Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 25 Nov 2015 14:34:15 +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/Nov/25/t1448462324glu2ar5g4yy7mpn.htm/, Retrieved Wed, 15 May 2024 16:22:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284133, Retrieved Wed, 15 May 2024 16:22:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-25 14:34:15] [bd97b182bc123d4050d70da6fa7efb72] [Current]
- R P     [Exponential Smoothing] [] [2015-12-12 13:26:58] [fbceac9f0608ffc2a284e55c3c8d1045]
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Dataseries X:
98.41
98.94
99.09
100.45
101.99
102.35
102.69
102.6
102.62
102.73
102.74
103.45
103.9
103.45
103.5
103.33
103.56
103.58
103.86
103.77
103.73
104.21
104.55
104.5
104.66
104.99
104.99
105.62
106.52
106.1
106.73
106.63
106.72
106.5
107.12
106.84
107.25
108.19
108.21
107.98
109.12
109.79
109.69
109.69
109.24
108.55
106.47
107.27
105.95
108.55
110.81
111.54
110.38
106.67
106.45
105.44
105.37
103.72
106.57
108.54
110.36
106.64
103.45
101.36
101.9
100.86
100.37
100.16
99.5
99.52
99.2
99.35
99.37
99.85
99.76
100.07
99.77
99.93
99.16
99.4
99.81
99.67
99.37
99.49
99.28
99.33
99.19
98.11
99.12
99.06
97.41
98.45
100.33
103.18
103.06
103.48
102.8
103.92
103.9
103.96
103.62
103.83
104.09
104.07
103.22
104.01
104.01
104.24




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284133&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284133&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284133&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.00456890294711491
gamma0.292744199899729

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00456890294711491 \tabularnewline
gamma & 0.292744199899729 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284133&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]0.00456890294711491[/C][/ROW]
[ROW][C]gamma[/C][C]0.292744199899729[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284133&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284133&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
beta0.00456890294711491
gamma0.292744199899729







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13103.9102.6300310822171.26996891778266
14103.45103.523328554876-0.0733285548759
15103.5103.575463644372-0.0754636443723058
16103.33103.392025378613-0.0620253786127165
17103.56103.592660586483-0.0326605864833169
18103.58103.630361653835-0.05036165383477
19103.86104.93109970856-1.07109970856042
20103.77103.5109791672880.259020832711826
21103.73103.5798496775690.150150322431486
22104.21103.7006980248730.509301975127229
23104.55104.200848904920.349151095080217
24104.5105.3242887241-0.824288724100498
25104.66105.020566241551-0.360566241551311
26104.99104.273525802510.716474197490271
27104.99105.112605072825-0.122605072824783
28105.62104.875630897520.744369102480121
29106.52105.8860118619560.633988138044316
30106.1106.591864618978-0.491864618978056
31106.73107.482150487449-0.752150487449413
32106.63106.3705457951940.259454204805579
33106.72106.4338042967060.286195703294183
34106.5106.689441664991-0.189441664990639
35107.12106.4881355947180.631864405282087
36106.84107.911613692872-1.07161369287212
37107.25107.369835065943-0.119835065943022
38108.19106.8523284534941.33767154650558
39108.21108.316500279816-0.106500279816231
40107.98108.092339669468-0.112339669467801
41109.12108.2495729198740.870427080126333
42109.79109.1918943884750.598105611525128
43109.69111.221770402302-1.53177040230223
44109.69109.3198854798290.370114520171214
45109.24109.48779257055-0.247792570550246
46108.55109.206734336582-0.656734336581749
47106.47108.534553564159-2.06455356415903
48107.27107.2453795884610.0246204115394875
49105.95107.793787919006-1.84378791900575
50108.55105.5438854783363.00611452166444
51110.81108.6686749417392.14132505826107
52111.54110.6879580103750.852041989624595
53110.38111.819786054687-1.4397860546873
54106.67110.447146049311-3.7771460493105
55106.45108.042420654047-1.59242065404719
56105.44106.071968563704-0.631968563703836
57105.37105.2239331083980.146066891602487
58103.72105.317438827829-1.59743882782949
59106.57103.6819411665282.88805883347207
60108.54107.337700459271.20229954072975
61110.36109.065191394661.29480860534012
62106.64109.94203631466-3.30203631466019
63103.45106.742087668144-3.29208766814362
64101.36103.305575426032-1.94557542603189
65101.9101.5756558943440.324344105655911
66100.86101.928389670835-1.06838967083534
67100.37102.131351814124-1.76135181412386
68100.1699.98660599437840.173394005621617
6999.599.9303680142574-0.430368014257411
7099.5299.4242555808420.0957444191579526
7199.299.462624244815-0.262624244815029
7299.3599.884064455884-0.534064455884007
7399.3799.7949583694811-0.424958369481089
7499.8598.95320516782420.896794832175814
7599.7699.9174912132886-0.157491213288608
76100.0799.60230554077550.467694459224489
7799.77100.272338367682-0.502338367681688
7899.9399.78450687772070.145493122279277
7999.16101.180266462639-2.02026646263886
8099.498.77098286621090.629017133789077
8199.8199.16347518001650.646524819983469
8299.6799.729099597457-0.0590995974570063
8399.3799.6070987987669-0.237098798766851
8499.49100.049862473051-0.559862473050686
8599.2899.930112230881-0.650112230880964
8699.3398.85736535724410.472634642755864
8799.1999.3894692591794-0.199469259179409
8898.1199.0254172932826-0.915417293282587
8999.1298.29582300776460.82417699223538
9099.0699.1264466099042-0.0664466099042045
9197.41100.290594867162-2.88059486716219
9298.4597.0160260632411.43397393675896
93100.3398.20682407386462.1231759261354
94103.18100.2449613291642.93503867083574
95103.06103.121626063161-0.0616260631614551
96103.48103.772530544507-0.292530544506718
97102.8103.94622138768-1.14622138768044
98103.92102.3691264410231.5508735589767
99103.9103.992702798754-0.0927027987541607
100103.96103.7384585017460.221541498254425
101103.62104.171983826879-0.551983826878981
102103.83103.6367386987530.193261301246892
103104.09105.130897864155-1.04089786415526
104104.07103.687190102180.382809897820025
105103.22103.826914506683-0.606914506682998
106104.01103.136399069380.873600930619716
107104.01103.947684728550.0623152714499469
108104.24104.726040457561-0.486040457561373

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 103.9 & 102.630031082217 & 1.26996891778266 \tabularnewline
14 & 103.45 & 103.523328554876 & -0.0733285548759 \tabularnewline
15 & 103.5 & 103.575463644372 & -0.0754636443723058 \tabularnewline
16 & 103.33 & 103.392025378613 & -0.0620253786127165 \tabularnewline
17 & 103.56 & 103.592660586483 & -0.0326605864833169 \tabularnewline
18 & 103.58 & 103.630361653835 & -0.05036165383477 \tabularnewline
19 & 103.86 & 104.93109970856 & -1.07109970856042 \tabularnewline
20 & 103.77 & 103.510979167288 & 0.259020832711826 \tabularnewline
21 & 103.73 & 103.579849677569 & 0.150150322431486 \tabularnewline
22 & 104.21 & 103.700698024873 & 0.509301975127229 \tabularnewline
23 & 104.55 & 104.20084890492 & 0.349151095080217 \tabularnewline
24 & 104.5 & 105.3242887241 & -0.824288724100498 \tabularnewline
25 & 104.66 & 105.020566241551 & -0.360566241551311 \tabularnewline
26 & 104.99 & 104.27352580251 & 0.716474197490271 \tabularnewline
27 & 104.99 & 105.112605072825 & -0.122605072824783 \tabularnewline
28 & 105.62 & 104.87563089752 & 0.744369102480121 \tabularnewline
29 & 106.52 & 105.886011861956 & 0.633988138044316 \tabularnewline
30 & 106.1 & 106.591864618978 & -0.491864618978056 \tabularnewline
31 & 106.73 & 107.482150487449 & -0.752150487449413 \tabularnewline
32 & 106.63 & 106.370545795194 & 0.259454204805579 \tabularnewline
33 & 106.72 & 106.433804296706 & 0.286195703294183 \tabularnewline
34 & 106.5 & 106.689441664991 & -0.189441664990639 \tabularnewline
35 & 107.12 & 106.488135594718 & 0.631864405282087 \tabularnewline
36 & 106.84 & 107.911613692872 & -1.07161369287212 \tabularnewline
37 & 107.25 & 107.369835065943 & -0.119835065943022 \tabularnewline
38 & 108.19 & 106.852328453494 & 1.33767154650558 \tabularnewline
39 & 108.21 & 108.316500279816 & -0.106500279816231 \tabularnewline
40 & 107.98 & 108.092339669468 & -0.112339669467801 \tabularnewline
41 & 109.12 & 108.249572919874 & 0.870427080126333 \tabularnewline
42 & 109.79 & 109.191894388475 & 0.598105611525128 \tabularnewline
43 & 109.69 & 111.221770402302 & -1.53177040230223 \tabularnewline
44 & 109.69 & 109.319885479829 & 0.370114520171214 \tabularnewline
45 & 109.24 & 109.48779257055 & -0.247792570550246 \tabularnewline
46 & 108.55 & 109.206734336582 & -0.656734336581749 \tabularnewline
47 & 106.47 & 108.534553564159 & -2.06455356415903 \tabularnewline
48 & 107.27 & 107.245379588461 & 0.0246204115394875 \tabularnewline
49 & 105.95 & 107.793787919006 & -1.84378791900575 \tabularnewline
50 & 108.55 & 105.543885478336 & 3.00611452166444 \tabularnewline
51 & 110.81 & 108.668674941739 & 2.14132505826107 \tabularnewline
52 & 111.54 & 110.687958010375 & 0.852041989624595 \tabularnewline
53 & 110.38 & 111.819786054687 & -1.4397860546873 \tabularnewline
54 & 106.67 & 110.447146049311 & -3.7771460493105 \tabularnewline
55 & 106.45 & 108.042420654047 & -1.59242065404719 \tabularnewline
56 & 105.44 & 106.071968563704 & -0.631968563703836 \tabularnewline
57 & 105.37 & 105.223933108398 & 0.146066891602487 \tabularnewline
58 & 103.72 & 105.317438827829 & -1.59743882782949 \tabularnewline
59 & 106.57 & 103.681941166528 & 2.88805883347207 \tabularnewline
60 & 108.54 & 107.33770045927 & 1.20229954072975 \tabularnewline
61 & 110.36 & 109.06519139466 & 1.29480860534012 \tabularnewline
62 & 106.64 & 109.94203631466 & -3.30203631466019 \tabularnewline
63 & 103.45 & 106.742087668144 & -3.29208766814362 \tabularnewline
64 & 101.36 & 103.305575426032 & -1.94557542603189 \tabularnewline
65 & 101.9 & 101.575655894344 & 0.324344105655911 \tabularnewline
66 & 100.86 & 101.928389670835 & -1.06838967083534 \tabularnewline
67 & 100.37 & 102.131351814124 & -1.76135181412386 \tabularnewline
68 & 100.16 & 99.9866059943784 & 0.173394005621617 \tabularnewline
69 & 99.5 & 99.9303680142574 & -0.430368014257411 \tabularnewline
70 & 99.52 & 99.424255580842 & 0.0957444191579526 \tabularnewline
71 & 99.2 & 99.462624244815 & -0.262624244815029 \tabularnewline
72 & 99.35 & 99.884064455884 & -0.534064455884007 \tabularnewline
73 & 99.37 & 99.7949583694811 & -0.424958369481089 \tabularnewline
74 & 99.85 & 98.9532051678242 & 0.896794832175814 \tabularnewline
75 & 99.76 & 99.9174912132886 & -0.157491213288608 \tabularnewline
76 & 100.07 & 99.6023055407755 & 0.467694459224489 \tabularnewline
77 & 99.77 & 100.272338367682 & -0.502338367681688 \tabularnewline
78 & 99.93 & 99.7845068777207 & 0.145493122279277 \tabularnewline
79 & 99.16 & 101.180266462639 & -2.02026646263886 \tabularnewline
80 & 99.4 & 98.7709828662109 & 0.629017133789077 \tabularnewline
81 & 99.81 & 99.1634751800165 & 0.646524819983469 \tabularnewline
82 & 99.67 & 99.729099597457 & -0.0590995974570063 \tabularnewline
83 & 99.37 & 99.6070987987669 & -0.237098798766851 \tabularnewline
84 & 99.49 & 100.049862473051 & -0.559862473050686 \tabularnewline
85 & 99.28 & 99.930112230881 & -0.650112230880964 \tabularnewline
86 & 99.33 & 98.8573653572441 & 0.472634642755864 \tabularnewline
87 & 99.19 & 99.3894692591794 & -0.199469259179409 \tabularnewline
88 & 98.11 & 99.0254172932826 & -0.915417293282587 \tabularnewline
89 & 99.12 & 98.2958230077646 & 0.82417699223538 \tabularnewline
90 & 99.06 & 99.1264466099042 & -0.0664466099042045 \tabularnewline
91 & 97.41 & 100.290594867162 & -2.88059486716219 \tabularnewline
92 & 98.45 & 97.016026063241 & 1.43397393675896 \tabularnewline
93 & 100.33 & 98.2068240738646 & 2.1231759261354 \tabularnewline
94 & 103.18 & 100.244961329164 & 2.93503867083574 \tabularnewline
95 & 103.06 & 103.121626063161 & -0.0616260631614551 \tabularnewline
96 & 103.48 & 103.772530544507 & -0.292530544506718 \tabularnewline
97 & 102.8 & 103.94622138768 & -1.14622138768044 \tabularnewline
98 & 103.92 & 102.369126441023 & 1.5508735589767 \tabularnewline
99 & 103.9 & 103.992702798754 & -0.0927027987541607 \tabularnewline
100 & 103.96 & 103.738458501746 & 0.221541498254425 \tabularnewline
101 & 103.62 & 104.171983826879 & -0.551983826878981 \tabularnewline
102 & 103.83 & 103.636738698753 & 0.193261301246892 \tabularnewline
103 & 104.09 & 105.130897864155 & -1.04089786415526 \tabularnewline
104 & 104.07 & 103.68719010218 & 0.382809897820025 \tabularnewline
105 & 103.22 & 103.826914506683 & -0.606914506682998 \tabularnewline
106 & 104.01 & 103.13639906938 & 0.873600930619716 \tabularnewline
107 & 104.01 & 103.94768472855 & 0.0623152714499469 \tabularnewline
108 & 104.24 & 104.726040457561 & -0.486040457561373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284133&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]103.9[/C][C]102.630031082217[/C][C]1.26996891778266[/C][/ROW]
[ROW][C]14[/C][C]103.45[/C][C]103.523328554876[/C][C]-0.0733285548759[/C][/ROW]
[ROW][C]15[/C][C]103.5[/C][C]103.575463644372[/C][C]-0.0754636443723058[/C][/ROW]
[ROW][C]16[/C][C]103.33[/C][C]103.392025378613[/C][C]-0.0620253786127165[/C][/ROW]
[ROW][C]17[/C][C]103.56[/C][C]103.592660586483[/C][C]-0.0326605864833169[/C][/ROW]
[ROW][C]18[/C][C]103.58[/C][C]103.630361653835[/C][C]-0.05036165383477[/C][/ROW]
[ROW][C]19[/C][C]103.86[/C][C]104.93109970856[/C][C]-1.07109970856042[/C][/ROW]
[ROW][C]20[/C][C]103.77[/C][C]103.510979167288[/C][C]0.259020832711826[/C][/ROW]
[ROW][C]21[/C][C]103.73[/C][C]103.579849677569[/C][C]0.150150322431486[/C][/ROW]
[ROW][C]22[/C][C]104.21[/C][C]103.700698024873[/C][C]0.509301975127229[/C][/ROW]
[ROW][C]23[/C][C]104.55[/C][C]104.20084890492[/C][C]0.349151095080217[/C][/ROW]
[ROW][C]24[/C][C]104.5[/C][C]105.3242887241[/C][C]-0.824288724100498[/C][/ROW]
[ROW][C]25[/C][C]104.66[/C][C]105.020566241551[/C][C]-0.360566241551311[/C][/ROW]
[ROW][C]26[/C][C]104.99[/C][C]104.27352580251[/C][C]0.716474197490271[/C][/ROW]
[ROW][C]27[/C][C]104.99[/C][C]105.112605072825[/C][C]-0.122605072824783[/C][/ROW]
[ROW][C]28[/C][C]105.62[/C][C]104.87563089752[/C][C]0.744369102480121[/C][/ROW]
[ROW][C]29[/C][C]106.52[/C][C]105.886011861956[/C][C]0.633988138044316[/C][/ROW]
[ROW][C]30[/C][C]106.1[/C][C]106.591864618978[/C][C]-0.491864618978056[/C][/ROW]
[ROW][C]31[/C][C]106.73[/C][C]107.482150487449[/C][C]-0.752150487449413[/C][/ROW]
[ROW][C]32[/C][C]106.63[/C][C]106.370545795194[/C][C]0.259454204805579[/C][/ROW]
[ROW][C]33[/C][C]106.72[/C][C]106.433804296706[/C][C]0.286195703294183[/C][/ROW]
[ROW][C]34[/C][C]106.5[/C][C]106.689441664991[/C][C]-0.189441664990639[/C][/ROW]
[ROW][C]35[/C][C]107.12[/C][C]106.488135594718[/C][C]0.631864405282087[/C][/ROW]
[ROW][C]36[/C][C]106.84[/C][C]107.911613692872[/C][C]-1.07161369287212[/C][/ROW]
[ROW][C]37[/C][C]107.25[/C][C]107.369835065943[/C][C]-0.119835065943022[/C][/ROW]
[ROW][C]38[/C][C]108.19[/C][C]106.852328453494[/C][C]1.33767154650558[/C][/ROW]
[ROW][C]39[/C][C]108.21[/C][C]108.316500279816[/C][C]-0.106500279816231[/C][/ROW]
[ROW][C]40[/C][C]107.98[/C][C]108.092339669468[/C][C]-0.112339669467801[/C][/ROW]
[ROW][C]41[/C][C]109.12[/C][C]108.249572919874[/C][C]0.870427080126333[/C][/ROW]
[ROW][C]42[/C][C]109.79[/C][C]109.191894388475[/C][C]0.598105611525128[/C][/ROW]
[ROW][C]43[/C][C]109.69[/C][C]111.221770402302[/C][C]-1.53177040230223[/C][/ROW]
[ROW][C]44[/C][C]109.69[/C][C]109.319885479829[/C][C]0.370114520171214[/C][/ROW]
[ROW][C]45[/C][C]109.24[/C][C]109.48779257055[/C][C]-0.247792570550246[/C][/ROW]
[ROW][C]46[/C][C]108.55[/C][C]109.206734336582[/C][C]-0.656734336581749[/C][/ROW]
[ROW][C]47[/C][C]106.47[/C][C]108.534553564159[/C][C]-2.06455356415903[/C][/ROW]
[ROW][C]48[/C][C]107.27[/C][C]107.245379588461[/C][C]0.0246204115394875[/C][/ROW]
[ROW][C]49[/C][C]105.95[/C][C]107.793787919006[/C][C]-1.84378791900575[/C][/ROW]
[ROW][C]50[/C][C]108.55[/C][C]105.543885478336[/C][C]3.00611452166444[/C][/ROW]
[ROW][C]51[/C][C]110.81[/C][C]108.668674941739[/C][C]2.14132505826107[/C][/ROW]
[ROW][C]52[/C][C]111.54[/C][C]110.687958010375[/C][C]0.852041989624595[/C][/ROW]
[ROW][C]53[/C][C]110.38[/C][C]111.819786054687[/C][C]-1.4397860546873[/C][/ROW]
[ROW][C]54[/C][C]106.67[/C][C]110.447146049311[/C][C]-3.7771460493105[/C][/ROW]
[ROW][C]55[/C][C]106.45[/C][C]108.042420654047[/C][C]-1.59242065404719[/C][/ROW]
[ROW][C]56[/C][C]105.44[/C][C]106.071968563704[/C][C]-0.631968563703836[/C][/ROW]
[ROW][C]57[/C][C]105.37[/C][C]105.223933108398[/C][C]0.146066891602487[/C][/ROW]
[ROW][C]58[/C][C]103.72[/C][C]105.317438827829[/C][C]-1.59743882782949[/C][/ROW]
[ROW][C]59[/C][C]106.57[/C][C]103.681941166528[/C][C]2.88805883347207[/C][/ROW]
[ROW][C]60[/C][C]108.54[/C][C]107.33770045927[/C][C]1.20229954072975[/C][/ROW]
[ROW][C]61[/C][C]110.36[/C][C]109.06519139466[/C][C]1.29480860534012[/C][/ROW]
[ROW][C]62[/C][C]106.64[/C][C]109.94203631466[/C][C]-3.30203631466019[/C][/ROW]
[ROW][C]63[/C][C]103.45[/C][C]106.742087668144[/C][C]-3.29208766814362[/C][/ROW]
[ROW][C]64[/C][C]101.36[/C][C]103.305575426032[/C][C]-1.94557542603189[/C][/ROW]
[ROW][C]65[/C][C]101.9[/C][C]101.575655894344[/C][C]0.324344105655911[/C][/ROW]
[ROW][C]66[/C][C]100.86[/C][C]101.928389670835[/C][C]-1.06838967083534[/C][/ROW]
[ROW][C]67[/C][C]100.37[/C][C]102.131351814124[/C][C]-1.76135181412386[/C][/ROW]
[ROW][C]68[/C][C]100.16[/C][C]99.9866059943784[/C][C]0.173394005621617[/C][/ROW]
[ROW][C]69[/C][C]99.5[/C][C]99.9303680142574[/C][C]-0.430368014257411[/C][/ROW]
[ROW][C]70[/C][C]99.52[/C][C]99.424255580842[/C][C]0.0957444191579526[/C][/ROW]
[ROW][C]71[/C][C]99.2[/C][C]99.462624244815[/C][C]-0.262624244815029[/C][/ROW]
[ROW][C]72[/C][C]99.35[/C][C]99.884064455884[/C][C]-0.534064455884007[/C][/ROW]
[ROW][C]73[/C][C]99.37[/C][C]99.7949583694811[/C][C]-0.424958369481089[/C][/ROW]
[ROW][C]74[/C][C]99.85[/C][C]98.9532051678242[/C][C]0.896794832175814[/C][/ROW]
[ROW][C]75[/C][C]99.76[/C][C]99.9174912132886[/C][C]-0.157491213288608[/C][/ROW]
[ROW][C]76[/C][C]100.07[/C][C]99.6023055407755[/C][C]0.467694459224489[/C][/ROW]
[ROW][C]77[/C][C]99.77[/C][C]100.272338367682[/C][C]-0.502338367681688[/C][/ROW]
[ROW][C]78[/C][C]99.93[/C][C]99.7845068777207[/C][C]0.145493122279277[/C][/ROW]
[ROW][C]79[/C][C]99.16[/C][C]101.180266462639[/C][C]-2.02026646263886[/C][/ROW]
[ROW][C]80[/C][C]99.4[/C][C]98.7709828662109[/C][C]0.629017133789077[/C][/ROW]
[ROW][C]81[/C][C]99.81[/C][C]99.1634751800165[/C][C]0.646524819983469[/C][/ROW]
[ROW][C]82[/C][C]99.67[/C][C]99.729099597457[/C][C]-0.0590995974570063[/C][/ROW]
[ROW][C]83[/C][C]99.37[/C][C]99.6070987987669[/C][C]-0.237098798766851[/C][/ROW]
[ROW][C]84[/C][C]99.49[/C][C]100.049862473051[/C][C]-0.559862473050686[/C][/ROW]
[ROW][C]85[/C][C]99.28[/C][C]99.930112230881[/C][C]-0.650112230880964[/C][/ROW]
[ROW][C]86[/C][C]99.33[/C][C]98.8573653572441[/C][C]0.472634642755864[/C][/ROW]
[ROW][C]87[/C][C]99.19[/C][C]99.3894692591794[/C][C]-0.199469259179409[/C][/ROW]
[ROW][C]88[/C][C]98.11[/C][C]99.0254172932826[/C][C]-0.915417293282587[/C][/ROW]
[ROW][C]89[/C][C]99.12[/C][C]98.2958230077646[/C][C]0.82417699223538[/C][/ROW]
[ROW][C]90[/C][C]99.06[/C][C]99.1264466099042[/C][C]-0.0664466099042045[/C][/ROW]
[ROW][C]91[/C][C]97.41[/C][C]100.290594867162[/C][C]-2.88059486716219[/C][/ROW]
[ROW][C]92[/C][C]98.45[/C][C]97.016026063241[/C][C]1.43397393675896[/C][/ROW]
[ROW][C]93[/C][C]100.33[/C][C]98.2068240738646[/C][C]2.1231759261354[/C][/ROW]
[ROW][C]94[/C][C]103.18[/C][C]100.244961329164[/C][C]2.93503867083574[/C][/ROW]
[ROW][C]95[/C][C]103.06[/C][C]103.121626063161[/C][C]-0.0616260631614551[/C][/ROW]
[ROW][C]96[/C][C]103.48[/C][C]103.772530544507[/C][C]-0.292530544506718[/C][/ROW]
[ROW][C]97[/C][C]102.8[/C][C]103.94622138768[/C][C]-1.14622138768044[/C][/ROW]
[ROW][C]98[/C][C]103.92[/C][C]102.369126441023[/C][C]1.5508735589767[/C][/ROW]
[ROW][C]99[/C][C]103.9[/C][C]103.992702798754[/C][C]-0.0927027987541607[/C][/ROW]
[ROW][C]100[/C][C]103.96[/C][C]103.738458501746[/C][C]0.221541498254425[/C][/ROW]
[ROW][C]101[/C][C]103.62[/C][C]104.171983826879[/C][C]-0.551983826878981[/C][/ROW]
[ROW][C]102[/C][C]103.83[/C][C]103.636738698753[/C][C]0.193261301246892[/C][/ROW]
[ROW][C]103[/C][C]104.09[/C][C]105.130897864155[/C][C]-1.04089786415526[/C][/ROW]
[ROW][C]104[/C][C]104.07[/C][C]103.68719010218[/C][C]0.382809897820025[/C][/ROW]
[ROW][C]105[/C][C]103.22[/C][C]103.826914506683[/C][C]-0.606914506682998[/C][/ROW]
[ROW][C]106[/C][C]104.01[/C][C]103.13639906938[/C][C]0.873600930619716[/C][/ROW]
[ROW][C]107[/C][C]104.01[/C][C]103.94768472855[/C][C]0.0623152714499469[/C][/ROW]
[ROW][C]108[/C][C]104.24[/C][C]104.726040457561[/C][C]-0.486040457561373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284133&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284133&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
13103.9102.6300310822171.26996891778266
14103.45103.523328554876-0.0733285548759
15103.5103.575463644372-0.0754636443723058
16103.33103.392025378613-0.0620253786127165
17103.56103.592660586483-0.0326605864833169
18103.58103.630361653835-0.05036165383477
19103.86104.93109970856-1.07109970856042
20103.77103.5109791672880.259020832711826
21103.73103.5798496775690.150150322431486
22104.21103.7006980248730.509301975127229
23104.55104.200848904920.349151095080217
24104.5105.3242887241-0.824288724100498
25104.66105.020566241551-0.360566241551311
26104.99104.273525802510.716474197490271
27104.99105.112605072825-0.122605072824783
28105.62104.875630897520.744369102480121
29106.52105.8860118619560.633988138044316
30106.1106.591864618978-0.491864618978056
31106.73107.482150487449-0.752150487449413
32106.63106.3705457951940.259454204805579
33106.72106.4338042967060.286195703294183
34106.5106.689441664991-0.189441664990639
35107.12106.4881355947180.631864405282087
36106.84107.911613692872-1.07161369287212
37107.25107.369835065943-0.119835065943022
38108.19106.8523284534941.33767154650558
39108.21108.316500279816-0.106500279816231
40107.98108.092339669468-0.112339669467801
41109.12108.2495729198740.870427080126333
42109.79109.1918943884750.598105611525128
43109.69111.221770402302-1.53177040230223
44109.69109.3198854798290.370114520171214
45109.24109.48779257055-0.247792570550246
46108.55109.206734336582-0.656734336581749
47106.47108.534553564159-2.06455356415903
48107.27107.2453795884610.0246204115394875
49105.95107.793787919006-1.84378791900575
50108.55105.5438854783363.00611452166444
51110.81108.6686749417392.14132505826107
52111.54110.6879580103750.852041989624595
53110.38111.819786054687-1.4397860546873
54106.67110.447146049311-3.7771460493105
55106.45108.042420654047-1.59242065404719
56105.44106.071968563704-0.631968563703836
57105.37105.2239331083980.146066891602487
58103.72105.317438827829-1.59743882782949
59106.57103.6819411665282.88805883347207
60108.54107.337700459271.20229954072975
61110.36109.065191394661.29480860534012
62106.64109.94203631466-3.30203631466019
63103.45106.742087668144-3.29208766814362
64101.36103.305575426032-1.94557542603189
65101.9101.5756558943440.324344105655911
66100.86101.928389670835-1.06838967083534
67100.37102.131351814124-1.76135181412386
68100.1699.98660599437840.173394005621617
6999.599.9303680142574-0.430368014257411
7099.5299.4242555808420.0957444191579526
7199.299.462624244815-0.262624244815029
7299.3599.884064455884-0.534064455884007
7399.3799.7949583694811-0.424958369481089
7499.8598.95320516782420.896794832175814
7599.7699.9174912132886-0.157491213288608
76100.0799.60230554077550.467694459224489
7799.77100.272338367682-0.502338367681688
7899.9399.78450687772070.145493122279277
7999.16101.180266462639-2.02026646263886
8099.498.77098286621090.629017133789077
8199.8199.16347518001650.646524819983469
8299.6799.729099597457-0.0590995974570063
8399.3799.6070987987669-0.237098798766851
8499.49100.049862473051-0.559862473050686
8599.2899.930112230881-0.650112230880964
8699.3398.85736535724410.472634642755864
8799.1999.3894692591794-0.199469259179409
8898.1199.0254172932826-0.915417293282587
8999.1298.29582300776460.82417699223538
9099.0699.1264466099042-0.0664466099042045
9197.41100.290594867162-2.88059486716219
9298.4597.0160260632411.43397393675896
93100.3398.20682407386462.1231759261354
94103.18100.2449613291642.93503867083574
95103.06103.121626063161-0.0616260631614551
96103.48103.772530544507-0.292530544506718
97102.8103.94622138768-1.14622138768044
98103.92102.3691264410231.5508735589767
99103.9103.992702798754-0.0927027987541607
100103.96103.7384585017460.221541498254425
101103.62104.171983826879-0.551983826878981
102103.83103.6367386987530.193261301246892
103104.09105.130897864155-1.04089786415526
104104.07103.687190102180.382809897820025
105103.22103.826914506683-0.606914506682998
106104.01103.136399069380.873600930619716
107104.01103.947684728550.0623152714499469
108104.24104.726040457561-0.486040457561373







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109104.705921059678102.346446935016107.06539518434
110104.267359759238100.931770156053107.602949362422
111104.335185129612100.238215126618108.432155132605
112104.1681849586399.4337857014395108.902584215821
113104.37504830412699.0622054095167109.687891198734
114104.38828235389798.5577427471086110.218821960686
115105.69183274600599.3156091343939112.068056357616
116105.28213335559798.4861527382941112.0781139729
117105.03418488860997.8335242342045112.234845543013
118104.94922862217897.3541100956904112.544347148665
119104.88339081813996.9101560679231112.856625568354
120105.60225142211383.2482532744109127.956249569816

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 104.705921059678 & 102.346446935016 & 107.06539518434 \tabularnewline
110 & 104.267359759238 & 100.931770156053 & 107.602949362422 \tabularnewline
111 & 104.335185129612 & 100.238215126618 & 108.432155132605 \tabularnewline
112 & 104.16818495863 & 99.4337857014395 & 108.902584215821 \tabularnewline
113 & 104.375048304126 & 99.0622054095167 & 109.687891198734 \tabularnewline
114 & 104.388282353897 & 98.5577427471086 & 110.218821960686 \tabularnewline
115 & 105.691832746005 & 99.3156091343939 & 112.068056357616 \tabularnewline
116 & 105.282133355597 & 98.4861527382941 & 112.0781139729 \tabularnewline
117 & 105.034184888609 & 97.8335242342045 & 112.234845543013 \tabularnewline
118 & 104.949228622178 & 97.3541100956904 & 112.544347148665 \tabularnewline
119 & 104.883390818139 & 96.9101560679231 & 112.856625568354 \tabularnewline
120 & 105.602251422113 & 83.2482532744109 & 127.956249569816 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284133&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]104.705921059678[/C][C]102.346446935016[/C][C]107.06539518434[/C][/ROW]
[ROW][C]110[/C][C]104.267359759238[/C][C]100.931770156053[/C][C]107.602949362422[/C][/ROW]
[ROW][C]111[/C][C]104.335185129612[/C][C]100.238215126618[/C][C]108.432155132605[/C][/ROW]
[ROW][C]112[/C][C]104.16818495863[/C][C]99.4337857014395[/C][C]108.902584215821[/C][/ROW]
[ROW][C]113[/C][C]104.375048304126[/C][C]99.0622054095167[/C][C]109.687891198734[/C][/ROW]
[ROW][C]114[/C][C]104.388282353897[/C][C]98.5577427471086[/C][C]110.218821960686[/C][/ROW]
[ROW][C]115[/C][C]105.691832746005[/C][C]99.3156091343939[/C][C]112.068056357616[/C][/ROW]
[ROW][C]116[/C][C]105.282133355597[/C][C]98.4861527382941[/C][C]112.0781139729[/C][/ROW]
[ROW][C]117[/C][C]105.034184888609[/C][C]97.8335242342045[/C][C]112.234845543013[/C][/ROW]
[ROW][C]118[/C][C]104.949228622178[/C][C]97.3541100956904[/C][C]112.544347148665[/C][/ROW]
[ROW][C]119[/C][C]104.883390818139[/C][C]96.9101560679231[/C][C]112.856625568354[/C][/ROW]
[ROW][C]120[/C][C]105.602251422113[/C][C]83.2482532744109[/C][C]127.956249569816[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284133&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284133&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
109104.705921059678102.346446935016107.06539518434
110104.267359759238100.931770156053107.602949362422
111104.335185129612100.238215126618108.432155132605
112104.1681849586399.4337857014395108.902584215821
113104.37504830412699.0622054095167109.687891198734
114104.38828235389798.5577427471086110.218821960686
115105.69183274600599.3156091343939112.068056357616
116105.28213335559798.4861527382941112.0781139729
117105.03418488860997.8335242342045112.234845543013
118104.94922862217897.3541100956904112.544347148665
119104.88339081813996.9101560679231112.856625568354
120105.60225142211383.2482532744109127.956249569816



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')