Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 06 Jun 2009 06:39:05 -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/06/t124429211466w3822ls9n8omw.htm/, Retrieved Mon, 29 Apr 2024 00:26:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41989, Retrieved Mon, 29 Apr 2024 00:26:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [datareeks-cinemap...] [2009-06-06 12:39:05] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
5.44
5.44
5.44
5.44
5.44
5.49
5.49
5.49
5.49
5.49
5.49
5.60
5.60
5.60
5.60
5.60
5.60
5.60
5.67
5.67
5.67
5.67
5.67
5.67
5.67
5.67
5.67
5.82
5.82
5.95
5.95
5.95
5.95
5.95
5.95
6.02
6.02
6.05
6.05
6.05
6.12
6.12
6.12
6.12
6.12
6.12
6.12
6.12
6.17
6.17
6.17
6.17
6.17
6.28
6.27
6.28
6.28
6.27
6.27
6.28
6.59
6.59
6.59
6.59
6.59
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.79
6.79
6.79
6.81
6.80
6.80
6.85
6.85
6.85
6.85
6.85
6.85
6.86
6.86
6.88
6.88
6.88
6.91
6.91
6.91
6.91
6.99
6.99
6.99
7.02
7.02
7.05
7.05
7.05
7.05
7.10
7.10
7.10
7.10
7.12
7.13
7.18




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41989&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41989&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41989&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 time3 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.800021697608403
beta0
gamma0.938182298582948

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.800021697608403 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.938182298582948 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41989&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]0.800021697608403[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.938182298582948[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41989&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41989&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
alpha0.800021697608403
beta0
gamma0.938182298582948







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135.65.525889950899060.074110049100943
145.65.58369606619930.0163039338007014
155.65.595229004324910.00477099567508521
165.65.597533212707970.00246678729202543
175.65.597996811118680.00200318888132411
185.65.60264896463026-0.00264896463025988
195.675.651245909811360.0187540901886427
205.675.665971579425310.00402842057468789
215.675.668909942539150.00109005746084989
225.675.669496819827310.000503180172692907
235.675.66961458659470.000385413405301627
245.675.78540913247381-0.115409132473809
255.675.70846222126103-0.0384622212610317
265.675.664992211985520.00500778801447943
275.675.665111307835210.00488869216478616
285.825.666887067780910.153112932219088
295.825.787275434307310.0327245656926864
305.955.81520430304810.134795696951902
315.955.98014370904363-0.0301437090436343
325.955.95215353141279-0.00215353141279451
335.955.948889163808950.00111083619105035
345.955.948701916972530.00129808302746781
355.955.948758957180620.00124104281937587
366.026.04710204611742-0.0271020461174167
376.026.05621048990421-0.0362104899042102
386.056.021558553038410.028441446961585
396.056.039252058833790.0107479411662101
406.056.07368537555861-0.0236853755586131
416.126.028464564614470.0915354353855315
426.126.12247130456343-0.0024713045634277
436.126.14699180601871-0.0269918060187146
446.126.12641899140255-0.00641899140254765
456.126.119941262878545.87371214564314e-05
466.126.118534848688240.00146515131176095
476.126.118305240311340.00169475968865918
486.126.21391319226207-0.09391319226207
496.176.168134127050650.00186587294935325
506.176.17587698996837-0.0058769899683675
516.176.162352723437680.00764727656232367
526.176.18794569341074-0.0179456934107405
536.176.168354083342480.00164591665751601
546.286.172724229826170.107275770173833
556.276.28061659094706-0.0106165909470644
566.286.276790274830960.00320972516904305
576.286.27887819945580.00112180054420463
586.276.27820520653592-0.00820520653592283
596.276.269917199747738.28002522705873e-05
606.286.34761656413826-0.0676165641382624
616.596.341795189346480.248204810653516
626.596.544635036268210.0453649637317906
636.596.573322832225380.0166771677746222
646.596.60140796860466-0.0114079686046589
656.596.58969329221360.00030670778639319
666.636.613152671936530.0168473280634744
676.636.625829454993420.00417054500658409
686.636.63607188217895-0.00607188217894716
696.636.629542555041140.000457444958857245
706.636.625655046985840.0043449530141606
716.636.628187358231050.00181264176895457
726.636.6974052631018-0.0674052631018025
736.636.75492951073505-0.124929510735055
746.636.620661053988880.00933894601112062
756.636.614982925944390.0150170740556073
766.636.63644494323795-0.00644494323795097
776.636.63081202185839-0.00081202185839313
786.636.65655126741056-0.0265512674105643
796.636.63211560629388-0.00211560629387808
806.636.63540589045668-0.00540589045668405
816.636.63063226754273-0.00063226754272705
826.636.6266015603580.00339843964199371
836.796.627902859515530.162097140484475
846.796.81305631113353-0.0230563111335300
856.796.89705711743291-0.107057117432912
866.816.801659880980650.00834011901935128
876.86.79555338587720.00444661412279768
886.86.80432465670647-0.00432465670646565
896.856.801112415697420.0488875843025749
906.856.86202239722673-0.0120223972267288
916.856.85338976835674-0.00338976835674210
926.856.85474010811502-0.00474010811502357
936.856.85096214536677-0.000962145366766087
946.856.846886566042980.00311343395702046
956.866.87762543910154-0.0176254391015398
966.866.88432842658235-0.024328426582346
976.886.9520991608042-0.0720991608041954
986.886.9062923434223-0.0262923434223046
996.886.871448986900640.00855101309935957
1006.916.881743284357440.0282567156425646
1016.916.91447689719075-0.00447689719075051
1026.916.92123518754496-0.011235187544961
1036.916.9147531730619-0.00475317306189993
1046.996.914673138620540.0753268613794598
1056.996.975427607215910.0145723927840855
1066.996.984225433586310.00577456641369167
1077.027.013417121557860.00658287844214289
1087.027.03835766823982-0.0183576682398172
1097.057.10336775614203-0.0533677561420314
1107.057.08130525442563-0.0313052544256349
1117.057.048455030233650.00154496976635166
1127.057.05666647299218-0.00666647299217793
1137.17.055123883742820.0448761162571767
1147.17.099979114730982.0885269019999e-05
1157.17.10344992850955-0.00344992850954551
1167.17.11945656199515-0.0194565619951472
1177.127.092579148996690.0274208510033080
1187.137.109685118235110.0203148817648904
1197.187.150879957375460.0291200426245446

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5.6 & 5.52588995089906 & 0.074110049100943 \tabularnewline
14 & 5.6 & 5.5836960661993 & 0.0163039338007014 \tabularnewline
15 & 5.6 & 5.59522900432491 & 0.00477099567508521 \tabularnewline
16 & 5.6 & 5.59753321270797 & 0.00246678729202543 \tabularnewline
17 & 5.6 & 5.59799681111868 & 0.00200318888132411 \tabularnewline
18 & 5.6 & 5.60264896463026 & -0.00264896463025988 \tabularnewline
19 & 5.67 & 5.65124590981136 & 0.0187540901886427 \tabularnewline
20 & 5.67 & 5.66597157942531 & 0.00402842057468789 \tabularnewline
21 & 5.67 & 5.66890994253915 & 0.00109005746084989 \tabularnewline
22 & 5.67 & 5.66949681982731 & 0.000503180172692907 \tabularnewline
23 & 5.67 & 5.6696145865947 & 0.000385413405301627 \tabularnewline
24 & 5.67 & 5.78540913247381 & -0.115409132473809 \tabularnewline
25 & 5.67 & 5.70846222126103 & -0.0384622212610317 \tabularnewline
26 & 5.67 & 5.66499221198552 & 0.00500778801447943 \tabularnewline
27 & 5.67 & 5.66511130783521 & 0.00488869216478616 \tabularnewline
28 & 5.82 & 5.66688706778091 & 0.153112932219088 \tabularnewline
29 & 5.82 & 5.78727543430731 & 0.0327245656926864 \tabularnewline
30 & 5.95 & 5.8152043030481 & 0.134795696951902 \tabularnewline
31 & 5.95 & 5.98014370904363 & -0.0301437090436343 \tabularnewline
32 & 5.95 & 5.95215353141279 & -0.00215353141279451 \tabularnewline
33 & 5.95 & 5.94888916380895 & 0.00111083619105035 \tabularnewline
34 & 5.95 & 5.94870191697253 & 0.00129808302746781 \tabularnewline
35 & 5.95 & 5.94875895718062 & 0.00124104281937587 \tabularnewline
36 & 6.02 & 6.04710204611742 & -0.0271020461174167 \tabularnewline
37 & 6.02 & 6.05621048990421 & -0.0362104899042102 \tabularnewline
38 & 6.05 & 6.02155855303841 & 0.028441446961585 \tabularnewline
39 & 6.05 & 6.03925205883379 & 0.0107479411662101 \tabularnewline
40 & 6.05 & 6.07368537555861 & -0.0236853755586131 \tabularnewline
41 & 6.12 & 6.02846456461447 & 0.0915354353855315 \tabularnewline
42 & 6.12 & 6.12247130456343 & -0.0024713045634277 \tabularnewline
43 & 6.12 & 6.14699180601871 & -0.0269918060187146 \tabularnewline
44 & 6.12 & 6.12641899140255 & -0.00641899140254765 \tabularnewline
45 & 6.12 & 6.11994126287854 & 5.87371214564314e-05 \tabularnewline
46 & 6.12 & 6.11853484868824 & 0.00146515131176095 \tabularnewline
47 & 6.12 & 6.11830524031134 & 0.00169475968865918 \tabularnewline
48 & 6.12 & 6.21391319226207 & -0.09391319226207 \tabularnewline
49 & 6.17 & 6.16813412705065 & 0.00186587294935325 \tabularnewline
50 & 6.17 & 6.17587698996837 & -0.0058769899683675 \tabularnewline
51 & 6.17 & 6.16235272343768 & 0.00764727656232367 \tabularnewline
52 & 6.17 & 6.18794569341074 & -0.0179456934107405 \tabularnewline
53 & 6.17 & 6.16835408334248 & 0.00164591665751601 \tabularnewline
54 & 6.28 & 6.17272422982617 & 0.107275770173833 \tabularnewline
55 & 6.27 & 6.28061659094706 & -0.0106165909470644 \tabularnewline
56 & 6.28 & 6.27679027483096 & 0.00320972516904305 \tabularnewline
57 & 6.28 & 6.2788781994558 & 0.00112180054420463 \tabularnewline
58 & 6.27 & 6.27820520653592 & -0.00820520653592283 \tabularnewline
59 & 6.27 & 6.26991719974773 & 8.28002522705873e-05 \tabularnewline
60 & 6.28 & 6.34761656413826 & -0.0676165641382624 \tabularnewline
61 & 6.59 & 6.34179518934648 & 0.248204810653516 \tabularnewline
62 & 6.59 & 6.54463503626821 & 0.0453649637317906 \tabularnewline
63 & 6.59 & 6.57332283222538 & 0.0166771677746222 \tabularnewline
64 & 6.59 & 6.60140796860466 & -0.0114079686046589 \tabularnewline
65 & 6.59 & 6.5896932922136 & 0.00030670778639319 \tabularnewline
66 & 6.63 & 6.61315267193653 & 0.0168473280634744 \tabularnewline
67 & 6.63 & 6.62582945499342 & 0.00417054500658409 \tabularnewline
68 & 6.63 & 6.63607188217895 & -0.00607188217894716 \tabularnewline
69 & 6.63 & 6.62954255504114 & 0.000457444958857245 \tabularnewline
70 & 6.63 & 6.62565504698584 & 0.0043449530141606 \tabularnewline
71 & 6.63 & 6.62818735823105 & 0.00181264176895457 \tabularnewline
72 & 6.63 & 6.6974052631018 & -0.0674052631018025 \tabularnewline
73 & 6.63 & 6.75492951073505 & -0.124929510735055 \tabularnewline
74 & 6.63 & 6.62066105398888 & 0.00933894601112062 \tabularnewline
75 & 6.63 & 6.61498292594439 & 0.0150170740556073 \tabularnewline
76 & 6.63 & 6.63644494323795 & -0.00644494323795097 \tabularnewline
77 & 6.63 & 6.63081202185839 & -0.00081202185839313 \tabularnewline
78 & 6.63 & 6.65655126741056 & -0.0265512674105643 \tabularnewline
79 & 6.63 & 6.63211560629388 & -0.00211560629387808 \tabularnewline
80 & 6.63 & 6.63540589045668 & -0.00540589045668405 \tabularnewline
81 & 6.63 & 6.63063226754273 & -0.00063226754272705 \tabularnewline
82 & 6.63 & 6.626601560358 & 0.00339843964199371 \tabularnewline
83 & 6.79 & 6.62790285951553 & 0.162097140484475 \tabularnewline
84 & 6.79 & 6.81305631113353 & -0.0230563111335300 \tabularnewline
85 & 6.79 & 6.89705711743291 & -0.107057117432912 \tabularnewline
86 & 6.81 & 6.80165988098065 & 0.00834011901935128 \tabularnewline
87 & 6.8 & 6.7955533858772 & 0.00444661412279768 \tabularnewline
88 & 6.8 & 6.80432465670647 & -0.00432465670646565 \tabularnewline
89 & 6.85 & 6.80111241569742 & 0.0488875843025749 \tabularnewline
90 & 6.85 & 6.86202239722673 & -0.0120223972267288 \tabularnewline
91 & 6.85 & 6.85338976835674 & -0.00338976835674210 \tabularnewline
92 & 6.85 & 6.85474010811502 & -0.00474010811502357 \tabularnewline
93 & 6.85 & 6.85096214536677 & -0.000962145366766087 \tabularnewline
94 & 6.85 & 6.84688656604298 & 0.00311343395702046 \tabularnewline
95 & 6.86 & 6.87762543910154 & -0.0176254391015398 \tabularnewline
96 & 6.86 & 6.88432842658235 & -0.024328426582346 \tabularnewline
97 & 6.88 & 6.9520991608042 & -0.0720991608041954 \tabularnewline
98 & 6.88 & 6.9062923434223 & -0.0262923434223046 \tabularnewline
99 & 6.88 & 6.87144898690064 & 0.00855101309935957 \tabularnewline
100 & 6.91 & 6.88174328435744 & 0.0282567156425646 \tabularnewline
101 & 6.91 & 6.91447689719075 & -0.00447689719075051 \tabularnewline
102 & 6.91 & 6.92123518754496 & -0.011235187544961 \tabularnewline
103 & 6.91 & 6.9147531730619 & -0.00475317306189993 \tabularnewline
104 & 6.99 & 6.91467313862054 & 0.0753268613794598 \tabularnewline
105 & 6.99 & 6.97542760721591 & 0.0145723927840855 \tabularnewline
106 & 6.99 & 6.98422543358631 & 0.00577456641369167 \tabularnewline
107 & 7.02 & 7.01341712155786 & 0.00658287844214289 \tabularnewline
108 & 7.02 & 7.03835766823982 & -0.0183576682398172 \tabularnewline
109 & 7.05 & 7.10336775614203 & -0.0533677561420314 \tabularnewline
110 & 7.05 & 7.08130525442563 & -0.0313052544256349 \tabularnewline
111 & 7.05 & 7.04845503023365 & 0.00154496976635166 \tabularnewline
112 & 7.05 & 7.05666647299218 & -0.00666647299217793 \tabularnewline
113 & 7.1 & 7.05512388374282 & 0.0448761162571767 \tabularnewline
114 & 7.1 & 7.09997911473098 & 2.0885269019999e-05 \tabularnewline
115 & 7.1 & 7.10344992850955 & -0.00344992850954551 \tabularnewline
116 & 7.1 & 7.11945656199515 & -0.0194565619951472 \tabularnewline
117 & 7.12 & 7.09257914899669 & 0.0274208510033080 \tabularnewline
118 & 7.13 & 7.10968511823511 & 0.0203148817648904 \tabularnewline
119 & 7.18 & 7.15087995737546 & 0.0291200426245446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41989&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]5.6[/C][C]5.52588995089906[/C][C]0.074110049100943[/C][/ROW]
[ROW][C]14[/C][C]5.6[/C][C]5.5836960661993[/C][C]0.0163039338007014[/C][/ROW]
[ROW][C]15[/C][C]5.6[/C][C]5.59522900432491[/C][C]0.00477099567508521[/C][/ROW]
[ROW][C]16[/C][C]5.6[/C][C]5.59753321270797[/C][C]0.00246678729202543[/C][/ROW]
[ROW][C]17[/C][C]5.6[/C][C]5.59799681111868[/C][C]0.00200318888132411[/C][/ROW]
[ROW][C]18[/C][C]5.6[/C][C]5.60264896463026[/C][C]-0.00264896463025988[/C][/ROW]
[ROW][C]19[/C][C]5.67[/C][C]5.65124590981136[/C][C]0.0187540901886427[/C][/ROW]
[ROW][C]20[/C][C]5.67[/C][C]5.66597157942531[/C][C]0.00402842057468789[/C][/ROW]
[ROW][C]21[/C][C]5.67[/C][C]5.66890994253915[/C][C]0.00109005746084989[/C][/ROW]
[ROW][C]22[/C][C]5.67[/C][C]5.66949681982731[/C][C]0.000503180172692907[/C][/ROW]
[ROW][C]23[/C][C]5.67[/C][C]5.6696145865947[/C][C]0.000385413405301627[/C][/ROW]
[ROW][C]24[/C][C]5.67[/C][C]5.78540913247381[/C][C]-0.115409132473809[/C][/ROW]
[ROW][C]25[/C][C]5.67[/C][C]5.70846222126103[/C][C]-0.0384622212610317[/C][/ROW]
[ROW][C]26[/C][C]5.67[/C][C]5.66499221198552[/C][C]0.00500778801447943[/C][/ROW]
[ROW][C]27[/C][C]5.67[/C][C]5.66511130783521[/C][C]0.00488869216478616[/C][/ROW]
[ROW][C]28[/C][C]5.82[/C][C]5.66688706778091[/C][C]0.153112932219088[/C][/ROW]
[ROW][C]29[/C][C]5.82[/C][C]5.78727543430731[/C][C]0.0327245656926864[/C][/ROW]
[ROW][C]30[/C][C]5.95[/C][C]5.8152043030481[/C][C]0.134795696951902[/C][/ROW]
[ROW][C]31[/C][C]5.95[/C][C]5.98014370904363[/C][C]-0.0301437090436343[/C][/ROW]
[ROW][C]32[/C][C]5.95[/C][C]5.95215353141279[/C][C]-0.00215353141279451[/C][/ROW]
[ROW][C]33[/C][C]5.95[/C][C]5.94888916380895[/C][C]0.00111083619105035[/C][/ROW]
[ROW][C]34[/C][C]5.95[/C][C]5.94870191697253[/C][C]0.00129808302746781[/C][/ROW]
[ROW][C]35[/C][C]5.95[/C][C]5.94875895718062[/C][C]0.00124104281937587[/C][/ROW]
[ROW][C]36[/C][C]6.02[/C][C]6.04710204611742[/C][C]-0.0271020461174167[/C][/ROW]
[ROW][C]37[/C][C]6.02[/C][C]6.05621048990421[/C][C]-0.0362104899042102[/C][/ROW]
[ROW][C]38[/C][C]6.05[/C][C]6.02155855303841[/C][C]0.028441446961585[/C][/ROW]
[ROW][C]39[/C][C]6.05[/C][C]6.03925205883379[/C][C]0.0107479411662101[/C][/ROW]
[ROW][C]40[/C][C]6.05[/C][C]6.07368537555861[/C][C]-0.0236853755586131[/C][/ROW]
[ROW][C]41[/C][C]6.12[/C][C]6.02846456461447[/C][C]0.0915354353855315[/C][/ROW]
[ROW][C]42[/C][C]6.12[/C][C]6.12247130456343[/C][C]-0.0024713045634277[/C][/ROW]
[ROW][C]43[/C][C]6.12[/C][C]6.14699180601871[/C][C]-0.0269918060187146[/C][/ROW]
[ROW][C]44[/C][C]6.12[/C][C]6.12641899140255[/C][C]-0.00641899140254765[/C][/ROW]
[ROW][C]45[/C][C]6.12[/C][C]6.11994126287854[/C][C]5.87371214564314e-05[/C][/ROW]
[ROW][C]46[/C][C]6.12[/C][C]6.11853484868824[/C][C]0.00146515131176095[/C][/ROW]
[ROW][C]47[/C][C]6.12[/C][C]6.11830524031134[/C][C]0.00169475968865918[/C][/ROW]
[ROW][C]48[/C][C]6.12[/C][C]6.21391319226207[/C][C]-0.09391319226207[/C][/ROW]
[ROW][C]49[/C][C]6.17[/C][C]6.16813412705065[/C][C]0.00186587294935325[/C][/ROW]
[ROW][C]50[/C][C]6.17[/C][C]6.17587698996837[/C][C]-0.0058769899683675[/C][/ROW]
[ROW][C]51[/C][C]6.17[/C][C]6.16235272343768[/C][C]0.00764727656232367[/C][/ROW]
[ROW][C]52[/C][C]6.17[/C][C]6.18794569341074[/C][C]-0.0179456934107405[/C][/ROW]
[ROW][C]53[/C][C]6.17[/C][C]6.16835408334248[/C][C]0.00164591665751601[/C][/ROW]
[ROW][C]54[/C][C]6.28[/C][C]6.17272422982617[/C][C]0.107275770173833[/C][/ROW]
[ROW][C]55[/C][C]6.27[/C][C]6.28061659094706[/C][C]-0.0106165909470644[/C][/ROW]
[ROW][C]56[/C][C]6.28[/C][C]6.27679027483096[/C][C]0.00320972516904305[/C][/ROW]
[ROW][C]57[/C][C]6.28[/C][C]6.2788781994558[/C][C]0.00112180054420463[/C][/ROW]
[ROW][C]58[/C][C]6.27[/C][C]6.27820520653592[/C][C]-0.00820520653592283[/C][/ROW]
[ROW][C]59[/C][C]6.27[/C][C]6.26991719974773[/C][C]8.28002522705873e-05[/C][/ROW]
[ROW][C]60[/C][C]6.28[/C][C]6.34761656413826[/C][C]-0.0676165641382624[/C][/ROW]
[ROW][C]61[/C][C]6.59[/C][C]6.34179518934648[/C][C]0.248204810653516[/C][/ROW]
[ROW][C]62[/C][C]6.59[/C][C]6.54463503626821[/C][C]0.0453649637317906[/C][/ROW]
[ROW][C]63[/C][C]6.59[/C][C]6.57332283222538[/C][C]0.0166771677746222[/C][/ROW]
[ROW][C]64[/C][C]6.59[/C][C]6.60140796860466[/C][C]-0.0114079686046589[/C][/ROW]
[ROW][C]65[/C][C]6.59[/C][C]6.5896932922136[/C][C]0.00030670778639319[/C][/ROW]
[ROW][C]66[/C][C]6.63[/C][C]6.61315267193653[/C][C]0.0168473280634744[/C][/ROW]
[ROW][C]67[/C][C]6.63[/C][C]6.62582945499342[/C][C]0.00417054500658409[/C][/ROW]
[ROW][C]68[/C][C]6.63[/C][C]6.63607188217895[/C][C]-0.00607188217894716[/C][/ROW]
[ROW][C]69[/C][C]6.63[/C][C]6.62954255504114[/C][C]0.000457444958857245[/C][/ROW]
[ROW][C]70[/C][C]6.63[/C][C]6.62565504698584[/C][C]0.0043449530141606[/C][/ROW]
[ROW][C]71[/C][C]6.63[/C][C]6.62818735823105[/C][C]0.00181264176895457[/C][/ROW]
[ROW][C]72[/C][C]6.63[/C][C]6.6974052631018[/C][C]-0.0674052631018025[/C][/ROW]
[ROW][C]73[/C][C]6.63[/C][C]6.75492951073505[/C][C]-0.124929510735055[/C][/ROW]
[ROW][C]74[/C][C]6.63[/C][C]6.62066105398888[/C][C]0.00933894601112062[/C][/ROW]
[ROW][C]75[/C][C]6.63[/C][C]6.61498292594439[/C][C]0.0150170740556073[/C][/ROW]
[ROW][C]76[/C][C]6.63[/C][C]6.63644494323795[/C][C]-0.00644494323795097[/C][/ROW]
[ROW][C]77[/C][C]6.63[/C][C]6.63081202185839[/C][C]-0.00081202185839313[/C][/ROW]
[ROW][C]78[/C][C]6.63[/C][C]6.65655126741056[/C][C]-0.0265512674105643[/C][/ROW]
[ROW][C]79[/C][C]6.63[/C][C]6.63211560629388[/C][C]-0.00211560629387808[/C][/ROW]
[ROW][C]80[/C][C]6.63[/C][C]6.63540589045668[/C][C]-0.00540589045668405[/C][/ROW]
[ROW][C]81[/C][C]6.63[/C][C]6.63063226754273[/C][C]-0.00063226754272705[/C][/ROW]
[ROW][C]82[/C][C]6.63[/C][C]6.626601560358[/C][C]0.00339843964199371[/C][/ROW]
[ROW][C]83[/C][C]6.79[/C][C]6.62790285951553[/C][C]0.162097140484475[/C][/ROW]
[ROW][C]84[/C][C]6.79[/C][C]6.81305631113353[/C][C]-0.0230563111335300[/C][/ROW]
[ROW][C]85[/C][C]6.79[/C][C]6.89705711743291[/C][C]-0.107057117432912[/C][/ROW]
[ROW][C]86[/C][C]6.81[/C][C]6.80165988098065[/C][C]0.00834011901935128[/C][/ROW]
[ROW][C]87[/C][C]6.8[/C][C]6.7955533858772[/C][C]0.00444661412279768[/C][/ROW]
[ROW][C]88[/C][C]6.8[/C][C]6.80432465670647[/C][C]-0.00432465670646565[/C][/ROW]
[ROW][C]89[/C][C]6.85[/C][C]6.80111241569742[/C][C]0.0488875843025749[/C][/ROW]
[ROW][C]90[/C][C]6.85[/C][C]6.86202239722673[/C][C]-0.0120223972267288[/C][/ROW]
[ROW][C]91[/C][C]6.85[/C][C]6.85338976835674[/C][C]-0.00338976835674210[/C][/ROW]
[ROW][C]92[/C][C]6.85[/C][C]6.85474010811502[/C][C]-0.00474010811502357[/C][/ROW]
[ROW][C]93[/C][C]6.85[/C][C]6.85096214536677[/C][C]-0.000962145366766087[/C][/ROW]
[ROW][C]94[/C][C]6.85[/C][C]6.84688656604298[/C][C]0.00311343395702046[/C][/ROW]
[ROW][C]95[/C][C]6.86[/C][C]6.87762543910154[/C][C]-0.0176254391015398[/C][/ROW]
[ROW][C]96[/C][C]6.86[/C][C]6.88432842658235[/C][C]-0.024328426582346[/C][/ROW]
[ROW][C]97[/C][C]6.88[/C][C]6.9520991608042[/C][C]-0.0720991608041954[/C][/ROW]
[ROW][C]98[/C][C]6.88[/C][C]6.9062923434223[/C][C]-0.0262923434223046[/C][/ROW]
[ROW][C]99[/C][C]6.88[/C][C]6.87144898690064[/C][C]0.00855101309935957[/C][/ROW]
[ROW][C]100[/C][C]6.91[/C][C]6.88174328435744[/C][C]0.0282567156425646[/C][/ROW]
[ROW][C]101[/C][C]6.91[/C][C]6.91447689719075[/C][C]-0.00447689719075051[/C][/ROW]
[ROW][C]102[/C][C]6.91[/C][C]6.92123518754496[/C][C]-0.011235187544961[/C][/ROW]
[ROW][C]103[/C][C]6.91[/C][C]6.9147531730619[/C][C]-0.00475317306189993[/C][/ROW]
[ROW][C]104[/C][C]6.99[/C][C]6.91467313862054[/C][C]0.0753268613794598[/C][/ROW]
[ROW][C]105[/C][C]6.99[/C][C]6.97542760721591[/C][C]0.0145723927840855[/C][/ROW]
[ROW][C]106[/C][C]6.99[/C][C]6.98422543358631[/C][C]0.00577456641369167[/C][/ROW]
[ROW][C]107[/C][C]7.02[/C][C]7.01341712155786[/C][C]0.00658287844214289[/C][/ROW]
[ROW][C]108[/C][C]7.02[/C][C]7.03835766823982[/C][C]-0.0183576682398172[/C][/ROW]
[ROW][C]109[/C][C]7.05[/C][C]7.10336775614203[/C][C]-0.0533677561420314[/C][/ROW]
[ROW][C]110[/C][C]7.05[/C][C]7.08130525442563[/C][C]-0.0313052544256349[/C][/ROW]
[ROW][C]111[/C][C]7.05[/C][C]7.04845503023365[/C][C]0.00154496976635166[/C][/ROW]
[ROW][C]112[/C][C]7.05[/C][C]7.05666647299218[/C][C]-0.00666647299217793[/C][/ROW]
[ROW][C]113[/C][C]7.1[/C][C]7.05512388374282[/C][C]0.0448761162571767[/C][/ROW]
[ROW][C]114[/C][C]7.1[/C][C]7.09997911473098[/C][C]2.0885269019999e-05[/C][/ROW]
[ROW][C]115[/C][C]7.1[/C][C]7.10344992850955[/C][C]-0.00344992850954551[/C][/ROW]
[ROW][C]116[/C][C]7.1[/C][C]7.11945656199515[/C][C]-0.0194565619951472[/C][/ROW]
[ROW][C]117[/C][C]7.12[/C][C]7.09257914899669[/C][C]0.0274208510033080[/C][/ROW]
[ROW][C]118[/C][C]7.13[/C][C]7.10968511823511[/C][C]0.0203148817648904[/C][/ROW]
[ROW][C]119[/C][C]7.18[/C][C]7.15087995737546[/C][C]0.0291200426245446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41989&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41989&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
135.65.525889950899060.074110049100943
145.65.58369606619930.0163039338007014
155.65.595229004324910.00477099567508521
165.65.597533212707970.00246678729202543
175.65.597996811118680.00200318888132411
185.65.60264896463026-0.00264896463025988
195.675.651245909811360.0187540901886427
205.675.665971579425310.00402842057468789
215.675.668909942539150.00109005746084989
225.675.669496819827310.000503180172692907
235.675.66961458659470.000385413405301627
245.675.78540913247381-0.115409132473809
255.675.70846222126103-0.0384622212610317
265.675.664992211985520.00500778801447943
275.675.665111307835210.00488869216478616
285.825.666887067780910.153112932219088
295.825.787275434307310.0327245656926864
305.955.81520430304810.134795696951902
315.955.98014370904363-0.0301437090436343
325.955.95215353141279-0.00215353141279451
335.955.948889163808950.00111083619105035
345.955.948701916972530.00129808302746781
355.955.948758957180620.00124104281937587
366.026.04710204611742-0.0271020461174167
376.026.05621048990421-0.0362104899042102
386.056.021558553038410.028441446961585
396.056.039252058833790.0107479411662101
406.056.07368537555861-0.0236853755586131
416.126.028464564614470.0915354353855315
426.126.12247130456343-0.0024713045634277
436.126.14699180601871-0.0269918060187146
446.126.12641899140255-0.00641899140254765
456.126.119941262878545.87371214564314e-05
466.126.118534848688240.00146515131176095
476.126.118305240311340.00169475968865918
486.126.21391319226207-0.09391319226207
496.176.168134127050650.00186587294935325
506.176.17587698996837-0.0058769899683675
516.176.162352723437680.00764727656232367
526.176.18794569341074-0.0179456934107405
536.176.168354083342480.00164591665751601
546.286.172724229826170.107275770173833
556.276.28061659094706-0.0106165909470644
566.286.276790274830960.00320972516904305
576.286.27887819945580.00112180054420463
586.276.27820520653592-0.00820520653592283
596.276.269917199747738.28002522705873e-05
606.286.34761656413826-0.0676165641382624
616.596.341795189346480.248204810653516
626.596.544635036268210.0453649637317906
636.596.573322832225380.0166771677746222
646.596.60140796860466-0.0114079686046589
656.596.58969329221360.00030670778639319
666.636.613152671936530.0168473280634744
676.636.625829454993420.00417054500658409
686.636.63607188217895-0.00607188217894716
696.636.629542555041140.000457444958857245
706.636.625655046985840.0043449530141606
716.636.628187358231050.00181264176895457
726.636.6974052631018-0.0674052631018025
736.636.75492951073505-0.124929510735055
746.636.620661053988880.00933894601112062
756.636.614982925944390.0150170740556073
766.636.63644494323795-0.00644494323795097
776.636.63081202185839-0.00081202185839313
786.636.65655126741056-0.0265512674105643
796.636.63211560629388-0.00211560629387808
806.636.63540589045668-0.00540589045668405
816.636.63063226754273-0.00063226754272705
826.636.6266015603580.00339843964199371
836.796.627902859515530.162097140484475
846.796.81305631113353-0.0230563111335300
856.796.89705711743291-0.107057117432912
866.816.801659880980650.00834011901935128
876.86.79555338587720.00444661412279768
886.86.80432465670647-0.00432465670646565
896.856.801112415697420.0488875843025749
906.856.86202239722673-0.0120223972267288
916.856.85338976835674-0.00338976835674210
926.856.85474010811502-0.00474010811502357
936.856.85096214536677-0.000962145366766087
946.856.846886566042980.00311343395702046
956.866.87762543910154-0.0176254391015398
966.866.88432842658235-0.024328426582346
976.886.9520991608042-0.0720991608041954
986.886.9062923434223-0.0262923434223046
996.886.871448986900640.00855101309935957
1006.916.881743284357440.0282567156425646
1016.916.91447689719075-0.00447689719075051
1026.916.92123518754496-0.011235187544961
1036.916.9147531730619-0.00475317306189993
1046.996.914673138620540.0753268613794598
1056.996.975427607215910.0145723927840855
1066.996.984225433586310.00577456641369167
1077.027.013417121557860.00658287844214289
1087.027.03835766823982-0.0183576682398172
1097.057.10336775614203-0.0533677561420314
1107.057.08130525442563-0.0313052544256349
1117.057.048455030233650.00154496976635166
1127.057.05666647299218-0.00666647299217793
1137.17.055123883742820.0448761162571767
1147.17.099979114730982.0885269019999e-05
1157.17.10344992850955-0.00344992850954551
1167.17.11945656199515-0.0194565619951472
1177.127.092579148996690.0274208510033080
1187.137.109685118235110.0203148817648904
1197.187.150879957375460.0291200426245446







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1207.189198581202887.095056000118937.28334116228684
1217.263698978820367.142137159357367.38526079828335
1227.288788371415377.145157085341497.43241965748926
1237.286633092573697.124245436296397.44902074885099
1247.291795646978527.112542443820397.47104885013665
1257.305210594020367.110412473915627.5000087141251
1267.305372933160677.096484271131017.51426159519033
1277.307866989233887.08576792747367.52996605099415
1287.323689256563067.088799660574367.55857885255175
1297.320653754604437.07417011240997.56713739679895
1307.313927744245877.05653194944217.57132353904964
1317.340844003772270.36939301929725414.3122949882473

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
120 & 7.18919858120288 & 7.09505600011893 & 7.28334116228684 \tabularnewline
121 & 7.26369897882036 & 7.14213715935736 & 7.38526079828335 \tabularnewline
122 & 7.28878837141537 & 7.14515708534149 & 7.43241965748926 \tabularnewline
123 & 7.28663309257369 & 7.12424543629639 & 7.44902074885099 \tabularnewline
124 & 7.29179564697852 & 7.11254244382039 & 7.47104885013665 \tabularnewline
125 & 7.30521059402036 & 7.11041247391562 & 7.5000087141251 \tabularnewline
126 & 7.30537293316067 & 7.09648427113101 & 7.51426159519033 \tabularnewline
127 & 7.30786698923388 & 7.0857679274736 & 7.52996605099415 \tabularnewline
128 & 7.32368925656306 & 7.08879966057436 & 7.55857885255175 \tabularnewline
129 & 7.32065375460443 & 7.0741701124099 & 7.56713739679895 \tabularnewline
130 & 7.31392774424587 & 7.0565319494421 & 7.57132353904964 \tabularnewline
131 & 7.34084400377227 & 0.369393019297254 & 14.3122949882473 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41989&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]120[/C][C]7.18919858120288[/C][C]7.09505600011893[/C][C]7.28334116228684[/C][/ROW]
[ROW][C]121[/C][C]7.26369897882036[/C][C]7.14213715935736[/C][C]7.38526079828335[/C][/ROW]
[ROW][C]122[/C][C]7.28878837141537[/C][C]7.14515708534149[/C][C]7.43241965748926[/C][/ROW]
[ROW][C]123[/C][C]7.28663309257369[/C][C]7.12424543629639[/C][C]7.44902074885099[/C][/ROW]
[ROW][C]124[/C][C]7.29179564697852[/C][C]7.11254244382039[/C][C]7.47104885013665[/C][/ROW]
[ROW][C]125[/C][C]7.30521059402036[/C][C]7.11041247391562[/C][C]7.5000087141251[/C][/ROW]
[ROW][C]126[/C][C]7.30537293316067[/C][C]7.09648427113101[/C][C]7.51426159519033[/C][/ROW]
[ROW][C]127[/C][C]7.30786698923388[/C][C]7.0857679274736[/C][C]7.52996605099415[/C][/ROW]
[ROW][C]128[/C][C]7.32368925656306[/C][C]7.08879966057436[/C][C]7.55857885255175[/C][/ROW]
[ROW][C]129[/C][C]7.32065375460443[/C][C]7.0741701124099[/C][C]7.56713739679895[/C][/ROW]
[ROW][C]130[/C][C]7.31392774424587[/C][C]7.0565319494421[/C][C]7.57132353904964[/C][/ROW]
[ROW][C]131[/C][C]7.34084400377227[/C][C]0.369393019297254[/C][C]14.3122949882473[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41989&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41989&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
1207.189198581202887.095056000118937.28334116228684
1217.263698978820367.142137159357367.38526079828335
1227.288788371415377.145157085341497.43241965748926
1237.286633092573697.124245436296397.44902074885099
1247.291795646978527.112542443820397.47104885013665
1257.305210594020367.110412473915627.5000087141251
1267.305372933160677.096484271131017.51426159519033
1277.307866989233887.08576792747367.52996605099415
1287.323689256563067.088799660574367.55857885255175
1297.320653754604437.07417011240997.56713739679895
1307.313927744245877.05653194944217.57132353904964
1317.340844003772270.36939301929725414.3122949882473



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