Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 02 Dec 2015 09:10:40 +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/2015/Dec/02/t1449047470i4hkd9nrucptvee.htm/, Retrieved Sat, 18 May 2024 16:44:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284793, Retrieved Sat, 18 May 2024 16:44:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-12-02 09:10:40] [047b71d569822bc9ea0d1a14ab5e311b] [Current]
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Dataseries X:
72.04
72.26
72.53
72.41
72.91
72.84
72.92
73.03
72.98
72.99
73.15
73.34
73.8
74.46
74.54
74.92
74.19
74.34
74.54
74.4
73.78
74.42
73.54
74.45
76.31
76.44
76.64
76.44
76.49
76.52
78.15
78.54
78.79
78.75
78.28
78.44
78.75
80.54
80.84
81.11
80.47
80.53
80.35
80.29
80.27
80.1
79.8
79.84
79.92
80.26
80.69
84.5
85.45
86.19
86.4
85.98
85.87
86.06
86.43
86.43
86.37
86.84
86.73
90.99
92.61
93.83
94.2
94.01
93.47
93.27
94.3
94.53
94.59
94.69
94.67
96.55
97.14
97.32
97.97
98.49
99.11
99.09
98.76
99.2
99.61
99.54
99.68
100.75
100.38
100.79
100.39
100.39
100.12
100
99.17
99.17
99.59
99.96
99.68
101.03
100.99
101.38
101.84
101.52
101.37
101.22
101.45
101.99




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284793&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284793&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284793&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.994336334612503
beta0.0217638859938461
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.994336334612503 \tabularnewline
beta & 0.0217638859938461 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284793&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]0.994336334612503[/C][/ROW]
[ROW][C]beta[/C][C]0.0217638859938461[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284793&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284793&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
alpha0.994336334612503
beta0.0217638859938461
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1373.872.90798062539270.892019374607287
1474.4674.4761166373183-0.0161166373183192
1574.5474.595358770105-0.0553587701049878
1674.9274.9720639728689-0.0520639728688508
1774.1974.2574570048232-0.0674570048232397
1874.3474.4195175288345-0.0795175288345291
1974.5474.44032548575230.0996745142477522
2074.474.6251714210555-0.225171421055535
2173.7874.3088376078929-0.528837607892882
2274.4273.72865850955710.691341490442895
2373.5474.5589692027444-1.01896920274443
2474.4573.73881243097760.711187569022385
2576.3174.92001722938671.38998277061333
2676.4477.0146149757524-0.574614975752439
2776.6476.58442741899810.0555725810019112
2876.4477.0883756689242-0.648375668924189
2976.4975.76035831195180.729641688048176
3076.5276.7309046924164-0.210904692416435
3178.1576.63135704928021.51864295071982
3278.5478.26357899511460.276421004885407
3378.7978.48320196210670.30679803789333
3478.7578.7988049268439-0.0488049268439283
3578.2878.9366856461582-0.656685646158181
3678.4478.5535869718347-0.113586971834692
3778.7578.980763060899-0.230763060899022
3880.5479.47872627509821.06127372490182
3980.8480.72262947662940.117370523370568
4081.1181.3457425678399-0.235742567839893
4180.4780.44019084534340.0298091546566042
4280.5380.7530273245871-0.223027324587051
4380.3580.6882557794165-0.338255779416485
4480.2980.4637572226015-0.173757222601495
4580.2780.21939619697830.0506038030216587
4680.180.2581499701439-0.158149970143924
4779.880.2646886339-0.464688633899968
4879.8480.0625672918622-0.222567291862205
4979.9280.3699100445081-0.449910044508115
5080.2680.6433915424687-0.383391542468701
5180.6980.39209596223510.297904037764937
5284.581.14245018699333.3575498130067
5385.4583.8032497568241.64675024317604
5486.1985.79067780064840.39932219935163
5586.486.418027476896-0.0180274768960373
5685.9886.5908060479002-0.610806047900198
5785.8785.9690144422112-0.0990144422111712
5886.0685.9145332326270.145466767372966
5986.4386.29687395429660.133126045703435
6086.4386.7882065014988-0.358206501498827
6186.3787.0767505173383-0.70675051733825
6286.8487.2233003233784-0.383300323378407
6386.7387.0572475891241-0.327247589124084
6490.9987.29538341158883.69461658841122
6592.6190.2872273294272.32277267057304
6693.8393.03699986846550.793000131534498
6794.294.14861921924270.0513807807573272
6894.0194.479956774186-0.469956774186045
6993.4794.0792567949336-0.609256794933614
7093.2793.5922503913985-0.32225039139847
7194.393.5895753936460.710424606353968
7294.5394.7552740792924-0.22527407929239
7394.5995.3081946304136-0.71819463041362
7494.6995.6015647181447-0.911564718144732
7594.6794.9957927944697-0.32579279446972
7696.5595.3773865933831.17261340661697
7797.1495.82485279636611.31514720363387
7897.3297.5779639751615-0.257963975161474
7997.9797.62578986967650.344210130323503
8098.4998.23527256763960.25472743236044
8199.1198.5497285011010.560271498898956
8299.0999.2483555160498-0.158355516049753
8398.7699.4517734380329-0.691773438032939
8499.299.2304460558283-0.0304460558283211
8599.61100.007267829256-0.397267829255853
8699.54100.673295730231-1.13329573023059
8799.6899.8640212495152-0.184021249515212
88100.75100.4337857588290.31621424117067
89100.3899.98363000948630.396369990513733
90100.79100.795703355606-0.00570335560632884
91100.39101.080478711829-0.690478711828703
92100.39100.620261867075-0.23026186707483
93100.12100.399957234614-0.27995723461423
94100100.190160348006-0.190160348006145
9599.17100.291640232996-1.12164023299613
9699.1799.5705669607839-0.400566960783905
9799.5999.8922185251249-0.302218525124943
9899.96100.564921857641-0.604921857641244
9999.68100.214360519952-0.534360519951505
100101.03100.3586543070360.671345692963527
101100.99100.1875846358180.802415364182011
102101.38101.3388577496720.041142250327681
103101.84101.604314885540.235685114459628
104101.52102.024677179154-0.504677179154342
105101.37101.480353480681-0.110353480681482
106101.22101.393082866988-0.173082866987841
107101.45101.462707245261-0.012707245260529
108101.99101.8318019769070.158198023093377

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 73.8 & 72.9079806253927 & 0.892019374607287 \tabularnewline
14 & 74.46 & 74.4761166373183 & -0.0161166373183192 \tabularnewline
15 & 74.54 & 74.595358770105 & -0.0553587701049878 \tabularnewline
16 & 74.92 & 74.9720639728689 & -0.0520639728688508 \tabularnewline
17 & 74.19 & 74.2574570048232 & -0.0674570048232397 \tabularnewline
18 & 74.34 & 74.4195175288345 & -0.0795175288345291 \tabularnewline
19 & 74.54 & 74.4403254857523 & 0.0996745142477522 \tabularnewline
20 & 74.4 & 74.6251714210555 & -0.225171421055535 \tabularnewline
21 & 73.78 & 74.3088376078929 & -0.528837607892882 \tabularnewline
22 & 74.42 & 73.7286585095571 & 0.691341490442895 \tabularnewline
23 & 73.54 & 74.5589692027444 & -1.01896920274443 \tabularnewline
24 & 74.45 & 73.7388124309776 & 0.711187569022385 \tabularnewline
25 & 76.31 & 74.9200172293867 & 1.38998277061333 \tabularnewline
26 & 76.44 & 77.0146149757524 & -0.574614975752439 \tabularnewline
27 & 76.64 & 76.5844274189981 & 0.0555725810019112 \tabularnewline
28 & 76.44 & 77.0883756689242 & -0.648375668924189 \tabularnewline
29 & 76.49 & 75.7603583119518 & 0.729641688048176 \tabularnewline
30 & 76.52 & 76.7309046924164 & -0.210904692416435 \tabularnewline
31 & 78.15 & 76.6313570492802 & 1.51864295071982 \tabularnewline
32 & 78.54 & 78.2635789951146 & 0.276421004885407 \tabularnewline
33 & 78.79 & 78.4832019621067 & 0.30679803789333 \tabularnewline
34 & 78.75 & 78.7988049268439 & -0.0488049268439283 \tabularnewline
35 & 78.28 & 78.9366856461582 & -0.656685646158181 \tabularnewline
36 & 78.44 & 78.5535869718347 & -0.113586971834692 \tabularnewline
37 & 78.75 & 78.980763060899 & -0.230763060899022 \tabularnewline
38 & 80.54 & 79.4787262750982 & 1.06127372490182 \tabularnewline
39 & 80.84 & 80.7226294766294 & 0.117370523370568 \tabularnewline
40 & 81.11 & 81.3457425678399 & -0.235742567839893 \tabularnewline
41 & 80.47 & 80.4401908453434 & 0.0298091546566042 \tabularnewline
42 & 80.53 & 80.7530273245871 & -0.223027324587051 \tabularnewline
43 & 80.35 & 80.6882557794165 & -0.338255779416485 \tabularnewline
44 & 80.29 & 80.4637572226015 & -0.173757222601495 \tabularnewline
45 & 80.27 & 80.2193961969783 & 0.0506038030216587 \tabularnewline
46 & 80.1 & 80.2581499701439 & -0.158149970143924 \tabularnewline
47 & 79.8 & 80.2646886339 & -0.464688633899968 \tabularnewline
48 & 79.84 & 80.0625672918622 & -0.222567291862205 \tabularnewline
49 & 79.92 & 80.3699100445081 & -0.449910044508115 \tabularnewline
50 & 80.26 & 80.6433915424687 & -0.383391542468701 \tabularnewline
51 & 80.69 & 80.3920959622351 & 0.297904037764937 \tabularnewline
52 & 84.5 & 81.1424501869933 & 3.3575498130067 \tabularnewline
53 & 85.45 & 83.803249756824 & 1.64675024317604 \tabularnewline
54 & 86.19 & 85.7906778006484 & 0.39932219935163 \tabularnewline
55 & 86.4 & 86.418027476896 & -0.0180274768960373 \tabularnewline
56 & 85.98 & 86.5908060479002 & -0.610806047900198 \tabularnewline
57 & 85.87 & 85.9690144422112 & -0.0990144422111712 \tabularnewline
58 & 86.06 & 85.914533232627 & 0.145466767372966 \tabularnewline
59 & 86.43 & 86.2968739542966 & 0.133126045703435 \tabularnewline
60 & 86.43 & 86.7882065014988 & -0.358206501498827 \tabularnewline
61 & 86.37 & 87.0767505173383 & -0.70675051733825 \tabularnewline
62 & 86.84 & 87.2233003233784 & -0.383300323378407 \tabularnewline
63 & 86.73 & 87.0572475891241 & -0.327247589124084 \tabularnewline
64 & 90.99 & 87.2953834115888 & 3.69461658841122 \tabularnewline
65 & 92.61 & 90.287227329427 & 2.32277267057304 \tabularnewline
66 & 93.83 & 93.0369998684655 & 0.793000131534498 \tabularnewline
67 & 94.2 & 94.1486192192427 & 0.0513807807573272 \tabularnewline
68 & 94.01 & 94.479956774186 & -0.469956774186045 \tabularnewline
69 & 93.47 & 94.0792567949336 & -0.609256794933614 \tabularnewline
70 & 93.27 & 93.5922503913985 & -0.32225039139847 \tabularnewline
71 & 94.3 & 93.589575393646 & 0.710424606353968 \tabularnewline
72 & 94.53 & 94.7552740792924 & -0.22527407929239 \tabularnewline
73 & 94.59 & 95.3081946304136 & -0.71819463041362 \tabularnewline
74 & 94.69 & 95.6015647181447 & -0.911564718144732 \tabularnewline
75 & 94.67 & 94.9957927944697 & -0.32579279446972 \tabularnewline
76 & 96.55 & 95.377386593383 & 1.17261340661697 \tabularnewline
77 & 97.14 & 95.8248527963661 & 1.31514720363387 \tabularnewline
78 & 97.32 & 97.5779639751615 & -0.257963975161474 \tabularnewline
79 & 97.97 & 97.6257898696765 & 0.344210130323503 \tabularnewline
80 & 98.49 & 98.2352725676396 & 0.25472743236044 \tabularnewline
81 & 99.11 & 98.549728501101 & 0.560271498898956 \tabularnewline
82 & 99.09 & 99.2483555160498 & -0.158355516049753 \tabularnewline
83 & 98.76 & 99.4517734380329 & -0.691773438032939 \tabularnewline
84 & 99.2 & 99.2304460558283 & -0.0304460558283211 \tabularnewline
85 & 99.61 & 100.007267829256 & -0.397267829255853 \tabularnewline
86 & 99.54 & 100.673295730231 & -1.13329573023059 \tabularnewline
87 & 99.68 & 99.8640212495152 & -0.184021249515212 \tabularnewline
88 & 100.75 & 100.433785758829 & 0.31621424117067 \tabularnewline
89 & 100.38 & 99.9836300094863 & 0.396369990513733 \tabularnewline
90 & 100.79 & 100.795703355606 & -0.00570335560632884 \tabularnewline
91 & 100.39 & 101.080478711829 & -0.690478711828703 \tabularnewline
92 & 100.39 & 100.620261867075 & -0.23026186707483 \tabularnewline
93 & 100.12 & 100.399957234614 & -0.27995723461423 \tabularnewline
94 & 100 & 100.190160348006 & -0.190160348006145 \tabularnewline
95 & 99.17 & 100.291640232996 & -1.12164023299613 \tabularnewline
96 & 99.17 & 99.5705669607839 & -0.400566960783905 \tabularnewline
97 & 99.59 & 99.8922185251249 & -0.302218525124943 \tabularnewline
98 & 99.96 & 100.564921857641 & -0.604921857641244 \tabularnewline
99 & 99.68 & 100.214360519952 & -0.534360519951505 \tabularnewline
100 & 101.03 & 100.358654307036 & 0.671345692963527 \tabularnewline
101 & 100.99 & 100.187584635818 & 0.802415364182011 \tabularnewline
102 & 101.38 & 101.338857749672 & 0.041142250327681 \tabularnewline
103 & 101.84 & 101.60431488554 & 0.235685114459628 \tabularnewline
104 & 101.52 & 102.024677179154 & -0.504677179154342 \tabularnewline
105 & 101.37 & 101.480353480681 & -0.110353480681482 \tabularnewline
106 & 101.22 & 101.393082866988 & -0.173082866987841 \tabularnewline
107 & 101.45 & 101.462707245261 & -0.012707245260529 \tabularnewline
108 & 101.99 & 101.831801976907 & 0.158198023093377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284793&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]73.8[/C][C]72.9079806253927[/C][C]0.892019374607287[/C][/ROW]
[ROW][C]14[/C][C]74.46[/C][C]74.4761166373183[/C][C]-0.0161166373183192[/C][/ROW]
[ROW][C]15[/C][C]74.54[/C][C]74.595358770105[/C][C]-0.0553587701049878[/C][/ROW]
[ROW][C]16[/C][C]74.92[/C][C]74.9720639728689[/C][C]-0.0520639728688508[/C][/ROW]
[ROW][C]17[/C][C]74.19[/C][C]74.2574570048232[/C][C]-0.0674570048232397[/C][/ROW]
[ROW][C]18[/C][C]74.34[/C][C]74.4195175288345[/C][C]-0.0795175288345291[/C][/ROW]
[ROW][C]19[/C][C]74.54[/C][C]74.4403254857523[/C][C]0.0996745142477522[/C][/ROW]
[ROW][C]20[/C][C]74.4[/C][C]74.6251714210555[/C][C]-0.225171421055535[/C][/ROW]
[ROW][C]21[/C][C]73.78[/C][C]74.3088376078929[/C][C]-0.528837607892882[/C][/ROW]
[ROW][C]22[/C][C]74.42[/C][C]73.7286585095571[/C][C]0.691341490442895[/C][/ROW]
[ROW][C]23[/C][C]73.54[/C][C]74.5589692027444[/C][C]-1.01896920274443[/C][/ROW]
[ROW][C]24[/C][C]74.45[/C][C]73.7388124309776[/C][C]0.711187569022385[/C][/ROW]
[ROW][C]25[/C][C]76.31[/C][C]74.9200172293867[/C][C]1.38998277061333[/C][/ROW]
[ROW][C]26[/C][C]76.44[/C][C]77.0146149757524[/C][C]-0.574614975752439[/C][/ROW]
[ROW][C]27[/C][C]76.64[/C][C]76.5844274189981[/C][C]0.0555725810019112[/C][/ROW]
[ROW][C]28[/C][C]76.44[/C][C]77.0883756689242[/C][C]-0.648375668924189[/C][/ROW]
[ROW][C]29[/C][C]76.49[/C][C]75.7603583119518[/C][C]0.729641688048176[/C][/ROW]
[ROW][C]30[/C][C]76.52[/C][C]76.7309046924164[/C][C]-0.210904692416435[/C][/ROW]
[ROW][C]31[/C][C]78.15[/C][C]76.6313570492802[/C][C]1.51864295071982[/C][/ROW]
[ROW][C]32[/C][C]78.54[/C][C]78.2635789951146[/C][C]0.276421004885407[/C][/ROW]
[ROW][C]33[/C][C]78.79[/C][C]78.4832019621067[/C][C]0.30679803789333[/C][/ROW]
[ROW][C]34[/C][C]78.75[/C][C]78.7988049268439[/C][C]-0.0488049268439283[/C][/ROW]
[ROW][C]35[/C][C]78.28[/C][C]78.9366856461582[/C][C]-0.656685646158181[/C][/ROW]
[ROW][C]36[/C][C]78.44[/C][C]78.5535869718347[/C][C]-0.113586971834692[/C][/ROW]
[ROW][C]37[/C][C]78.75[/C][C]78.980763060899[/C][C]-0.230763060899022[/C][/ROW]
[ROW][C]38[/C][C]80.54[/C][C]79.4787262750982[/C][C]1.06127372490182[/C][/ROW]
[ROW][C]39[/C][C]80.84[/C][C]80.7226294766294[/C][C]0.117370523370568[/C][/ROW]
[ROW][C]40[/C][C]81.11[/C][C]81.3457425678399[/C][C]-0.235742567839893[/C][/ROW]
[ROW][C]41[/C][C]80.47[/C][C]80.4401908453434[/C][C]0.0298091546566042[/C][/ROW]
[ROW][C]42[/C][C]80.53[/C][C]80.7530273245871[/C][C]-0.223027324587051[/C][/ROW]
[ROW][C]43[/C][C]80.35[/C][C]80.6882557794165[/C][C]-0.338255779416485[/C][/ROW]
[ROW][C]44[/C][C]80.29[/C][C]80.4637572226015[/C][C]-0.173757222601495[/C][/ROW]
[ROW][C]45[/C][C]80.27[/C][C]80.2193961969783[/C][C]0.0506038030216587[/C][/ROW]
[ROW][C]46[/C][C]80.1[/C][C]80.2581499701439[/C][C]-0.158149970143924[/C][/ROW]
[ROW][C]47[/C][C]79.8[/C][C]80.2646886339[/C][C]-0.464688633899968[/C][/ROW]
[ROW][C]48[/C][C]79.84[/C][C]80.0625672918622[/C][C]-0.222567291862205[/C][/ROW]
[ROW][C]49[/C][C]79.92[/C][C]80.3699100445081[/C][C]-0.449910044508115[/C][/ROW]
[ROW][C]50[/C][C]80.26[/C][C]80.6433915424687[/C][C]-0.383391542468701[/C][/ROW]
[ROW][C]51[/C][C]80.69[/C][C]80.3920959622351[/C][C]0.297904037764937[/C][/ROW]
[ROW][C]52[/C][C]84.5[/C][C]81.1424501869933[/C][C]3.3575498130067[/C][/ROW]
[ROW][C]53[/C][C]85.45[/C][C]83.803249756824[/C][C]1.64675024317604[/C][/ROW]
[ROW][C]54[/C][C]86.19[/C][C]85.7906778006484[/C][C]0.39932219935163[/C][/ROW]
[ROW][C]55[/C][C]86.4[/C][C]86.418027476896[/C][C]-0.0180274768960373[/C][/ROW]
[ROW][C]56[/C][C]85.98[/C][C]86.5908060479002[/C][C]-0.610806047900198[/C][/ROW]
[ROW][C]57[/C][C]85.87[/C][C]85.9690144422112[/C][C]-0.0990144422111712[/C][/ROW]
[ROW][C]58[/C][C]86.06[/C][C]85.914533232627[/C][C]0.145466767372966[/C][/ROW]
[ROW][C]59[/C][C]86.43[/C][C]86.2968739542966[/C][C]0.133126045703435[/C][/ROW]
[ROW][C]60[/C][C]86.43[/C][C]86.7882065014988[/C][C]-0.358206501498827[/C][/ROW]
[ROW][C]61[/C][C]86.37[/C][C]87.0767505173383[/C][C]-0.70675051733825[/C][/ROW]
[ROW][C]62[/C][C]86.84[/C][C]87.2233003233784[/C][C]-0.383300323378407[/C][/ROW]
[ROW][C]63[/C][C]86.73[/C][C]87.0572475891241[/C][C]-0.327247589124084[/C][/ROW]
[ROW][C]64[/C][C]90.99[/C][C]87.2953834115888[/C][C]3.69461658841122[/C][/ROW]
[ROW][C]65[/C][C]92.61[/C][C]90.287227329427[/C][C]2.32277267057304[/C][/ROW]
[ROW][C]66[/C][C]93.83[/C][C]93.0369998684655[/C][C]0.793000131534498[/C][/ROW]
[ROW][C]67[/C][C]94.2[/C][C]94.1486192192427[/C][C]0.0513807807573272[/C][/ROW]
[ROW][C]68[/C][C]94.01[/C][C]94.479956774186[/C][C]-0.469956774186045[/C][/ROW]
[ROW][C]69[/C][C]93.47[/C][C]94.0792567949336[/C][C]-0.609256794933614[/C][/ROW]
[ROW][C]70[/C][C]93.27[/C][C]93.5922503913985[/C][C]-0.32225039139847[/C][/ROW]
[ROW][C]71[/C][C]94.3[/C][C]93.589575393646[/C][C]0.710424606353968[/C][/ROW]
[ROW][C]72[/C][C]94.53[/C][C]94.7552740792924[/C][C]-0.22527407929239[/C][/ROW]
[ROW][C]73[/C][C]94.59[/C][C]95.3081946304136[/C][C]-0.71819463041362[/C][/ROW]
[ROW][C]74[/C][C]94.69[/C][C]95.6015647181447[/C][C]-0.911564718144732[/C][/ROW]
[ROW][C]75[/C][C]94.67[/C][C]94.9957927944697[/C][C]-0.32579279446972[/C][/ROW]
[ROW][C]76[/C][C]96.55[/C][C]95.377386593383[/C][C]1.17261340661697[/C][/ROW]
[ROW][C]77[/C][C]97.14[/C][C]95.8248527963661[/C][C]1.31514720363387[/C][/ROW]
[ROW][C]78[/C][C]97.32[/C][C]97.5779639751615[/C][C]-0.257963975161474[/C][/ROW]
[ROW][C]79[/C][C]97.97[/C][C]97.6257898696765[/C][C]0.344210130323503[/C][/ROW]
[ROW][C]80[/C][C]98.49[/C][C]98.2352725676396[/C][C]0.25472743236044[/C][/ROW]
[ROW][C]81[/C][C]99.11[/C][C]98.549728501101[/C][C]0.560271498898956[/C][/ROW]
[ROW][C]82[/C][C]99.09[/C][C]99.2483555160498[/C][C]-0.158355516049753[/C][/ROW]
[ROW][C]83[/C][C]98.76[/C][C]99.4517734380329[/C][C]-0.691773438032939[/C][/ROW]
[ROW][C]84[/C][C]99.2[/C][C]99.2304460558283[/C][C]-0.0304460558283211[/C][/ROW]
[ROW][C]85[/C][C]99.61[/C][C]100.007267829256[/C][C]-0.397267829255853[/C][/ROW]
[ROW][C]86[/C][C]99.54[/C][C]100.673295730231[/C][C]-1.13329573023059[/C][/ROW]
[ROW][C]87[/C][C]99.68[/C][C]99.8640212495152[/C][C]-0.184021249515212[/C][/ROW]
[ROW][C]88[/C][C]100.75[/C][C]100.433785758829[/C][C]0.31621424117067[/C][/ROW]
[ROW][C]89[/C][C]100.38[/C][C]99.9836300094863[/C][C]0.396369990513733[/C][/ROW]
[ROW][C]90[/C][C]100.79[/C][C]100.795703355606[/C][C]-0.00570335560632884[/C][/ROW]
[ROW][C]91[/C][C]100.39[/C][C]101.080478711829[/C][C]-0.690478711828703[/C][/ROW]
[ROW][C]92[/C][C]100.39[/C][C]100.620261867075[/C][C]-0.23026186707483[/C][/ROW]
[ROW][C]93[/C][C]100.12[/C][C]100.399957234614[/C][C]-0.27995723461423[/C][/ROW]
[ROW][C]94[/C][C]100[/C][C]100.190160348006[/C][C]-0.190160348006145[/C][/ROW]
[ROW][C]95[/C][C]99.17[/C][C]100.291640232996[/C][C]-1.12164023299613[/C][/ROW]
[ROW][C]96[/C][C]99.17[/C][C]99.5705669607839[/C][C]-0.400566960783905[/C][/ROW]
[ROW][C]97[/C][C]99.59[/C][C]99.8922185251249[/C][C]-0.302218525124943[/C][/ROW]
[ROW][C]98[/C][C]99.96[/C][C]100.564921857641[/C][C]-0.604921857641244[/C][/ROW]
[ROW][C]99[/C][C]99.68[/C][C]100.214360519952[/C][C]-0.534360519951505[/C][/ROW]
[ROW][C]100[/C][C]101.03[/C][C]100.358654307036[/C][C]0.671345692963527[/C][/ROW]
[ROW][C]101[/C][C]100.99[/C][C]100.187584635818[/C][C]0.802415364182011[/C][/ROW]
[ROW][C]102[/C][C]101.38[/C][C]101.338857749672[/C][C]0.041142250327681[/C][/ROW]
[ROW][C]103[/C][C]101.84[/C][C]101.60431488554[/C][C]0.235685114459628[/C][/ROW]
[ROW][C]104[/C][C]101.52[/C][C]102.024677179154[/C][C]-0.504677179154342[/C][/ROW]
[ROW][C]105[/C][C]101.37[/C][C]101.480353480681[/C][C]-0.110353480681482[/C][/ROW]
[ROW][C]106[/C][C]101.22[/C][C]101.393082866988[/C][C]-0.173082866987841[/C][/ROW]
[ROW][C]107[/C][C]101.45[/C][C]101.462707245261[/C][C]-0.012707245260529[/C][/ROW]
[ROW][C]108[/C][C]101.99[/C][C]101.831801976907[/C][C]0.158198023093377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284793&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284793&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
1373.872.90798062539270.892019374607287
1474.4674.4761166373183-0.0161166373183192
1574.5474.595358770105-0.0553587701049878
1674.9274.9720639728689-0.0520639728688508
1774.1974.2574570048232-0.0674570048232397
1874.3474.4195175288345-0.0795175288345291
1974.5474.44032548575230.0996745142477522
2074.474.6251714210555-0.225171421055535
2173.7874.3088376078929-0.528837607892882
2274.4273.72865850955710.691341490442895
2373.5474.5589692027444-1.01896920274443
2474.4573.73881243097760.711187569022385
2576.3174.92001722938671.38998277061333
2676.4477.0146149757524-0.574614975752439
2776.6476.58442741899810.0555725810019112
2876.4477.0883756689242-0.648375668924189
2976.4975.76035831195180.729641688048176
3076.5276.7309046924164-0.210904692416435
3178.1576.63135704928021.51864295071982
3278.5478.26357899511460.276421004885407
3378.7978.48320196210670.30679803789333
3478.7578.7988049268439-0.0488049268439283
3578.2878.9366856461582-0.656685646158181
3678.4478.5535869718347-0.113586971834692
3778.7578.980763060899-0.230763060899022
3880.5479.47872627509821.06127372490182
3980.8480.72262947662940.117370523370568
4081.1181.3457425678399-0.235742567839893
4180.4780.44019084534340.0298091546566042
4280.5380.7530273245871-0.223027324587051
4380.3580.6882557794165-0.338255779416485
4480.2980.4637572226015-0.173757222601495
4580.2780.21939619697830.0506038030216587
4680.180.2581499701439-0.158149970143924
4779.880.2646886339-0.464688633899968
4879.8480.0625672918622-0.222567291862205
4979.9280.3699100445081-0.449910044508115
5080.2680.6433915424687-0.383391542468701
5180.6980.39209596223510.297904037764937
5284.581.14245018699333.3575498130067
5385.4583.8032497568241.64675024317604
5486.1985.79067780064840.39932219935163
5586.486.418027476896-0.0180274768960373
5685.9886.5908060479002-0.610806047900198
5785.8785.9690144422112-0.0990144422111712
5886.0685.9145332326270.145466767372966
5986.4386.29687395429660.133126045703435
6086.4386.7882065014988-0.358206501498827
6186.3787.0767505173383-0.70675051733825
6286.8487.2233003233784-0.383300323378407
6386.7387.0572475891241-0.327247589124084
6490.9987.29538341158883.69461658841122
6592.6190.2872273294272.32277267057304
6693.8393.03699986846550.793000131534498
6794.294.14861921924270.0513807807573272
6894.0194.479956774186-0.469956774186045
6993.4794.0792567949336-0.609256794933614
7093.2793.5922503913985-0.32225039139847
7194.393.5895753936460.710424606353968
7294.5394.7552740792924-0.22527407929239
7394.5995.3081946304136-0.71819463041362
7494.6995.6015647181447-0.911564718144732
7594.6794.9957927944697-0.32579279446972
7696.5595.3773865933831.17261340661697
7797.1495.82485279636611.31514720363387
7897.3297.5779639751615-0.257963975161474
7997.9797.62578986967650.344210130323503
8098.4998.23527256763960.25472743236044
8199.1198.5497285011010.560271498898956
8299.0999.2483555160498-0.158355516049753
8398.7699.4517734380329-0.691773438032939
8499.299.2304460558283-0.0304460558283211
8599.61100.007267829256-0.397267829255853
8699.54100.673295730231-1.13329573023059
8799.6899.8640212495152-0.184021249515212
88100.75100.4337857588290.31621424117067
89100.3899.98363000948630.396369990513733
90100.79100.795703355606-0.00570335560632884
91100.39101.080478711829-0.690478711828703
92100.39100.620261867075-0.23026186707483
93100.12100.399957234614-0.27995723461423
94100100.190160348006-0.190160348006145
9599.17100.291640232996-1.12164023299613
9699.1799.5705669607839-0.400566960783905
9799.5999.8922185251249-0.302218525124943
9899.96100.564921857641-0.604921857641244
9999.68100.214360519952-0.534360519951505
100101.03100.3586543070360.671345692963527
101100.99100.1875846358180.802415364182011
102101.38101.3388577496720.041142250327681
103101.84101.604314885540.235685114459628
104101.52102.024677179154-0.504677179154342
105101.37101.480353480681-0.110353480681482
106101.22101.393082866988-0.173082866987841
107101.45101.462707245261-0.012707245260529
108101.99101.8318019769070.158198023093377







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109102.715124178517101.169036489941104.261211867093
110103.70799993159101.496034178841105.919965684338
111103.971604690012101.238906614159106.704302765865
112104.696990026151101.500156253148107.893823799155
113103.828830835237100.252762360977107.404899309497
114104.172118564256100.20864727753108.135589850982
115104.387611971555100.062069484727108.713154458383
116104.55307954135199.8833052410096109.222853841692
117104.50064641799199.5085163119546109.492776524027
118104.51468643790299.2075381519423109.821834723862
119104.7599050171499.1347265915796110.385083442701
120105.15003108020996.9830123405824113.317049819835

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 102.715124178517 & 101.169036489941 & 104.261211867093 \tabularnewline
110 & 103.70799993159 & 101.496034178841 & 105.919965684338 \tabularnewline
111 & 103.971604690012 & 101.238906614159 & 106.704302765865 \tabularnewline
112 & 104.696990026151 & 101.500156253148 & 107.893823799155 \tabularnewline
113 & 103.828830835237 & 100.252762360977 & 107.404899309497 \tabularnewline
114 & 104.172118564256 & 100.20864727753 & 108.135589850982 \tabularnewline
115 & 104.387611971555 & 100.062069484727 & 108.713154458383 \tabularnewline
116 & 104.553079541351 & 99.8833052410096 & 109.222853841692 \tabularnewline
117 & 104.500646417991 & 99.5085163119546 & 109.492776524027 \tabularnewline
118 & 104.514686437902 & 99.2075381519423 & 109.821834723862 \tabularnewline
119 & 104.75990501714 & 99.1347265915796 & 110.385083442701 \tabularnewline
120 & 105.150031080209 & 96.9830123405824 & 113.317049819835 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284793&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]102.715124178517[/C][C]101.169036489941[/C][C]104.261211867093[/C][/ROW]
[ROW][C]110[/C][C]103.70799993159[/C][C]101.496034178841[/C][C]105.919965684338[/C][/ROW]
[ROW][C]111[/C][C]103.971604690012[/C][C]101.238906614159[/C][C]106.704302765865[/C][/ROW]
[ROW][C]112[/C][C]104.696990026151[/C][C]101.500156253148[/C][C]107.893823799155[/C][/ROW]
[ROW][C]113[/C][C]103.828830835237[/C][C]100.252762360977[/C][C]107.404899309497[/C][/ROW]
[ROW][C]114[/C][C]104.172118564256[/C][C]100.20864727753[/C][C]108.135589850982[/C][/ROW]
[ROW][C]115[/C][C]104.387611971555[/C][C]100.062069484727[/C][C]108.713154458383[/C][/ROW]
[ROW][C]116[/C][C]104.553079541351[/C][C]99.8833052410096[/C][C]109.222853841692[/C][/ROW]
[ROW][C]117[/C][C]104.500646417991[/C][C]99.5085163119546[/C][C]109.492776524027[/C][/ROW]
[ROW][C]118[/C][C]104.514686437902[/C][C]99.2075381519423[/C][C]109.821834723862[/C][/ROW]
[ROW][C]119[/C][C]104.75990501714[/C][C]99.1347265915796[/C][C]110.385083442701[/C][/ROW]
[ROW][C]120[/C][C]105.150031080209[/C][C]96.9830123405824[/C][C]113.317049819835[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284793&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284793&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
109102.715124178517101.169036489941104.261211867093
110103.70799993159101.496034178841105.919965684338
111103.971604690012101.238906614159106.704302765865
112104.696990026151101.500156253148107.893823799155
113103.828830835237100.252762360977107.404899309497
114104.172118564256100.20864727753108.135589850982
115104.387611971555100.062069484727108.713154458383
116104.55307954135199.8833052410096109.222853841692
117104.50064641799199.5085163119546109.492776524027
118104.51468643790299.2075381519423109.821834723862
119104.7599050171499.1347265915796110.385083442701
120105.15003108020996.9830123405824113.317049819835



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):
par3 <- 'additive'
par2 <- 'Triple'
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')