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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 09 Jan 2017 11:00:40 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Jan/09/t1483959691mm5aw5uk4elnbcc.htm/, Retrieved Tue, 14 May 2024 19:57:53 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 19:57:53 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
94,46
96,91
101,92
104,53
105,85
106,39
106,08
106,42
106,51
106,59
105,71
104,41
103,04
100,99
100,93
99,31
99,79
99,57
99,11
98,96
97,72
99,35
98,15
97,64
97,49
97,94
98,03
98,05
97,54
98,71
99,33
99,16
98,41
98,43
97,02
97,89
97,92
97,37
97,42
96,12
96,72
96,64
95,28
95,3
95,02
95,57
94,78
95,27
96,14
96,16
95,08
94,39
94,15
94,58
94,16
95,02
94,86
94,49
94,81
94,16
94,83
96,02
95,97
95,88
95,97
97,55
97,49
98,4
98,2
97,16
96,96
96,37
96,34
96,86
96,32
95,44
92,85
92,56
91,74
92,44
93,19
92,62
94,04
93,8
96,73
98,99
100,38
101,07
99,92
101,78
100,91
100,49
101,17
100,25
98,94
99,4
100,02
99,91
99,22
98,84
98,42
97,59
97,07
96,59
95,96
94,22
94,48
93,14
93,73
94,24
98,52
99,09
99,84
99,13
100,88
100,83
101,6
101,8
102,77
103,14

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.917897731960009
beta0.0306973701880003
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.917897731960009 \tabularnewline
beta & 0.0306973701880003 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.917897731960009[/C][/ROW]
[ROW][C]beta[/C][C]0.0306973701880003[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.917897731960009
beta0.0306973701880003
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13103.04105.055364197453-2.01536419745312
14100.99101.234097492041-0.244097492041206
15100.93101.099955993039-0.169955993039238
1699.3199.4584315219442-0.14843152194419
1799.7999.8832589184353-0.0932589184352821
1899.5799.6367582088831-0.0667582088830585
1999.11101.112681213834-2.00268121383367
2098.9698.48590872795850.47409127204152
2197.7298.2917872794031-0.571787279403068
2299.3597.47305451799141.87694548200861
2398.1598.2666726386161-0.11667263861608
2497.6496.90112604406140.738873955938587
2597.4996.15298028186461.33701971813541
2697.9495.65432262887752.28567737112252
2798.0397.92830253601740.101697463982617
2898.0596.67202215121791.37797784878214
2997.5498.6383712066469-1.09837120664689
3098.7197.58650491295791.12349508704212
3199.33100.134364924594-0.804364924594225
3299.1699.00426323573070.155736764269307
3398.4198.6158655890423-0.205865589042304
3498.4398.530731027288-0.100731027287978
3597.0297.4893554050744-0.469355405074367
3697.8996.00524669033041.88475330966961
3797.9296.51496132303631.40503867696368
3897.3796.30794107308181.06205892691821
3997.4297.40167697936270.0183230206373111
4096.1296.2990244533907-0.17902445339071
4196.7296.69324790713460.0267520928653511
4296.6496.9616657256385-0.32166572563851
4395.2898.0593021569692-2.77930215696919
4495.395.20698722054760.0930127794523514
4595.0294.75109484555020.268905154449826
4695.5795.11939888280560.450601117194353
4794.7894.61284983151940.167150168480632
4895.2793.97390974614671.29609025385328
4996.1493.97039096536782.16960903463217
5096.1694.5240073927841.63599260721598
5195.0896.1346017551066-1.05460175510663
5294.3994.09998877844830.29001122155168
5394.1594.9890503920407-0.839050392040704
5494.5894.45990842593990.12009157406014
5594.1695.775483282491-1.61548328249101
5695.0294.30921206237910.710787937620864
5794.8694.53788399019410.322116009805939
5894.4995.0734823088023-0.583482308802303
5994.8193.67574954812841.13425045187161
6094.1694.11810639927450.0418936007255297
6194.8393.10678800879431.72321199120566
6296.0293.27589048924462.74410951075541
6395.9795.76540184321980.204598156780179
6495.8895.10891598165370.771084018346329
6595.9796.4910441465401-0.521044146540135
6697.5596.48704592591931.06295407408074
6797.4998.7357744132-1.2457744132
6898.498.00160330918890.398396690811126
6998.298.07986358207040.120136417929615
7097.1698.5404196605701-1.38041966057006
7196.9696.68481288586170.275187114138276
7296.3796.36078537519940.00921462480062019
7396.3495.5594280019120.78057199808805
7496.8695.01588909148811.84411090851191
7596.3296.5362485251122-0.216248525112249
7695.4495.5909355650319-0.150935565031901
7792.8596.0456449859097-3.19564498590971
7892.5693.6467285055935-1.08672850559347
7991.7493.563110145117-1.82311014511703
8092.4492.26867929966120.171320700338782
8193.1991.9946944750911.19530552490896
8292.6293.1970494440134-0.577049444013369
8394.0492.1486893231811.89131067681903
8493.893.26644427957960.533555720420395
8596.7393.00627946671923.72372053328083
8698.9995.31085445601483.67914554398516
87100.3898.45536083369431.92463916630571
88101.0799.62666221446531.44333778553469
8999.92101.529417105084-1.60941710508435
90101.78101.0925799250860.687420074914343
91100.91102.997983565862-2.08798356586158
92100.49102.020087933709-1.53008793370948
93101.17100.525085721770.644914278230416
94100.25101.342845447786-1.09284544778556
9598.94100.250292127739-1.31029212773889
9699.498.43373479117180.966265208828233
97100.0298.9591776975341.06082230246601
9899.9198.85091149658921.05908850341079
9999.2299.4467700472317-0.226770047231682
10098.8498.55703023497210.282969765027858
10198.4299.0515310542991-0.631531054299074
10297.5999.6244751164777-2.03447511647765
10397.0798.626183579555-1.55618357955501
10496.5998.0227046468215-1.43270464682153
10595.9696.6714666337335-0.711466633733494
10694.2295.9387188452703-1.71871884527033
10794.4894.08217397464090.397826025359123
10893.1493.909265060338-0.769265060338043
10993.7392.6936954806191.03630451938102
11094.2492.45710001588391.78289998411611
11198.5293.4887095744365.03129042556404
11299.0997.46878727580981.62121272419016
11399.8499.14808568807220.691914311927761
11499.13100.900907933136-1.77090793313621
115100.88100.2756519895910.604348010409353
116100.83101.838435700377-1.00843570037746
117101.6101.0930511510040.506948848996146
118101.8101.5774190902020.222580909797642
119102.77101.9227941927490.847205807250717
120103.14102.2771879087250.862812091274677

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 103.04 & 105.055364197453 & -2.01536419745312 \tabularnewline
14 & 100.99 & 101.234097492041 & -0.244097492041206 \tabularnewline
15 & 100.93 & 101.099955993039 & -0.169955993039238 \tabularnewline
16 & 99.31 & 99.4584315219442 & -0.14843152194419 \tabularnewline
17 & 99.79 & 99.8832589184353 & -0.0932589184352821 \tabularnewline
18 & 99.57 & 99.6367582088831 & -0.0667582088830585 \tabularnewline
19 & 99.11 & 101.112681213834 & -2.00268121383367 \tabularnewline
20 & 98.96 & 98.4859087279585 & 0.47409127204152 \tabularnewline
21 & 97.72 & 98.2917872794031 & -0.571787279403068 \tabularnewline
22 & 99.35 & 97.4730545179914 & 1.87694548200861 \tabularnewline
23 & 98.15 & 98.2666726386161 & -0.11667263861608 \tabularnewline
24 & 97.64 & 96.9011260440614 & 0.738873955938587 \tabularnewline
25 & 97.49 & 96.1529802818646 & 1.33701971813541 \tabularnewline
26 & 97.94 & 95.6543226288775 & 2.28567737112252 \tabularnewline
27 & 98.03 & 97.9283025360174 & 0.101697463982617 \tabularnewline
28 & 98.05 & 96.6720221512179 & 1.37797784878214 \tabularnewline
29 & 97.54 & 98.6383712066469 & -1.09837120664689 \tabularnewline
30 & 98.71 & 97.5865049129579 & 1.12349508704212 \tabularnewline
31 & 99.33 & 100.134364924594 & -0.804364924594225 \tabularnewline
32 & 99.16 & 99.0042632357307 & 0.155736764269307 \tabularnewline
33 & 98.41 & 98.6158655890423 & -0.205865589042304 \tabularnewline
34 & 98.43 & 98.530731027288 & -0.100731027287978 \tabularnewline
35 & 97.02 & 97.4893554050744 & -0.469355405074367 \tabularnewline
36 & 97.89 & 96.0052466903304 & 1.88475330966961 \tabularnewline
37 & 97.92 & 96.5149613230363 & 1.40503867696368 \tabularnewline
38 & 97.37 & 96.3079410730818 & 1.06205892691821 \tabularnewline
39 & 97.42 & 97.4016769793627 & 0.0183230206373111 \tabularnewline
40 & 96.12 & 96.2990244533907 & -0.17902445339071 \tabularnewline
41 & 96.72 & 96.6932479071346 & 0.0267520928653511 \tabularnewline
42 & 96.64 & 96.9616657256385 & -0.32166572563851 \tabularnewline
43 & 95.28 & 98.0593021569692 & -2.77930215696919 \tabularnewline
44 & 95.3 & 95.2069872205476 & 0.0930127794523514 \tabularnewline
45 & 95.02 & 94.7510948455502 & 0.268905154449826 \tabularnewline
46 & 95.57 & 95.1193988828056 & 0.450601117194353 \tabularnewline
47 & 94.78 & 94.6128498315194 & 0.167150168480632 \tabularnewline
48 & 95.27 & 93.9739097461467 & 1.29609025385328 \tabularnewline
49 & 96.14 & 93.9703909653678 & 2.16960903463217 \tabularnewline
50 & 96.16 & 94.524007392784 & 1.63599260721598 \tabularnewline
51 & 95.08 & 96.1346017551066 & -1.05460175510663 \tabularnewline
52 & 94.39 & 94.0999887784483 & 0.29001122155168 \tabularnewline
53 & 94.15 & 94.9890503920407 & -0.839050392040704 \tabularnewline
54 & 94.58 & 94.4599084259399 & 0.12009157406014 \tabularnewline
55 & 94.16 & 95.775483282491 & -1.61548328249101 \tabularnewline
56 & 95.02 & 94.3092120623791 & 0.710787937620864 \tabularnewline
57 & 94.86 & 94.5378839901941 & 0.322116009805939 \tabularnewline
58 & 94.49 & 95.0734823088023 & -0.583482308802303 \tabularnewline
59 & 94.81 & 93.6757495481284 & 1.13425045187161 \tabularnewline
60 & 94.16 & 94.1181063992745 & 0.0418936007255297 \tabularnewline
61 & 94.83 & 93.1067880087943 & 1.72321199120566 \tabularnewline
62 & 96.02 & 93.2758904892446 & 2.74410951075541 \tabularnewline
63 & 95.97 & 95.7654018432198 & 0.204598156780179 \tabularnewline
64 & 95.88 & 95.1089159816537 & 0.771084018346329 \tabularnewline
65 & 95.97 & 96.4910441465401 & -0.521044146540135 \tabularnewline
66 & 97.55 & 96.4870459259193 & 1.06295407408074 \tabularnewline
67 & 97.49 & 98.7357744132 & -1.2457744132 \tabularnewline
68 & 98.4 & 98.0016033091889 & 0.398396690811126 \tabularnewline
69 & 98.2 & 98.0798635820704 & 0.120136417929615 \tabularnewline
70 & 97.16 & 98.5404196605701 & -1.38041966057006 \tabularnewline
71 & 96.96 & 96.6848128858617 & 0.275187114138276 \tabularnewline
72 & 96.37 & 96.3607853751994 & 0.00921462480062019 \tabularnewline
73 & 96.34 & 95.559428001912 & 0.78057199808805 \tabularnewline
74 & 96.86 & 95.0158890914881 & 1.84411090851191 \tabularnewline
75 & 96.32 & 96.5362485251122 & -0.216248525112249 \tabularnewline
76 & 95.44 & 95.5909355650319 & -0.150935565031901 \tabularnewline
77 & 92.85 & 96.0456449859097 & -3.19564498590971 \tabularnewline
78 & 92.56 & 93.6467285055935 & -1.08672850559347 \tabularnewline
79 & 91.74 & 93.563110145117 & -1.82311014511703 \tabularnewline
80 & 92.44 & 92.2686792996612 & 0.171320700338782 \tabularnewline
81 & 93.19 & 91.994694475091 & 1.19530552490896 \tabularnewline
82 & 92.62 & 93.1970494440134 & -0.577049444013369 \tabularnewline
83 & 94.04 & 92.148689323181 & 1.89131067681903 \tabularnewline
84 & 93.8 & 93.2664442795796 & 0.533555720420395 \tabularnewline
85 & 96.73 & 93.0062794667192 & 3.72372053328083 \tabularnewline
86 & 98.99 & 95.3108544560148 & 3.67914554398516 \tabularnewline
87 & 100.38 & 98.4553608336943 & 1.92463916630571 \tabularnewline
88 & 101.07 & 99.6266622144653 & 1.44333778553469 \tabularnewline
89 & 99.92 & 101.529417105084 & -1.60941710508435 \tabularnewline
90 & 101.78 & 101.092579925086 & 0.687420074914343 \tabularnewline
91 & 100.91 & 102.997983565862 & -2.08798356586158 \tabularnewline
92 & 100.49 & 102.020087933709 & -1.53008793370948 \tabularnewline
93 & 101.17 & 100.52508572177 & 0.644914278230416 \tabularnewline
94 & 100.25 & 101.342845447786 & -1.09284544778556 \tabularnewline
95 & 98.94 & 100.250292127739 & -1.31029212773889 \tabularnewline
96 & 99.4 & 98.4337347911718 & 0.966265208828233 \tabularnewline
97 & 100.02 & 98.959177697534 & 1.06082230246601 \tabularnewline
98 & 99.91 & 98.8509114965892 & 1.05908850341079 \tabularnewline
99 & 99.22 & 99.4467700472317 & -0.226770047231682 \tabularnewline
100 & 98.84 & 98.5570302349721 & 0.282969765027858 \tabularnewline
101 & 98.42 & 99.0515310542991 & -0.631531054299074 \tabularnewline
102 & 97.59 & 99.6244751164777 & -2.03447511647765 \tabularnewline
103 & 97.07 & 98.626183579555 & -1.55618357955501 \tabularnewline
104 & 96.59 & 98.0227046468215 & -1.43270464682153 \tabularnewline
105 & 95.96 & 96.6714666337335 & -0.711466633733494 \tabularnewline
106 & 94.22 & 95.9387188452703 & -1.71871884527033 \tabularnewline
107 & 94.48 & 94.0821739746409 & 0.397826025359123 \tabularnewline
108 & 93.14 & 93.909265060338 & -0.769265060338043 \tabularnewline
109 & 93.73 & 92.693695480619 & 1.03630451938102 \tabularnewline
110 & 94.24 & 92.4571000158839 & 1.78289998411611 \tabularnewline
111 & 98.52 & 93.488709574436 & 5.03129042556404 \tabularnewline
112 & 99.09 & 97.4687872758098 & 1.62121272419016 \tabularnewline
113 & 99.84 & 99.1480856880722 & 0.691914311927761 \tabularnewline
114 & 99.13 & 100.900907933136 & -1.77090793313621 \tabularnewline
115 & 100.88 & 100.275651989591 & 0.604348010409353 \tabularnewline
116 & 100.83 & 101.838435700377 & -1.00843570037746 \tabularnewline
117 & 101.6 & 101.093051151004 & 0.506948848996146 \tabularnewline
118 & 101.8 & 101.577419090202 & 0.222580909797642 \tabularnewline
119 & 102.77 & 101.922794192749 & 0.847205807250717 \tabularnewline
120 & 103.14 & 102.277187908725 & 0.862812091274677 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]103.04[/C][C]105.055364197453[/C][C]-2.01536419745312[/C][/ROW]
[ROW][C]14[/C][C]100.99[/C][C]101.234097492041[/C][C]-0.244097492041206[/C][/ROW]
[ROW][C]15[/C][C]100.93[/C][C]101.099955993039[/C][C]-0.169955993039238[/C][/ROW]
[ROW][C]16[/C][C]99.31[/C][C]99.4584315219442[/C][C]-0.14843152194419[/C][/ROW]
[ROW][C]17[/C][C]99.79[/C][C]99.8832589184353[/C][C]-0.0932589184352821[/C][/ROW]
[ROW][C]18[/C][C]99.57[/C][C]99.6367582088831[/C][C]-0.0667582088830585[/C][/ROW]
[ROW][C]19[/C][C]99.11[/C][C]101.112681213834[/C][C]-2.00268121383367[/C][/ROW]
[ROW][C]20[/C][C]98.96[/C][C]98.4859087279585[/C][C]0.47409127204152[/C][/ROW]
[ROW][C]21[/C][C]97.72[/C][C]98.2917872794031[/C][C]-0.571787279403068[/C][/ROW]
[ROW][C]22[/C][C]99.35[/C][C]97.4730545179914[/C][C]1.87694548200861[/C][/ROW]
[ROW][C]23[/C][C]98.15[/C][C]98.2666726386161[/C][C]-0.11667263861608[/C][/ROW]
[ROW][C]24[/C][C]97.64[/C][C]96.9011260440614[/C][C]0.738873955938587[/C][/ROW]
[ROW][C]25[/C][C]97.49[/C][C]96.1529802818646[/C][C]1.33701971813541[/C][/ROW]
[ROW][C]26[/C][C]97.94[/C][C]95.6543226288775[/C][C]2.28567737112252[/C][/ROW]
[ROW][C]27[/C][C]98.03[/C][C]97.9283025360174[/C][C]0.101697463982617[/C][/ROW]
[ROW][C]28[/C][C]98.05[/C][C]96.6720221512179[/C][C]1.37797784878214[/C][/ROW]
[ROW][C]29[/C][C]97.54[/C][C]98.6383712066469[/C][C]-1.09837120664689[/C][/ROW]
[ROW][C]30[/C][C]98.71[/C][C]97.5865049129579[/C][C]1.12349508704212[/C][/ROW]
[ROW][C]31[/C][C]99.33[/C][C]100.134364924594[/C][C]-0.804364924594225[/C][/ROW]
[ROW][C]32[/C][C]99.16[/C][C]99.0042632357307[/C][C]0.155736764269307[/C][/ROW]
[ROW][C]33[/C][C]98.41[/C][C]98.6158655890423[/C][C]-0.205865589042304[/C][/ROW]
[ROW][C]34[/C][C]98.43[/C][C]98.530731027288[/C][C]-0.100731027287978[/C][/ROW]
[ROW][C]35[/C][C]97.02[/C][C]97.4893554050744[/C][C]-0.469355405074367[/C][/ROW]
[ROW][C]36[/C][C]97.89[/C][C]96.0052466903304[/C][C]1.88475330966961[/C][/ROW]
[ROW][C]37[/C][C]97.92[/C][C]96.5149613230363[/C][C]1.40503867696368[/C][/ROW]
[ROW][C]38[/C][C]97.37[/C][C]96.3079410730818[/C][C]1.06205892691821[/C][/ROW]
[ROW][C]39[/C][C]97.42[/C][C]97.4016769793627[/C][C]0.0183230206373111[/C][/ROW]
[ROW][C]40[/C][C]96.12[/C][C]96.2990244533907[/C][C]-0.17902445339071[/C][/ROW]
[ROW][C]41[/C][C]96.72[/C][C]96.6932479071346[/C][C]0.0267520928653511[/C][/ROW]
[ROW][C]42[/C][C]96.64[/C][C]96.9616657256385[/C][C]-0.32166572563851[/C][/ROW]
[ROW][C]43[/C][C]95.28[/C][C]98.0593021569692[/C][C]-2.77930215696919[/C][/ROW]
[ROW][C]44[/C][C]95.3[/C][C]95.2069872205476[/C][C]0.0930127794523514[/C][/ROW]
[ROW][C]45[/C][C]95.02[/C][C]94.7510948455502[/C][C]0.268905154449826[/C][/ROW]
[ROW][C]46[/C][C]95.57[/C][C]95.1193988828056[/C][C]0.450601117194353[/C][/ROW]
[ROW][C]47[/C][C]94.78[/C][C]94.6128498315194[/C][C]0.167150168480632[/C][/ROW]
[ROW][C]48[/C][C]95.27[/C][C]93.9739097461467[/C][C]1.29609025385328[/C][/ROW]
[ROW][C]49[/C][C]96.14[/C][C]93.9703909653678[/C][C]2.16960903463217[/C][/ROW]
[ROW][C]50[/C][C]96.16[/C][C]94.524007392784[/C][C]1.63599260721598[/C][/ROW]
[ROW][C]51[/C][C]95.08[/C][C]96.1346017551066[/C][C]-1.05460175510663[/C][/ROW]
[ROW][C]52[/C][C]94.39[/C][C]94.0999887784483[/C][C]0.29001122155168[/C][/ROW]
[ROW][C]53[/C][C]94.15[/C][C]94.9890503920407[/C][C]-0.839050392040704[/C][/ROW]
[ROW][C]54[/C][C]94.58[/C][C]94.4599084259399[/C][C]0.12009157406014[/C][/ROW]
[ROW][C]55[/C][C]94.16[/C][C]95.775483282491[/C][C]-1.61548328249101[/C][/ROW]
[ROW][C]56[/C][C]95.02[/C][C]94.3092120623791[/C][C]0.710787937620864[/C][/ROW]
[ROW][C]57[/C][C]94.86[/C][C]94.5378839901941[/C][C]0.322116009805939[/C][/ROW]
[ROW][C]58[/C][C]94.49[/C][C]95.0734823088023[/C][C]-0.583482308802303[/C][/ROW]
[ROW][C]59[/C][C]94.81[/C][C]93.6757495481284[/C][C]1.13425045187161[/C][/ROW]
[ROW][C]60[/C][C]94.16[/C][C]94.1181063992745[/C][C]0.0418936007255297[/C][/ROW]
[ROW][C]61[/C][C]94.83[/C][C]93.1067880087943[/C][C]1.72321199120566[/C][/ROW]
[ROW][C]62[/C][C]96.02[/C][C]93.2758904892446[/C][C]2.74410951075541[/C][/ROW]
[ROW][C]63[/C][C]95.97[/C][C]95.7654018432198[/C][C]0.204598156780179[/C][/ROW]
[ROW][C]64[/C][C]95.88[/C][C]95.1089159816537[/C][C]0.771084018346329[/C][/ROW]
[ROW][C]65[/C][C]95.97[/C][C]96.4910441465401[/C][C]-0.521044146540135[/C][/ROW]
[ROW][C]66[/C][C]97.55[/C][C]96.4870459259193[/C][C]1.06295407408074[/C][/ROW]
[ROW][C]67[/C][C]97.49[/C][C]98.7357744132[/C][C]-1.2457744132[/C][/ROW]
[ROW][C]68[/C][C]98.4[/C][C]98.0016033091889[/C][C]0.398396690811126[/C][/ROW]
[ROW][C]69[/C][C]98.2[/C][C]98.0798635820704[/C][C]0.120136417929615[/C][/ROW]
[ROW][C]70[/C][C]97.16[/C][C]98.5404196605701[/C][C]-1.38041966057006[/C][/ROW]
[ROW][C]71[/C][C]96.96[/C][C]96.6848128858617[/C][C]0.275187114138276[/C][/ROW]
[ROW][C]72[/C][C]96.37[/C][C]96.3607853751994[/C][C]0.00921462480062019[/C][/ROW]
[ROW][C]73[/C][C]96.34[/C][C]95.559428001912[/C][C]0.78057199808805[/C][/ROW]
[ROW][C]74[/C][C]96.86[/C][C]95.0158890914881[/C][C]1.84411090851191[/C][/ROW]
[ROW][C]75[/C][C]96.32[/C][C]96.5362485251122[/C][C]-0.216248525112249[/C][/ROW]
[ROW][C]76[/C][C]95.44[/C][C]95.5909355650319[/C][C]-0.150935565031901[/C][/ROW]
[ROW][C]77[/C][C]92.85[/C][C]96.0456449859097[/C][C]-3.19564498590971[/C][/ROW]
[ROW][C]78[/C][C]92.56[/C][C]93.6467285055935[/C][C]-1.08672850559347[/C][/ROW]
[ROW][C]79[/C][C]91.74[/C][C]93.563110145117[/C][C]-1.82311014511703[/C][/ROW]
[ROW][C]80[/C][C]92.44[/C][C]92.2686792996612[/C][C]0.171320700338782[/C][/ROW]
[ROW][C]81[/C][C]93.19[/C][C]91.994694475091[/C][C]1.19530552490896[/C][/ROW]
[ROW][C]82[/C][C]92.62[/C][C]93.1970494440134[/C][C]-0.577049444013369[/C][/ROW]
[ROW][C]83[/C][C]94.04[/C][C]92.148689323181[/C][C]1.89131067681903[/C][/ROW]
[ROW][C]84[/C][C]93.8[/C][C]93.2664442795796[/C][C]0.533555720420395[/C][/ROW]
[ROW][C]85[/C][C]96.73[/C][C]93.0062794667192[/C][C]3.72372053328083[/C][/ROW]
[ROW][C]86[/C][C]98.99[/C][C]95.3108544560148[/C][C]3.67914554398516[/C][/ROW]
[ROW][C]87[/C][C]100.38[/C][C]98.4553608336943[/C][C]1.92463916630571[/C][/ROW]
[ROW][C]88[/C][C]101.07[/C][C]99.6266622144653[/C][C]1.44333778553469[/C][/ROW]
[ROW][C]89[/C][C]99.92[/C][C]101.529417105084[/C][C]-1.60941710508435[/C][/ROW]
[ROW][C]90[/C][C]101.78[/C][C]101.092579925086[/C][C]0.687420074914343[/C][/ROW]
[ROW][C]91[/C][C]100.91[/C][C]102.997983565862[/C][C]-2.08798356586158[/C][/ROW]
[ROW][C]92[/C][C]100.49[/C][C]102.020087933709[/C][C]-1.53008793370948[/C][/ROW]
[ROW][C]93[/C][C]101.17[/C][C]100.52508572177[/C][C]0.644914278230416[/C][/ROW]
[ROW][C]94[/C][C]100.25[/C][C]101.342845447786[/C][C]-1.09284544778556[/C][/ROW]
[ROW][C]95[/C][C]98.94[/C][C]100.250292127739[/C][C]-1.31029212773889[/C][/ROW]
[ROW][C]96[/C][C]99.4[/C][C]98.4337347911718[/C][C]0.966265208828233[/C][/ROW]
[ROW][C]97[/C][C]100.02[/C][C]98.959177697534[/C][C]1.06082230246601[/C][/ROW]
[ROW][C]98[/C][C]99.91[/C][C]98.8509114965892[/C][C]1.05908850341079[/C][/ROW]
[ROW][C]99[/C][C]99.22[/C][C]99.4467700472317[/C][C]-0.226770047231682[/C][/ROW]
[ROW][C]100[/C][C]98.84[/C][C]98.5570302349721[/C][C]0.282969765027858[/C][/ROW]
[ROW][C]101[/C][C]98.42[/C][C]99.0515310542991[/C][C]-0.631531054299074[/C][/ROW]
[ROW][C]102[/C][C]97.59[/C][C]99.6244751164777[/C][C]-2.03447511647765[/C][/ROW]
[ROW][C]103[/C][C]97.07[/C][C]98.626183579555[/C][C]-1.55618357955501[/C][/ROW]
[ROW][C]104[/C][C]96.59[/C][C]98.0227046468215[/C][C]-1.43270464682153[/C][/ROW]
[ROW][C]105[/C][C]95.96[/C][C]96.6714666337335[/C][C]-0.711466633733494[/C][/ROW]
[ROW][C]106[/C][C]94.22[/C][C]95.9387188452703[/C][C]-1.71871884527033[/C][/ROW]
[ROW][C]107[/C][C]94.48[/C][C]94.0821739746409[/C][C]0.397826025359123[/C][/ROW]
[ROW][C]108[/C][C]93.14[/C][C]93.909265060338[/C][C]-0.769265060338043[/C][/ROW]
[ROW][C]109[/C][C]93.73[/C][C]92.693695480619[/C][C]1.03630451938102[/C][/ROW]
[ROW][C]110[/C][C]94.24[/C][C]92.4571000158839[/C][C]1.78289998411611[/C][/ROW]
[ROW][C]111[/C][C]98.52[/C][C]93.488709574436[/C][C]5.03129042556404[/C][/ROW]
[ROW][C]112[/C][C]99.09[/C][C]97.4687872758098[/C][C]1.62121272419016[/C][/ROW]
[ROW][C]113[/C][C]99.84[/C][C]99.1480856880722[/C][C]0.691914311927761[/C][/ROW]
[ROW][C]114[/C][C]99.13[/C][C]100.900907933136[/C][C]-1.77090793313621[/C][/ROW]
[ROW][C]115[/C][C]100.88[/C][C]100.275651989591[/C][C]0.604348010409353[/C][/ROW]
[ROW][C]116[/C][C]100.83[/C][C]101.838435700377[/C][C]-1.00843570037746[/C][/ROW]
[ROW][C]117[/C][C]101.6[/C][C]101.093051151004[/C][C]0.506948848996146[/C][/ROW]
[ROW][C]118[/C][C]101.8[/C][C]101.577419090202[/C][C]0.222580909797642[/C][/ROW]
[ROW][C]119[/C][C]102.77[/C][C]101.922794192749[/C][C]0.847205807250717[/C][/ROW]
[ROW][C]120[/C][C]103.14[/C][C]102.277187908725[/C][C]0.862812091274677[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13103.04105.055364197453-2.01536419745312
14100.99101.234097492041-0.244097492041206
15100.93101.099955993039-0.169955993039238
1699.3199.4584315219442-0.14843152194419
1799.7999.8832589184353-0.0932589184352821
1899.5799.6367582088831-0.0667582088830585
1999.11101.112681213834-2.00268121383367
2098.9698.48590872795850.47409127204152
2197.7298.2917872794031-0.571787279403068
2299.3597.47305451799141.87694548200861
2398.1598.2666726386161-0.11667263861608
2497.6496.90112604406140.738873955938587
2597.4996.15298028186461.33701971813541
2697.9495.65432262887752.28567737112252
2798.0397.92830253601740.101697463982617
2898.0596.67202215121791.37797784878214
2997.5498.6383712066469-1.09837120664689
3098.7197.58650491295791.12349508704212
3199.33100.134364924594-0.804364924594225
3299.1699.00426323573070.155736764269307
3398.4198.6158655890423-0.205865589042304
3498.4398.530731027288-0.100731027287978
3597.0297.4893554050744-0.469355405074367
3697.8996.00524669033041.88475330966961
3797.9296.51496132303631.40503867696368
3897.3796.30794107308181.06205892691821
3997.4297.40167697936270.0183230206373111
4096.1296.2990244533907-0.17902445339071
4196.7296.69324790713460.0267520928653511
4296.6496.9616657256385-0.32166572563851
4395.2898.0593021569692-2.77930215696919
4495.395.20698722054760.0930127794523514
4595.0294.75109484555020.268905154449826
4695.5795.11939888280560.450601117194353
4794.7894.61284983151940.167150168480632
4895.2793.97390974614671.29609025385328
4996.1493.97039096536782.16960903463217
5096.1694.5240073927841.63599260721598
5195.0896.1346017551066-1.05460175510663
5294.3994.09998877844830.29001122155168
5394.1594.9890503920407-0.839050392040704
5494.5894.45990842593990.12009157406014
5594.1695.775483282491-1.61548328249101
5695.0294.30921206237910.710787937620864
5794.8694.53788399019410.322116009805939
5894.4995.0734823088023-0.583482308802303
5994.8193.67574954812841.13425045187161
6094.1694.11810639927450.0418936007255297
6194.8393.10678800879431.72321199120566
6296.0293.27589048924462.74410951075541
6395.9795.76540184321980.204598156780179
6495.8895.10891598165370.771084018346329
6595.9796.4910441465401-0.521044146540135
6697.5596.48704592591931.06295407408074
6797.4998.7357744132-1.2457744132
6898.498.00160330918890.398396690811126
6998.298.07986358207040.120136417929615
7097.1698.5404196605701-1.38041966057006
7196.9696.68481288586170.275187114138276
7296.3796.36078537519940.00921462480062019
7396.3495.5594280019120.78057199808805
7496.8695.01588909148811.84411090851191
7596.3296.5362485251122-0.216248525112249
7695.4495.5909355650319-0.150935565031901
7792.8596.0456449859097-3.19564498590971
7892.5693.6467285055935-1.08672850559347
7991.7493.563110145117-1.82311014511703
8092.4492.26867929966120.171320700338782
8193.1991.9946944750911.19530552490896
8292.6293.1970494440134-0.577049444013369
8394.0492.1486893231811.89131067681903
8493.893.26644427957960.533555720420395
8596.7393.00627946671923.72372053328083
8698.9995.31085445601483.67914554398516
87100.3898.45536083369431.92463916630571
88101.0799.62666221446531.44333778553469
8999.92101.529417105084-1.60941710508435
90101.78101.0925799250860.687420074914343
91100.91102.997983565862-2.08798356586158
92100.49102.020087933709-1.53008793370948
93101.17100.525085721770.644914278230416
94100.25101.342845447786-1.09284544778556
9598.94100.250292127739-1.31029212773889
9699.498.43373479117180.966265208828233
97100.0298.9591776975341.06082230246601
9899.9198.85091149658921.05908850341079
9999.2299.4467700472317-0.226770047231682
10098.8498.55703023497210.282969765027858
10198.4299.0515310542991-0.631531054299074
10297.5999.6244751164777-2.03447511647765
10397.0798.626183579555-1.55618357955501
10496.5998.0227046468215-1.43270464682153
10595.9696.6714666337335-0.711466633733494
10694.2295.9387188452703-1.71871884527033
10794.4894.08217397464090.397826025359123
10893.1493.909265060338-0.769265060338043
10993.7392.6936954806191.03630451938102
11094.2492.45710001588391.78289998411611
11198.5293.4887095744365.03129042556404
11299.0997.46878727580981.62121272419016
11399.8499.14808568807220.691914311927761
11499.13100.900907933136-1.77090793313621
115100.88100.2756519895910.604348010409353
116100.83101.838435700377-1.00843570037746
117101.6101.0930511510040.506948848996146
118101.8101.5774190902020.222580909797642
119102.77101.9227941927490.847205807250717
120103.14102.2771879087250.862812091274677






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121102.985596145957100.343044540843105.628147751071
122102.02565932223898.4057761167701105.645542527706
123101.86156142915197.4282430955429106.29487976276
124100.98058124814195.8544874648246106.106675031458
125101.12164529058695.3187589576159106.924531623557
126102.05167563380495.5690021484204108.534349119188
127103.33719737009796.1769422184294110.497452521765
128104.27184286326696.471373427734112.072312298799
129104.65395760425796.2637028593113113.044212349204
130104.70216451199295.757675116489113.646653907495
131104.94583981187895.439352330472114.452327293284
132104.53675566232979.4930017082386129.58050961642

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 102.985596145957 & 100.343044540843 & 105.628147751071 \tabularnewline
122 & 102.025659322238 & 98.4057761167701 & 105.645542527706 \tabularnewline
123 & 101.861561429151 & 97.4282430955429 & 106.29487976276 \tabularnewline
124 & 100.980581248141 & 95.8544874648246 & 106.106675031458 \tabularnewline
125 & 101.121645290586 & 95.3187589576159 & 106.924531623557 \tabularnewline
126 & 102.051675633804 & 95.5690021484204 & 108.534349119188 \tabularnewline
127 & 103.337197370097 & 96.1769422184294 & 110.497452521765 \tabularnewline
128 & 104.271842863266 & 96.471373427734 & 112.072312298799 \tabularnewline
129 & 104.653957604257 & 96.2637028593113 & 113.044212349204 \tabularnewline
130 & 104.702164511992 & 95.757675116489 & 113.646653907495 \tabularnewline
131 & 104.945839811878 & 95.439352330472 & 114.452327293284 \tabularnewline
132 & 104.536755662329 & 79.4930017082386 & 129.58050961642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]121[/C][C]102.985596145957[/C][C]100.343044540843[/C][C]105.628147751071[/C][/ROW]
[ROW][C]122[/C][C]102.025659322238[/C][C]98.4057761167701[/C][C]105.645542527706[/C][/ROW]
[ROW][C]123[/C][C]101.861561429151[/C][C]97.4282430955429[/C][C]106.29487976276[/C][/ROW]
[ROW][C]124[/C][C]100.980581248141[/C][C]95.8544874648246[/C][C]106.106675031458[/C][/ROW]
[ROW][C]125[/C][C]101.121645290586[/C][C]95.3187589576159[/C][C]106.924531623557[/C][/ROW]
[ROW][C]126[/C][C]102.051675633804[/C][C]95.5690021484204[/C][C]108.534349119188[/C][/ROW]
[ROW][C]127[/C][C]103.337197370097[/C][C]96.1769422184294[/C][C]110.497452521765[/C][/ROW]
[ROW][C]128[/C][C]104.271842863266[/C][C]96.471373427734[/C][C]112.072312298799[/C][/ROW]
[ROW][C]129[/C][C]104.653957604257[/C][C]96.2637028593113[/C][C]113.044212349204[/C][/ROW]
[ROW][C]130[/C][C]104.702164511992[/C][C]95.757675116489[/C][C]113.646653907495[/C][/ROW]
[ROW][C]131[/C][C]104.945839811878[/C][C]95.439352330472[/C][C]114.452327293284[/C][/ROW]
[ROW][C]132[/C][C]104.536755662329[/C][C]79.4930017082386[/C][C]129.58050961642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121102.985596145957100.343044540843105.628147751071
122102.02565932223898.4057761167701105.645542527706
123101.86156142915197.4282430955429106.29487976276
124100.98058124814195.8544874648246106.106675031458
125101.12164529058695.3187589576159106.924531623557
126102.05167563380495.5690021484204108.534349119188
127103.33719737009796.1769422184294110.497452521765
128104.27184286326696.471373427734112.072312298799
129104.65395760425796.2637028593113113.044212349204
130104.70216451199295.757675116489113.646653907495
131104.94583981187895.439352330472114.452327293284
132104.53675566232979.4930017082386129.58050961642


Figures (Output of Computation)

Input Parameters & R Code

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=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')