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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 computationMon, 29 Nov 2010 10:02:53 +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/2010/Nov/29/t1291025503wlnua7wqlwucc2f.htm/, Retrieved Mon, 29 Apr 2024 11:37:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102792, Retrieved Mon, 29 Apr 2024 11:37:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact168
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [W8 (3)] [2010-11-29 10:02:53] [c9b1b69acb8f4b2b921fdfd5091a94b7] [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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102792&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102792&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102792&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.380859354912001
beta0.0316088853012633
gamma0.733581043315084

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.380859354912001 \tabularnewline
beta & 0.0316088853012633 \tabularnewline
gamma & 0.733581043315084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102792&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]0.380859354912001[/C][/ROW]
[ROW][C]beta[/C][C]0.0316088853012633[/C][/ROW]
[ROW][C]gamma[/C][C]0.733581043315084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102792&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102792&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
alpha0.380859354912001
beta0.0316088853012633
gamma0.733581043315084







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138065.953525641025714.0464743589743
144232.44671481726019.55328518273991
155447.13530513160956.86469486839045
166660.590894908015.40910509199001
178179.72389409402461.2761059059754
186369.4231643277681-6.42316432776809
19137111.48776994845825.5122300515419
207280.1890659314056-8.18906593140558
2110786.45632367155220.5436763284479
225868.1223642893241-10.1223642893241
233697.153764642369-61.1537646423691
2452157.471510088699-105.471510088699
257965.853803915793113.1461960842069
267728.650494978248748.3495050217513
275456.0480501431291-2.04805014312910
288464.494919076742319.5050809232577
294886.3359268092791-38.3359268092791
309656.191372995912939.8086270040871
3183129.664803267216-46.6648032672161
326653.99739133105812.002608668942
336179.6754118037384-18.6754118037384
345330.674606122684922.3253938773151
353047.4750331630982-17.4750331630982
3674103.414328539587-29.4143285395875
376994.6690520639822-25.6690520639822
385958.23468268167360.765317318326439
394243.609557805132-1.60955780513198
406561.0081831412343.99181685876599
417049.478803349931820.5211966500682
4210076.760334137812323.2396658621877
4363103.965837074180-40.9658370741803
4410556.50154942884248.498450571158
458281.97154136393560.0284586360644283
468158.767430267256822.2325697327432
477557.505438458549117.4945615414509
48102121.811391006691-19.8113910066906
49121119.0110215464311.98897845356879
5098106.036128029648-8.03612802964805
517687.7937238475118-11.7937238475118
5277104.548576897235-27.5485768972347
536388.8253943324124-25.8253943324124
543799.4433230770057-62.4433230770057
553563.5759025308631-28.5759025308631
562360.3350961492543-37.3350961492543
574028.937578654051311.0624213459487
582917.991147653551511.0088523464485
59378.1378362318391328.8621637681609
605157.8014044626805-6.8014044626805
612067.986280314369-47.9862803143689
622828.951675237226-0.95167523722598
63139.313210565713963.68678943428604
642222.6070517338644-0.607051733864424
652516.05057370461658.94942629538355
661321.8230856739742-8.82308567397422
671620.9469405271599-4.94694052715987
681322.1988348562020-9.19883485620204
691623.3093821664651-7.30938216646515
70174.9308234847238512.0691765152762
7193.192179909837565.80782009016244
721727.201755489461-10.2017554894610
732516.66938856479288.33061143520722
741420.4077763690616-6.40777636906155
7580.6939026256049847.30609737439502
76713.3553977851489-6.3553977851489
77108.820287664657131.17971233534287
7873.338225050026453.66177494997355
79108.904549139224121.09545086077588
80310.5263066432461-7.5263066432461

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 80 & 65.9535256410257 & 14.0464743589743 \tabularnewline
14 & 42 & 32.4467148172601 & 9.55328518273991 \tabularnewline
15 & 54 & 47.1353051316095 & 6.86469486839045 \tabularnewline
16 & 66 & 60.59089490801 & 5.40910509199001 \tabularnewline
17 & 81 & 79.7238940940246 & 1.2761059059754 \tabularnewline
18 & 63 & 69.4231643277681 & -6.42316432776809 \tabularnewline
19 & 137 & 111.487769948458 & 25.5122300515419 \tabularnewline
20 & 72 & 80.1890659314056 & -8.18906593140558 \tabularnewline
21 & 107 & 86.456323671552 & 20.5436763284479 \tabularnewline
22 & 58 & 68.1223642893241 & -10.1223642893241 \tabularnewline
23 & 36 & 97.153764642369 & -61.1537646423691 \tabularnewline
24 & 52 & 157.471510088699 & -105.471510088699 \tabularnewline
25 & 79 & 65.8538039157931 & 13.1461960842069 \tabularnewline
26 & 77 & 28.6504949782487 & 48.3495050217513 \tabularnewline
27 & 54 & 56.0480501431291 & -2.04805014312910 \tabularnewline
28 & 84 & 64.4949190767423 & 19.5050809232577 \tabularnewline
29 & 48 & 86.3359268092791 & -38.3359268092791 \tabularnewline
30 & 96 & 56.1913729959129 & 39.8086270040871 \tabularnewline
31 & 83 & 129.664803267216 & -46.6648032672161 \tabularnewline
32 & 66 & 53.997391331058 & 12.002608668942 \tabularnewline
33 & 61 & 79.6754118037384 & -18.6754118037384 \tabularnewline
34 & 53 & 30.6746061226849 & 22.3253938773151 \tabularnewline
35 & 30 & 47.4750331630982 & -17.4750331630982 \tabularnewline
36 & 74 & 103.414328539587 & -29.4143285395875 \tabularnewline
37 & 69 & 94.6690520639822 & -25.6690520639822 \tabularnewline
38 & 59 & 58.2346826816736 & 0.765317318326439 \tabularnewline
39 & 42 & 43.609557805132 & -1.60955780513198 \tabularnewline
40 & 65 & 61.008183141234 & 3.99181685876599 \tabularnewline
41 & 70 & 49.4788033499318 & 20.5211966500682 \tabularnewline
42 & 100 & 76.7603341378123 & 23.2396658621877 \tabularnewline
43 & 63 & 103.965837074180 & -40.9658370741803 \tabularnewline
44 & 105 & 56.501549428842 & 48.498450571158 \tabularnewline
45 & 82 & 81.9715413639356 & 0.0284586360644283 \tabularnewline
46 & 81 & 58.7674302672568 & 22.2325697327432 \tabularnewline
47 & 75 & 57.5054384585491 & 17.4945615414509 \tabularnewline
48 & 102 & 121.811391006691 & -19.8113910066906 \tabularnewline
49 & 121 & 119.011021546431 & 1.98897845356879 \tabularnewline
50 & 98 & 106.036128029648 & -8.03612802964805 \tabularnewline
51 & 76 & 87.7937238475118 & -11.7937238475118 \tabularnewline
52 & 77 & 104.548576897235 & -27.5485768972347 \tabularnewline
53 & 63 & 88.8253943324124 & -25.8253943324124 \tabularnewline
54 & 37 & 99.4433230770057 & -62.4433230770057 \tabularnewline
55 & 35 & 63.5759025308631 & -28.5759025308631 \tabularnewline
56 & 23 & 60.3350961492543 & -37.3350961492543 \tabularnewline
57 & 40 & 28.9375786540513 & 11.0624213459487 \tabularnewline
58 & 29 & 17.9911476535515 & 11.0088523464485 \tabularnewline
59 & 37 & 8.13783623183913 & 28.8621637681609 \tabularnewline
60 & 51 & 57.8014044626805 & -6.8014044626805 \tabularnewline
61 & 20 & 67.986280314369 & -47.9862803143689 \tabularnewline
62 & 28 & 28.951675237226 & -0.95167523722598 \tabularnewline
63 & 13 & 9.31321056571396 & 3.68678943428604 \tabularnewline
64 & 22 & 22.6070517338644 & -0.607051733864424 \tabularnewline
65 & 25 & 16.0505737046165 & 8.94942629538355 \tabularnewline
66 & 13 & 21.8230856739742 & -8.82308567397422 \tabularnewline
67 & 16 & 20.9469405271599 & -4.94694052715987 \tabularnewline
68 & 13 & 22.1988348562020 & -9.19883485620204 \tabularnewline
69 & 16 & 23.3093821664651 & -7.30938216646515 \tabularnewline
70 & 17 & 4.93082348472385 & 12.0691765152762 \tabularnewline
71 & 9 & 3.19217990983756 & 5.80782009016244 \tabularnewline
72 & 17 & 27.201755489461 & -10.2017554894610 \tabularnewline
73 & 25 & 16.6693885647928 & 8.33061143520722 \tabularnewline
74 & 14 & 20.4077763690616 & -6.40777636906155 \tabularnewline
75 & 8 & 0.693902625604984 & 7.30609737439502 \tabularnewline
76 & 7 & 13.3553977851489 & -6.3553977851489 \tabularnewline
77 & 10 & 8.82028766465713 & 1.17971233534287 \tabularnewline
78 & 7 & 3.33822505002645 & 3.66177494997355 \tabularnewline
79 & 10 & 8.90454913922412 & 1.09545086077588 \tabularnewline
80 & 3 & 10.5263066432461 & -7.5263066432461 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102792&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]65.9535256410257[/C][C]14.0464743589743[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]32.4467148172601[/C][C]9.55328518273991[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]47.1353051316095[/C][C]6.86469486839045[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]60.59089490801[/C][C]5.40910509199001[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]79.7238940940246[/C][C]1.2761059059754[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]69.4231643277681[/C][C]-6.42316432776809[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]111.487769948458[/C][C]25.5122300515419[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]80.1890659314056[/C][C]-8.18906593140558[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]86.456323671552[/C][C]20.5436763284479[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]68.1223642893241[/C][C]-10.1223642893241[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]97.153764642369[/C][C]-61.1537646423691[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]157.471510088699[/C][C]-105.471510088699[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]65.8538039157931[/C][C]13.1461960842069[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]28.6504949782487[/C][C]48.3495050217513[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]56.0480501431291[/C][C]-2.04805014312910[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]64.4949190767423[/C][C]19.5050809232577[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]86.3359268092791[/C][C]-38.3359268092791[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]56.1913729959129[/C][C]39.8086270040871[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]129.664803267216[/C][C]-46.6648032672161[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]53.997391331058[/C][C]12.002608668942[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]79.6754118037384[/C][C]-18.6754118037384[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]30.6746061226849[/C][C]22.3253938773151[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]47.4750331630982[/C][C]-17.4750331630982[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]103.414328539587[/C][C]-29.4143285395875[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]94.6690520639822[/C][C]-25.6690520639822[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]58.2346826816736[/C][C]0.765317318326439[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]43.609557805132[/C][C]-1.60955780513198[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]61.008183141234[/C][C]3.99181685876599[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]49.4788033499318[/C][C]20.5211966500682[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]76.7603341378123[/C][C]23.2396658621877[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]103.965837074180[/C][C]-40.9658370741803[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]56.501549428842[/C][C]48.498450571158[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]81.9715413639356[/C][C]0.0284586360644283[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]58.7674302672568[/C][C]22.2325697327432[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]57.5054384585491[/C][C]17.4945615414509[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]121.811391006691[/C][C]-19.8113910066906[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]119.011021546431[/C][C]1.98897845356879[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]106.036128029648[/C][C]-8.03612802964805[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]87.7937238475118[/C][C]-11.7937238475118[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]104.548576897235[/C][C]-27.5485768972347[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]88.8253943324124[/C][C]-25.8253943324124[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]99.4433230770057[/C][C]-62.4433230770057[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]63.5759025308631[/C][C]-28.5759025308631[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]60.3350961492543[/C][C]-37.3350961492543[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]28.9375786540513[/C][C]11.0624213459487[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]17.9911476535515[/C][C]11.0088523464485[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]8.13783623183913[/C][C]28.8621637681609[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]57.8014044626805[/C][C]-6.8014044626805[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]67.986280314369[/C][C]-47.9862803143689[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]28.951675237226[/C][C]-0.95167523722598[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]9.31321056571396[/C][C]3.68678943428604[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]22.6070517338644[/C][C]-0.607051733864424[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]16.0505737046165[/C][C]8.94942629538355[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]21.8230856739742[/C][C]-8.82308567397422[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]20.9469405271599[/C][C]-4.94694052715987[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]22.1988348562020[/C][C]-9.19883485620204[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]23.3093821664651[/C][C]-7.30938216646515[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]4.93082348472385[/C][C]12.0691765152762[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]3.19217990983756[/C][C]5.80782009016244[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]27.201755489461[/C][C]-10.2017554894610[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]16.6693885647928[/C][C]8.33061143520722[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]20.4077763690616[/C][C]-6.40777636906155[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]0.693902625604984[/C][C]7.30609737439502[/C][/ROW]
[ROW][C]76[/C][C]7[/C][C]13.3553977851489[/C][C]-6.3553977851489[/C][/ROW]
[ROW][C]77[/C][C]10[/C][C]8.82028766465713[/C][C]1.17971233534287[/C][/ROW]
[ROW][C]78[/C][C]7[/C][C]3.33822505002645[/C][C]3.66177494997355[/C][/ROW]
[ROW][C]79[/C][C]10[/C][C]8.90454913922412[/C][C]1.09545086077588[/C][/ROW]
[ROW][C]80[/C][C]3[/C][C]10.5263066432461[/C][C]-7.5263066432461[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102792&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102792&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
138065.953525641025714.0464743589743
144232.44671481726019.55328518273991
155447.13530513160956.86469486839045
166660.590894908015.40910509199001
178179.72389409402461.2761059059754
186369.4231643277681-6.42316432776809
19137111.48776994845825.5122300515419
207280.1890659314056-8.18906593140558
2110786.45632367155220.5436763284479
225868.1223642893241-10.1223642893241
233697.153764642369-61.1537646423691
2452157.471510088699-105.471510088699
257965.853803915793113.1461960842069
267728.650494978248748.3495050217513
275456.0480501431291-2.04805014312910
288464.494919076742319.5050809232577
294886.3359268092791-38.3359268092791
309656.191372995912939.8086270040871
3183129.664803267216-46.6648032672161
326653.99739133105812.002608668942
336179.6754118037384-18.6754118037384
345330.674606122684922.3253938773151
353047.4750331630982-17.4750331630982
3674103.414328539587-29.4143285395875
376994.6690520639822-25.6690520639822
385958.23468268167360.765317318326439
394243.609557805132-1.60955780513198
406561.0081831412343.99181685876599
417049.478803349931820.5211966500682
4210076.760334137812323.2396658621877
4363103.965837074180-40.9658370741803
4410556.50154942884248.498450571158
458281.97154136393560.0284586360644283
468158.767430267256822.2325697327432
477557.505438458549117.4945615414509
48102121.811391006691-19.8113910066906
49121119.0110215464311.98897845356879
5098106.036128029648-8.03612802964805
517687.7937238475118-11.7937238475118
5277104.548576897235-27.5485768972347
536388.8253943324124-25.8253943324124
543799.4433230770057-62.4433230770057
553563.5759025308631-28.5759025308631
562360.3350961492543-37.3350961492543
574028.937578654051311.0624213459487
582917.991147653551511.0088523464485
59378.1378362318391328.8621637681609
605157.8014044626805-6.8014044626805
612067.986280314369-47.9862803143689
622828.951675237226-0.95167523722598
63139.313210565713963.68678943428604
642222.6070517338644-0.607051733864424
652516.05057370461658.94942629538355
661321.8230856739742-8.82308567397422
671620.9469405271599-4.94694052715987
681322.1988348562020-9.19883485620204
691623.3093821664651-7.30938216646515
70174.9308234847238512.0691765152762
7193.192179909837565.80782009016244
721727.201755489461-10.2017554894610
732516.66938856479288.33061143520722
741420.4077763690616-6.40777636906155
7580.6939026256049847.30609737439502
76713.3553977851489-6.3553977851489
77108.820287664657131.17971233534287
7873.338225050026453.66177494997355
79108.904549139224121.09545086077588
80310.5263066432461-7.5263066432461







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8113.1518860780379-37.446598918895763.7503710749715
826.46657662737189-47.897222023720360.8303752784641
83-2.75000728509995-60.846725736882455.3467111666825
8411.6688643515566-50.140253426642173.4779821297553
8513.4546037022310-52.055546076287878.9647534807497
867.24134529398266-61.96565455853776.4483451465023
87-3.81105338954830-76.716447137432969.0943403583363
88-0.232709452860554-76.842660726262776.3772418205416
891.05592991450302-79.268509091258781.3803689202648
90-3.78144524582828-87.833400150117980.2705096584614
91-0.852758842772003-88.64782466259586.942306977051
92-3.6547344525488-95.210646124488587.9011772193909

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 13.1518860780379 & -37.4465989188957 & 63.7503710749715 \tabularnewline
82 & 6.46657662737189 & -47.8972220237203 & 60.8303752784641 \tabularnewline
83 & -2.75000728509995 & -60.8467257368824 & 55.3467111666825 \tabularnewline
84 & 11.6688643515566 & -50.1402534266421 & 73.4779821297553 \tabularnewline
85 & 13.4546037022310 & -52.0555460762878 & 78.9647534807497 \tabularnewline
86 & 7.24134529398266 & -61.965654558537 & 76.4483451465023 \tabularnewline
87 & -3.81105338954830 & -76.7164471374329 & 69.0943403583363 \tabularnewline
88 & -0.232709452860554 & -76.8426607262627 & 76.3772418205416 \tabularnewline
89 & 1.05592991450302 & -79.2685090912587 & 81.3803689202648 \tabularnewline
90 & -3.78144524582828 & -87.8334001501179 & 80.2705096584614 \tabularnewline
91 & -0.852758842772003 & -88.647824662595 & 86.942306977051 \tabularnewline
92 & -3.6547344525488 & -95.2106461244885 & 87.9011772193909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102792&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]13.1518860780379[/C][C]-37.4465989188957[/C][C]63.7503710749715[/C][/ROW]
[ROW][C]82[/C][C]6.46657662737189[/C][C]-47.8972220237203[/C][C]60.8303752784641[/C][/ROW]
[ROW][C]83[/C][C]-2.75000728509995[/C][C]-60.8467257368824[/C][C]55.3467111666825[/C][/ROW]
[ROW][C]84[/C][C]11.6688643515566[/C][C]-50.1402534266421[/C][C]73.4779821297553[/C][/ROW]
[ROW][C]85[/C][C]13.4546037022310[/C][C]-52.0555460762878[/C][C]78.9647534807497[/C][/ROW]
[ROW][C]86[/C][C]7.24134529398266[/C][C]-61.965654558537[/C][C]76.4483451465023[/C][/ROW]
[ROW][C]87[/C][C]-3.81105338954830[/C][C]-76.7164471374329[/C][C]69.0943403583363[/C][/ROW]
[ROW][C]88[/C][C]-0.232709452860554[/C][C]-76.8426607262627[/C][C]76.3772418205416[/C][/ROW]
[ROW][C]89[/C][C]1.05592991450302[/C][C]-79.2685090912587[/C][C]81.3803689202648[/C][/ROW]
[ROW][C]90[/C][C]-3.78144524582828[/C][C]-87.8334001501179[/C][C]80.2705096584614[/C][/ROW]
[ROW][C]91[/C][C]-0.852758842772003[/C][C]-88.647824662595[/C][C]86.942306977051[/C][/ROW]
[ROW][C]92[/C][C]-3.6547344525488[/C][C]-95.2106461244885[/C][C]87.9011772193909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102792&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102792&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
8113.1518860780379-37.446598918895763.7503710749715
826.46657662737189-47.897222023720360.8303752784641
83-2.75000728509995-60.846725736882455.3467111666825
8411.6688643515566-50.140253426642173.4779821297553
8513.4546037022310-52.055546076287878.9647534807497
867.24134529398266-61.96565455853776.4483451465023
87-3.81105338954830-76.716447137432969.0943403583363
88-0.232709452860554-76.842660726262776.3772418205416
891.05592991450302-79.268509091258781.3803689202648
90-3.78144524582828-87.833400150117980.2705096584614
91-0.852758842772003-88.64782466259586.942306977051
92-3.6547344525488-95.210646124488587.9011772193909



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')