Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 13 Aug 2016 12:29:39 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Aug/13/t147108787336k4p14qtztm38r.htm/, Retrieved Wed, 01 May 2024 19:26:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296506, Retrieved Wed, 01 May 2024 19:26:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean versus Median] [mean vs median va...] [2016-08-11 11:22:45] [4c392b130fccc63297597dd6ffb6df17]
- RMP   [Mean Plot] [mean en meadian p...] [2016-08-11 22:10:26] [4c392b130fccc63297597dd6ffb6df17]
- RMP     [(Partial) Autocorrelation Function] [autocorrelation a...] [2016-08-11 22:42:14] [4c392b130fccc63297597dd6ffb6df17]
- RMP         [Exponential Smoothing] [exponential smoot...] [2016-08-13 11:29:39] [d7adcc7732e5b057da1b42af54844e1a] [Current]
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Dataseries X:
77
85
85
78
89
87
80
83
88
86
81
94
79
85
83
81
90
85
83
89
94
80
82
91
80
86
87
87
91
88
77
79
99
78
88
91
76
81
88
88
91
91
79
79
97
77
86
93
74
74
88
86
94
88
81
75
100
76
86
91
79
71
87
86
98
83
76
74
99
72
83
89
79
65
91
85
94
78
79
76
105
76
84
93
79
65
91
82
94
73
81
77
105
74
82
93
83
66
86
83
93
72
78
79
105
72
82
92




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296506&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296506&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296506&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00614643894836553
beta0.681427670122723
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00614643894836553 \tabularnewline
beta & 0.681427670122723 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296506&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]0.00614643894836553[/C][/ROW]
[ROW][C]beta[/C][C]0.681427670122723[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296506&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296506&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
alpha0.00614643894836553
beta0.681427670122723
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137978.98958333333340.0104166666666003
148584.71885765408880.281142345911178
158382.32597349725220.674026502747779
168180.43832724020990.561672759790071
179089.76067622518910.239323774810913
188584.95704628439910.0429537156008877
198380.86072260571042.13927739428956
208983.9112439026455.088756097355
219489.16787416680224.83212583319779
228087.3181657202029-7.31816572020294
238282.2381251828302-0.238125182830188
249195.4089376632455-4.40893766324552
258080.4626676175013-0.462667617501324
268686.4640909698897-0.464090969889696
278784.45996943462542.54003056537458
288782.48281860917414.51718139082585
299191.5363685876239-0.536368587623883
308886.55681533236171.44318466763831
317784.5824090171307-7.58240901713071
327990.4936807905572-11.4936807905572
339995.31303642429463.68696357570543
347881.295583642632-3.295583642632
358883.20854401988674.79145598011328
369192.2179122009618-1.21791220096176
377681.1794538023774-5.1794538023774
388187.0968992104806-6.09689921048064
398887.96664875426890.0333512457310974
408887.85142621210150.148573787898513
419191.7496759414111-0.74967594141107
429188.62934402375332.37065597624665
437977.58755087405081.41244912594919
447979.6015822038433-0.601582203843279
459799.5555474692567-2.55554746925672
467778.5142747632064-1.51427476320642
478688.4371564323664-2.43715643236642
489391.36102589571421.63897410428577
497476.3462640701074-2.34626407010741
507481.3245126438921-7.32451264389206
518888.2293418274718-0.229341827471842
528688.1759725855105-2.17597258551052
539491.10642351145482.89357648854516
548891.0641144109773-3.06411441097725
558178.96831354705272.03168645294731
567578.9188064175105-3.91880641751048
5710096.83084116715353.16915883284648
587676.8040186374495-0.804018637449545
598685.76142245461090.238577545389148
609192.7113877580325-1.7113877580325
617973.65983024182485.34016975817515
627173.7144066968917-2.71440669689167
638787.6951749089822-0.695174908982196
648685.6983679794380.301632020561954
659893.68690527305244.3130947269476
668387.7426628049569-4.74266280495688
677680.7044082929952-4.70440829299521
687474.6747501047054-0.674750104705367
699999.6398814736191-0.639881473619099
707275.6136944456232-3.61369444562322
718385.5510528882577-2.55105288825773
728990.4952441764458-1.49524417644578
737978.40348824639990.596511753600083
746570.3542280119605-5.35422801196052
759186.24492432891274.75507567108727
768585.2144576273136-0.214457627313621
779497.1266282161554-3.12662821615535
787882.0453997969022-4.04539979690216
797974.96120945920874.03879054079134
807672.9385596639033.06144033609695
8110597.92533681389987.07466318610015
827670.98737059368965.01262940631041
838482.06632884160571.93367115839429
849388.1386566068194.86134339318104
857978.24274591681910.757254083180911
866564.35885879681360.641141203186407
879190.43723250425030.562767495749725
888284.5281105565779-2.52811055657786
899493.60819979788050.391800202119484
907377.7266196880587-4.72661968805872
918178.76103735074772.23896264925229
927775.83673744779841.16326255220163
93105104.873208550940.126791449059709
947475.8868830690534-1.88688306905337
958283.8782076908522-1.87820769085218
969392.83562538028670.164374619713271
978378.81115064563224.18884935436783
986664.82649851427361.1735014857264
998690.8260241636313-4.8260241636313
1008381.78510182331551.21489817668451
1019393.7790396341417-0.779039634141739
1027272.7872779921034-0.78727799210337
1037880.7691515427888-2.7691515427888
1047976.72447960069892.27552039930107
105105104.72184356220.278156437800106
1067273.7199417456326-1.71994174563258
1078281.70640462717380.293595372826232
1089292.7017852633347-0.701785263334685

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 79 & 78.9895833333334 & 0.0104166666666003 \tabularnewline
14 & 85 & 84.7188576540888 & 0.281142345911178 \tabularnewline
15 & 83 & 82.3259734972522 & 0.674026502747779 \tabularnewline
16 & 81 & 80.4383272402099 & 0.561672759790071 \tabularnewline
17 & 90 & 89.7606762251891 & 0.239323774810913 \tabularnewline
18 & 85 & 84.9570462843991 & 0.0429537156008877 \tabularnewline
19 & 83 & 80.8607226057104 & 2.13927739428956 \tabularnewline
20 & 89 & 83.911243902645 & 5.088756097355 \tabularnewline
21 & 94 & 89.1678741668022 & 4.83212583319779 \tabularnewline
22 & 80 & 87.3181657202029 & -7.31816572020294 \tabularnewline
23 & 82 & 82.2381251828302 & -0.238125182830188 \tabularnewline
24 & 91 & 95.4089376632455 & -4.40893766324552 \tabularnewline
25 & 80 & 80.4626676175013 & -0.462667617501324 \tabularnewline
26 & 86 & 86.4640909698897 & -0.464090969889696 \tabularnewline
27 & 87 & 84.4599694346254 & 2.54003056537458 \tabularnewline
28 & 87 & 82.4828186091741 & 4.51718139082585 \tabularnewline
29 & 91 & 91.5363685876239 & -0.536368587623883 \tabularnewline
30 & 88 & 86.5568153323617 & 1.44318466763831 \tabularnewline
31 & 77 & 84.5824090171307 & -7.58240901713071 \tabularnewline
32 & 79 & 90.4936807905572 & -11.4936807905572 \tabularnewline
33 & 99 & 95.3130364242946 & 3.68696357570543 \tabularnewline
34 & 78 & 81.295583642632 & -3.295583642632 \tabularnewline
35 & 88 & 83.2085440198867 & 4.79145598011328 \tabularnewline
36 & 91 & 92.2179122009618 & -1.21791220096176 \tabularnewline
37 & 76 & 81.1794538023774 & -5.1794538023774 \tabularnewline
38 & 81 & 87.0968992104806 & -6.09689921048064 \tabularnewline
39 & 88 & 87.9666487542689 & 0.0333512457310974 \tabularnewline
40 & 88 & 87.8514262121015 & 0.148573787898513 \tabularnewline
41 & 91 & 91.7496759414111 & -0.74967594141107 \tabularnewline
42 & 91 & 88.6293440237533 & 2.37065597624665 \tabularnewline
43 & 79 & 77.5875508740508 & 1.41244912594919 \tabularnewline
44 & 79 & 79.6015822038433 & -0.601582203843279 \tabularnewline
45 & 97 & 99.5555474692567 & -2.55554746925672 \tabularnewline
46 & 77 & 78.5142747632064 & -1.51427476320642 \tabularnewline
47 & 86 & 88.4371564323664 & -2.43715643236642 \tabularnewline
48 & 93 & 91.3610258957142 & 1.63897410428577 \tabularnewline
49 & 74 & 76.3462640701074 & -2.34626407010741 \tabularnewline
50 & 74 & 81.3245126438921 & -7.32451264389206 \tabularnewline
51 & 88 & 88.2293418274718 & -0.229341827471842 \tabularnewline
52 & 86 & 88.1759725855105 & -2.17597258551052 \tabularnewline
53 & 94 & 91.1064235114548 & 2.89357648854516 \tabularnewline
54 & 88 & 91.0641144109773 & -3.06411441097725 \tabularnewline
55 & 81 & 78.9683135470527 & 2.03168645294731 \tabularnewline
56 & 75 & 78.9188064175105 & -3.91880641751048 \tabularnewline
57 & 100 & 96.8308411671535 & 3.16915883284648 \tabularnewline
58 & 76 & 76.8040186374495 & -0.804018637449545 \tabularnewline
59 & 86 & 85.7614224546109 & 0.238577545389148 \tabularnewline
60 & 91 & 92.7113877580325 & -1.7113877580325 \tabularnewline
61 & 79 & 73.6598302418248 & 5.34016975817515 \tabularnewline
62 & 71 & 73.7144066968917 & -2.71440669689167 \tabularnewline
63 & 87 & 87.6951749089822 & -0.695174908982196 \tabularnewline
64 & 86 & 85.698367979438 & 0.301632020561954 \tabularnewline
65 & 98 & 93.6869052730524 & 4.3130947269476 \tabularnewline
66 & 83 & 87.7426628049569 & -4.74266280495688 \tabularnewline
67 & 76 & 80.7044082929952 & -4.70440829299521 \tabularnewline
68 & 74 & 74.6747501047054 & -0.674750104705367 \tabularnewline
69 & 99 & 99.6398814736191 & -0.639881473619099 \tabularnewline
70 & 72 & 75.6136944456232 & -3.61369444562322 \tabularnewline
71 & 83 & 85.5510528882577 & -2.55105288825773 \tabularnewline
72 & 89 & 90.4952441764458 & -1.49524417644578 \tabularnewline
73 & 79 & 78.4034882463999 & 0.596511753600083 \tabularnewline
74 & 65 & 70.3542280119605 & -5.35422801196052 \tabularnewline
75 & 91 & 86.2449243289127 & 4.75507567108727 \tabularnewline
76 & 85 & 85.2144576273136 & -0.214457627313621 \tabularnewline
77 & 94 & 97.1266282161554 & -3.12662821615535 \tabularnewline
78 & 78 & 82.0453997969022 & -4.04539979690216 \tabularnewline
79 & 79 & 74.9612094592087 & 4.03879054079134 \tabularnewline
80 & 76 & 72.938559663903 & 3.06144033609695 \tabularnewline
81 & 105 & 97.9253368138998 & 7.07466318610015 \tabularnewline
82 & 76 & 70.9873705936896 & 5.01262940631041 \tabularnewline
83 & 84 & 82.0663288416057 & 1.93367115839429 \tabularnewline
84 & 93 & 88.138656606819 & 4.86134339318104 \tabularnewline
85 & 79 & 78.2427459168191 & 0.757254083180911 \tabularnewline
86 & 65 & 64.3588587968136 & 0.641141203186407 \tabularnewline
87 & 91 & 90.4372325042503 & 0.562767495749725 \tabularnewline
88 & 82 & 84.5281105565779 & -2.52811055657786 \tabularnewline
89 & 94 & 93.6081997978805 & 0.391800202119484 \tabularnewline
90 & 73 & 77.7266196880587 & -4.72661968805872 \tabularnewline
91 & 81 & 78.7610373507477 & 2.23896264925229 \tabularnewline
92 & 77 & 75.8367374477984 & 1.16326255220163 \tabularnewline
93 & 105 & 104.87320855094 & 0.126791449059709 \tabularnewline
94 & 74 & 75.8868830690534 & -1.88688306905337 \tabularnewline
95 & 82 & 83.8782076908522 & -1.87820769085218 \tabularnewline
96 & 93 & 92.8356253802867 & 0.164374619713271 \tabularnewline
97 & 83 & 78.8111506456322 & 4.18884935436783 \tabularnewline
98 & 66 & 64.8264985142736 & 1.1735014857264 \tabularnewline
99 & 86 & 90.8260241636313 & -4.8260241636313 \tabularnewline
100 & 83 & 81.7851018233155 & 1.21489817668451 \tabularnewline
101 & 93 & 93.7790396341417 & -0.779039634141739 \tabularnewline
102 & 72 & 72.7872779921034 & -0.78727799210337 \tabularnewline
103 & 78 & 80.7691515427888 & -2.7691515427888 \tabularnewline
104 & 79 & 76.7244796006989 & 2.27552039930107 \tabularnewline
105 & 105 & 104.7218435622 & 0.278156437800106 \tabularnewline
106 & 72 & 73.7199417456326 & -1.71994174563258 \tabularnewline
107 & 82 & 81.7064046271738 & 0.293595372826232 \tabularnewline
108 & 92 & 92.7017852633347 & -0.701785263334685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296506&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]79[/C][C]78.9895833333334[/C][C]0.0104166666666003[/C][/ROW]
[ROW][C]14[/C][C]85[/C][C]84.7188576540888[/C][C]0.281142345911178[/C][/ROW]
[ROW][C]15[/C][C]83[/C][C]82.3259734972522[/C][C]0.674026502747779[/C][/ROW]
[ROW][C]16[/C][C]81[/C][C]80.4383272402099[/C][C]0.561672759790071[/C][/ROW]
[ROW][C]17[/C][C]90[/C][C]89.7606762251891[/C][C]0.239323774810913[/C][/ROW]
[ROW][C]18[/C][C]85[/C][C]84.9570462843991[/C][C]0.0429537156008877[/C][/ROW]
[ROW][C]19[/C][C]83[/C][C]80.8607226057104[/C][C]2.13927739428956[/C][/ROW]
[ROW][C]20[/C][C]89[/C][C]83.911243902645[/C][C]5.088756097355[/C][/ROW]
[ROW][C]21[/C][C]94[/C][C]89.1678741668022[/C][C]4.83212583319779[/C][/ROW]
[ROW][C]22[/C][C]80[/C][C]87.3181657202029[/C][C]-7.31816572020294[/C][/ROW]
[ROW][C]23[/C][C]82[/C][C]82.2381251828302[/C][C]-0.238125182830188[/C][/ROW]
[ROW][C]24[/C][C]91[/C][C]95.4089376632455[/C][C]-4.40893766324552[/C][/ROW]
[ROW][C]25[/C][C]80[/C][C]80.4626676175013[/C][C]-0.462667617501324[/C][/ROW]
[ROW][C]26[/C][C]86[/C][C]86.4640909698897[/C][C]-0.464090969889696[/C][/ROW]
[ROW][C]27[/C][C]87[/C][C]84.4599694346254[/C][C]2.54003056537458[/C][/ROW]
[ROW][C]28[/C][C]87[/C][C]82.4828186091741[/C][C]4.51718139082585[/C][/ROW]
[ROW][C]29[/C][C]91[/C][C]91.5363685876239[/C][C]-0.536368587623883[/C][/ROW]
[ROW][C]30[/C][C]88[/C][C]86.5568153323617[/C][C]1.44318466763831[/C][/ROW]
[ROW][C]31[/C][C]77[/C][C]84.5824090171307[/C][C]-7.58240901713071[/C][/ROW]
[ROW][C]32[/C][C]79[/C][C]90.4936807905572[/C][C]-11.4936807905572[/C][/ROW]
[ROW][C]33[/C][C]99[/C][C]95.3130364242946[/C][C]3.68696357570543[/C][/ROW]
[ROW][C]34[/C][C]78[/C][C]81.295583642632[/C][C]-3.295583642632[/C][/ROW]
[ROW][C]35[/C][C]88[/C][C]83.2085440198867[/C][C]4.79145598011328[/C][/ROW]
[ROW][C]36[/C][C]91[/C][C]92.2179122009618[/C][C]-1.21791220096176[/C][/ROW]
[ROW][C]37[/C][C]76[/C][C]81.1794538023774[/C][C]-5.1794538023774[/C][/ROW]
[ROW][C]38[/C][C]81[/C][C]87.0968992104806[/C][C]-6.09689921048064[/C][/ROW]
[ROW][C]39[/C][C]88[/C][C]87.9666487542689[/C][C]0.0333512457310974[/C][/ROW]
[ROW][C]40[/C][C]88[/C][C]87.8514262121015[/C][C]0.148573787898513[/C][/ROW]
[ROW][C]41[/C][C]91[/C][C]91.7496759414111[/C][C]-0.74967594141107[/C][/ROW]
[ROW][C]42[/C][C]91[/C][C]88.6293440237533[/C][C]2.37065597624665[/C][/ROW]
[ROW][C]43[/C][C]79[/C][C]77.5875508740508[/C][C]1.41244912594919[/C][/ROW]
[ROW][C]44[/C][C]79[/C][C]79.6015822038433[/C][C]-0.601582203843279[/C][/ROW]
[ROW][C]45[/C][C]97[/C][C]99.5555474692567[/C][C]-2.55554746925672[/C][/ROW]
[ROW][C]46[/C][C]77[/C][C]78.5142747632064[/C][C]-1.51427476320642[/C][/ROW]
[ROW][C]47[/C][C]86[/C][C]88.4371564323664[/C][C]-2.43715643236642[/C][/ROW]
[ROW][C]48[/C][C]93[/C][C]91.3610258957142[/C][C]1.63897410428577[/C][/ROW]
[ROW][C]49[/C][C]74[/C][C]76.3462640701074[/C][C]-2.34626407010741[/C][/ROW]
[ROW][C]50[/C][C]74[/C][C]81.3245126438921[/C][C]-7.32451264389206[/C][/ROW]
[ROW][C]51[/C][C]88[/C][C]88.2293418274718[/C][C]-0.229341827471842[/C][/ROW]
[ROW][C]52[/C][C]86[/C][C]88.1759725855105[/C][C]-2.17597258551052[/C][/ROW]
[ROW][C]53[/C][C]94[/C][C]91.1064235114548[/C][C]2.89357648854516[/C][/ROW]
[ROW][C]54[/C][C]88[/C][C]91.0641144109773[/C][C]-3.06411441097725[/C][/ROW]
[ROW][C]55[/C][C]81[/C][C]78.9683135470527[/C][C]2.03168645294731[/C][/ROW]
[ROW][C]56[/C][C]75[/C][C]78.9188064175105[/C][C]-3.91880641751048[/C][/ROW]
[ROW][C]57[/C][C]100[/C][C]96.8308411671535[/C][C]3.16915883284648[/C][/ROW]
[ROW][C]58[/C][C]76[/C][C]76.8040186374495[/C][C]-0.804018637449545[/C][/ROW]
[ROW][C]59[/C][C]86[/C][C]85.7614224546109[/C][C]0.238577545389148[/C][/ROW]
[ROW][C]60[/C][C]91[/C][C]92.7113877580325[/C][C]-1.7113877580325[/C][/ROW]
[ROW][C]61[/C][C]79[/C][C]73.6598302418248[/C][C]5.34016975817515[/C][/ROW]
[ROW][C]62[/C][C]71[/C][C]73.7144066968917[/C][C]-2.71440669689167[/C][/ROW]
[ROW][C]63[/C][C]87[/C][C]87.6951749089822[/C][C]-0.695174908982196[/C][/ROW]
[ROW][C]64[/C][C]86[/C][C]85.698367979438[/C][C]0.301632020561954[/C][/ROW]
[ROW][C]65[/C][C]98[/C][C]93.6869052730524[/C][C]4.3130947269476[/C][/ROW]
[ROW][C]66[/C][C]83[/C][C]87.7426628049569[/C][C]-4.74266280495688[/C][/ROW]
[ROW][C]67[/C][C]76[/C][C]80.7044082929952[/C][C]-4.70440829299521[/C][/ROW]
[ROW][C]68[/C][C]74[/C][C]74.6747501047054[/C][C]-0.674750104705367[/C][/ROW]
[ROW][C]69[/C][C]99[/C][C]99.6398814736191[/C][C]-0.639881473619099[/C][/ROW]
[ROW][C]70[/C][C]72[/C][C]75.6136944456232[/C][C]-3.61369444562322[/C][/ROW]
[ROW][C]71[/C][C]83[/C][C]85.5510528882577[/C][C]-2.55105288825773[/C][/ROW]
[ROW][C]72[/C][C]89[/C][C]90.4952441764458[/C][C]-1.49524417644578[/C][/ROW]
[ROW][C]73[/C][C]79[/C][C]78.4034882463999[/C][C]0.596511753600083[/C][/ROW]
[ROW][C]74[/C][C]65[/C][C]70.3542280119605[/C][C]-5.35422801196052[/C][/ROW]
[ROW][C]75[/C][C]91[/C][C]86.2449243289127[/C][C]4.75507567108727[/C][/ROW]
[ROW][C]76[/C][C]85[/C][C]85.2144576273136[/C][C]-0.214457627313621[/C][/ROW]
[ROW][C]77[/C][C]94[/C][C]97.1266282161554[/C][C]-3.12662821615535[/C][/ROW]
[ROW][C]78[/C][C]78[/C][C]82.0453997969022[/C][C]-4.04539979690216[/C][/ROW]
[ROW][C]79[/C][C]79[/C][C]74.9612094592087[/C][C]4.03879054079134[/C][/ROW]
[ROW][C]80[/C][C]76[/C][C]72.938559663903[/C][C]3.06144033609695[/C][/ROW]
[ROW][C]81[/C][C]105[/C][C]97.9253368138998[/C][C]7.07466318610015[/C][/ROW]
[ROW][C]82[/C][C]76[/C][C]70.9873705936896[/C][C]5.01262940631041[/C][/ROW]
[ROW][C]83[/C][C]84[/C][C]82.0663288416057[/C][C]1.93367115839429[/C][/ROW]
[ROW][C]84[/C][C]93[/C][C]88.138656606819[/C][C]4.86134339318104[/C][/ROW]
[ROW][C]85[/C][C]79[/C][C]78.2427459168191[/C][C]0.757254083180911[/C][/ROW]
[ROW][C]86[/C][C]65[/C][C]64.3588587968136[/C][C]0.641141203186407[/C][/ROW]
[ROW][C]87[/C][C]91[/C][C]90.4372325042503[/C][C]0.562767495749725[/C][/ROW]
[ROW][C]88[/C][C]82[/C][C]84.5281105565779[/C][C]-2.52811055657786[/C][/ROW]
[ROW][C]89[/C][C]94[/C][C]93.6081997978805[/C][C]0.391800202119484[/C][/ROW]
[ROW][C]90[/C][C]73[/C][C]77.7266196880587[/C][C]-4.72661968805872[/C][/ROW]
[ROW][C]91[/C][C]81[/C][C]78.7610373507477[/C][C]2.23896264925229[/C][/ROW]
[ROW][C]92[/C][C]77[/C][C]75.8367374477984[/C][C]1.16326255220163[/C][/ROW]
[ROW][C]93[/C][C]105[/C][C]104.87320855094[/C][C]0.126791449059709[/C][/ROW]
[ROW][C]94[/C][C]74[/C][C]75.8868830690534[/C][C]-1.88688306905337[/C][/ROW]
[ROW][C]95[/C][C]82[/C][C]83.8782076908522[/C][C]-1.87820769085218[/C][/ROW]
[ROW][C]96[/C][C]93[/C][C]92.8356253802867[/C][C]0.164374619713271[/C][/ROW]
[ROW][C]97[/C][C]83[/C][C]78.8111506456322[/C][C]4.18884935436783[/C][/ROW]
[ROW][C]98[/C][C]66[/C][C]64.8264985142736[/C][C]1.1735014857264[/C][/ROW]
[ROW][C]99[/C][C]86[/C][C]90.8260241636313[/C][C]-4.8260241636313[/C][/ROW]
[ROW][C]100[/C][C]83[/C][C]81.7851018233155[/C][C]1.21489817668451[/C][/ROW]
[ROW][C]101[/C][C]93[/C][C]93.7790396341417[/C][C]-0.779039634141739[/C][/ROW]
[ROW][C]102[/C][C]72[/C][C]72.7872779921034[/C][C]-0.78727799210337[/C][/ROW]
[ROW][C]103[/C][C]78[/C][C]80.7691515427888[/C][C]-2.7691515427888[/C][/ROW]
[ROW][C]104[/C][C]79[/C][C]76.7244796006989[/C][C]2.27552039930107[/C][/ROW]
[ROW][C]105[/C][C]105[/C][C]104.7218435622[/C][C]0.278156437800106[/C][/ROW]
[ROW][C]106[/C][C]72[/C][C]73.7199417456326[/C][C]-1.71994174563258[/C][/ROW]
[ROW][C]107[/C][C]82[/C][C]81.7064046271738[/C][C]0.293595372826232[/C][/ROW]
[ROW][C]108[/C][C]92[/C][C]92.7017852633347[/C][C]-0.701785263334685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296506&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296506&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
137978.98958333333340.0104166666666003
148584.71885765408880.281142345911178
158382.32597349725220.674026502747779
168180.43832724020990.561672759790071
179089.76067622518910.239323774810913
188584.95704628439910.0429537156008877
198380.86072260571042.13927739428956
208983.9112439026455.088756097355
219489.16787416680224.83212583319779
228087.3181657202029-7.31816572020294
238282.2381251828302-0.238125182830188
249195.4089376632455-4.40893766324552
258080.4626676175013-0.462667617501324
268686.4640909698897-0.464090969889696
278784.45996943462542.54003056537458
288782.48281860917414.51718139082585
299191.5363685876239-0.536368587623883
308886.55681533236171.44318466763831
317784.5824090171307-7.58240901713071
327990.4936807905572-11.4936807905572
339995.31303642429463.68696357570543
347881.295583642632-3.295583642632
358883.20854401988674.79145598011328
369192.2179122009618-1.21791220096176
377681.1794538023774-5.1794538023774
388187.0968992104806-6.09689921048064
398887.96664875426890.0333512457310974
408887.85142621210150.148573787898513
419191.7496759414111-0.74967594141107
429188.62934402375332.37065597624665
437977.58755087405081.41244912594919
447979.6015822038433-0.601582203843279
459799.5555474692567-2.55554746925672
467778.5142747632064-1.51427476320642
478688.4371564323664-2.43715643236642
489391.36102589571421.63897410428577
497476.3462640701074-2.34626407010741
507481.3245126438921-7.32451264389206
518888.2293418274718-0.229341827471842
528688.1759725855105-2.17597258551052
539491.10642351145482.89357648854516
548891.0641144109773-3.06411441097725
558178.96831354705272.03168645294731
567578.9188064175105-3.91880641751048
5710096.83084116715353.16915883284648
587676.8040186374495-0.804018637449545
598685.76142245461090.238577545389148
609192.7113877580325-1.7113877580325
617973.65983024182485.34016975817515
627173.7144066968917-2.71440669689167
638787.6951749089822-0.695174908982196
648685.6983679794380.301632020561954
659893.68690527305244.3130947269476
668387.7426628049569-4.74266280495688
677680.7044082929952-4.70440829299521
687474.6747501047054-0.674750104705367
699999.6398814736191-0.639881473619099
707275.6136944456232-3.61369444562322
718385.5510528882577-2.55105288825773
728990.4952441764458-1.49524417644578
737978.40348824639990.596511753600083
746570.3542280119605-5.35422801196052
759186.24492432891274.75507567108727
768585.2144576273136-0.214457627313621
779497.1266282161554-3.12662821615535
787882.0453997969022-4.04539979690216
797974.96120945920874.03879054079134
807672.9385596639033.06144033609695
8110597.92533681389987.07466318610015
827670.98737059368965.01262940631041
838482.06632884160571.93367115839429
849388.1386566068194.86134339318104
857978.24274591681910.757254083180911
866564.35885879681360.641141203186407
879190.43723250425030.562767495749725
888284.5281105565779-2.52811055657786
899493.60819979788050.391800202119484
907377.7266196880587-4.72661968805872
918178.76103735074772.23896264925229
927775.83673744779841.16326255220163
93105104.873208550940.126791449059709
947475.8868830690534-1.88688306905337
958283.8782076908522-1.87820769085218
969392.83562538028670.164374619713271
978378.81115064563224.18884935436783
986664.82649851427361.1735014857264
998690.8260241636313-4.8260241636313
1008381.78510182331551.21489817668451
1019393.7790396341417-0.779039634141739
1027272.7872779921034-0.78727799210337
1037880.7691515427888-2.7691515427888
1047976.72447960069892.27552039930107
105105104.72184356220.278156437800106
1067273.7199417456326-1.71994174563258
1078281.70640462717380.293595372826232
1089292.7017852633347-0.701785263334685







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10982.662683881089176.232001112071789.0933666501064
11065.628885248545559.197859064719672.0599114323715
11185.627047294985379.19534299762292.0587515923486
11282.608292276613576.17546250049289.041122052735
11392.596704452144686.162189323995999.0312195802934
11471.588430157674565.151557542498878.0253027728503
11577.595634726577671.155620580999384.0356488721559
11678.583430713130172.139379564517185.0274818617431
117104.57397269133798.1248782608066111.023067121867
11871.575630840530865.120376827176378.0308848538852
11981.572116630910175.109477673575388.034755588245
12091.573490786371585.102133618086498.0448479546567

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 82.6626838810891 & 76.2320011120717 & 89.0933666501064 \tabularnewline
110 & 65.6288852485455 & 59.1978590647196 & 72.0599114323715 \tabularnewline
111 & 85.6270472949853 & 79.195342997622 & 92.0587515923486 \tabularnewline
112 & 82.6082922766135 & 76.175462500492 & 89.041122052735 \tabularnewline
113 & 92.5967044521446 & 86.1621893239959 & 99.0312195802934 \tabularnewline
114 & 71.5884301576745 & 65.1515575424988 & 78.0253027728503 \tabularnewline
115 & 77.5956347265776 & 71.1556205809993 & 84.0356488721559 \tabularnewline
116 & 78.5834307131301 & 72.1393795645171 & 85.0274818617431 \tabularnewline
117 & 104.573972691337 & 98.1248782608066 & 111.023067121867 \tabularnewline
118 & 71.5756308405308 & 65.1203768271763 & 78.0308848538852 \tabularnewline
119 & 81.5721166309101 & 75.1094776735753 & 88.034755588245 \tabularnewline
120 & 91.5734907863715 & 85.1021336180864 & 98.0448479546567 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296506&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]109[/C][C]82.6626838810891[/C][C]76.2320011120717[/C][C]89.0933666501064[/C][/ROW]
[ROW][C]110[/C][C]65.6288852485455[/C][C]59.1978590647196[/C][C]72.0599114323715[/C][/ROW]
[ROW][C]111[/C][C]85.6270472949853[/C][C]79.195342997622[/C][C]92.0587515923486[/C][/ROW]
[ROW][C]112[/C][C]82.6082922766135[/C][C]76.175462500492[/C][C]89.041122052735[/C][/ROW]
[ROW][C]113[/C][C]92.5967044521446[/C][C]86.1621893239959[/C][C]99.0312195802934[/C][/ROW]
[ROW][C]114[/C][C]71.5884301576745[/C][C]65.1515575424988[/C][C]78.0253027728503[/C][/ROW]
[ROW][C]115[/C][C]77.5956347265776[/C][C]71.1556205809993[/C][C]84.0356488721559[/C][/ROW]
[ROW][C]116[/C][C]78.5834307131301[/C][C]72.1393795645171[/C][C]85.0274818617431[/C][/ROW]
[ROW][C]117[/C][C]104.573972691337[/C][C]98.1248782608066[/C][C]111.023067121867[/C][/ROW]
[ROW][C]118[/C][C]71.5756308405308[/C][C]65.1203768271763[/C][C]78.0308848538852[/C][/ROW]
[ROW][C]119[/C][C]81.5721166309101[/C][C]75.1094776735753[/C][C]88.034755588245[/C][/ROW]
[ROW][C]120[/C][C]91.5734907863715[/C][C]85.1021336180864[/C][C]98.0448479546567[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296506&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296506&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
10982.662683881089176.232001112071789.0933666501064
11065.628885248545559.197859064719672.0599114323715
11185.627047294985379.19534299762292.0587515923486
11282.608292276613576.17546250049289.041122052735
11392.596704452144686.162189323995999.0312195802934
11471.588430157674565.151557542498878.0253027728503
11577.595634726577671.155620580999384.0356488721559
11678.583430713130172.139379564517185.0274818617431
117104.57397269133798.1248782608066111.023067121867
11871.575630840530865.120376827176378.0308848538852
11981.572116630910175.109477673575388.034755588245
12091.573490786371585.102133618086498.0448479546567



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')