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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 26 Nov 2011 12:44:54 -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/26/t132232953220i6ads0gqj9uwx.htm/, Retrieved Mon, 30 Jan 2023 00:36:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147430, Retrieved Mon, 30 Jan 2023 00:36:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [WS8 Smoothing] [2011-11-26 17:44:54] [3208276753335f0b81f0071d45b8bac9] [Current]
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Dataseries X:
37
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147430&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147430&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147430&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.380859354911949
beta0.0316088853012832
gamma0.733581043314767

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.380859354911949 \tabularnewline
beta & 0.0316088853012832 \tabularnewline
gamma & 0.733581043314767 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147430&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]0.380859354911949[/C][/ROW]
[ROW][C]beta[/C][C]0.0316088853012832[/C][/ROW]
[ROW][C]gamma[/C][C]0.733581043314767[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147430&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147430&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
alpha0.380859354911949
beta0.0316088853012832
gamma0.733581043314767







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138065.953525641025614.0464743589744
144232.44671481725949.55328518274057
155447.13530513160886.86469486839122
166660.59089490800945.40910509199063
178179.72389409402421.27610590597584
186369.423164327768-6.42316432776798
19137111.48776994845925.5122300515414
207280.189065931405-8.18906593140491
2110786.456323671552420.5436763284476
225868.1223642893237-10.1223642893237
233697.1537646423697-61.1537646423697
2452157.471510088703-105.471510088703
257965.853803915797913.1461960842021
267728.650494978251348.3495050217487
275456.0480501431283-2.04805014312831
288464.494919076741719.5050809232583
294886.335926809278-38.335926809278
309656.191372995914739.8086270040853
3183129.66480326721-46.6648032672097
326653.997391331061812.0026086689382
336179.6754118037346-18.6754118037346
345330.674606122688322.3253938773117
353047.4750331631063-17.4750331631063
3674103.414328539598-29.4143285395985
376994.669052063968-25.669052063968
385958.23468268166160.765317318338404
394243.6095578051338-1.60955780513378
406561.00818314123113.99181685876892
417049.47880334993920.521196650061
4210076.760334137802423.2396658621976
4363103.965837074185-40.9658370741847
4410556.50154942883848.498450571162
458281.97154136393350.0284586360665458
468158.767430267250622.2325697327494
477557.505438458555717.4945615414443
48102121.8113910067-19.8113910066999
49121119.0110215464271.9889784535731
5098106.036128029636-8.03612802963619
517687.7937238475087-11.7937238475087
5277104.548576897231-27.5485768972311
536388.825394332414-25.825394332414
543799.4433230770021-62.4433230770021
553563.5759025308791-28.5759025308791
562360.3350961492459-37.3350961492459
574028.937578654056711.0624213459433
582917.991147653546811.0088523464532
59378.1378362318411228.8621637681589
605157.8014044626901-6.80140446269012
612067.986280314366-47.986280314366
622828.9516752372214-0.95167523722138
63139.313210565710433.68678943428957
642222.6070517338614-0.607051733861354
652516.05057370461348.94942629538664
661321.8230856739734-8.82308567397342
671620.9469405271601-4.94694052716012
681322.1988348561951-9.19883485619508
691623.3093821664561-7.30938216645614
70174.9308234847158712.0691765152841
7193.192179909831775.80782009016823
721727.2017554894693-10.2017554894693
732516.66938856480168.33061143519844
741420.4077763690549-6.40777636905491
7580.6939026255995497.30609737440045
76713.3553977851453-6.35539778514529
77108.820287664652811.17971233534719
7873.338225050027363.66177494997264
79108.904549139224041.09545086077596
80310.526306643243-7.52630664324296

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 80 & 65.9535256410256 & 14.0464743589744 \tabularnewline
14 & 42 & 32.4467148172594 & 9.55328518274057 \tabularnewline
15 & 54 & 47.1353051316088 & 6.86469486839122 \tabularnewline
16 & 66 & 60.5908949080094 & 5.40910509199063 \tabularnewline
17 & 81 & 79.7238940940242 & 1.27610590597584 \tabularnewline
18 & 63 & 69.423164327768 & -6.42316432776798 \tabularnewline
19 & 137 & 111.487769948459 & 25.5122300515414 \tabularnewline
20 & 72 & 80.189065931405 & -8.18906593140491 \tabularnewline
21 & 107 & 86.4563236715524 & 20.5436763284476 \tabularnewline
22 & 58 & 68.1223642893237 & -10.1223642893237 \tabularnewline
23 & 36 & 97.1537646423697 & -61.1537646423697 \tabularnewline
24 & 52 & 157.471510088703 & -105.471510088703 \tabularnewline
25 & 79 & 65.8538039157979 & 13.1461960842021 \tabularnewline
26 & 77 & 28.6504949782513 & 48.3495050217487 \tabularnewline
27 & 54 & 56.0480501431283 & -2.04805014312831 \tabularnewline
28 & 84 & 64.4949190767417 & 19.5050809232583 \tabularnewline
29 & 48 & 86.335926809278 & -38.335926809278 \tabularnewline
30 & 96 & 56.1913729959147 & 39.8086270040853 \tabularnewline
31 & 83 & 129.66480326721 & -46.6648032672097 \tabularnewline
32 & 66 & 53.9973913310618 & 12.0026086689382 \tabularnewline
33 & 61 & 79.6754118037346 & -18.6754118037346 \tabularnewline
34 & 53 & 30.6746061226883 & 22.3253938773117 \tabularnewline
35 & 30 & 47.4750331631063 & -17.4750331631063 \tabularnewline
36 & 74 & 103.414328539598 & -29.4143285395985 \tabularnewline
37 & 69 & 94.669052063968 & -25.669052063968 \tabularnewline
38 & 59 & 58.2346826816616 & 0.765317318338404 \tabularnewline
39 & 42 & 43.6095578051338 & -1.60955780513378 \tabularnewline
40 & 65 & 61.0081831412311 & 3.99181685876892 \tabularnewline
41 & 70 & 49.478803349939 & 20.521196650061 \tabularnewline
42 & 100 & 76.7603341378024 & 23.2396658621976 \tabularnewline
43 & 63 & 103.965837074185 & -40.9658370741847 \tabularnewline
44 & 105 & 56.501549428838 & 48.498450571162 \tabularnewline
45 & 82 & 81.9715413639335 & 0.0284586360665458 \tabularnewline
46 & 81 & 58.7674302672506 & 22.2325697327494 \tabularnewline
47 & 75 & 57.5054384585557 & 17.4945615414443 \tabularnewline
48 & 102 & 121.8113910067 & -19.8113910066999 \tabularnewline
49 & 121 & 119.011021546427 & 1.9889784535731 \tabularnewline
50 & 98 & 106.036128029636 & -8.03612802963619 \tabularnewline
51 & 76 & 87.7937238475087 & -11.7937238475087 \tabularnewline
52 & 77 & 104.548576897231 & -27.5485768972311 \tabularnewline
53 & 63 & 88.825394332414 & -25.825394332414 \tabularnewline
54 & 37 & 99.4433230770021 & -62.4433230770021 \tabularnewline
55 & 35 & 63.5759025308791 & -28.5759025308791 \tabularnewline
56 & 23 & 60.3350961492459 & -37.3350961492459 \tabularnewline
57 & 40 & 28.9375786540567 & 11.0624213459433 \tabularnewline
58 & 29 & 17.9911476535468 & 11.0088523464532 \tabularnewline
59 & 37 & 8.13783623184112 & 28.8621637681589 \tabularnewline
60 & 51 & 57.8014044626901 & -6.80140446269012 \tabularnewline
61 & 20 & 67.986280314366 & -47.986280314366 \tabularnewline
62 & 28 & 28.9516752372214 & -0.95167523722138 \tabularnewline
63 & 13 & 9.31321056571043 & 3.68678943428957 \tabularnewline
64 & 22 & 22.6070517338614 & -0.607051733861354 \tabularnewline
65 & 25 & 16.0505737046134 & 8.94942629538664 \tabularnewline
66 & 13 & 21.8230856739734 & -8.82308567397342 \tabularnewline
67 & 16 & 20.9469405271601 & -4.94694052716012 \tabularnewline
68 & 13 & 22.1988348561951 & -9.19883485619508 \tabularnewline
69 & 16 & 23.3093821664561 & -7.30938216645614 \tabularnewline
70 & 17 & 4.93082348471587 & 12.0691765152841 \tabularnewline
71 & 9 & 3.19217990983177 & 5.80782009016823 \tabularnewline
72 & 17 & 27.2017554894693 & -10.2017554894693 \tabularnewline
73 & 25 & 16.6693885648016 & 8.33061143519844 \tabularnewline
74 & 14 & 20.4077763690549 & -6.40777636905491 \tabularnewline
75 & 8 & 0.693902625599549 & 7.30609737440045 \tabularnewline
76 & 7 & 13.3553977851453 & -6.35539778514529 \tabularnewline
77 & 10 & 8.82028766465281 & 1.17971233534719 \tabularnewline
78 & 7 & 3.33822505002736 & 3.66177494997264 \tabularnewline
79 & 10 & 8.90454913922404 & 1.09545086077596 \tabularnewline
80 & 3 & 10.526306643243 & -7.52630664324296 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147430&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]80[/C][C]65.9535256410256[/C][C]14.0464743589744[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]32.4467148172594[/C][C]9.55328518274057[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]47.1353051316088[/C][C]6.86469486839122[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]60.5908949080094[/C][C]5.40910509199063[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]79.7238940940242[/C][C]1.27610590597584[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]69.423164327768[/C][C]-6.42316432776798[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]111.487769948459[/C][C]25.5122300515414[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]80.189065931405[/C][C]-8.18906593140491[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]86.4563236715524[/C][C]20.5436763284476[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]68.1223642893237[/C][C]-10.1223642893237[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]97.1537646423697[/C][C]-61.1537646423697[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]157.471510088703[/C][C]-105.471510088703[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]65.8538039157979[/C][C]13.1461960842021[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]28.6504949782513[/C][C]48.3495050217487[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]56.0480501431283[/C][C]-2.04805014312831[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]64.4949190767417[/C][C]19.5050809232583[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]86.335926809278[/C][C]-38.335926809278[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]56.1913729959147[/C][C]39.8086270040853[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]129.66480326721[/C][C]-46.6648032672097[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]53.9973913310618[/C][C]12.0026086689382[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]79.6754118037346[/C][C]-18.6754118037346[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]30.6746061226883[/C][C]22.3253938773117[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]47.4750331631063[/C][C]-17.4750331631063[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]103.414328539598[/C][C]-29.4143285395985[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]94.669052063968[/C][C]-25.669052063968[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]58.2346826816616[/C][C]0.765317318338404[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]43.6095578051338[/C][C]-1.60955780513378[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]61.0081831412311[/C][C]3.99181685876892[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]49.478803349939[/C][C]20.521196650061[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]76.7603341378024[/C][C]23.2396658621976[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]103.965837074185[/C][C]-40.9658370741847[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]56.501549428838[/C][C]48.498450571162[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]81.9715413639335[/C][C]0.0284586360665458[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]58.7674302672506[/C][C]22.2325697327494[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]57.5054384585557[/C][C]17.4945615414443[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]121.8113910067[/C][C]-19.8113910066999[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]119.011021546427[/C][C]1.9889784535731[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]106.036128029636[/C][C]-8.03612802963619[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]87.7937238475087[/C][C]-11.7937238475087[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]104.548576897231[/C][C]-27.5485768972311[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]88.825394332414[/C][C]-25.825394332414[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]99.4433230770021[/C][C]-62.4433230770021[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]63.5759025308791[/C][C]-28.5759025308791[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]60.3350961492459[/C][C]-37.3350961492459[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]28.9375786540567[/C][C]11.0624213459433[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]17.9911476535468[/C][C]11.0088523464532[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]8.13783623184112[/C][C]28.8621637681589[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]57.8014044626901[/C][C]-6.80140446269012[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]67.986280314366[/C][C]-47.986280314366[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]28.9516752372214[/C][C]-0.95167523722138[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]9.31321056571043[/C][C]3.68678943428957[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]22.6070517338614[/C][C]-0.607051733861354[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]16.0505737046134[/C][C]8.94942629538664[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]21.8230856739734[/C][C]-8.82308567397342[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]20.9469405271601[/C][C]-4.94694052716012[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]22.1988348561951[/C][C]-9.19883485619508[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]23.3093821664561[/C][C]-7.30938216645614[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]4.93082348471587[/C][C]12.0691765152841[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]3.19217990983177[/C][C]5.80782009016823[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]27.2017554894693[/C][C]-10.2017554894693[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]16.6693885648016[/C][C]8.33061143519844[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]20.4077763690549[/C][C]-6.40777636905491[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]0.693902625599549[/C][C]7.30609737440045[/C][/ROW]
[ROW][C]76[/C][C]7[/C][C]13.3553977851453[/C][C]-6.35539778514529[/C][/ROW]
[ROW][C]77[/C][C]10[/C][C]8.82028766465281[/C][C]1.17971233534719[/C][/ROW]
[ROW][C]78[/C][C]7[/C][C]3.33822505002736[/C][C]3.66177494997264[/C][/ROW]
[ROW][C]79[/C][C]10[/C][C]8.90454913922404[/C][C]1.09545086077596[/C][/ROW]
[ROW][C]80[/C][C]3[/C][C]10.526306643243[/C][C]-7.52630664324296[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147430&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147430&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
138065.953525641025614.0464743589744
144232.44671481725949.55328518274057
155447.13530513160886.86469486839122
166660.59089490800945.40910509199063
178179.72389409402421.27610590597584
186369.423164327768-6.42316432776798
19137111.48776994845925.5122300515414
207280.189065931405-8.18906593140491
2110786.456323671552420.5436763284476
225868.1223642893237-10.1223642893237
233697.1537646423697-61.1537646423697
2452157.471510088703-105.471510088703
257965.853803915797913.1461960842021
267728.650494978251348.3495050217487
275456.0480501431283-2.04805014312831
288464.494919076741719.5050809232583
294886.335926809278-38.335926809278
309656.191372995914739.8086270040853
3183129.66480326721-46.6648032672097
326653.997391331061812.0026086689382
336179.6754118037346-18.6754118037346
345330.674606122688322.3253938773117
353047.4750331631063-17.4750331631063
3674103.414328539598-29.4143285395985
376994.669052063968-25.669052063968
385958.23468268166160.765317318338404
394243.6095578051338-1.60955780513378
406561.00818314123113.99181685876892
417049.47880334993920.521196650061
4210076.760334137802423.2396658621976
4363103.965837074185-40.9658370741847
4410556.50154942883848.498450571162
458281.97154136393350.0284586360665458
468158.767430267250622.2325697327494
477557.505438458555717.4945615414443
48102121.8113910067-19.8113910066999
49121119.0110215464271.9889784535731
5098106.036128029636-8.03612802963619
517687.7937238475087-11.7937238475087
5277104.548576897231-27.5485768972311
536388.825394332414-25.825394332414
543799.4433230770021-62.4433230770021
553563.5759025308791-28.5759025308791
562360.3350961492459-37.3350961492459
574028.937578654056711.0624213459433
582917.991147653546811.0088523464532
59378.1378362318411228.8621637681589
605157.8014044626901-6.80140446269012
612067.986280314366-47.986280314366
622828.9516752372214-0.95167523722138
63139.313210565710433.68678943428957
642222.6070517338614-0.607051733861354
652516.05057370461348.94942629538664
661321.8230856739734-8.82308567397342
671620.9469405271601-4.94694052716012
681322.1988348561951-9.19883485619508
691623.3093821664561-7.30938216645614
70174.9308234847158712.0691765152841
7193.192179909831775.80782009016823
721727.2017554894693-10.2017554894693
732516.66938856480168.33061143519844
741420.4077763690549-6.40777636905491
7580.6939026255995497.30609737440045
76713.3553977851453-6.35539778514529
77108.820287664652811.17971233534719
7873.338225050027363.66177494997264
79108.904549139224041.09545086077596
80310.526306643243-7.52630664324296







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8113.1518860780322-37.446598918901763.750371074966
826.4665766273601-47.897222023731660.8303752784518
83-2.75000728511186-60.846725736893155.3467111666694
8411.6688643515531-50.140253426643973.47798212975
8513.4546037022275-52.055546076289278.9647534807443
867.24134529397715-61.965654558540376.4483451464945
87-3.811053389558-76.716447137440269.0943403583242
88-0.232709452868718-76.842660726268576.377241820531
891.05592991449164-79.268509091267881.3803689202511
90-3.78144524583877-87.833400150126380.2705096584488
91-0.852758842782082-88.647824662603186.942306977039
92-3.65473445255916-95.210646124497387.901177219379

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 13.1518860780322 & -37.4465989189017 & 63.750371074966 \tabularnewline
82 & 6.4665766273601 & -47.8972220237316 & 60.8303752784518 \tabularnewline
83 & -2.75000728511186 & -60.8467257368931 & 55.3467111666694 \tabularnewline
84 & 11.6688643515531 & -50.1402534266439 & 73.47798212975 \tabularnewline
85 & 13.4546037022275 & -52.0555460762892 & 78.9647534807443 \tabularnewline
86 & 7.24134529397715 & -61.9656545585403 & 76.4483451464945 \tabularnewline
87 & -3.811053389558 & -76.7164471374402 & 69.0943403583242 \tabularnewline
88 & -0.232709452868718 & -76.8426607262685 & 76.377241820531 \tabularnewline
89 & 1.05592991449164 & -79.2685090912678 & 81.3803689202511 \tabularnewline
90 & -3.78144524583877 & -87.8334001501263 & 80.2705096584488 \tabularnewline
91 & -0.852758842782082 & -88.6478246626031 & 86.942306977039 \tabularnewline
92 & -3.65473445255916 & -95.2106461244973 & 87.901177219379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147430&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]81[/C][C]13.1518860780322[/C][C]-37.4465989189017[/C][C]63.750371074966[/C][/ROW]
[ROW][C]82[/C][C]6.4665766273601[/C][C]-47.8972220237316[/C][C]60.8303752784518[/C][/ROW]
[ROW][C]83[/C][C]-2.75000728511186[/C][C]-60.8467257368931[/C][C]55.3467111666694[/C][/ROW]
[ROW][C]84[/C][C]11.6688643515531[/C][C]-50.1402534266439[/C][C]73.47798212975[/C][/ROW]
[ROW][C]85[/C][C]13.4546037022275[/C][C]-52.0555460762892[/C][C]78.9647534807443[/C][/ROW]
[ROW][C]86[/C][C]7.24134529397715[/C][C]-61.9656545585403[/C][C]76.4483451464945[/C][/ROW]
[ROW][C]87[/C][C]-3.811053389558[/C][C]-76.7164471374402[/C][C]69.0943403583242[/C][/ROW]
[ROW][C]88[/C][C]-0.232709452868718[/C][C]-76.8426607262685[/C][C]76.377241820531[/C][/ROW]
[ROW][C]89[/C][C]1.05592991449164[/C][C]-79.2685090912678[/C][C]81.3803689202511[/C][/ROW]
[ROW][C]90[/C][C]-3.78144524583877[/C][C]-87.8334001501263[/C][C]80.2705096584488[/C][/ROW]
[ROW][C]91[/C][C]-0.852758842782082[/C][C]-88.6478246626031[/C][C]86.942306977039[/C][/ROW]
[ROW][C]92[/C][C]-3.65473445255916[/C][C]-95.2106461244973[/C][C]87.901177219379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147430&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147430&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
8113.1518860780322-37.446598918901763.750371074966
826.4665766273601-47.897222023731660.8303752784518
83-2.75000728511186-60.846725736893155.3467111666694
8411.6688643515531-50.140253426643973.47798212975
8513.4546037022275-52.055546076289278.9647534807443
867.24134529397715-61.965654558540376.4483451464945
87-3.811053389558-76.716447137440269.0943403583242
88-0.232709452868718-76.842660726268576.377241820531
891.05592991449164-79.268509091267881.3803689202511
90-3.78144524583877-87.833400150126380.2705096584488
91-0.852758842782082-88.647824662603186.942306977039
92-3.65473445255916-95.210646124497387.901177219379



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')