 & -557 \tabularnewline
3 & 15220 & 15554.0368215775 & -334.036821577472 \tabularnewline
4 & 14807 & 15220.0220821593 & -413.022082159254 \tabularnewline
5 & 14291 & 14807.0273036348 & -516.027303634823 \tabularnewline
6 & 14653 & 14291.034112997 & 361.965887002982 \tabularnewline
7 & 17006 & 14652.9760715351 & 2353.0239284649 \tabularnewline
8 & 18032 & 17005.8444487381 & 1026.1555512619 \tabularnewline
9 & 16558 & 18031.9321639746 & -1473.93216397463 \tabularnewline
10 & 16102 & 16558.0974371766 & -456.097437176599 \tabularnewline
11 & 15055 & 16102.0301512157 & -1047.03015121565 \tabularnewline
12 & 15484 & 15055.0692159817 & 428.930784018259 \tabularnewline
13 & 14596 & 15483.9716446892 & -887.971644689238 \tabularnewline
14 & 14609 & 14596.0587011072 & 12.9412988928034 \tabularnewline
15 & 13923 & 14608.9991444901 & -685.999144490053 \tabularnewline
16 & 14226 & 13923.0453493189 & 302.954650681068 \tabularnewline
17 & 14056 & 14225.9799725886 & -169.979972588617 \tabularnewline
18 & 14278 & 14056.0112368595 & 221.988763140522 \tabularnewline
19 & 16142 & 14277.9853249974 & 1864.01467500259 \tabularnewline
20 & 16509 & 16141.8767756539 & 367.12322434608 \tabularnewline
21 & 15680 & 16508.9757305992 & -828.975730599195 \tabularnewline
22 & 14086 & 15680.0548010666 & -1594.05480106658 \tabularnewline
23 & 13129 & 14086.1053781191 & -957.105378119128 \tabularnewline
24 & 13086 & 13129.0632713282 & -43.0632713282412 \tabularnewline
25 & 13096 & 13086.002846782 & 9.99715321798612 \tabularnewline
26 & 12280 & 13095.9993391186 & -815.999339118578 \tabularnewline
27 & 11534 & 12280.0539432368 & -746.053943236775 \tabularnewline
28 & 11135 & 11534.0493193592 & -399.049319359192 \tabularnewline
29 & 10903 & 11135.0263799379 & -232.026379937932 \tabularnewline
30 & 10926 & 10903.0153385589 & 22.984661441069 \tabularnewline
31 & 13220 & 10925.9984805539 & 2294.00151944612 \tabularnewline
32 & 13581 & 13219.8483505302 & 361.151649469788 \tabularnewline
33 & 11788 & 13580.9761253619 & -1792.97612536187 \tabularnewline
34 & 11088 & 11788.1185282034 & -700.118528203424 \tabularnewline
35 & 10434 & 11088.0462827085 & -654.046282708485 \tabularnewline
36 & 11061 & 10434.0432370123 & 626.956762987667 \tabularnewline
37 & 10828 & 11060.9585537935 & -232.9585537935 \tabularnewline
38 & 10270 & 10828.0154001821 & -558.015400182112 \tabularnewline
39 & 10360 & 10270.0368887025 & 89.9631112975057 \tabularnewline
40 & 9899 & 10359.9940528121 & -460.994052812079 \tabularnewline
41 & 9395 & 9899.03047491603 & -504.030474916033 \tabularnewline
42 & 9944 & 9395.03331992313 & 548.966680076874 \tabularnewline
43 & 12117 & 9943.9637094809 & 2173.0362905191 \tabularnewline
44 & 12474 & 12116.8563471739 & 357.143652826073 \tabularnewline
45 & 11106 & 12473.9763903183 & -1367.97639031834 \tabularnewline
46 & 10643 & 11106.0904327624 & -463.090432762365 \tabularnewline
47 & 10227 & 10643.0306135013 & -416.030613501342 \tabularnewline
48 & 11273 & 10227.0275025197 & 1045.97249748031 \tabularnewline
49 & 11516 & 11272.9308539365 & 243.069146063466 \tabularnewline
50 & 11583 & 11515.9839314374 & 67.0160685626452 \tabularnewline
51 & 11605 & 11582.9955697713 & 22.0044302286551 \tabularnewline
52 & 11414 & 11604.998545354 & -190.998545353981 \tabularnewline
53 & 11181 & 11414.0126263335 & -233.012626333457 \tabularnewline
54 & 12000 & 11181.0154037567 & 818.984596243317 \tabularnewline
55 & 14007 & 11999.9458594169 & 2007.05414058305 \tabularnewline
56 & 14582 & 14006.8673197495 & 575.132680250503 \tabularnewline
57 & 13251 & 14581.9619797261 & -1330.96197972613 \tabularnewline
58 & 12806 & 13251.0879858522 & -445.087985852155 \tabularnewline
59 & 12645 & 12806.0294234143 & -161.029423414278 \tabularnewline
60 & 13869 & 12645.0106451659 & 1223.98935483413 \tabularnewline
61 & 13342 & 13868.919085783 & -526.919085783025 \tabularnewline
62 & 13079 & 13342.0348330196 & -263.034833019639 \tabularnewline
63 & 12513 & 13079.0173884335 & -566.01738843354 \tabularnewline
64 & 12331 & 12513.0374176896 & -182.037417689622 \tabularnewline
65 & 11882 & 12331.0120339405 & -449.012033940537 \tabularnewline
66 & 12388 & 11882.0296828212 & 505.970317178826 \tabularnewline
67 & 14394 & 12387.9665518398 & 2006.0334481602 \tabularnewline
68 & 14635 & 14393.8673872244 & 241.132612775627 \tabularnewline
69 & 13218 & 14634.9840594557 & -1416.98405945569 \tabularnewline
70 & 12554 & 13218.0936725105 & -664.093672510455 \tabularnewline
71 & 12031 & 12554.0439012147 & -523.043901214744 \tabularnewline
72 & 12429 & 12031.034576843 & 397.965423157037 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148184&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]15554[/C][C]16111[/C][C]-557[/C][/ROW]
[ROW][C]3[/C][C]15220[/C][C]15554.0368215775[/C][C]-334.036821577472[/C][/ROW]
[ROW][C]4[/C][C]14807[/C][C]15220.0220821593[/C][C]-413.022082159254[/C][/ROW]
[ROW][C]5[/C][C]14291[/C][C]14807.0273036348[/C][C]-516.027303634823[/C][/ROW]
[ROW][C]6[/C][C]14653[/C][C]14291.034112997[/C][C]361.965887002982[/C][/ROW]
[ROW][C]7[/C][C]17006[/C][C]14652.9760715351[/C][C]2353.0239284649[/C][/ROW]
[ROW][C]8[/C][C]18032[/C][C]17005.8444487381[/C][C]1026.1555512619[/C][/ROW]
[ROW][C]9[/C][C]16558[/C][C]18031.9321639746[/C][C]-1473.93216397463[/C][/ROW]
[ROW][C]10[/C][C]16102[/C][C]16558.0974371766[/C][C]-456.097437176599[/C][/ROW]
[ROW][C]11[/C][C]15055[/C][C]16102.0301512157[/C][C]-1047.03015121565[/C][/ROW]
[ROW][C]12[/C][C]15484[/C][C]15055.0692159817[/C][C]428.930784018259[/C][/ROW]
[ROW][C]13[/C][C]14596[/C][C]15483.9716446892[/C][C]-887.971644689238[/C][/ROW]
[ROW][C]14[/C][C]14609[/C][C]14596.0587011072[/C][C]12.9412988928034[/C][/ROW]
[ROW][C]15[/C][C]13923[/C][C]14608.9991444901[/C][C]-685.999144490053[/C][/ROW]
[ROW][C]16[/C][C]14226[/C][C]13923.0453493189[/C][C]302.954650681068[/C][/ROW]
[ROW][C]17[/C][C]14056[/C][C]14225.9799725886[/C][C]-169.979972588617[/C][/ROW]
[ROW][C]18[/C][C]14278[/C][C]14056.0112368595[/C][C]221.988763140522[/C][/ROW]
[ROW][C]19[/C][C]16142[/C][C]14277.9853249974[/C][C]1864.01467500259[/C][/ROW]
[ROW][C]20[/C][C]16509[/C][C]16141.8767756539[/C][C]367.12322434608[/C][/ROW]
[ROW][C]21[/C][C]15680[/C][C]16508.9757305992[/C][C]-828.975730599195[/C][/ROW]
[ROW][C]22[/C][C]14086[/C][C]15680.0548010666[/C][C]-1594.05480106658[/C][/ROW]
[ROW][C]23[/C][C]13129[/C][C]14086.1053781191[/C][C]-957.105378119128[/C][/ROW]
[ROW][C]24[/C][C]13086[/C][C]13129.0632713282[/C][C]-43.0632713282412[/C][/ROW]
[ROW][C]25[/C][C]13096[/C][C]13086.002846782[/C][C]9.99715321798612[/C][/ROW]
[ROW][C]26[/C][C]12280[/C][C]13095.9993391186[/C][C]-815.999339118578[/C][/ROW]
[ROW][C]27[/C][C]11534[/C][C]12280.0539432368[/C][C]-746.053943236775[/C][/ROW]
[ROW][C]28[/C][C]11135[/C][C]11534.0493193592[/C][C]-399.049319359192[/C][/ROW]
[ROW][C]29[/C][C]10903[/C][C]11135.0263799379[/C][C]-232.026379937932[/C][/ROW]
[ROW][C]30[/C][C]10926[/C][C]10903.0153385589[/C][C]22.984661441069[/C][/ROW]
[ROW][C]31[/C][C]13220[/C][C]10925.9984805539[/C][C]2294.00151944612[/C][/ROW]
[ROW][C]32[/C][C]13581[/C][C]13219.8483505302[/C][C]361.151649469788[/C][/ROW]
[ROW][C]33[/C][C]11788[/C][C]13580.9761253619[/C][C]-1792.97612536187[/C][/ROW]
[ROW][C]34[/C][C]11088[/C][C]11788.1185282034[/C][C]-700.118528203424[/C][/ROW]
[ROW][C]35[/C][C]10434[/C][C]11088.0462827085[/C][C]-654.046282708485[/C][/ROW]
[ROW][C]36[/C][C]11061[/C][C]10434.0432370123[/C][C]626.956762987667[/C][/ROW]
[ROW][C]37[/C][C]10828[/C][C]11060.9585537935[/C][C]-232.9585537935[/C][/ROW]
[ROW][C]38[/C][C]10270[/C][C]10828.0154001821[/C][C]-558.015400182112[/C][/ROW]
[ROW][C]39[/C][C]10360[/C][C]10270.0368887025[/C][C]89.9631112975057[/C][/ROW]
[ROW][C]40[/C][C]9899[/C][C]10359.9940528121[/C][C]-460.994052812079[/C][/ROW]
[ROW][C]41[/C][C]9395[/C][C]9899.03047491603[/C][C]-504.030474916033[/C][/ROW]
[ROW][C]42[/C][C]9944[/C][C]9395.03331992313[/C][C]548.966680076874[/C][/ROW]
[ROW][C]43[/C][C]12117[/C][C]9943.9637094809[/C][C]2173.0362905191[/C][/ROW]
[ROW][C]44[/C][C]12474[/C][C]12116.8563471739[/C][C]357.143652826073[/C][/ROW]
[ROW][C]45[/C][C]11106[/C][C]12473.9763903183[/C][C]-1367.97639031834[/C][/ROW]
[ROW][C]46[/C][C]10643[/C][C]11106.0904327624[/C][C]-463.090432762365[/C][/ROW]
[ROW][C]47[/C][C]10227[/C][C]10643.0306135013[/C][C]-416.030613501342[/C][/ROW]
[ROW][C]48[/C][C]11273[/C][C]10227.0275025197[/C][C]1045.97249748031[/C][/ROW]
[ROW][C]49[/C][C]11516[/C][C]11272.9308539365[/C][C]243.069146063466[/C][/ROW]
[ROW][C]50[/C][C]11583[/C][C]11515.9839314374[/C][C]67.0160685626452[/C][/ROW]
[ROW][C]51[/C][C]11605[/C][C]11582.9955697713[/C][C]22.0044302286551[/C][/ROW]
[ROW][C]52[/C][C]11414[/C][C]11604.998545354[/C][C]-190.998545353981[/C][/ROW]
[ROW][C]53[/C][C]11181[/C][C]11414.0126263335[/C][C]-233.012626333457[/C][/ROW]
[ROW][C]54[/C][C]12000[/C][C]11181.0154037567[/C][C]818.984596243317[/C][/ROW]
[ROW][C]55[/C][C]14007[/C][C]11999.9458594169[/C][C]2007.05414058305[/C][/ROW]
[ROW][C]56[/C][C]14582[/C][C]14006.8673197495[/C][C]575.132680250503[/C][/ROW]
[ROW][C]57[/C][C]13251[/C][C]14581.9619797261[/C][C]-1330.96197972613[/C][/ROW]
[ROW][C]58[/C][C]12806[/C][C]13251.0879858522[/C][C]-445.087985852155[/C][/ROW]
[ROW][C]59[/C][C]12645[/C][C]12806.0294234143[/C][C]-161.029423414278[/C][/ROW]
[ROW][C]60[/C][C]13869[/C][C]12645.0106451659[/C][C]1223.98935483413[/C][/ROW]
[ROW][C]61[/C][C]13342[/C][C]13868.919085783[/C][C]-526.919085783025[/C][/ROW]
[ROW][C]62[/C][C]13079[/C][C]13342.0348330196[/C][C]-263.034833019639[/C][/ROW]
[ROW][C]63[/C][C]12513[/C][C]13079.0173884335[/C][C]-566.01738843354[/C][/ROW]
[ROW][C]64[/C][C]12331[/C][C]12513.0374176896[/C][C]-182.037417689622[/C][/ROW]
[ROW][C]65[/C][C]11882[/C][C]12331.0120339405[/C][C]-449.012033940537[/C][/ROW]
[ROW][C]66[/C][C]12388[/C][C]11882.0296828212[/C][C]505.970317178826[/C][/ROW]
[ROW][C]67[/C][C]14394[/C][C]12387.9665518398[/C][C]2006.0334481602[/C][/ROW]
[ROW][C]68[/C][C]14635[/C][C]14393.8673872244[/C][C]241.132612775627[/C][/ROW]
[ROW][C]69[/C][C]13218[/C][C]14634.9840594557[/C][C]-1416.98405945569[/C][/ROW]
[ROW][C]70[/C][C]12554[/C][C]13218.0936725105[/C][C]-664.093672510455[/C][/ROW]
[ROW][C]71[/C][C]12031[/C][C]12554.0439012147[/C][C]-523.043901214744[/C][/ROW]
[ROW][C]72[/C][C]12429[/C][C]12031.034576843[/C][C]397.965423157037[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148184&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148184&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
21555416111-557
31522015554.0368215775-334.036821577472
41480715220.0220821593-413.022082159254
51429114807.0273036348-516.027303634823
61465314291.034112997361.965887002982
71700614652.97607153512353.0239284649
81803217005.84444873811026.1555512619
91655818031.9321639746-1473.93216397463
101610216558.0974371766-456.097437176599
111505516102.0301512157-1047.03015121565
121548415055.0692159817428.930784018259
131459615483.9716446892-887.971644689238
141460914596.058701107212.9412988928034
151392314608.9991444901-685.999144490053
161422613923.0453493189302.954650681068
171405614225.9799725886-169.979972588617
181427814056.0112368595221.988763140522
191614214277.98532499741864.01467500259
201650916141.8767756539367.12322434608
211568016508.9757305992-828.975730599195
221408615680.0548010666-1594.05480106658
231312914086.1053781191-957.105378119128
241308613129.0632713282-43.0632713282412
251309613086.0028467829.99715321798612
261228013095.9993391186-815.999339118578
271153412280.0539432368-746.053943236775
281113511534.0493193592-399.049319359192
291090311135.0263799379-232.026379937932
301092610903.015338558922.984661441069
311322010925.99848055392294.00151944612
321358113219.8483505302361.151649469788
331178813580.9761253619-1792.97612536187
341108811788.1185282034-700.118528203424
351043411088.0462827085-654.046282708485
361106110434.0432370123626.956762987667
371082811060.9585537935-232.9585537935
381027010828.0154001821-558.015400182112
391036010270.036888702589.9631112975057
40989910359.9940528121-460.994052812079
4193959899.03047491603-504.030474916033
4299449395.03331992313548.966680076874
43121179943.96370948092173.0362905191
441247412116.8563471739357.143652826073
451110612473.9763903183-1367.97639031834
461064311106.0904327624-463.090432762365
471022710643.0306135013-416.030613501342
481127310227.02750251971045.97249748031
491151611272.9308539365243.069146063466
501158311515.983931437467.0160685626452
511160511582.995569771322.0044302286551
521141411604.998545354-190.998545353981
531118111414.0126263335-233.012626333457
541200011181.0154037567818.984596243317
551400711999.94585941692007.05414058305
561458214006.8673197495575.132680250503
571325114581.9619797261-1330.96197972613
581280613251.0879858522-445.087985852155
591264512806.0294234143-161.029423414278
601386912645.01064516591223.98935483413
611334213868.919085783-526.919085783025
621307913342.0348330196-263.034833019639
631251313079.0173884335-566.01738843354
641233112513.0374176896-182.037417689622
651188212331.0120339405-449.012033940537
661238811882.0296828212505.970317178826
671439412387.96655183982006.0334481602
681463514393.8673872244241.132612775627
691321814634.9840594557-1416.98405945569
701255413218.0936725105-664.093672510455
711203112554.0439012147-523.043901214744
721242912031.034576843397.965423157037







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7312428.973691715210649.020893585214208.9264898451
7412428.97369171529911.8235061658514946.1238772644
7512428.97369171529346.1408792436215511.8065041867
7612428.97369171528869.2445949029615988.7027885273
7712428.97369171528449.0887265771416408.8586568532
7812428.97369171528069.2377560452116788.7096273851
7912428.97369171527719.9280854577517138.0192979726
8012428.97369171527394.7981271512417463.1492562791
8112428.97369171527089.4290755617617768.5183078685
8212428.97369171526800.6036078513618057.3437755789
8312428.97369171526525.8928948792218332.0544885511
8412428.97369171526263.4099715827118594.5374118476

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 12428.9736917152 & 10649.0208935852 & 14208.9264898451 \tabularnewline
74 & 12428.9736917152 & 9911.82350616585 & 14946.1238772644 \tabularnewline
75 & 12428.9736917152 & 9346.14087924362 & 15511.8065041867 \tabularnewline
76 & 12428.9736917152 & 8869.24459490296 & 15988.7027885273 \tabularnewline
77 & 12428.9736917152 & 8449.08872657714 & 16408.8586568532 \tabularnewline
78 & 12428.9736917152 & 8069.23775604521 & 16788.7096273851 \tabularnewline
79 & 12428.9736917152 & 7719.92808545775 & 17138.0192979726 \tabularnewline
80 & 12428.9736917152 & 7394.79812715124 & 17463.1492562791 \tabularnewline
81 & 12428.9736917152 & 7089.42907556176 & 17768.5183078685 \tabularnewline
82 & 12428.9736917152 & 6800.60360785136 & 18057.3437755789 \tabularnewline
83 & 12428.9736917152 & 6525.89289487922 & 18332.0544885511 \tabularnewline
84 & 12428.9736917152 & 6263.40997158271 & 18594.5374118476 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148184&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]73[/C][C]12428.9736917152[/C][C]10649.0208935852[/C][C]14208.9264898451[/C][/ROW]
[ROW][C]74[/C][C]12428.9736917152[/C][C]9911.82350616585[/C][C]14946.1238772644[/C][/ROW]
[ROW][C]75[/C][C]12428.9736917152[/C][C]9346.14087924362[/C][C]15511.8065041867[/C][/ROW]
[ROW][C]76[/C][C]12428.9736917152[/C][C]8869.24459490296[/C][C]15988.7027885273[/C][/ROW]
[ROW][C]77[/C][C]12428.9736917152[/C][C]8449.08872657714[/C][C]16408.8586568532[/C][/ROW]
[ROW][C]78[/C][C]12428.9736917152[/C][C]8069.23775604521[/C][C]16788.7096273851[/C][/ROW]
[ROW][C]79[/C][C]12428.9736917152[/C][C]7719.92808545775[/C][C]17138.0192979726[/C][/ROW]
[ROW][C]80[/C][C]12428.9736917152[/C][C]7394.79812715124[/C][C]17463.1492562791[/C][/ROW]
[ROW][C]81[/C][C]12428.9736917152[/C][C]7089.42907556176[/C][C]17768.5183078685[/C][/ROW]
[ROW][C]82[/C][C]12428.9736917152[/C][C]6800.60360785136[/C][C]18057.3437755789[/C][/ROW]
[ROW][C]83[/C][C]12428.9736917152[/C][C]6525.89289487922[/C][C]18332.0544885511[/C][/ROW]
[ROW][C]84[/C][C]12428.9736917152[/C][C]6263.40997158271[/C][C]18594.5374118476[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148184&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148184&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
7312428.973691715210649.020893585214208.9264898451
7412428.97369171529911.8235061658514946.1238772644
7512428.97369171529346.1408792436215511.8065041867
7612428.97369171528869.2445949029615988.7027885273
7712428.97369171528449.0887265771416408.8586568532
7812428.97369171528069.2377560452116788.7096273851
7912428.97369171527719.9280854577517138.0192979726
8012428.97369171527394.7981271512417463.1492562791
8112428.97369171527089.4290755617617768.5183078685
8212428.97369171526800.6036078513618057.3437755789
8312428.97369171526525.8928948792218332.0544885511
8412428.97369171526263.4099715827118594.5374118476



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')