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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 20 Jan 2009 07:20:52 -0700
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/Jan/20/t1232461282bif80sks7fnzu24.htm/, Retrieved Sat, 04 May 2024 01:46:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36930, Retrieved Sat, 04 May 2024 01:46:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact208
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 - oef 2...] [2009-01-20 14:20:52] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2.13
1.87
2.23
3
2.12
1.6
1.17
1.02
1.22
1.8
2.13
2.21
2.38
1.99
1.82
2.47
1.94
1.39
1.11
0.97
1.38
2.39
1.88
2.11
2.11
2.17
2.54
3.13
2.25
1.39
1.36
1.33
1.6
1.95
2.23
2.53
2.36
1.95
2.16
2.76
2.09
1.49
1.17
1.3
1.26
2.17
2.03
2.18
2.61
2.58
3.86
3.81
2.41
1.47
1.33
1.38
1.57
2.6
2.18
2.36
2.24
2.41
2.51
2.98
1.87
1.9
1.47
1.45
2.71
2.9
2.11
2.18
2.24
2.05
2.42
2.77
1.99
1.47
1.09
0.93
1.32
2.03
2.04
2.78
2.8
3.03
3.11
2.75
2.78
1.76
1.29
1.28
1.43
1.71
1.89
1.84




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36930&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36930&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36930&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.520425617529786
beta0
gamma0.561201006499266

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.520425617529786 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.561201006499266 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36930&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]0.520425617529786[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.561201006499266[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36930&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36930&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
alpha0.520425617529786
beta0
gamma0.561201006499266







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132.382.39998328408389-0.0199832840838923
141.992.00313498691079-0.0131349869107866
151.821.82109270008571-0.00109270008571416
162.472.428375489463270.041624510536729
171.941.909488631834430.030511368165574
181.391.39054951559396-0.00054951559396299
191.111.11967755683772-0.0096775568377201
200.970.97608033956112-0.00608033956112053
211.381.355964481399960.0240355186000416
222.392.298280613406880.0917193865931232
231.881.806945832165340.0730541678346568
242.112.056980433740460.0530195662595374
252.112.55543567295012-0.445435672950124
262.171.948775700498340.221224299501662
272.541.885801696962060.65419830303794
283.132.983646559660550.146353440339451
292.252.38399955359399-0.133999553593986
301.391.66414412563453-0.274144125634533
311.361.222616190740620.137383809259379
321.331.133986894276850.196013105723152
331.61.73368281761453-0.133682817614531
341.952.81090881714227-0.860908817142275
352.231.820171393396880.409828606603123
362.532.258582403596660.271417596403336
372.362.77115619594074-0.411156195940741
381.952.32656311019377-0.376563110193769
392.162.041790861705000.118209138295002
402.762.645894575165340.114105424834664
412.092.048552429667870.0414475703321342
421.491.438821655081340.051178344918664
431.171.2729812597176-0.102981259717599
441.31.083163956370170.21683604362983
451.261.57413829407315-0.314138294073152
462.172.19662014535545-0.0266201453554524
472.031.965362677944090.0646373220559062
482.182.170180378976880.0098196210231194
492.612.332182406582780.277817593417220
502.582.243286254921860.336713745078145
513.862.470284615065491.38971538493451
523.814.00241743196746-0.192417431967456
532.412.93754895891679-0.527548958916794
541.471.85827856196712-0.388278561967121
551.331.39288739028636-0.0628873902863631
561.381.296635612603530.08336438739647
571.571.58083669736747-0.0108366973674736
582.62.60066068272966-0.000660682729659356
592.182.36947786358222-0.189477863582215
602.362.44702799086976-0.0870279908697649
612.242.64947693824172-0.409476938241721
622.412.222299115484220.187700884515777
632.512.55156201626627-0.0415620162662731
642.982.800649542816080.179350457183921
651.872.09011516470113-0.220115164701126
661.91.364334520666150.535665479333854
671.471.456579262813230.0134207371867678
681.451.436446099457580.0135539005424161
692.711.671768255776051.03823174422395
702.93.65870085771060-0.758700857710595
712.112.90752100729388-0.797521007293879
722.182.72072515495033-0.540725154950332
732.242.59451730431754-0.354517304317538
742.052.35253803832019-0.302538038320189
752.422.35230585295990.0676941470401022
762.772.699033298028010.0709667019719884
771.991.885288027461120.104711972538879
781.471.50221228335625-0.0322122833562548
791.091.21358566768870-0.123585667688698
800.931.12804081910118-0.198040819101177
811.321.33363715434135-0.0136371543413532
822.031.826104221050180.203895778949824
832.041.678017858429640.361982141570361
842.782.096303154574460.68369684542554
852.82.663794576541190.136205423458809
863.032.676396286718620.35360371328138
873.113.20766495379542-0.0976649537954168
882.753.56640310427847-0.816403104278469
892.782.180974410612420.599025589387579
901.761.89167208016354-0.131672080163539
911.291.45486270338064-0.164862703380636
921.281.31186545340233-0.0318654534023308
931.431.77287304609525-0.342873046095252
941.712.26348219764550-0.553482197645503
951.891.755249866963990.134750133036012
961.842.09473316847462-0.254733168474621

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2.38 & 2.39998328408389 & -0.0199832840838923 \tabularnewline
14 & 1.99 & 2.00313498691079 & -0.0131349869107866 \tabularnewline
15 & 1.82 & 1.82109270008571 & -0.00109270008571416 \tabularnewline
16 & 2.47 & 2.42837548946327 & 0.041624510536729 \tabularnewline
17 & 1.94 & 1.90948863183443 & 0.030511368165574 \tabularnewline
18 & 1.39 & 1.39054951559396 & -0.00054951559396299 \tabularnewline
19 & 1.11 & 1.11967755683772 & -0.0096775568377201 \tabularnewline
20 & 0.97 & 0.97608033956112 & -0.00608033956112053 \tabularnewline
21 & 1.38 & 1.35596448139996 & 0.0240355186000416 \tabularnewline
22 & 2.39 & 2.29828061340688 & 0.0917193865931232 \tabularnewline
23 & 1.88 & 1.80694583216534 & 0.0730541678346568 \tabularnewline
24 & 2.11 & 2.05698043374046 & 0.0530195662595374 \tabularnewline
25 & 2.11 & 2.55543567295012 & -0.445435672950124 \tabularnewline
26 & 2.17 & 1.94877570049834 & 0.221224299501662 \tabularnewline
27 & 2.54 & 1.88580169696206 & 0.65419830303794 \tabularnewline
28 & 3.13 & 2.98364655966055 & 0.146353440339451 \tabularnewline
29 & 2.25 & 2.38399955359399 & -0.133999553593986 \tabularnewline
30 & 1.39 & 1.66414412563453 & -0.274144125634533 \tabularnewline
31 & 1.36 & 1.22261619074062 & 0.137383809259379 \tabularnewline
32 & 1.33 & 1.13398689427685 & 0.196013105723152 \tabularnewline
33 & 1.6 & 1.73368281761453 & -0.133682817614531 \tabularnewline
34 & 1.95 & 2.81090881714227 & -0.860908817142275 \tabularnewline
35 & 2.23 & 1.82017139339688 & 0.409828606603123 \tabularnewline
36 & 2.53 & 2.25858240359666 & 0.271417596403336 \tabularnewline
37 & 2.36 & 2.77115619594074 & -0.411156195940741 \tabularnewline
38 & 1.95 & 2.32656311019377 & -0.376563110193769 \tabularnewline
39 & 2.16 & 2.04179086170500 & 0.118209138295002 \tabularnewline
40 & 2.76 & 2.64589457516534 & 0.114105424834664 \tabularnewline
41 & 2.09 & 2.04855242966787 & 0.0414475703321342 \tabularnewline
42 & 1.49 & 1.43882165508134 & 0.051178344918664 \tabularnewline
43 & 1.17 & 1.2729812597176 & -0.102981259717599 \tabularnewline
44 & 1.3 & 1.08316395637017 & 0.21683604362983 \tabularnewline
45 & 1.26 & 1.57413829407315 & -0.314138294073152 \tabularnewline
46 & 2.17 & 2.19662014535545 & -0.0266201453554524 \tabularnewline
47 & 2.03 & 1.96536267794409 & 0.0646373220559062 \tabularnewline
48 & 2.18 & 2.17018037897688 & 0.0098196210231194 \tabularnewline
49 & 2.61 & 2.33218240658278 & 0.277817593417220 \tabularnewline
50 & 2.58 & 2.24328625492186 & 0.336713745078145 \tabularnewline
51 & 3.86 & 2.47028461506549 & 1.38971538493451 \tabularnewline
52 & 3.81 & 4.00241743196746 & -0.192417431967456 \tabularnewline
53 & 2.41 & 2.93754895891679 & -0.527548958916794 \tabularnewline
54 & 1.47 & 1.85827856196712 & -0.388278561967121 \tabularnewline
55 & 1.33 & 1.39288739028636 & -0.0628873902863631 \tabularnewline
56 & 1.38 & 1.29663561260353 & 0.08336438739647 \tabularnewline
57 & 1.57 & 1.58083669736747 & -0.0108366973674736 \tabularnewline
58 & 2.6 & 2.60066068272966 & -0.000660682729659356 \tabularnewline
59 & 2.18 & 2.36947786358222 & -0.189477863582215 \tabularnewline
60 & 2.36 & 2.44702799086976 & -0.0870279908697649 \tabularnewline
61 & 2.24 & 2.64947693824172 & -0.409476938241721 \tabularnewline
62 & 2.41 & 2.22229911548422 & 0.187700884515777 \tabularnewline
63 & 2.51 & 2.55156201626627 & -0.0415620162662731 \tabularnewline
64 & 2.98 & 2.80064954281608 & 0.179350457183921 \tabularnewline
65 & 1.87 & 2.09011516470113 & -0.220115164701126 \tabularnewline
66 & 1.9 & 1.36433452066615 & 0.535665479333854 \tabularnewline
67 & 1.47 & 1.45657926281323 & 0.0134207371867678 \tabularnewline
68 & 1.45 & 1.43644609945758 & 0.0135539005424161 \tabularnewline
69 & 2.71 & 1.67176825577605 & 1.03823174422395 \tabularnewline
70 & 2.9 & 3.65870085771060 & -0.758700857710595 \tabularnewline
71 & 2.11 & 2.90752100729388 & -0.797521007293879 \tabularnewline
72 & 2.18 & 2.72072515495033 & -0.540725154950332 \tabularnewline
73 & 2.24 & 2.59451730431754 & -0.354517304317538 \tabularnewline
74 & 2.05 & 2.35253803832019 & -0.302538038320189 \tabularnewline
75 & 2.42 & 2.3523058529599 & 0.0676941470401022 \tabularnewline
76 & 2.77 & 2.69903329802801 & 0.0709667019719884 \tabularnewline
77 & 1.99 & 1.88528802746112 & 0.104711972538879 \tabularnewline
78 & 1.47 & 1.50221228335625 & -0.0322122833562548 \tabularnewline
79 & 1.09 & 1.21358566768870 & -0.123585667688698 \tabularnewline
80 & 0.93 & 1.12804081910118 & -0.198040819101177 \tabularnewline
81 & 1.32 & 1.33363715434135 & -0.0136371543413532 \tabularnewline
82 & 2.03 & 1.82610422105018 & 0.203895778949824 \tabularnewline
83 & 2.04 & 1.67801785842964 & 0.361982141570361 \tabularnewline
84 & 2.78 & 2.09630315457446 & 0.68369684542554 \tabularnewline
85 & 2.8 & 2.66379457654119 & 0.136205423458809 \tabularnewline
86 & 3.03 & 2.67639628671862 & 0.35360371328138 \tabularnewline
87 & 3.11 & 3.20766495379542 & -0.0976649537954168 \tabularnewline
88 & 2.75 & 3.56640310427847 & -0.816403104278469 \tabularnewline
89 & 2.78 & 2.18097441061242 & 0.599025589387579 \tabularnewline
90 & 1.76 & 1.89167208016354 & -0.131672080163539 \tabularnewline
91 & 1.29 & 1.45486270338064 & -0.164862703380636 \tabularnewline
92 & 1.28 & 1.31186545340233 & -0.0318654534023308 \tabularnewline
93 & 1.43 & 1.77287304609525 & -0.342873046095252 \tabularnewline
94 & 1.71 & 2.26348219764550 & -0.553482197645503 \tabularnewline
95 & 1.89 & 1.75524986696399 & 0.134750133036012 \tabularnewline
96 & 1.84 & 2.09473316847462 & -0.254733168474621 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36930&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]2.38[/C][C]2.39998328408389[/C][C]-0.0199832840838923[/C][/ROW]
[ROW][C]14[/C][C]1.99[/C][C]2.00313498691079[/C][C]-0.0131349869107866[/C][/ROW]
[ROW][C]15[/C][C]1.82[/C][C]1.82109270008571[/C][C]-0.00109270008571416[/C][/ROW]
[ROW][C]16[/C][C]2.47[/C][C]2.42837548946327[/C][C]0.041624510536729[/C][/ROW]
[ROW][C]17[/C][C]1.94[/C][C]1.90948863183443[/C][C]0.030511368165574[/C][/ROW]
[ROW][C]18[/C][C]1.39[/C][C]1.39054951559396[/C][C]-0.00054951559396299[/C][/ROW]
[ROW][C]19[/C][C]1.11[/C][C]1.11967755683772[/C][C]-0.0096775568377201[/C][/ROW]
[ROW][C]20[/C][C]0.97[/C][C]0.97608033956112[/C][C]-0.00608033956112053[/C][/ROW]
[ROW][C]21[/C][C]1.38[/C][C]1.35596448139996[/C][C]0.0240355186000416[/C][/ROW]
[ROW][C]22[/C][C]2.39[/C][C]2.29828061340688[/C][C]0.0917193865931232[/C][/ROW]
[ROW][C]23[/C][C]1.88[/C][C]1.80694583216534[/C][C]0.0730541678346568[/C][/ROW]
[ROW][C]24[/C][C]2.11[/C][C]2.05698043374046[/C][C]0.0530195662595374[/C][/ROW]
[ROW][C]25[/C][C]2.11[/C][C]2.55543567295012[/C][C]-0.445435672950124[/C][/ROW]
[ROW][C]26[/C][C]2.17[/C][C]1.94877570049834[/C][C]0.221224299501662[/C][/ROW]
[ROW][C]27[/C][C]2.54[/C][C]1.88580169696206[/C][C]0.65419830303794[/C][/ROW]
[ROW][C]28[/C][C]3.13[/C][C]2.98364655966055[/C][C]0.146353440339451[/C][/ROW]
[ROW][C]29[/C][C]2.25[/C][C]2.38399955359399[/C][C]-0.133999553593986[/C][/ROW]
[ROW][C]30[/C][C]1.39[/C][C]1.66414412563453[/C][C]-0.274144125634533[/C][/ROW]
[ROW][C]31[/C][C]1.36[/C][C]1.22261619074062[/C][C]0.137383809259379[/C][/ROW]
[ROW][C]32[/C][C]1.33[/C][C]1.13398689427685[/C][C]0.196013105723152[/C][/ROW]
[ROW][C]33[/C][C]1.6[/C][C]1.73368281761453[/C][C]-0.133682817614531[/C][/ROW]
[ROW][C]34[/C][C]1.95[/C][C]2.81090881714227[/C][C]-0.860908817142275[/C][/ROW]
[ROW][C]35[/C][C]2.23[/C][C]1.82017139339688[/C][C]0.409828606603123[/C][/ROW]
[ROW][C]36[/C][C]2.53[/C][C]2.25858240359666[/C][C]0.271417596403336[/C][/ROW]
[ROW][C]37[/C][C]2.36[/C][C]2.77115619594074[/C][C]-0.411156195940741[/C][/ROW]
[ROW][C]38[/C][C]1.95[/C][C]2.32656311019377[/C][C]-0.376563110193769[/C][/ROW]
[ROW][C]39[/C][C]2.16[/C][C]2.04179086170500[/C][C]0.118209138295002[/C][/ROW]
[ROW][C]40[/C][C]2.76[/C][C]2.64589457516534[/C][C]0.114105424834664[/C][/ROW]
[ROW][C]41[/C][C]2.09[/C][C]2.04855242966787[/C][C]0.0414475703321342[/C][/ROW]
[ROW][C]42[/C][C]1.49[/C][C]1.43882165508134[/C][C]0.051178344918664[/C][/ROW]
[ROW][C]43[/C][C]1.17[/C][C]1.2729812597176[/C][C]-0.102981259717599[/C][/ROW]
[ROW][C]44[/C][C]1.3[/C][C]1.08316395637017[/C][C]0.21683604362983[/C][/ROW]
[ROW][C]45[/C][C]1.26[/C][C]1.57413829407315[/C][C]-0.314138294073152[/C][/ROW]
[ROW][C]46[/C][C]2.17[/C][C]2.19662014535545[/C][C]-0.0266201453554524[/C][/ROW]
[ROW][C]47[/C][C]2.03[/C][C]1.96536267794409[/C][C]0.0646373220559062[/C][/ROW]
[ROW][C]48[/C][C]2.18[/C][C]2.17018037897688[/C][C]0.0098196210231194[/C][/ROW]
[ROW][C]49[/C][C]2.61[/C][C]2.33218240658278[/C][C]0.277817593417220[/C][/ROW]
[ROW][C]50[/C][C]2.58[/C][C]2.24328625492186[/C][C]0.336713745078145[/C][/ROW]
[ROW][C]51[/C][C]3.86[/C][C]2.47028461506549[/C][C]1.38971538493451[/C][/ROW]
[ROW][C]52[/C][C]3.81[/C][C]4.00241743196746[/C][C]-0.192417431967456[/C][/ROW]
[ROW][C]53[/C][C]2.41[/C][C]2.93754895891679[/C][C]-0.527548958916794[/C][/ROW]
[ROW][C]54[/C][C]1.47[/C][C]1.85827856196712[/C][C]-0.388278561967121[/C][/ROW]
[ROW][C]55[/C][C]1.33[/C][C]1.39288739028636[/C][C]-0.0628873902863631[/C][/ROW]
[ROW][C]56[/C][C]1.38[/C][C]1.29663561260353[/C][C]0.08336438739647[/C][/ROW]
[ROW][C]57[/C][C]1.57[/C][C]1.58083669736747[/C][C]-0.0108366973674736[/C][/ROW]
[ROW][C]58[/C][C]2.6[/C][C]2.60066068272966[/C][C]-0.000660682729659356[/C][/ROW]
[ROW][C]59[/C][C]2.18[/C][C]2.36947786358222[/C][C]-0.189477863582215[/C][/ROW]
[ROW][C]60[/C][C]2.36[/C][C]2.44702799086976[/C][C]-0.0870279908697649[/C][/ROW]
[ROW][C]61[/C][C]2.24[/C][C]2.64947693824172[/C][C]-0.409476938241721[/C][/ROW]
[ROW][C]62[/C][C]2.41[/C][C]2.22229911548422[/C][C]0.187700884515777[/C][/ROW]
[ROW][C]63[/C][C]2.51[/C][C]2.55156201626627[/C][C]-0.0415620162662731[/C][/ROW]
[ROW][C]64[/C][C]2.98[/C][C]2.80064954281608[/C][C]0.179350457183921[/C][/ROW]
[ROW][C]65[/C][C]1.87[/C][C]2.09011516470113[/C][C]-0.220115164701126[/C][/ROW]
[ROW][C]66[/C][C]1.9[/C][C]1.36433452066615[/C][C]0.535665479333854[/C][/ROW]
[ROW][C]67[/C][C]1.47[/C][C]1.45657926281323[/C][C]0.0134207371867678[/C][/ROW]
[ROW][C]68[/C][C]1.45[/C][C]1.43644609945758[/C][C]0.0135539005424161[/C][/ROW]
[ROW][C]69[/C][C]2.71[/C][C]1.67176825577605[/C][C]1.03823174422395[/C][/ROW]
[ROW][C]70[/C][C]2.9[/C][C]3.65870085771060[/C][C]-0.758700857710595[/C][/ROW]
[ROW][C]71[/C][C]2.11[/C][C]2.90752100729388[/C][C]-0.797521007293879[/C][/ROW]
[ROW][C]72[/C][C]2.18[/C][C]2.72072515495033[/C][C]-0.540725154950332[/C][/ROW]
[ROW][C]73[/C][C]2.24[/C][C]2.59451730431754[/C][C]-0.354517304317538[/C][/ROW]
[ROW][C]74[/C][C]2.05[/C][C]2.35253803832019[/C][C]-0.302538038320189[/C][/ROW]
[ROW][C]75[/C][C]2.42[/C][C]2.3523058529599[/C][C]0.0676941470401022[/C][/ROW]
[ROW][C]76[/C][C]2.77[/C][C]2.69903329802801[/C][C]0.0709667019719884[/C][/ROW]
[ROW][C]77[/C][C]1.99[/C][C]1.88528802746112[/C][C]0.104711972538879[/C][/ROW]
[ROW][C]78[/C][C]1.47[/C][C]1.50221228335625[/C][C]-0.0322122833562548[/C][/ROW]
[ROW][C]79[/C][C]1.09[/C][C]1.21358566768870[/C][C]-0.123585667688698[/C][/ROW]
[ROW][C]80[/C][C]0.93[/C][C]1.12804081910118[/C][C]-0.198040819101177[/C][/ROW]
[ROW][C]81[/C][C]1.32[/C][C]1.33363715434135[/C][C]-0.0136371543413532[/C][/ROW]
[ROW][C]82[/C][C]2.03[/C][C]1.82610422105018[/C][C]0.203895778949824[/C][/ROW]
[ROW][C]83[/C][C]2.04[/C][C]1.67801785842964[/C][C]0.361982141570361[/C][/ROW]
[ROW][C]84[/C][C]2.78[/C][C]2.09630315457446[/C][C]0.68369684542554[/C][/ROW]
[ROW][C]85[/C][C]2.8[/C][C]2.66379457654119[/C][C]0.136205423458809[/C][/ROW]
[ROW][C]86[/C][C]3.03[/C][C]2.67639628671862[/C][C]0.35360371328138[/C][/ROW]
[ROW][C]87[/C][C]3.11[/C][C]3.20766495379542[/C][C]-0.0976649537954168[/C][/ROW]
[ROW][C]88[/C][C]2.75[/C][C]3.56640310427847[/C][C]-0.816403104278469[/C][/ROW]
[ROW][C]89[/C][C]2.78[/C][C]2.18097441061242[/C][C]0.599025589387579[/C][/ROW]
[ROW][C]90[/C][C]1.76[/C][C]1.89167208016354[/C][C]-0.131672080163539[/C][/ROW]
[ROW][C]91[/C][C]1.29[/C][C]1.45486270338064[/C][C]-0.164862703380636[/C][/ROW]
[ROW][C]92[/C][C]1.28[/C][C]1.31186545340233[/C][C]-0.0318654534023308[/C][/ROW]
[ROW][C]93[/C][C]1.43[/C][C]1.77287304609525[/C][C]-0.342873046095252[/C][/ROW]
[ROW][C]94[/C][C]1.71[/C][C]2.26348219764550[/C][C]-0.553482197645503[/C][/ROW]
[ROW][C]95[/C][C]1.89[/C][C]1.75524986696399[/C][C]0.134750133036012[/C][/ROW]
[ROW][C]96[/C][C]1.84[/C][C]2.09473316847462[/C][C]-0.254733168474621[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36930&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36930&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
132.382.39998328408389-0.0199832840838923
141.992.00313498691079-0.0131349869107866
151.821.82109270008571-0.00109270008571416
162.472.428375489463270.041624510536729
171.941.909488631834430.030511368165574
181.391.39054951559396-0.00054951559396299
191.111.11967755683772-0.0096775568377201
200.970.97608033956112-0.00608033956112053
211.381.355964481399960.0240355186000416
222.392.298280613406880.0917193865931232
231.881.806945832165340.0730541678346568
242.112.056980433740460.0530195662595374
252.112.55543567295012-0.445435672950124
262.171.948775700498340.221224299501662
272.541.885801696962060.65419830303794
283.132.983646559660550.146353440339451
292.252.38399955359399-0.133999553593986
301.391.66414412563453-0.274144125634533
311.361.222616190740620.137383809259379
321.331.133986894276850.196013105723152
331.61.73368281761453-0.133682817614531
341.952.81090881714227-0.860908817142275
352.231.820171393396880.409828606603123
362.532.258582403596660.271417596403336
372.362.77115619594074-0.411156195940741
381.952.32656311019377-0.376563110193769
392.162.041790861705000.118209138295002
402.762.645894575165340.114105424834664
412.092.048552429667870.0414475703321342
421.491.438821655081340.051178344918664
431.171.2729812597176-0.102981259717599
441.31.083163956370170.21683604362983
451.261.57413829407315-0.314138294073152
462.172.19662014535545-0.0266201453554524
472.031.965362677944090.0646373220559062
482.182.170180378976880.0098196210231194
492.612.332182406582780.277817593417220
502.582.243286254921860.336713745078145
513.862.470284615065491.38971538493451
523.814.00241743196746-0.192417431967456
532.412.93754895891679-0.527548958916794
541.471.85827856196712-0.388278561967121
551.331.39288739028636-0.0628873902863631
561.381.296635612603530.08336438739647
571.571.58083669736747-0.0108366973674736
582.62.60066068272966-0.000660682729659356
592.182.36947786358222-0.189477863582215
602.362.44702799086976-0.0870279908697649
612.242.64947693824172-0.409476938241721
622.412.222299115484220.187700884515777
632.512.55156201626627-0.0415620162662731
642.982.800649542816080.179350457183921
651.872.09011516470113-0.220115164701126
661.91.364334520666150.535665479333854
671.471.456579262813230.0134207371867678
681.451.436446099457580.0135539005424161
692.711.671768255776051.03823174422395
702.93.65870085771060-0.758700857710595
712.112.90752100729388-0.797521007293879
722.182.72072515495033-0.540725154950332
732.242.59451730431754-0.354517304317538
742.052.35253803832019-0.302538038320189
752.422.35230585295990.0676941470401022
762.772.699033298028010.0709667019719884
771.991.885288027461120.104711972538879
781.471.50221228335625-0.0322122833562548
791.091.21358566768870-0.123585667688698
800.931.12804081910118-0.198040819101177
811.321.33363715434135-0.0136371543413532
822.031.826104221050180.203895778949824
832.041.678017858429640.361982141570361
842.782.096303154574460.68369684542554
852.82.663794576541190.136205423458809
863.032.676396286718620.35360371328138
873.113.20766495379542-0.0976649537954168
882.753.56640310427847-0.816403104278469
892.782.180974410612420.599025589387579
901.761.89167208016354-0.131672080163539
911.291.45486270338064-0.164862703380636
921.281.31186545340233-0.0318654534023308
931.431.77287304609525-0.342873046095252
941.712.26348219764550-0.553482197645503
951.891.755249866963990.134750133036012
961.842.09473316847462-0.254733168474621







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
972.009337544978031.450585098681032.56808999127504
982.005062958900441.319996209834872.69012970796602
992.157951724106571.357416598019082.95848685019405
1002.286447304447871.508343578297073.06455103059866
1011.817099577174431.094805224600002.53939392974886
1021.270012950303910.5446070392993881.99541886130842
1031.000057541696950.1934675973941331.80664748599977
1040.98381608164466-0.07020178347151152.03783394676083
1051.27708624912585-0.1809447584593442.73511725671104
1061.779235493997630.3011704935126053.25730049448265
1071.743825522991130.1067281088612833.38092293712097
1081.89360522170516NANA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 2.00933754497803 & 1.45058509868103 & 2.56808999127504 \tabularnewline
98 & 2.00506295890044 & 1.31999620983487 & 2.69012970796602 \tabularnewline
99 & 2.15795172410657 & 1.35741659801908 & 2.95848685019405 \tabularnewline
100 & 2.28644730444787 & 1.50834357829707 & 3.06455103059866 \tabularnewline
101 & 1.81709957717443 & 1.09480522460000 & 2.53939392974886 \tabularnewline
102 & 1.27001295030391 & 0.544607039299388 & 1.99541886130842 \tabularnewline
103 & 1.00005754169695 & 0.193467597394133 & 1.80664748599977 \tabularnewline
104 & 0.98381608164466 & -0.0702017834715115 & 2.03783394676083 \tabularnewline
105 & 1.27708624912585 & -0.180944758459344 & 2.73511725671104 \tabularnewline
106 & 1.77923549399763 & 0.301170493512605 & 3.25730049448265 \tabularnewline
107 & 1.74382552299113 & 0.106728108861283 & 3.38092293712097 \tabularnewline
108 & 1.89360522170516 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36930&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]97[/C][C]2.00933754497803[/C][C]1.45058509868103[/C][C]2.56808999127504[/C][/ROW]
[ROW][C]98[/C][C]2.00506295890044[/C][C]1.31999620983487[/C][C]2.69012970796602[/C][/ROW]
[ROW][C]99[/C][C]2.15795172410657[/C][C]1.35741659801908[/C][C]2.95848685019405[/C][/ROW]
[ROW][C]100[/C][C]2.28644730444787[/C][C]1.50834357829707[/C][C]3.06455103059866[/C][/ROW]
[ROW][C]101[/C][C]1.81709957717443[/C][C]1.09480522460000[/C][C]2.53939392974886[/C][/ROW]
[ROW][C]102[/C][C]1.27001295030391[/C][C]0.544607039299388[/C][C]1.99541886130842[/C][/ROW]
[ROW][C]103[/C][C]1.00005754169695[/C][C]0.193467597394133[/C][C]1.80664748599977[/C][/ROW]
[ROW][C]104[/C][C]0.98381608164466[/C][C]-0.0702017834715115[/C][C]2.03783394676083[/C][/ROW]
[ROW][C]105[/C][C]1.27708624912585[/C][C]-0.180944758459344[/C][C]2.73511725671104[/C][/ROW]
[ROW][C]106[/C][C]1.77923549399763[/C][C]0.301170493512605[/C][C]3.25730049448265[/C][/ROW]
[ROW][C]107[/C][C]1.74382552299113[/C][C]0.106728108861283[/C][C]3.38092293712097[/C][/ROW]
[ROW][C]108[/C][C]1.89360522170516[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36930&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36930&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
972.009337544978031.450585098681032.56808999127504
982.005062958900441.319996209834872.69012970796602
992.157951724106571.357416598019082.95848685019405
1002.286447304447871.508343578297073.06455103059866
1011.817099577174431.094805224600002.53939392974886
1021.270012950303910.5446070392993881.99541886130842
1031.000057541696950.1934675973941331.80664748599977
1040.98381608164466-0.07020178347151152.03783394676083
1051.27708624912585-0.1809447584593442.73511725671104
1061.779235493997630.3011704935126053.25730049448265
1071.743825522991130.1067281088612833.38092293712097
1081.89360522170516NANA



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')