Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 22 Dec 2015 17:04:08 +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/2015/Dec/22/t1450803986ir0ghwdcicoual7.htm/, Retrieved Fri, 17 May 2024 00:47:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287037, Retrieved Fri, 17 May 2024 00:47:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Consumptieprijsin...] [2015-12-22 17:04:08] [91f26e786dd8a1c147ebc049dd81fbad] [Current]
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Dataseries X:
73.97
75.01
75.98
78.85
79.34
79.62
79.76
79.62
79.89
79.88
79.97
79.63
80.04
80.23
80.44
81.78
82.51
82.43
82.35
82.53
82.08
82.73
82.46
81.98
82.11
82.26
82.51
82.89
83.83
84.73
84.48
84.84
84.99
84.7
84.54
84.73
84.51
84.54
84.27
84.47
84.25
84.33
84.29
84.53
84.01
84.18
84.08
83.44
83.61
83.89
83.4
82.96
82.76
83.35
87.78
88.99
88.92
88.91
89.79
90.54
93.15
92.79
93.21
95.35
100.91
103.69
104.04
104.16
104.71
105.18
104.92
104.83
104.9
105.05
104.6
103.21
102.52
101.09
101.19
102.34
102.62
102.47
101.82
101.86
101.54
101.98
101.23
100.4
99.94
99.94
100
98.8
99.07
99.46
99.18
98.47
97.12
96.91
96.09
97.17
96.8
97.13
99.9
100.56
100.84
99.81
100.44
100.07




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287037&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287037&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287037&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.204653834068023
gamma0.458845688061906

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.204653834068023 \tabularnewline
gamma & 0.458845688061906 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287037&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.204653834068023[/C][/ROW]
[ROW][C]gamma[/C][C]0.458845688061906[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287037&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287037&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
alpha1
beta0.204653834068023
gamma0.458845688061906







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1380.0478.30774572649581.73225427350425
1480.2380.6129273970683-0.382927397068286
1580.4480.7612265037552-0.321226503755241
1681.7882.0379862681575-0.257986268157453
1782.5182.7026883892421-0.192688389242136
1882.4382.6040873049367-0.174087304936677
1982.3583.0859596705188-0.735959670518824
2082.5381.92909270222770.600907297772309
2182.0882.7091540179696-0.629154017969583
2282.7381.94581190263950.784188097360541
2382.4682.9100490033948-0.450049003394824
2481.9882.1229447493316-0.142944749331576
2582.1182.3878572249877-0.277857224987656
2682.2682.23682601190380.0231739880962465
2782.5182.4282353240850.0817646759150392
2882.8983.8274687785023-0.937468778502307
2983.8383.39311219866270.436887801337249
3084.7383.63335629559731.09664370440271
3184.4885.3552886343099-0.875288634309868
3284.8483.99990745938220.840092540617803
3384.9985.0089189521249-0.0189189521249062
3484.784.9704637827027-0.270463782702649
3584.5484.778862332596-0.238862332596014
3684.7384.14497824041580.585021759584166
3784.5185.2288718531946-0.718871853194614
3884.5484.6375853055681-0.0975853055680886
3984.2784.6842807653016-0.414280765301555
4084.4785.4619966183019-0.991996618301926
4184.2584.8364807069839-0.586480706983949
4284.3383.70728851502610.622711484973919
4384.2984.5122288079442-0.222228807944177
4484.5383.50049883035811.02950116964195
4584.0184.4282735252361-0.418273525236103
4684.1883.63808891127410.541911088725939
4784.0884.07274309330580.00725690669419521
4883.4483.5492282470843-0.10922824708426
4983.6183.6610409341966-0.0510409341965925
5083.8983.59642854465220.293571455347816
5183.483.9731757352287-0.573175735228702
5282.9684.4983731234194-1.5383731234194
5382.7683.1210391654844-0.361039165484414
5483.3582.05798444935261.29201555064735
5587.7883.50990038546814.27009961453189
5688.9987.88754264343451.10245735656552
5788.9289.8002481016854-0.880248101685424
5888.9189.3655186194111-0.45551861941108
5989.7989.41604498745920.37395501254079
6090.5489.94757631454470.59242368545533
6193.1591.59298475983251.55701524016753
6292.7994.2974672317684-1.50746723176843
6393.2193.6656249497218-0.455624949721795
6495.3595.12487955686410.22512044313585
65100.9196.6884513186794.221548681321
66103.69102.3232407753491.36675922465051
67104.04105.980453290922-1.94045329092204
68104.16105.007082085105-0.847082085104958
69104.71105.430806821951-0.720806821951214
70105.18105.648707608883-0.46870760888315
71104.92106.176534799668-1.25653479966839
72104.83105.234380135276-0.404380135276369
73104.9105.835788856838-0.93578885683776
74105.05105.490109412741-0.440109412741137
75104.6105.586706000681-0.986706000680897
76103.21106.067272834544-2.85727283454361
77102.52103.470020993976-0.950020993975855
78101.09101.796428888447-0.706428888446908
79101.19100.819355507930.370644492070156
80102.34100.0689593243082.27104067569181
81102.62102.1608198392460.459180160753718
82102.47102.3502094863390.119790513660831
83101.82102.378475074245-0.558475074244839
84101.86101.1891810090690.670818990930783
85101.54102.140633354196-0.600633354195509
86101.98101.4735447687240.506455231276391
87101.23102.053859440255-0.823859440254779
88100.4102.267753447074-1.8677534470735
8999.94100.433010543036-0.493010543036164
9099.9499.08294737850120.857052621498823
9110099.85584648348890.144153516511054
9298.899.0190980533373-0.219098053337333
9399.0798.25134213001830.818657869981664
9499.4698.50430026856670.955699731433299
9599.1899.2436378828223-0.0636378828222917
9698.4798.5256141461108-0.0556141461107842
9797.1298.5783991645474-1.45839916454743
9896.9196.70576551725450.204234482745449
9996.0996.574229553864-0.484229553863955
10097.1796.78763011909660.382369880903354
10196.897.3233835812557-0.523383581255672
10297.1396.05710445799681.07289554200324
10399.997.20417664422222.69582335577779
104100.5699.59963722995230.960362770047723
105100.84100.933262486272-0.093262486272053
10699.81101.009592627548-1.19959262754843
107100.4499.88784139700090.552158602999086
108100.07100.205842772118-0.135842772118338

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 80.04 & 78.3077457264958 & 1.73225427350425 \tabularnewline
14 & 80.23 & 80.6129273970683 & -0.382927397068286 \tabularnewline
15 & 80.44 & 80.7612265037552 & -0.321226503755241 \tabularnewline
16 & 81.78 & 82.0379862681575 & -0.257986268157453 \tabularnewline
17 & 82.51 & 82.7026883892421 & -0.192688389242136 \tabularnewline
18 & 82.43 & 82.6040873049367 & -0.174087304936677 \tabularnewline
19 & 82.35 & 83.0859596705188 & -0.735959670518824 \tabularnewline
20 & 82.53 & 81.9290927022277 & 0.600907297772309 \tabularnewline
21 & 82.08 & 82.7091540179696 & -0.629154017969583 \tabularnewline
22 & 82.73 & 81.9458119026395 & 0.784188097360541 \tabularnewline
23 & 82.46 & 82.9100490033948 & -0.450049003394824 \tabularnewline
24 & 81.98 & 82.1229447493316 & -0.142944749331576 \tabularnewline
25 & 82.11 & 82.3878572249877 & -0.277857224987656 \tabularnewline
26 & 82.26 & 82.2368260119038 & 0.0231739880962465 \tabularnewline
27 & 82.51 & 82.428235324085 & 0.0817646759150392 \tabularnewline
28 & 82.89 & 83.8274687785023 & -0.937468778502307 \tabularnewline
29 & 83.83 & 83.3931121986627 & 0.436887801337249 \tabularnewline
30 & 84.73 & 83.6333562955973 & 1.09664370440271 \tabularnewline
31 & 84.48 & 85.3552886343099 & -0.875288634309868 \tabularnewline
32 & 84.84 & 83.9999074593822 & 0.840092540617803 \tabularnewline
33 & 84.99 & 85.0089189521249 & -0.0189189521249062 \tabularnewline
34 & 84.7 & 84.9704637827027 & -0.270463782702649 \tabularnewline
35 & 84.54 & 84.778862332596 & -0.238862332596014 \tabularnewline
36 & 84.73 & 84.1449782404158 & 0.585021759584166 \tabularnewline
37 & 84.51 & 85.2288718531946 & -0.718871853194614 \tabularnewline
38 & 84.54 & 84.6375853055681 & -0.0975853055680886 \tabularnewline
39 & 84.27 & 84.6842807653016 & -0.414280765301555 \tabularnewline
40 & 84.47 & 85.4619966183019 & -0.991996618301926 \tabularnewline
41 & 84.25 & 84.8364807069839 & -0.586480706983949 \tabularnewline
42 & 84.33 & 83.7072885150261 & 0.622711484973919 \tabularnewline
43 & 84.29 & 84.5122288079442 & -0.222228807944177 \tabularnewline
44 & 84.53 & 83.5004988303581 & 1.02950116964195 \tabularnewline
45 & 84.01 & 84.4282735252361 & -0.418273525236103 \tabularnewline
46 & 84.18 & 83.6380889112741 & 0.541911088725939 \tabularnewline
47 & 84.08 & 84.0727430933058 & 0.00725690669419521 \tabularnewline
48 & 83.44 & 83.5492282470843 & -0.10922824708426 \tabularnewline
49 & 83.61 & 83.6610409341966 & -0.0510409341965925 \tabularnewline
50 & 83.89 & 83.5964285446522 & 0.293571455347816 \tabularnewline
51 & 83.4 & 83.9731757352287 & -0.573175735228702 \tabularnewline
52 & 82.96 & 84.4983731234194 & -1.5383731234194 \tabularnewline
53 & 82.76 & 83.1210391654844 & -0.361039165484414 \tabularnewline
54 & 83.35 & 82.0579844493526 & 1.29201555064735 \tabularnewline
55 & 87.78 & 83.5099003854681 & 4.27009961453189 \tabularnewline
56 & 88.99 & 87.8875426434345 & 1.10245735656552 \tabularnewline
57 & 88.92 & 89.8002481016854 & -0.880248101685424 \tabularnewline
58 & 88.91 & 89.3655186194111 & -0.45551861941108 \tabularnewline
59 & 89.79 & 89.4160449874592 & 0.37395501254079 \tabularnewline
60 & 90.54 & 89.9475763145447 & 0.59242368545533 \tabularnewline
61 & 93.15 & 91.5929847598325 & 1.55701524016753 \tabularnewline
62 & 92.79 & 94.2974672317684 & -1.50746723176843 \tabularnewline
63 & 93.21 & 93.6656249497218 & -0.455624949721795 \tabularnewline
64 & 95.35 & 95.1248795568641 & 0.22512044313585 \tabularnewline
65 & 100.91 & 96.688451318679 & 4.221548681321 \tabularnewline
66 & 103.69 & 102.323240775349 & 1.36675922465051 \tabularnewline
67 & 104.04 & 105.980453290922 & -1.94045329092204 \tabularnewline
68 & 104.16 & 105.007082085105 & -0.847082085104958 \tabularnewline
69 & 104.71 & 105.430806821951 & -0.720806821951214 \tabularnewline
70 & 105.18 & 105.648707608883 & -0.46870760888315 \tabularnewline
71 & 104.92 & 106.176534799668 & -1.25653479966839 \tabularnewline
72 & 104.83 & 105.234380135276 & -0.404380135276369 \tabularnewline
73 & 104.9 & 105.835788856838 & -0.93578885683776 \tabularnewline
74 & 105.05 & 105.490109412741 & -0.440109412741137 \tabularnewline
75 & 104.6 & 105.586706000681 & -0.986706000680897 \tabularnewline
76 & 103.21 & 106.067272834544 & -2.85727283454361 \tabularnewline
77 & 102.52 & 103.470020993976 & -0.950020993975855 \tabularnewline
78 & 101.09 & 101.796428888447 & -0.706428888446908 \tabularnewline
79 & 101.19 & 100.81935550793 & 0.370644492070156 \tabularnewline
80 & 102.34 & 100.068959324308 & 2.27104067569181 \tabularnewline
81 & 102.62 & 102.160819839246 & 0.459180160753718 \tabularnewline
82 & 102.47 & 102.350209486339 & 0.119790513660831 \tabularnewline
83 & 101.82 & 102.378475074245 & -0.558475074244839 \tabularnewline
84 & 101.86 & 101.189181009069 & 0.670818990930783 \tabularnewline
85 & 101.54 & 102.140633354196 & -0.600633354195509 \tabularnewline
86 & 101.98 & 101.473544768724 & 0.506455231276391 \tabularnewline
87 & 101.23 & 102.053859440255 & -0.823859440254779 \tabularnewline
88 & 100.4 & 102.267753447074 & -1.8677534470735 \tabularnewline
89 & 99.94 & 100.433010543036 & -0.493010543036164 \tabularnewline
90 & 99.94 & 99.0829473785012 & 0.857052621498823 \tabularnewline
91 & 100 & 99.8558464834889 & 0.144153516511054 \tabularnewline
92 & 98.8 & 99.0190980533373 & -0.219098053337333 \tabularnewline
93 & 99.07 & 98.2513421300183 & 0.818657869981664 \tabularnewline
94 & 99.46 & 98.5043002685667 & 0.955699731433299 \tabularnewline
95 & 99.18 & 99.2436378828223 & -0.0636378828222917 \tabularnewline
96 & 98.47 & 98.5256141461108 & -0.0556141461107842 \tabularnewline
97 & 97.12 & 98.5783991645474 & -1.45839916454743 \tabularnewline
98 & 96.91 & 96.7057655172545 & 0.204234482745449 \tabularnewline
99 & 96.09 & 96.574229553864 & -0.484229553863955 \tabularnewline
100 & 97.17 & 96.7876301190966 & 0.382369880903354 \tabularnewline
101 & 96.8 & 97.3233835812557 & -0.523383581255672 \tabularnewline
102 & 97.13 & 96.0571044579968 & 1.07289554200324 \tabularnewline
103 & 99.9 & 97.2041766442222 & 2.69582335577779 \tabularnewline
104 & 100.56 & 99.5996372299523 & 0.960362770047723 \tabularnewline
105 & 100.84 & 100.933262486272 & -0.093262486272053 \tabularnewline
106 & 99.81 & 101.009592627548 & -1.19959262754843 \tabularnewline
107 & 100.44 & 99.8878413970009 & 0.552158602999086 \tabularnewline
108 & 100.07 & 100.205842772118 & -0.135842772118338 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287037&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]80.04[/C][C]78.3077457264958[/C][C]1.73225427350425[/C][/ROW]
[ROW][C]14[/C][C]80.23[/C][C]80.6129273970683[/C][C]-0.382927397068286[/C][/ROW]
[ROW][C]15[/C][C]80.44[/C][C]80.7612265037552[/C][C]-0.321226503755241[/C][/ROW]
[ROW][C]16[/C][C]81.78[/C][C]82.0379862681575[/C][C]-0.257986268157453[/C][/ROW]
[ROW][C]17[/C][C]82.51[/C][C]82.7026883892421[/C][C]-0.192688389242136[/C][/ROW]
[ROW][C]18[/C][C]82.43[/C][C]82.6040873049367[/C][C]-0.174087304936677[/C][/ROW]
[ROW][C]19[/C][C]82.35[/C][C]83.0859596705188[/C][C]-0.735959670518824[/C][/ROW]
[ROW][C]20[/C][C]82.53[/C][C]81.9290927022277[/C][C]0.600907297772309[/C][/ROW]
[ROW][C]21[/C][C]82.08[/C][C]82.7091540179696[/C][C]-0.629154017969583[/C][/ROW]
[ROW][C]22[/C][C]82.73[/C][C]81.9458119026395[/C][C]0.784188097360541[/C][/ROW]
[ROW][C]23[/C][C]82.46[/C][C]82.9100490033948[/C][C]-0.450049003394824[/C][/ROW]
[ROW][C]24[/C][C]81.98[/C][C]82.1229447493316[/C][C]-0.142944749331576[/C][/ROW]
[ROW][C]25[/C][C]82.11[/C][C]82.3878572249877[/C][C]-0.277857224987656[/C][/ROW]
[ROW][C]26[/C][C]82.26[/C][C]82.2368260119038[/C][C]0.0231739880962465[/C][/ROW]
[ROW][C]27[/C][C]82.51[/C][C]82.428235324085[/C][C]0.0817646759150392[/C][/ROW]
[ROW][C]28[/C][C]82.89[/C][C]83.8274687785023[/C][C]-0.937468778502307[/C][/ROW]
[ROW][C]29[/C][C]83.83[/C][C]83.3931121986627[/C][C]0.436887801337249[/C][/ROW]
[ROW][C]30[/C][C]84.73[/C][C]83.6333562955973[/C][C]1.09664370440271[/C][/ROW]
[ROW][C]31[/C][C]84.48[/C][C]85.3552886343099[/C][C]-0.875288634309868[/C][/ROW]
[ROW][C]32[/C][C]84.84[/C][C]83.9999074593822[/C][C]0.840092540617803[/C][/ROW]
[ROW][C]33[/C][C]84.99[/C][C]85.0089189521249[/C][C]-0.0189189521249062[/C][/ROW]
[ROW][C]34[/C][C]84.7[/C][C]84.9704637827027[/C][C]-0.270463782702649[/C][/ROW]
[ROW][C]35[/C][C]84.54[/C][C]84.778862332596[/C][C]-0.238862332596014[/C][/ROW]
[ROW][C]36[/C][C]84.73[/C][C]84.1449782404158[/C][C]0.585021759584166[/C][/ROW]
[ROW][C]37[/C][C]84.51[/C][C]85.2288718531946[/C][C]-0.718871853194614[/C][/ROW]
[ROW][C]38[/C][C]84.54[/C][C]84.6375853055681[/C][C]-0.0975853055680886[/C][/ROW]
[ROW][C]39[/C][C]84.27[/C][C]84.6842807653016[/C][C]-0.414280765301555[/C][/ROW]
[ROW][C]40[/C][C]84.47[/C][C]85.4619966183019[/C][C]-0.991996618301926[/C][/ROW]
[ROW][C]41[/C][C]84.25[/C][C]84.8364807069839[/C][C]-0.586480706983949[/C][/ROW]
[ROW][C]42[/C][C]84.33[/C][C]83.7072885150261[/C][C]0.622711484973919[/C][/ROW]
[ROW][C]43[/C][C]84.29[/C][C]84.5122288079442[/C][C]-0.222228807944177[/C][/ROW]
[ROW][C]44[/C][C]84.53[/C][C]83.5004988303581[/C][C]1.02950116964195[/C][/ROW]
[ROW][C]45[/C][C]84.01[/C][C]84.4282735252361[/C][C]-0.418273525236103[/C][/ROW]
[ROW][C]46[/C][C]84.18[/C][C]83.6380889112741[/C][C]0.541911088725939[/C][/ROW]
[ROW][C]47[/C][C]84.08[/C][C]84.0727430933058[/C][C]0.00725690669419521[/C][/ROW]
[ROW][C]48[/C][C]83.44[/C][C]83.5492282470843[/C][C]-0.10922824708426[/C][/ROW]
[ROW][C]49[/C][C]83.61[/C][C]83.6610409341966[/C][C]-0.0510409341965925[/C][/ROW]
[ROW][C]50[/C][C]83.89[/C][C]83.5964285446522[/C][C]0.293571455347816[/C][/ROW]
[ROW][C]51[/C][C]83.4[/C][C]83.9731757352287[/C][C]-0.573175735228702[/C][/ROW]
[ROW][C]52[/C][C]82.96[/C][C]84.4983731234194[/C][C]-1.5383731234194[/C][/ROW]
[ROW][C]53[/C][C]82.76[/C][C]83.1210391654844[/C][C]-0.361039165484414[/C][/ROW]
[ROW][C]54[/C][C]83.35[/C][C]82.0579844493526[/C][C]1.29201555064735[/C][/ROW]
[ROW][C]55[/C][C]87.78[/C][C]83.5099003854681[/C][C]4.27009961453189[/C][/ROW]
[ROW][C]56[/C][C]88.99[/C][C]87.8875426434345[/C][C]1.10245735656552[/C][/ROW]
[ROW][C]57[/C][C]88.92[/C][C]89.8002481016854[/C][C]-0.880248101685424[/C][/ROW]
[ROW][C]58[/C][C]88.91[/C][C]89.3655186194111[/C][C]-0.45551861941108[/C][/ROW]
[ROW][C]59[/C][C]89.79[/C][C]89.4160449874592[/C][C]0.37395501254079[/C][/ROW]
[ROW][C]60[/C][C]90.54[/C][C]89.9475763145447[/C][C]0.59242368545533[/C][/ROW]
[ROW][C]61[/C][C]93.15[/C][C]91.5929847598325[/C][C]1.55701524016753[/C][/ROW]
[ROW][C]62[/C][C]92.79[/C][C]94.2974672317684[/C][C]-1.50746723176843[/C][/ROW]
[ROW][C]63[/C][C]93.21[/C][C]93.6656249497218[/C][C]-0.455624949721795[/C][/ROW]
[ROW][C]64[/C][C]95.35[/C][C]95.1248795568641[/C][C]0.22512044313585[/C][/ROW]
[ROW][C]65[/C][C]100.91[/C][C]96.688451318679[/C][C]4.221548681321[/C][/ROW]
[ROW][C]66[/C][C]103.69[/C][C]102.323240775349[/C][C]1.36675922465051[/C][/ROW]
[ROW][C]67[/C][C]104.04[/C][C]105.980453290922[/C][C]-1.94045329092204[/C][/ROW]
[ROW][C]68[/C][C]104.16[/C][C]105.007082085105[/C][C]-0.847082085104958[/C][/ROW]
[ROW][C]69[/C][C]104.71[/C][C]105.430806821951[/C][C]-0.720806821951214[/C][/ROW]
[ROW][C]70[/C][C]105.18[/C][C]105.648707608883[/C][C]-0.46870760888315[/C][/ROW]
[ROW][C]71[/C][C]104.92[/C][C]106.176534799668[/C][C]-1.25653479966839[/C][/ROW]
[ROW][C]72[/C][C]104.83[/C][C]105.234380135276[/C][C]-0.404380135276369[/C][/ROW]
[ROW][C]73[/C][C]104.9[/C][C]105.835788856838[/C][C]-0.93578885683776[/C][/ROW]
[ROW][C]74[/C][C]105.05[/C][C]105.490109412741[/C][C]-0.440109412741137[/C][/ROW]
[ROW][C]75[/C][C]104.6[/C][C]105.586706000681[/C][C]-0.986706000680897[/C][/ROW]
[ROW][C]76[/C][C]103.21[/C][C]106.067272834544[/C][C]-2.85727283454361[/C][/ROW]
[ROW][C]77[/C][C]102.52[/C][C]103.470020993976[/C][C]-0.950020993975855[/C][/ROW]
[ROW][C]78[/C][C]101.09[/C][C]101.796428888447[/C][C]-0.706428888446908[/C][/ROW]
[ROW][C]79[/C][C]101.19[/C][C]100.81935550793[/C][C]0.370644492070156[/C][/ROW]
[ROW][C]80[/C][C]102.34[/C][C]100.068959324308[/C][C]2.27104067569181[/C][/ROW]
[ROW][C]81[/C][C]102.62[/C][C]102.160819839246[/C][C]0.459180160753718[/C][/ROW]
[ROW][C]82[/C][C]102.47[/C][C]102.350209486339[/C][C]0.119790513660831[/C][/ROW]
[ROW][C]83[/C][C]101.82[/C][C]102.378475074245[/C][C]-0.558475074244839[/C][/ROW]
[ROW][C]84[/C][C]101.86[/C][C]101.189181009069[/C][C]0.670818990930783[/C][/ROW]
[ROW][C]85[/C][C]101.54[/C][C]102.140633354196[/C][C]-0.600633354195509[/C][/ROW]
[ROW][C]86[/C][C]101.98[/C][C]101.473544768724[/C][C]0.506455231276391[/C][/ROW]
[ROW][C]87[/C][C]101.23[/C][C]102.053859440255[/C][C]-0.823859440254779[/C][/ROW]
[ROW][C]88[/C][C]100.4[/C][C]102.267753447074[/C][C]-1.8677534470735[/C][/ROW]
[ROW][C]89[/C][C]99.94[/C][C]100.433010543036[/C][C]-0.493010543036164[/C][/ROW]
[ROW][C]90[/C][C]99.94[/C][C]99.0829473785012[/C][C]0.857052621498823[/C][/ROW]
[ROW][C]91[/C][C]100[/C][C]99.8558464834889[/C][C]0.144153516511054[/C][/ROW]
[ROW][C]92[/C][C]98.8[/C][C]99.0190980533373[/C][C]-0.219098053337333[/C][/ROW]
[ROW][C]93[/C][C]99.07[/C][C]98.2513421300183[/C][C]0.818657869981664[/C][/ROW]
[ROW][C]94[/C][C]99.46[/C][C]98.5043002685667[/C][C]0.955699731433299[/C][/ROW]
[ROW][C]95[/C][C]99.18[/C][C]99.2436378828223[/C][C]-0.0636378828222917[/C][/ROW]
[ROW][C]96[/C][C]98.47[/C][C]98.5256141461108[/C][C]-0.0556141461107842[/C][/ROW]
[ROW][C]97[/C][C]97.12[/C][C]98.5783991645474[/C][C]-1.45839916454743[/C][/ROW]
[ROW][C]98[/C][C]96.91[/C][C]96.7057655172545[/C][C]0.204234482745449[/C][/ROW]
[ROW][C]99[/C][C]96.09[/C][C]96.574229553864[/C][C]-0.484229553863955[/C][/ROW]
[ROW][C]100[/C][C]97.17[/C][C]96.7876301190966[/C][C]0.382369880903354[/C][/ROW]
[ROW][C]101[/C][C]96.8[/C][C]97.3233835812557[/C][C]-0.523383581255672[/C][/ROW]
[ROW][C]102[/C][C]97.13[/C][C]96.0571044579968[/C][C]1.07289554200324[/C][/ROW]
[ROW][C]103[/C][C]99.9[/C][C]97.2041766442222[/C][C]2.69582335577779[/C][/ROW]
[ROW][C]104[/C][C]100.56[/C][C]99.5996372299523[/C][C]0.960362770047723[/C][/ROW]
[ROW][C]105[/C][C]100.84[/C][C]100.933262486272[/C][C]-0.093262486272053[/C][/ROW]
[ROW][C]106[/C][C]99.81[/C][C]101.009592627548[/C][C]-1.19959262754843[/C][/ROW]
[ROW][C]107[/C][C]100.44[/C][C]99.8878413970009[/C][C]0.552158602999086[/C][/ROW]
[ROW][C]108[/C][C]100.07[/C][C]100.205842772118[/C][C]-0.135842772118338[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287037&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287037&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
1380.0478.30774572649581.73225427350425
1480.2380.6129273970683-0.382927397068286
1580.4480.7612265037552-0.321226503755241
1681.7882.0379862681575-0.257986268157453
1782.5182.7026883892421-0.192688389242136
1882.4382.6040873049367-0.174087304936677
1982.3583.0859596705188-0.735959670518824
2082.5381.92909270222770.600907297772309
2182.0882.7091540179696-0.629154017969583
2282.7381.94581190263950.784188097360541
2382.4682.9100490033948-0.450049003394824
2481.9882.1229447493316-0.142944749331576
2582.1182.3878572249877-0.277857224987656
2682.2682.23682601190380.0231739880962465
2782.5182.4282353240850.0817646759150392
2882.8983.8274687785023-0.937468778502307
2983.8383.39311219866270.436887801337249
3084.7383.63335629559731.09664370440271
3184.4885.3552886343099-0.875288634309868
3284.8483.99990745938220.840092540617803
3384.9985.0089189521249-0.0189189521249062
3484.784.9704637827027-0.270463782702649
3584.5484.778862332596-0.238862332596014
3684.7384.14497824041580.585021759584166
3784.5185.2288718531946-0.718871853194614
3884.5484.6375853055681-0.0975853055680886
3984.2784.6842807653016-0.414280765301555
4084.4785.4619966183019-0.991996618301926
4184.2584.8364807069839-0.586480706983949
4284.3383.70728851502610.622711484973919
4384.2984.5122288079442-0.222228807944177
4484.5383.50049883035811.02950116964195
4584.0184.4282735252361-0.418273525236103
4684.1883.63808891127410.541911088725939
4784.0884.07274309330580.00725690669419521
4883.4483.5492282470843-0.10922824708426
4983.6183.6610409341966-0.0510409341965925
5083.8983.59642854465220.293571455347816
5183.483.9731757352287-0.573175735228702
5282.9684.4983731234194-1.5383731234194
5382.7683.1210391654844-0.361039165484414
5483.3582.05798444935261.29201555064735
5587.7883.50990038546814.27009961453189
5688.9987.88754264343451.10245735656552
5788.9289.8002481016854-0.880248101685424
5888.9189.3655186194111-0.45551861941108
5989.7989.41604498745920.37395501254079
6090.5489.94757631454470.59242368545533
6193.1591.59298475983251.55701524016753
6292.7994.2974672317684-1.50746723176843
6393.2193.6656249497218-0.455624949721795
6495.3595.12487955686410.22512044313585
65100.9196.6884513186794.221548681321
66103.69102.3232407753491.36675922465051
67104.04105.980453290922-1.94045329092204
68104.16105.007082085105-0.847082085104958
69104.71105.430806821951-0.720806821951214
70105.18105.648707608883-0.46870760888315
71104.92106.176534799668-1.25653479966839
72104.83105.234380135276-0.404380135276369
73104.9105.835788856838-0.93578885683776
74105.05105.490109412741-0.440109412741137
75104.6105.586706000681-0.986706000680897
76103.21106.067272834544-2.85727283454361
77102.52103.470020993976-0.950020993975855
78101.09101.796428888447-0.706428888446908
79101.19100.819355507930.370644492070156
80102.34100.0689593243082.27104067569181
81102.62102.1608198392460.459180160753718
82102.47102.3502094863390.119790513660831
83101.82102.378475074245-0.558475074244839
84101.86101.1891810090690.670818990930783
85101.54102.140633354196-0.600633354195509
86101.98101.4735447687240.506455231276391
87101.23102.053859440255-0.823859440254779
88100.4102.267753447074-1.8677534470735
8999.94100.433010543036-0.493010543036164
9099.9499.08294737850120.857052621498823
9110099.85584648348890.144153516511054
9298.899.0190980533373-0.219098053337333
9399.0798.25134213001830.818657869981664
9499.4698.50430026856670.955699731433299
9599.1899.2436378828223-0.0636378828222917
9698.4798.5256141461108-0.0556141461107842
9797.1298.5783991645474-1.45839916454743
9896.9196.70576551725450.204234482745449
9996.0996.574229553864-0.484229553863955
10097.1796.78763011909660.382369880903354
10196.897.3233835812557-0.523383581255672
10297.1396.05710445799681.07289554200324
10399.997.20417664422222.69582335577779
104100.5699.59963722995230.960362770047723
105100.84100.933262486272-0.093262486272053
10699.81101.009592627548-1.19959262754843
107100.4499.88784139700090.552158602999086
108100.07100.205842772118-0.135842772118338







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109100.58220869464198.4713850549408102.69303233434
110100.87025072261497.5654862468372104.175015198392
111101.19495941725596.7485110668996105.64140776761
112102.65216811189597.0506408166824108.253695407109
113103.48687680653696.6961985572502110.277555055822
114103.5324188345195.5104029035644111.554434765455
115104.17546086248494.8766103369014113.474311388066
116103.89225289045893.2699093113453114.51459646957
117104.08612825176592.0935199796604116.078736523869
118104.09542027973990.6861973794925117.504643179985
119104.25846230771389.3869718814382119.129952733987
120103.99650433568687.6179272661103120.375081405263

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 100.582208694641 & 98.4713850549408 & 102.69303233434 \tabularnewline
110 & 100.870250722614 & 97.5654862468372 & 104.175015198392 \tabularnewline
111 & 101.194959417255 & 96.7485110668996 & 105.64140776761 \tabularnewline
112 & 102.652168111895 & 97.0506408166824 & 108.253695407109 \tabularnewline
113 & 103.486876806536 & 96.6961985572502 & 110.277555055822 \tabularnewline
114 & 103.53241883451 & 95.5104029035644 & 111.554434765455 \tabularnewline
115 & 104.175460862484 & 94.8766103369014 & 113.474311388066 \tabularnewline
116 & 103.892252890458 & 93.2699093113453 & 114.51459646957 \tabularnewline
117 & 104.086128251765 & 92.0935199796604 & 116.078736523869 \tabularnewline
118 & 104.095420279739 & 90.6861973794925 & 117.504643179985 \tabularnewline
119 & 104.258462307713 & 89.3869718814382 & 119.129952733987 \tabularnewline
120 & 103.996504335686 & 87.6179272661103 & 120.375081405263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287037&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]100.582208694641[/C][C]98.4713850549408[/C][C]102.69303233434[/C][/ROW]
[ROW][C]110[/C][C]100.870250722614[/C][C]97.5654862468372[/C][C]104.175015198392[/C][/ROW]
[ROW][C]111[/C][C]101.194959417255[/C][C]96.7485110668996[/C][C]105.64140776761[/C][/ROW]
[ROW][C]112[/C][C]102.652168111895[/C][C]97.0506408166824[/C][C]108.253695407109[/C][/ROW]
[ROW][C]113[/C][C]103.486876806536[/C][C]96.6961985572502[/C][C]110.277555055822[/C][/ROW]
[ROW][C]114[/C][C]103.53241883451[/C][C]95.5104029035644[/C][C]111.554434765455[/C][/ROW]
[ROW][C]115[/C][C]104.175460862484[/C][C]94.8766103369014[/C][C]113.474311388066[/C][/ROW]
[ROW][C]116[/C][C]103.892252890458[/C][C]93.2699093113453[/C][C]114.51459646957[/C][/ROW]
[ROW][C]117[/C][C]104.086128251765[/C][C]92.0935199796604[/C][C]116.078736523869[/C][/ROW]
[ROW][C]118[/C][C]104.095420279739[/C][C]90.6861973794925[/C][C]117.504643179985[/C][/ROW]
[ROW][C]119[/C][C]104.258462307713[/C][C]89.3869718814382[/C][C]119.129952733987[/C][/ROW]
[ROW][C]120[/C][C]103.996504335686[/C][C]87.6179272661103[/C][C]120.375081405263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287037&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287037&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
109100.58220869464198.4713850549408102.69303233434
110100.87025072261497.5654862468372104.175015198392
111101.19495941725596.7485110668996105.64140776761
112102.65216811189597.0506408166824108.253695407109
113103.48687680653696.6961985572502110.277555055822
114103.5324188345195.5104029035644111.554434765455
115104.17546086248494.8766103369014113.474311388066
116103.89225289045893.2699093113453114.51459646957
117104.08612825176592.0935199796604116.078736523869
118104.09542027973990.6861973794925117.504643179985
119104.25846230771389.3869718814382119.129952733987
120103.99650433568687.6179272661103120.375081405263



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')