Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 31 May 2010 19:28:56 +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/May/31/t1275334295ev3chbedt8d00q7.htm/, Retrieved Mon, 29 Apr 2024 13:41:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76785, Retrieved Mon, 29 Apr 2024 13:41:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10, oef. 2] [2010-05-31 19:28:56] [7305f5ba5e018172148a6d5988ec7f42] [Current]
Feedback Forum

Post a new message
Dataseries X:
164
96
73
49
39
59
169
169
210
278
298
245
200
188
90
79
78
91
167
169
289
247
275
203
223
104
107
85
75
99
135
211
335
488
326
346
261
224
141
148
145
223
272
445
560
612
467
404
518
404
300
210
196
186
247
343
464
680
711
610
513
292
273
322
189
257
324
404
677
858
895
664
628
308
324
248
272




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76785&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76785&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76785&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' @ 72.249.127.135







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=76785&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=76785&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76785&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
296164-68
37396.004495273372-23.0044952733719
44973.00152075728-24.0015207572799
53949.0015866676051-10.0015866676051
65939.000661174503319.9993388254967
716958.9986779044812110.001322095519
8169168.9927281468520.00727185314843837
9210168.9999995192841.0000004807201
10278209.99728961455368.0027103854472
11298277.99550454745320.0044954525473
12245297.998677563592-52.9986775635923
13200245.003503581529-45.0035035815294
14188200.002975044872-12.002975044872
1590188.000793480207-98.0007934802074
167990.006478534667-11.0064785346671
177879.0007276048511-1.00072760485111
189178.000066155061112.9999338449389
1916790.999140613875776.0008593861243
20169166.9949758141262.00502418587416
21289168.999867453944120.000132546056
22247288.992067155876-41.9920671558755
23275247.00277596796127.9972240320394
24203274.998149188593-71.9981491885929
25223203.00475957886619.9952404211342
26104222.998678175414-118.998678175414
27107104.0078666410192.99213335898092
2885106.999802199156-21.9998021991557
297585.0014543400737-10.0014543400737
309975.000661165755523.9993388342445
3113598.998413476635236.0015865233648
32211134.99762004451176.0023799554889
33335210.994975713606124.005024286394
34488334.991802404652153.008197595348
35326487.989885092995-161.989885092995
36346326.01070865907319.9892913409267
37261345.99867856869-84.9986785686899
38224261.005619004359-37.0056190043591
39141224.002446329025-83.0024463290253
40148141.0054870395126.9945129604884
41145147.999537614002-2.99953761400207
42223145.00019829031777.9998017096829
43272222.99484367012349.0051563298771
44445271.996760418024173.003239581976
45560444.988563281527115.011436718473
46612559.99239694339852.0076030566021
47467611.996561935395-144.996561935395
48404467.009585282116-63.009585282116
49518404.004165372219113.995834627781
50404517.992464081766-113.992464081766
51300404.007535695417-104.007535695417
52210300.006875622143-90.0068756221425
53196210.005950081048-14.0059500810482
54186196.000925890801-10.0009258908007
55247186.00066113082160.9993388691786
56343246.99596751906396.0040324809371
57464342.993653465135121.006346534865
58680463.992000638126216.007999361874
59711679.98572036753531.0142796324654
60610710.997949740215-100.997949740215
61513610.00667666756-97.0066766675601
62292513.006412816625-221.006412816625
63273292.014610062391-19.0146100623905
64322273.00125699809348.9987430019075
65189321.99676084199-132.99676084199
66257189.00879201172967.9912079882711
67324256.99550530784167.0044946921587
68404323.99557053645980.004429463541
69677403.994711150273273.005288849727
70858676.981952449921181.018047550079
71895857.98803344692737.0119665530734
72664894.997553251358-230.997553251358
73628664.015270546325-36.0152705463252
74308628.002380860098-320.002380860098
75324308.02115438502415.9788456149760
76248323.998943687070-75.9989436870705
77272248.00502405923323.9949759407669

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 96 & 164 & -68 \tabularnewline
3 & 73 & 96.004495273372 & -23.0044952733719 \tabularnewline
4 & 49 & 73.00152075728 & -24.0015207572799 \tabularnewline
5 & 39 & 49.0015866676051 & -10.0015866676051 \tabularnewline
6 & 59 & 39.0006611745033 & 19.9993388254967 \tabularnewline
7 & 169 & 58.9986779044812 & 110.001322095519 \tabularnewline
8 & 169 & 168.992728146852 & 0.00727185314843837 \tabularnewline
9 & 210 & 168.99999951928 & 41.0000004807201 \tabularnewline
10 & 278 & 209.997289614553 & 68.0027103854472 \tabularnewline
11 & 298 & 277.995504547453 & 20.0044954525473 \tabularnewline
12 & 245 & 297.998677563592 & -52.9986775635923 \tabularnewline
13 & 200 & 245.003503581529 & -45.0035035815294 \tabularnewline
14 & 188 & 200.002975044872 & -12.002975044872 \tabularnewline
15 & 90 & 188.000793480207 & -98.0007934802074 \tabularnewline
16 & 79 & 90.006478534667 & -11.0064785346671 \tabularnewline
17 & 78 & 79.0007276048511 & -1.00072760485111 \tabularnewline
18 & 91 & 78.0000661550611 & 12.9999338449389 \tabularnewline
19 & 167 & 90.9991406138757 & 76.0008593861243 \tabularnewline
20 & 169 & 166.994975814126 & 2.00502418587416 \tabularnewline
21 & 289 & 168.999867453944 & 120.000132546056 \tabularnewline
22 & 247 & 288.992067155876 & -41.9920671558755 \tabularnewline
23 & 275 & 247.002775967961 & 27.9972240320394 \tabularnewline
24 & 203 & 274.998149188593 & -71.9981491885929 \tabularnewline
25 & 223 & 203.004759578866 & 19.9952404211342 \tabularnewline
26 & 104 & 222.998678175414 & -118.998678175414 \tabularnewline
27 & 107 & 104.007866641019 & 2.99213335898092 \tabularnewline
28 & 85 & 106.999802199156 & -21.9998021991557 \tabularnewline
29 & 75 & 85.0014543400737 & -10.0014543400737 \tabularnewline
30 & 99 & 75.0006611657555 & 23.9993388342445 \tabularnewline
31 & 135 & 98.9984134766352 & 36.0015865233648 \tabularnewline
32 & 211 & 134.997620044511 & 76.0023799554889 \tabularnewline
33 & 335 & 210.994975713606 & 124.005024286394 \tabularnewline
34 & 488 & 334.991802404652 & 153.008197595348 \tabularnewline
35 & 326 & 487.989885092995 & -161.989885092995 \tabularnewline
36 & 346 & 326.010708659073 & 19.9892913409267 \tabularnewline
37 & 261 & 345.99867856869 & -84.9986785686899 \tabularnewline
38 & 224 & 261.005619004359 & -37.0056190043591 \tabularnewline
39 & 141 & 224.002446329025 & -83.0024463290253 \tabularnewline
40 & 148 & 141.005487039512 & 6.9945129604884 \tabularnewline
41 & 145 & 147.999537614002 & -2.99953761400207 \tabularnewline
42 & 223 & 145.000198290317 & 77.9998017096829 \tabularnewline
43 & 272 & 222.994843670123 & 49.0051563298771 \tabularnewline
44 & 445 & 271.996760418024 & 173.003239581976 \tabularnewline
45 & 560 & 444.988563281527 & 115.011436718473 \tabularnewline
46 & 612 & 559.992396943398 & 52.0076030566021 \tabularnewline
47 & 467 & 611.996561935395 & -144.996561935395 \tabularnewline
48 & 404 & 467.009585282116 & -63.009585282116 \tabularnewline
49 & 518 & 404.004165372219 & 113.995834627781 \tabularnewline
50 & 404 & 517.992464081766 & -113.992464081766 \tabularnewline
51 & 300 & 404.007535695417 & -104.007535695417 \tabularnewline
52 & 210 & 300.006875622143 & -90.0068756221425 \tabularnewline
53 & 196 & 210.005950081048 & -14.0059500810482 \tabularnewline
54 & 186 & 196.000925890801 & -10.0009258908007 \tabularnewline
55 & 247 & 186.000661130821 & 60.9993388691786 \tabularnewline
56 & 343 & 246.995967519063 & 96.0040324809371 \tabularnewline
57 & 464 & 342.993653465135 & 121.006346534865 \tabularnewline
58 & 680 & 463.992000638126 & 216.007999361874 \tabularnewline
59 & 711 & 679.985720367535 & 31.0142796324654 \tabularnewline
60 & 610 & 710.997949740215 & -100.997949740215 \tabularnewline
61 & 513 & 610.00667666756 & -97.0066766675601 \tabularnewline
62 & 292 & 513.006412816625 & -221.006412816625 \tabularnewline
63 & 273 & 292.014610062391 & -19.0146100623905 \tabularnewline
64 & 322 & 273.001256998093 & 48.9987430019075 \tabularnewline
65 & 189 & 321.99676084199 & -132.99676084199 \tabularnewline
66 & 257 & 189.008792011729 & 67.9912079882711 \tabularnewline
67 & 324 & 256.995505307841 & 67.0044946921587 \tabularnewline
68 & 404 & 323.995570536459 & 80.004429463541 \tabularnewline
69 & 677 & 403.994711150273 & 273.005288849727 \tabularnewline
70 & 858 & 676.981952449921 & 181.018047550079 \tabularnewline
71 & 895 & 857.988033446927 & 37.0119665530734 \tabularnewline
72 & 664 & 894.997553251358 & -230.997553251358 \tabularnewline
73 & 628 & 664.015270546325 & -36.0152705463252 \tabularnewline
74 & 308 & 628.002380860098 & -320.002380860098 \tabularnewline
75 & 324 & 308.021154385024 & 15.9788456149760 \tabularnewline
76 & 248 & 323.998943687070 & -75.9989436870705 \tabularnewline
77 & 272 & 248.005024059233 & 23.9949759407669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76785&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]96[/C][C]164[/C][C]-68[/C][/ROW]
[ROW][C]3[/C][C]73[/C][C]96.004495273372[/C][C]-23.0044952733719[/C][/ROW]
[ROW][C]4[/C][C]49[/C][C]73.00152075728[/C][C]-24.0015207572799[/C][/ROW]
[ROW][C]5[/C][C]39[/C][C]49.0015866676051[/C][C]-10.0015866676051[/C][/ROW]
[ROW][C]6[/C][C]59[/C][C]39.0006611745033[/C][C]19.9993388254967[/C][/ROW]
[ROW][C]7[/C][C]169[/C][C]58.9986779044812[/C][C]110.001322095519[/C][/ROW]
[ROW][C]8[/C][C]169[/C][C]168.992728146852[/C][C]0.00727185314843837[/C][/ROW]
[ROW][C]9[/C][C]210[/C][C]168.99999951928[/C][C]41.0000004807201[/C][/ROW]
[ROW][C]10[/C][C]278[/C][C]209.997289614553[/C][C]68.0027103854472[/C][/ROW]
[ROW][C]11[/C][C]298[/C][C]277.995504547453[/C][C]20.0044954525473[/C][/ROW]
[ROW][C]12[/C][C]245[/C][C]297.998677563592[/C][C]-52.9986775635923[/C][/ROW]
[ROW][C]13[/C][C]200[/C][C]245.003503581529[/C][C]-45.0035035815294[/C][/ROW]
[ROW][C]14[/C][C]188[/C][C]200.002975044872[/C][C]-12.002975044872[/C][/ROW]
[ROW][C]15[/C][C]90[/C][C]188.000793480207[/C][C]-98.0007934802074[/C][/ROW]
[ROW][C]16[/C][C]79[/C][C]90.006478534667[/C][C]-11.0064785346671[/C][/ROW]
[ROW][C]17[/C][C]78[/C][C]79.0007276048511[/C][C]-1.00072760485111[/C][/ROW]
[ROW][C]18[/C][C]91[/C][C]78.0000661550611[/C][C]12.9999338449389[/C][/ROW]
[ROW][C]19[/C][C]167[/C][C]90.9991406138757[/C][C]76.0008593861243[/C][/ROW]
[ROW][C]20[/C][C]169[/C][C]166.994975814126[/C][C]2.00502418587416[/C][/ROW]
[ROW][C]21[/C][C]289[/C][C]168.999867453944[/C][C]120.000132546056[/C][/ROW]
[ROW][C]22[/C][C]247[/C][C]288.992067155876[/C][C]-41.9920671558755[/C][/ROW]
[ROW][C]23[/C][C]275[/C][C]247.002775967961[/C][C]27.9972240320394[/C][/ROW]
[ROW][C]24[/C][C]203[/C][C]274.998149188593[/C][C]-71.9981491885929[/C][/ROW]
[ROW][C]25[/C][C]223[/C][C]203.004759578866[/C][C]19.9952404211342[/C][/ROW]
[ROW][C]26[/C][C]104[/C][C]222.998678175414[/C][C]-118.998678175414[/C][/ROW]
[ROW][C]27[/C][C]107[/C][C]104.007866641019[/C][C]2.99213335898092[/C][/ROW]
[ROW][C]28[/C][C]85[/C][C]106.999802199156[/C][C]-21.9998021991557[/C][/ROW]
[ROW][C]29[/C][C]75[/C][C]85.0014543400737[/C][C]-10.0014543400737[/C][/ROW]
[ROW][C]30[/C][C]99[/C][C]75.0006611657555[/C][C]23.9993388342445[/C][/ROW]
[ROW][C]31[/C][C]135[/C][C]98.9984134766352[/C][C]36.0015865233648[/C][/ROW]
[ROW][C]32[/C][C]211[/C][C]134.997620044511[/C][C]76.0023799554889[/C][/ROW]
[ROW][C]33[/C][C]335[/C][C]210.994975713606[/C][C]124.005024286394[/C][/ROW]
[ROW][C]34[/C][C]488[/C][C]334.991802404652[/C][C]153.008197595348[/C][/ROW]
[ROW][C]35[/C][C]326[/C][C]487.989885092995[/C][C]-161.989885092995[/C][/ROW]
[ROW][C]36[/C][C]346[/C][C]326.010708659073[/C][C]19.9892913409267[/C][/ROW]
[ROW][C]37[/C][C]261[/C][C]345.99867856869[/C][C]-84.9986785686899[/C][/ROW]
[ROW][C]38[/C][C]224[/C][C]261.005619004359[/C][C]-37.0056190043591[/C][/ROW]
[ROW][C]39[/C][C]141[/C][C]224.002446329025[/C][C]-83.0024463290253[/C][/ROW]
[ROW][C]40[/C][C]148[/C][C]141.005487039512[/C][C]6.9945129604884[/C][/ROW]
[ROW][C]41[/C][C]145[/C][C]147.999537614002[/C][C]-2.99953761400207[/C][/ROW]
[ROW][C]42[/C][C]223[/C][C]145.000198290317[/C][C]77.9998017096829[/C][/ROW]
[ROW][C]43[/C][C]272[/C][C]222.994843670123[/C][C]49.0051563298771[/C][/ROW]
[ROW][C]44[/C][C]445[/C][C]271.996760418024[/C][C]173.003239581976[/C][/ROW]
[ROW][C]45[/C][C]560[/C][C]444.988563281527[/C][C]115.011436718473[/C][/ROW]
[ROW][C]46[/C][C]612[/C][C]559.992396943398[/C][C]52.0076030566021[/C][/ROW]
[ROW][C]47[/C][C]467[/C][C]611.996561935395[/C][C]-144.996561935395[/C][/ROW]
[ROW][C]48[/C][C]404[/C][C]467.009585282116[/C][C]-63.009585282116[/C][/ROW]
[ROW][C]49[/C][C]518[/C][C]404.004165372219[/C][C]113.995834627781[/C][/ROW]
[ROW][C]50[/C][C]404[/C][C]517.992464081766[/C][C]-113.992464081766[/C][/ROW]
[ROW][C]51[/C][C]300[/C][C]404.007535695417[/C][C]-104.007535695417[/C][/ROW]
[ROW][C]52[/C][C]210[/C][C]300.006875622143[/C][C]-90.0068756221425[/C][/ROW]
[ROW][C]53[/C][C]196[/C][C]210.005950081048[/C][C]-14.0059500810482[/C][/ROW]
[ROW][C]54[/C][C]186[/C][C]196.000925890801[/C][C]-10.0009258908007[/C][/ROW]
[ROW][C]55[/C][C]247[/C][C]186.000661130821[/C][C]60.9993388691786[/C][/ROW]
[ROW][C]56[/C][C]343[/C][C]246.995967519063[/C][C]96.0040324809371[/C][/ROW]
[ROW][C]57[/C][C]464[/C][C]342.993653465135[/C][C]121.006346534865[/C][/ROW]
[ROW][C]58[/C][C]680[/C][C]463.992000638126[/C][C]216.007999361874[/C][/ROW]
[ROW][C]59[/C][C]711[/C][C]679.985720367535[/C][C]31.0142796324654[/C][/ROW]
[ROW][C]60[/C][C]610[/C][C]710.997949740215[/C][C]-100.997949740215[/C][/ROW]
[ROW][C]61[/C][C]513[/C][C]610.00667666756[/C][C]-97.0066766675601[/C][/ROW]
[ROW][C]62[/C][C]292[/C][C]513.006412816625[/C][C]-221.006412816625[/C][/ROW]
[ROW][C]63[/C][C]273[/C][C]292.014610062391[/C][C]-19.0146100623905[/C][/ROW]
[ROW][C]64[/C][C]322[/C][C]273.001256998093[/C][C]48.9987430019075[/C][/ROW]
[ROW][C]65[/C][C]189[/C][C]321.99676084199[/C][C]-132.99676084199[/C][/ROW]
[ROW][C]66[/C][C]257[/C][C]189.008792011729[/C][C]67.9912079882711[/C][/ROW]
[ROW][C]67[/C][C]324[/C][C]256.995505307841[/C][C]67.0044946921587[/C][/ROW]
[ROW][C]68[/C][C]404[/C][C]323.995570536459[/C][C]80.004429463541[/C][/ROW]
[ROW][C]69[/C][C]677[/C][C]403.994711150273[/C][C]273.005288849727[/C][/ROW]
[ROW][C]70[/C][C]858[/C][C]676.981952449921[/C][C]181.018047550079[/C][/ROW]
[ROW][C]71[/C][C]895[/C][C]857.988033446927[/C][C]37.0119665530734[/C][/ROW]
[ROW][C]72[/C][C]664[/C][C]894.997553251358[/C][C]-230.997553251358[/C][/ROW]
[ROW][C]73[/C][C]628[/C][C]664.015270546325[/C][C]-36.0152705463252[/C][/ROW]
[ROW][C]74[/C][C]308[/C][C]628.002380860098[/C][C]-320.002380860098[/C][/ROW]
[ROW][C]75[/C][C]324[/C][C]308.021154385024[/C][C]15.9788456149760[/C][/ROW]
[ROW][C]76[/C][C]248[/C][C]323.998943687070[/C][C]-75.9989436870705[/C][/ROW]
[ROW][C]77[/C][C]272[/C][C]248.005024059233[/C][C]23.9949759407669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76785&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76785&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
296164-68
37396.004495273372-23.0044952733719
44973.00152075728-24.0015207572799
53949.0015866676051-10.0015866676051
65939.000661174503319.9993388254967
716958.9986779044812110.001322095519
8169168.9927281468520.00727185314843837
9210168.9999995192841.0000004807201
10278209.99728961455368.0027103854472
11298277.99550454745320.0044954525473
12245297.998677563592-52.9986775635923
13200245.003503581529-45.0035035815294
14188200.002975044872-12.002975044872
1590188.000793480207-98.0007934802074
167990.006478534667-11.0064785346671
177879.0007276048511-1.00072760485111
189178.000066155061112.9999338449389
1916790.999140613875776.0008593861243
20169166.9949758141262.00502418587416
21289168.999867453944120.000132546056
22247288.992067155876-41.9920671558755
23275247.00277596796127.9972240320394
24203274.998149188593-71.9981491885929
25223203.00475957886619.9952404211342
26104222.998678175414-118.998678175414
27107104.0078666410192.99213335898092
2885106.999802199156-21.9998021991557
297585.0014543400737-10.0014543400737
309975.000661165755523.9993388342445
3113598.998413476635236.0015865233648
32211134.99762004451176.0023799554889
33335210.994975713606124.005024286394
34488334.991802404652153.008197595348
35326487.989885092995-161.989885092995
36346326.01070865907319.9892913409267
37261345.99867856869-84.9986785686899
38224261.005619004359-37.0056190043591
39141224.002446329025-83.0024463290253
40148141.0054870395126.9945129604884
41145147.999537614002-2.99953761400207
42223145.00019829031777.9998017096829
43272222.99484367012349.0051563298771
44445271.996760418024173.003239581976
45560444.988563281527115.011436718473
46612559.99239694339852.0076030566021
47467611.996561935395-144.996561935395
48404467.009585282116-63.009585282116
49518404.004165372219113.995834627781
50404517.992464081766-113.992464081766
51300404.007535695417-104.007535695417
52210300.006875622143-90.0068756221425
53196210.005950081048-14.0059500810482
54186196.000925890801-10.0009258908007
55247186.00066113082160.9993388691786
56343246.99596751906396.0040324809371
57464342.993653465135121.006346534865
58680463.992000638126216.007999361874
59711679.98572036753531.0142796324654
60610710.997949740215-100.997949740215
61513610.00667666756-97.0066766675601
62292513.006412816625-221.006412816625
63273292.014610062391-19.0146100623905
64322273.00125699809348.9987430019075
65189321.99676084199-132.99676084199
66257189.00879201172967.9912079882711
67324256.99550530784167.0044946921587
68404323.99557053645980.004429463541
69677403.994711150273273.005288849727
70858676.981952449921181.018047550079
71895857.98803344692737.0119665530734
72664894.997553251358-230.997553251358
73628664.015270546325-36.0152705463252
74308628.002380860098-320.002380860098
75324308.02115438502415.9788456149760
76248323.998943687070-75.9989436870705
77272248.00502405923323.9949759407669







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
78271.99841376505376.271369101634467.725458428472
79271.998413765053-4.79227827417157548.789105804277
80271.998413765053-66.9958315938169610.992659123923
81271.998413765053-119.436267341906663.433094872011
82271.998413765053-165.637417446450709.634244976556
83271.998413765053-207.406563208549751.403390738655
84271.998413765053-245.817328689671789.814156219777
85271.998413765053-281.569246345989825.566073876094
86271.998413765053-315.148216564791859.145044094897
87271.998413765053-346.908022374181890.904849904286
88271.998413765053-377.115742513674921.11257004378
89271.998413765053-405.978871303054949.97569883316

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
78 & 271.998413765053 & 76.271369101634 & 467.725458428472 \tabularnewline
79 & 271.998413765053 & -4.79227827417157 & 548.789105804277 \tabularnewline
80 & 271.998413765053 & -66.9958315938169 & 610.992659123923 \tabularnewline
81 & 271.998413765053 & -119.436267341906 & 663.433094872011 \tabularnewline
82 & 271.998413765053 & -165.637417446450 & 709.634244976556 \tabularnewline
83 & 271.998413765053 & -207.406563208549 & 751.403390738655 \tabularnewline
84 & 271.998413765053 & -245.817328689671 & 789.814156219777 \tabularnewline
85 & 271.998413765053 & -281.569246345989 & 825.566073876094 \tabularnewline
86 & 271.998413765053 & -315.148216564791 & 859.145044094897 \tabularnewline
87 & 271.998413765053 & -346.908022374181 & 890.904849904286 \tabularnewline
88 & 271.998413765053 & -377.115742513674 & 921.11257004378 \tabularnewline
89 & 271.998413765053 & -405.978871303054 & 949.97569883316 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76785&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]78[/C][C]271.998413765053[/C][C]76.271369101634[/C][C]467.725458428472[/C][/ROW]
[ROW][C]79[/C][C]271.998413765053[/C][C]-4.79227827417157[/C][C]548.789105804277[/C][/ROW]
[ROW][C]80[/C][C]271.998413765053[/C][C]-66.9958315938169[/C][C]610.992659123923[/C][/ROW]
[ROW][C]81[/C][C]271.998413765053[/C][C]-119.436267341906[/C][C]663.433094872011[/C][/ROW]
[ROW][C]82[/C][C]271.998413765053[/C][C]-165.637417446450[/C][C]709.634244976556[/C][/ROW]
[ROW][C]83[/C][C]271.998413765053[/C][C]-207.406563208549[/C][C]751.403390738655[/C][/ROW]
[ROW][C]84[/C][C]271.998413765053[/C][C]-245.817328689671[/C][C]789.814156219777[/C][/ROW]
[ROW][C]85[/C][C]271.998413765053[/C][C]-281.569246345989[/C][C]825.566073876094[/C][/ROW]
[ROW][C]86[/C][C]271.998413765053[/C][C]-315.148216564791[/C][C]859.145044094897[/C][/ROW]
[ROW][C]87[/C][C]271.998413765053[/C][C]-346.908022374181[/C][C]890.904849904286[/C][/ROW]
[ROW][C]88[/C][C]271.998413765053[/C][C]-377.115742513674[/C][C]921.11257004378[/C][/ROW]
[ROW][C]89[/C][C]271.998413765053[/C][C]-405.978871303054[/C][C]949.97569883316[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76785&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76785&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
78271.99841376505376.271369101634467.725458428472
79271.998413765053-4.79227827417157548.789105804277
80271.998413765053-66.9958315938169610.992659123923
81271.998413765053-119.436267341906663.433094872011
82271.998413765053-165.637417446450709.634244976556
83271.998413765053-207.406563208549751.403390738655
84271.998413765053-245.817328689671789.814156219777
85271.998413765053-281.569246345989825.566073876094
86271.998413765053-315.148216564791859.145044094897
87271.998413765053-346.908022374181890.904849904286
88271.998413765053-377.115742513674921.11257004378
89271.998413765053-405.978871303054949.97569883316



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