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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 11:46:39 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t1243964910yjzeacjoq5mez1s.htm/, Retrieved Thu, 09 May 2024 23:02:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41342, Retrieved Thu, 09 May 2024 23:02:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2009-06-02 17:46:39] [46186faee359a0c92d914c5fc942bc84] [Current]
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Dataseries X:
666.27
664.45
660.76
660.40
660.69
660.69
662.23
661.41
659.02
655.43
652.59
652.59
648.20
645.84
644.67
642.71
640.14
640.14
639.64
630.28
614.57
614.70
615.08
615.08
614.43
604.55
598.98
594.05
593.05
593.05
593.34
584.72
580.70
577.08
569.92
569.92
568.86
559.38
548.22
545.61
545.33
530.30
527.76
521.41
1601.93
1577.49
1551.43
1551.43
1516.88
1485.95
1438.22
1385.06
1329.49
1329.49
1276.16
1242.34
1181.59
1160.21
1135.18
1135.18
1084.96
1077.35
1061.13
1029.98
1013.08
1013.08
996.04
975.02
951.89
944.40
932.47
932.47
920.44
900.18
886.90




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41342&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41342&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41342&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.987057390298826
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.987057390298826 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41342&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]0.987057390298826[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41342&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41342&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
alpha0.987057390298826
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2664.45666.27-1.81999999999994
3660.76664.473555549656-3.71355554965623
4660.4660.808063100083-0.408063100082813
5660.69660.4052814014380.284718598562222
6660.69660.6863149983040.00368500169588515
7662.23660.6899523064611.54004769353867
8661.41662.210067763781-0.800067763781385
9659.02661.420354964801-2.40035496480107
10655.43659.051066857454-3.62106685745368
11652.59655.476866055038-2.88686605503779
12652.59652.62736358061-0.0373635806099628
13648.2652.590483582241-4.3904835822409
14645.84648.256824315404-2.41682431540437
15644.67645.87128001383-1.20128001383068
16642.71644.685547698361-1.97554769836074
17640.14642.735568742806-2.59556874280599
18640.14640.173593433191-0.0335934331907310
19639.64640.140434786694-0.500434786694314
20630.28639.646476932125-9.36647693212512
21614.57630.401226655208-15.8312266552075
22614.7614.774897387689-0.0748973876891341
23615.08614.7009693676570.379030632343529
24615.08615.0750943544610.00490564553922468
25614.43615.079936508144-0.649936508144492
26604.55614.438411874555-9.88841187455546
27598.98604.677981855457-5.69798185545676
28594.05599.05374675524-5.0037467552396
29593.05594.114761541297-1.06476154129655
30593.05593.063780793054-0.0137807930537974
31593.34593.0501783594260.289821640574246
32584.72593.336248951623-8.6162489516231
33580.7584.831516747269-4.13151674726896
34577.08580.753472608734-3.67347260873373
35569.92577.127544322223-7.20754432222293
36569.92570.013284433066-0.0932844330664011
37568.86569.921207344008-1.06120734400827
38559.38568.873734792465-9.49373479246549
39548.22559.502873704025-11.2828737040253
40545.61548.366029830659-2.75602983065880
41545.33545.645670218423-0.315670218422952
42530.3545.334085596431-15.0340855964314
43527.76530.494580302089-2.7345803020886
44521.41527.795392605546-6.38539260554649
451601.93521.4926436442821080.43735635572
461577.491587.94632099012-10.4563209901194
471551.431577.62533208149-26.1953320814853
481551.431551.76903595912-0.339035959123294
491516.881551.43438801009-34.5543880100936
501485.951517.32722395748-31.3772239574776
511438.221486.35610316319-48.136103163188
521385.061438.84300679578-53.7830067957766
531329.491385.75609246551-56.2660924655133
541329.491330.21823007419-0.728230074191288
551276.161329.49942519762-53.3394251976229
561242.341276.85035136202-34.5103513620179
571181.591242.78665400833-61.196654008329
581160.211182.38204440785-22.1720444078476
591135.181160.49696411705-25.3169641170477
601135.181135.50766758539-0.327667585385598
611084.961135.18424087367-50.2242408736695
621077.351085.61003274717-8.26003274716572
631061.131077.45690637997-16.3269063799653
641029.981061.34131277690-31.3613127769036
651013.081030.38589723099-17.3058972309879
661013.081013.30398347339-0.223983473389353
67996.041013.08289893068-17.0428989306756
68975.02996.260579589036-21.2405795890363
69951.89975.294908531448-23.4049085314476
70944.4952.192920596214-7.79292059621423
71932.47944.50086072971-12.0308607297090
72932.47932.625710734794-0.155710734793843
73920.44932.472015303267-12.0320153032667
74900.18920.595725677989-20.4157256779888
75886.9900.444232769216-13.5442327692165

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 664.45 & 666.27 & -1.81999999999994 \tabularnewline
3 & 660.76 & 664.473555549656 & -3.71355554965623 \tabularnewline
4 & 660.4 & 660.808063100083 & -0.408063100082813 \tabularnewline
5 & 660.69 & 660.405281401438 & 0.284718598562222 \tabularnewline
6 & 660.69 & 660.686314998304 & 0.00368500169588515 \tabularnewline
7 & 662.23 & 660.689952306461 & 1.54004769353867 \tabularnewline
8 & 661.41 & 662.210067763781 & -0.800067763781385 \tabularnewline
9 & 659.02 & 661.420354964801 & -2.40035496480107 \tabularnewline
10 & 655.43 & 659.051066857454 & -3.62106685745368 \tabularnewline
11 & 652.59 & 655.476866055038 & -2.88686605503779 \tabularnewline
12 & 652.59 & 652.62736358061 & -0.0373635806099628 \tabularnewline
13 & 648.2 & 652.590483582241 & -4.3904835822409 \tabularnewline
14 & 645.84 & 648.256824315404 & -2.41682431540437 \tabularnewline
15 & 644.67 & 645.87128001383 & -1.20128001383068 \tabularnewline
16 & 642.71 & 644.685547698361 & -1.97554769836074 \tabularnewline
17 & 640.14 & 642.735568742806 & -2.59556874280599 \tabularnewline
18 & 640.14 & 640.173593433191 & -0.0335934331907310 \tabularnewline
19 & 639.64 & 640.140434786694 & -0.500434786694314 \tabularnewline
20 & 630.28 & 639.646476932125 & -9.36647693212512 \tabularnewline
21 & 614.57 & 630.401226655208 & -15.8312266552075 \tabularnewline
22 & 614.7 & 614.774897387689 & -0.0748973876891341 \tabularnewline
23 & 615.08 & 614.700969367657 & 0.379030632343529 \tabularnewline
24 & 615.08 & 615.075094354461 & 0.00490564553922468 \tabularnewline
25 & 614.43 & 615.079936508144 & -0.649936508144492 \tabularnewline
26 & 604.55 & 614.438411874555 & -9.88841187455546 \tabularnewline
27 & 598.98 & 604.677981855457 & -5.69798185545676 \tabularnewline
28 & 594.05 & 599.05374675524 & -5.0037467552396 \tabularnewline
29 & 593.05 & 594.114761541297 & -1.06476154129655 \tabularnewline
30 & 593.05 & 593.063780793054 & -0.0137807930537974 \tabularnewline
31 & 593.34 & 593.050178359426 & 0.289821640574246 \tabularnewline
32 & 584.72 & 593.336248951623 & -8.6162489516231 \tabularnewline
33 & 580.7 & 584.831516747269 & -4.13151674726896 \tabularnewline
34 & 577.08 & 580.753472608734 & -3.67347260873373 \tabularnewline
35 & 569.92 & 577.127544322223 & -7.20754432222293 \tabularnewline
36 & 569.92 & 570.013284433066 & -0.0932844330664011 \tabularnewline
37 & 568.86 & 569.921207344008 & -1.06120734400827 \tabularnewline
38 & 559.38 & 568.873734792465 & -9.49373479246549 \tabularnewline
39 & 548.22 & 559.502873704025 & -11.2828737040253 \tabularnewline
40 & 545.61 & 548.366029830659 & -2.75602983065880 \tabularnewline
41 & 545.33 & 545.645670218423 & -0.315670218422952 \tabularnewline
42 & 530.3 & 545.334085596431 & -15.0340855964314 \tabularnewline
43 & 527.76 & 530.494580302089 & -2.7345803020886 \tabularnewline
44 & 521.41 & 527.795392605546 & -6.38539260554649 \tabularnewline
45 & 1601.93 & 521.492643644282 & 1080.43735635572 \tabularnewline
46 & 1577.49 & 1587.94632099012 & -10.4563209901194 \tabularnewline
47 & 1551.43 & 1577.62533208149 & -26.1953320814853 \tabularnewline
48 & 1551.43 & 1551.76903595912 & -0.339035959123294 \tabularnewline
49 & 1516.88 & 1551.43438801009 & -34.5543880100936 \tabularnewline
50 & 1485.95 & 1517.32722395748 & -31.3772239574776 \tabularnewline
51 & 1438.22 & 1486.35610316319 & -48.136103163188 \tabularnewline
52 & 1385.06 & 1438.84300679578 & -53.7830067957766 \tabularnewline
53 & 1329.49 & 1385.75609246551 & -56.2660924655133 \tabularnewline
54 & 1329.49 & 1330.21823007419 & -0.728230074191288 \tabularnewline
55 & 1276.16 & 1329.49942519762 & -53.3394251976229 \tabularnewline
56 & 1242.34 & 1276.85035136202 & -34.5103513620179 \tabularnewline
57 & 1181.59 & 1242.78665400833 & -61.196654008329 \tabularnewline
58 & 1160.21 & 1182.38204440785 & -22.1720444078476 \tabularnewline
59 & 1135.18 & 1160.49696411705 & -25.3169641170477 \tabularnewline
60 & 1135.18 & 1135.50766758539 & -0.327667585385598 \tabularnewline
61 & 1084.96 & 1135.18424087367 & -50.2242408736695 \tabularnewline
62 & 1077.35 & 1085.61003274717 & -8.26003274716572 \tabularnewline
63 & 1061.13 & 1077.45690637997 & -16.3269063799653 \tabularnewline
64 & 1029.98 & 1061.34131277690 & -31.3613127769036 \tabularnewline
65 & 1013.08 & 1030.38589723099 & -17.3058972309879 \tabularnewline
66 & 1013.08 & 1013.30398347339 & -0.223983473389353 \tabularnewline
67 & 996.04 & 1013.08289893068 & -17.0428989306756 \tabularnewline
68 & 975.02 & 996.260579589036 & -21.2405795890363 \tabularnewline
69 & 951.89 & 975.294908531448 & -23.4049085314476 \tabularnewline
70 & 944.4 & 952.192920596214 & -7.79292059621423 \tabularnewline
71 & 932.47 & 944.50086072971 & -12.0308607297090 \tabularnewline
72 & 932.47 & 932.625710734794 & -0.155710734793843 \tabularnewline
73 & 920.44 & 932.472015303267 & -12.0320153032667 \tabularnewline
74 & 900.18 & 920.595725677989 & -20.4157256779888 \tabularnewline
75 & 886.9 & 900.444232769216 & -13.5442327692165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41342&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]664.45[/C][C]666.27[/C][C]-1.81999999999994[/C][/ROW]
[ROW][C]3[/C][C]660.76[/C][C]664.473555549656[/C][C]-3.71355554965623[/C][/ROW]
[ROW][C]4[/C][C]660.4[/C][C]660.808063100083[/C][C]-0.408063100082813[/C][/ROW]
[ROW][C]5[/C][C]660.69[/C][C]660.405281401438[/C][C]0.284718598562222[/C][/ROW]
[ROW][C]6[/C][C]660.69[/C][C]660.686314998304[/C][C]0.00368500169588515[/C][/ROW]
[ROW][C]7[/C][C]662.23[/C][C]660.689952306461[/C][C]1.54004769353867[/C][/ROW]
[ROW][C]8[/C][C]661.41[/C][C]662.210067763781[/C][C]-0.800067763781385[/C][/ROW]
[ROW][C]9[/C][C]659.02[/C][C]661.420354964801[/C][C]-2.40035496480107[/C][/ROW]
[ROW][C]10[/C][C]655.43[/C][C]659.051066857454[/C][C]-3.62106685745368[/C][/ROW]
[ROW][C]11[/C][C]652.59[/C][C]655.476866055038[/C][C]-2.88686605503779[/C][/ROW]
[ROW][C]12[/C][C]652.59[/C][C]652.62736358061[/C][C]-0.0373635806099628[/C][/ROW]
[ROW][C]13[/C][C]648.2[/C][C]652.590483582241[/C][C]-4.3904835822409[/C][/ROW]
[ROW][C]14[/C][C]645.84[/C][C]648.256824315404[/C][C]-2.41682431540437[/C][/ROW]
[ROW][C]15[/C][C]644.67[/C][C]645.87128001383[/C][C]-1.20128001383068[/C][/ROW]
[ROW][C]16[/C][C]642.71[/C][C]644.685547698361[/C][C]-1.97554769836074[/C][/ROW]
[ROW][C]17[/C][C]640.14[/C][C]642.735568742806[/C][C]-2.59556874280599[/C][/ROW]
[ROW][C]18[/C][C]640.14[/C][C]640.173593433191[/C][C]-0.0335934331907310[/C][/ROW]
[ROW][C]19[/C][C]639.64[/C][C]640.140434786694[/C][C]-0.500434786694314[/C][/ROW]
[ROW][C]20[/C][C]630.28[/C][C]639.646476932125[/C][C]-9.36647693212512[/C][/ROW]
[ROW][C]21[/C][C]614.57[/C][C]630.401226655208[/C][C]-15.8312266552075[/C][/ROW]
[ROW][C]22[/C][C]614.7[/C][C]614.774897387689[/C][C]-0.0748973876891341[/C][/ROW]
[ROW][C]23[/C][C]615.08[/C][C]614.700969367657[/C][C]0.379030632343529[/C][/ROW]
[ROW][C]24[/C][C]615.08[/C][C]615.075094354461[/C][C]0.00490564553922468[/C][/ROW]
[ROW][C]25[/C][C]614.43[/C][C]615.079936508144[/C][C]-0.649936508144492[/C][/ROW]
[ROW][C]26[/C][C]604.55[/C][C]614.438411874555[/C][C]-9.88841187455546[/C][/ROW]
[ROW][C]27[/C][C]598.98[/C][C]604.677981855457[/C][C]-5.69798185545676[/C][/ROW]
[ROW][C]28[/C][C]594.05[/C][C]599.05374675524[/C][C]-5.0037467552396[/C][/ROW]
[ROW][C]29[/C][C]593.05[/C][C]594.114761541297[/C][C]-1.06476154129655[/C][/ROW]
[ROW][C]30[/C][C]593.05[/C][C]593.063780793054[/C][C]-0.0137807930537974[/C][/ROW]
[ROW][C]31[/C][C]593.34[/C][C]593.050178359426[/C][C]0.289821640574246[/C][/ROW]
[ROW][C]32[/C][C]584.72[/C][C]593.336248951623[/C][C]-8.6162489516231[/C][/ROW]
[ROW][C]33[/C][C]580.7[/C][C]584.831516747269[/C][C]-4.13151674726896[/C][/ROW]
[ROW][C]34[/C][C]577.08[/C][C]580.753472608734[/C][C]-3.67347260873373[/C][/ROW]
[ROW][C]35[/C][C]569.92[/C][C]577.127544322223[/C][C]-7.20754432222293[/C][/ROW]
[ROW][C]36[/C][C]569.92[/C][C]570.013284433066[/C][C]-0.0932844330664011[/C][/ROW]
[ROW][C]37[/C][C]568.86[/C][C]569.921207344008[/C][C]-1.06120734400827[/C][/ROW]
[ROW][C]38[/C][C]559.38[/C][C]568.873734792465[/C][C]-9.49373479246549[/C][/ROW]
[ROW][C]39[/C][C]548.22[/C][C]559.502873704025[/C][C]-11.2828737040253[/C][/ROW]
[ROW][C]40[/C][C]545.61[/C][C]548.366029830659[/C][C]-2.75602983065880[/C][/ROW]
[ROW][C]41[/C][C]545.33[/C][C]545.645670218423[/C][C]-0.315670218422952[/C][/ROW]
[ROW][C]42[/C][C]530.3[/C][C]545.334085596431[/C][C]-15.0340855964314[/C][/ROW]
[ROW][C]43[/C][C]527.76[/C][C]530.494580302089[/C][C]-2.7345803020886[/C][/ROW]
[ROW][C]44[/C][C]521.41[/C][C]527.795392605546[/C][C]-6.38539260554649[/C][/ROW]
[ROW][C]45[/C][C]1601.93[/C][C]521.492643644282[/C][C]1080.43735635572[/C][/ROW]
[ROW][C]46[/C][C]1577.49[/C][C]1587.94632099012[/C][C]-10.4563209901194[/C][/ROW]
[ROW][C]47[/C][C]1551.43[/C][C]1577.62533208149[/C][C]-26.1953320814853[/C][/ROW]
[ROW][C]48[/C][C]1551.43[/C][C]1551.76903595912[/C][C]-0.339035959123294[/C][/ROW]
[ROW][C]49[/C][C]1516.88[/C][C]1551.43438801009[/C][C]-34.5543880100936[/C][/ROW]
[ROW][C]50[/C][C]1485.95[/C][C]1517.32722395748[/C][C]-31.3772239574776[/C][/ROW]
[ROW][C]51[/C][C]1438.22[/C][C]1486.35610316319[/C][C]-48.136103163188[/C][/ROW]
[ROW][C]52[/C][C]1385.06[/C][C]1438.84300679578[/C][C]-53.7830067957766[/C][/ROW]
[ROW][C]53[/C][C]1329.49[/C][C]1385.75609246551[/C][C]-56.2660924655133[/C][/ROW]
[ROW][C]54[/C][C]1329.49[/C][C]1330.21823007419[/C][C]-0.728230074191288[/C][/ROW]
[ROW][C]55[/C][C]1276.16[/C][C]1329.49942519762[/C][C]-53.3394251976229[/C][/ROW]
[ROW][C]56[/C][C]1242.34[/C][C]1276.85035136202[/C][C]-34.5103513620179[/C][/ROW]
[ROW][C]57[/C][C]1181.59[/C][C]1242.78665400833[/C][C]-61.196654008329[/C][/ROW]
[ROW][C]58[/C][C]1160.21[/C][C]1182.38204440785[/C][C]-22.1720444078476[/C][/ROW]
[ROW][C]59[/C][C]1135.18[/C][C]1160.49696411705[/C][C]-25.3169641170477[/C][/ROW]
[ROW][C]60[/C][C]1135.18[/C][C]1135.50766758539[/C][C]-0.327667585385598[/C][/ROW]
[ROW][C]61[/C][C]1084.96[/C][C]1135.18424087367[/C][C]-50.2242408736695[/C][/ROW]
[ROW][C]62[/C][C]1077.35[/C][C]1085.61003274717[/C][C]-8.26003274716572[/C][/ROW]
[ROW][C]63[/C][C]1061.13[/C][C]1077.45690637997[/C][C]-16.3269063799653[/C][/ROW]
[ROW][C]64[/C][C]1029.98[/C][C]1061.34131277690[/C][C]-31.3613127769036[/C][/ROW]
[ROW][C]65[/C][C]1013.08[/C][C]1030.38589723099[/C][C]-17.3058972309879[/C][/ROW]
[ROW][C]66[/C][C]1013.08[/C][C]1013.30398347339[/C][C]-0.223983473389353[/C][/ROW]
[ROW][C]67[/C][C]996.04[/C][C]1013.08289893068[/C][C]-17.0428989306756[/C][/ROW]
[ROW][C]68[/C][C]975.02[/C][C]996.260579589036[/C][C]-21.2405795890363[/C][/ROW]
[ROW][C]69[/C][C]951.89[/C][C]975.294908531448[/C][C]-23.4049085314476[/C][/ROW]
[ROW][C]70[/C][C]944.4[/C][C]952.192920596214[/C][C]-7.79292059621423[/C][/ROW]
[ROW][C]71[/C][C]932.47[/C][C]944.50086072971[/C][C]-12.0308607297090[/C][/ROW]
[ROW][C]72[/C][C]932.47[/C][C]932.625710734794[/C][C]-0.155710734793843[/C][/ROW]
[ROW][C]73[/C][C]920.44[/C][C]932.472015303267[/C][C]-12.0320153032667[/C][/ROW]
[ROW][C]74[/C][C]900.18[/C][C]920.595725677989[/C][C]-20.4157256779888[/C][/ROW]
[ROW][C]75[/C][C]886.9[/C][C]900.444232769216[/C][C]-13.5442327692165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41342&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41342&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
2664.45666.27-1.81999999999994
3660.76664.473555549656-3.71355554965623
4660.4660.808063100083-0.408063100082813
5660.69660.4052814014380.284718598562222
6660.69660.6863149983040.00368500169588515
7662.23660.6899523064611.54004769353867
8661.41662.210067763781-0.800067763781385
9659.02661.420354964801-2.40035496480107
10655.43659.051066857454-3.62106685745368
11652.59655.476866055038-2.88686605503779
12652.59652.62736358061-0.0373635806099628
13648.2652.590483582241-4.3904835822409
14645.84648.256824315404-2.41682431540437
15644.67645.87128001383-1.20128001383068
16642.71644.685547698361-1.97554769836074
17640.14642.735568742806-2.59556874280599
18640.14640.173593433191-0.0335934331907310
19639.64640.140434786694-0.500434786694314
20630.28639.646476932125-9.36647693212512
21614.57630.401226655208-15.8312266552075
22614.7614.774897387689-0.0748973876891341
23615.08614.7009693676570.379030632343529
24615.08615.0750943544610.00490564553922468
25614.43615.079936508144-0.649936508144492
26604.55614.438411874555-9.88841187455546
27598.98604.677981855457-5.69798185545676
28594.05599.05374675524-5.0037467552396
29593.05594.114761541297-1.06476154129655
30593.05593.063780793054-0.0137807930537974
31593.34593.0501783594260.289821640574246
32584.72593.336248951623-8.6162489516231
33580.7584.831516747269-4.13151674726896
34577.08580.753472608734-3.67347260873373
35569.92577.127544322223-7.20754432222293
36569.92570.013284433066-0.0932844330664011
37568.86569.921207344008-1.06120734400827
38559.38568.873734792465-9.49373479246549
39548.22559.502873704025-11.2828737040253
40545.61548.366029830659-2.75602983065880
41545.33545.645670218423-0.315670218422952
42530.3545.334085596431-15.0340855964314
43527.76530.494580302089-2.7345803020886
44521.41527.795392605546-6.38539260554649
451601.93521.4926436442821080.43735635572
461577.491587.94632099012-10.4563209901194
471551.431577.62533208149-26.1953320814853
481551.431551.76903595912-0.339035959123294
491516.881551.43438801009-34.5543880100936
501485.951517.32722395748-31.3772239574776
511438.221486.35610316319-48.136103163188
521385.061438.84300679578-53.7830067957766
531329.491385.75609246551-56.2660924655133
541329.491330.21823007419-0.728230074191288
551276.161329.49942519762-53.3394251976229
561242.341276.85035136202-34.5103513620179
571181.591242.78665400833-61.196654008329
581160.211182.38204440785-22.1720444078476
591135.181160.49696411705-25.3169641170477
601135.181135.50766758539-0.327667585385598
611084.961135.18424087367-50.2242408736695
621077.351085.61003274717-8.26003274716572
631061.131077.45690637997-16.3269063799653
641029.981061.34131277690-31.3613127769036
651013.081030.38589723099-17.3058972309879
661013.081013.30398347339-0.223983473389353
67996.041013.08289893068-17.0428989306756
68975.02996.260579589036-21.2405795890363
69951.89975.294908531448-23.4049085314476
70944.4952.192920596214-7.79292059621423
71932.47944.50086072971-12.0308607297090
72932.47932.625710734794-0.155710734793843
73920.44932.472015303267-12.0320153032667
74900.18920.595725677989-20.4157256779888
75886.9900.444232769216-13.5442327692165







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
76887.075297718434636.3553135845831137.79528185228
77887.075297718434534.7907641100121239.35983132686
78887.075297718434456.554363505791317.59623193108
79887.075297718434390.4948339756961383.65576146117
80887.075297718434332.2455588375971441.90503659927
81887.075297718434279.5558154611141494.59477997575
82887.075297718434231.0845938987631543.06600153810
83887.075297718434185.9564164483231588.19417898854
84887.075297718434143.5623066758591630.58828876101
85887.075297718434103.4583951284621670.69220030841
86887.07529771843465.309313876121708.84128156075
87887.07529771843428.85433877140911745.29625666546

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 887.075297718434 & 636.355313584583 & 1137.79528185228 \tabularnewline
77 & 887.075297718434 & 534.790764110012 & 1239.35983132686 \tabularnewline
78 & 887.075297718434 & 456.55436350579 & 1317.59623193108 \tabularnewline
79 & 887.075297718434 & 390.494833975696 & 1383.65576146117 \tabularnewline
80 & 887.075297718434 & 332.245558837597 & 1441.90503659927 \tabularnewline
81 & 887.075297718434 & 279.555815461114 & 1494.59477997575 \tabularnewline
82 & 887.075297718434 & 231.084593898763 & 1543.06600153810 \tabularnewline
83 & 887.075297718434 & 185.956416448323 & 1588.19417898854 \tabularnewline
84 & 887.075297718434 & 143.562306675859 & 1630.58828876101 \tabularnewline
85 & 887.075297718434 & 103.458395128462 & 1670.69220030841 \tabularnewline
86 & 887.075297718434 & 65.30931387612 & 1708.84128156075 \tabularnewline
87 & 887.075297718434 & 28.8543387714091 & 1745.29625666546 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41342&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]76[/C][C]887.075297718434[/C][C]636.355313584583[/C][C]1137.79528185228[/C][/ROW]
[ROW][C]77[/C][C]887.075297718434[/C][C]534.790764110012[/C][C]1239.35983132686[/C][/ROW]
[ROW][C]78[/C][C]887.075297718434[/C][C]456.55436350579[/C][C]1317.59623193108[/C][/ROW]
[ROW][C]79[/C][C]887.075297718434[/C][C]390.494833975696[/C][C]1383.65576146117[/C][/ROW]
[ROW][C]80[/C][C]887.075297718434[/C][C]332.245558837597[/C][C]1441.90503659927[/C][/ROW]
[ROW][C]81[/C][C]887.075297718434[/C][C]279.555815461114[/C][C]1494.59477997575[/C][/ROW]
[ROW][C]82[/C][C]887.075297718434[/C][C]231.084593898763[/C][C]1543.06600153810[/C][/ROW]
[ROW][C]83[/C][C]887.075297718434[/C][C]185.956416448323[/C][C]1588.19417898854[/C][/ROW]
[ROW][C]84[/C][C]887.075297718434[/C][C]143.562306675859[/C][C]1630.58828876101[/C][/ROW]
[ROW][C]85[/C][C]887.075297718434[/C][C]103.458395128462[/C][C]1670.69220030841[/C][/ROW]
[ROW][C]86[/C][C]887.075297718434[/C][C]65.30931387612[/C][C]1708.84128156075[/C][/ROW]
[ROW][C]87[/C][C]887.075297718434[/C][C]28.8543387714091[/C][C]1745.29625666546[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41342&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41342&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
76887.075297718434636.3553135845831137.79528185228
77887.075297718434534.7907641100121239.35983132686
78887.075297718434456.554363505791317.59623193108
79887.075297718434390.4948339756961383.65576146117
80887.075297718434332.2455588375971441.90503659927
81887.075297718434279.5558154611141494.59477997575
82887.075297718434231.0845938987631543.06600153810
83887.075297718434185.9564164483231588.19417898854
84887.075297718434143.5623066758591630.58828876101
85887.075297718434103.4583951284621670.69220030841
86887.07529771843465.309313876121708.84128156075
87887.07529771843428.85433877140911745.29625666546



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')