Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 03 May 2017 07:47:46 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/May/03/t1493794083urq0f0hs9u7y705.htm/, Retrieved Fri, 17 May 2024 08:08:16 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 08:08:16 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
92.49
92.46
92.55
92.24
92.41
92.83
92.85
93.04
93.04
92.83
92.96
92.83
93.01
93.21
93.58
94.07
94.57
95.03
95.21
95.89
96.43
96.35
96.71
96.32
97.23
97.88
98.2
98.56
99.31
99.69
99.77
101.06
101.77
101.91
102.52
102.09
102.22
102.74
103.56
104.4
104.76
104.86
104.84
104.96
104.83
104.58
104.8
104.17
104.63
105.32
106.16
107.22
107.51
107.87
107.79
108.04
107.74
107.71
111.19
110.82
113.65
114.72
114.32
116.76
116.47
117.34
116.92
116.48
115.07
116.45
116.84
114.31




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

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

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

As an alternative you can also use a QR Code:  

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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999946270518707
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999946270518707 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.999946270518707[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

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

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999946270518707
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
292.4692.49-0.0300000000000011
392.5592.46000161188440.0899983881155606
492.2492.5499951644333-0.309995164433289
592.4192.24001665587940.16998334412061
692.8392.40999086688310.420009133116906
792.8592.82997743312710.0200225668728535
893.0492.84999892419790.190001075802144
993.0493.03998979134081.02086592477235e-05
1092.8393.0399999994515-0.209999999451512
1192.9692.8300112831910.129988716808953
1292.8392.9599930157737-0.129993015773678
1393.0192.83000698445730.179993015542692
1493.2193.00999032906860.200009670931351
1593.5893.20998925358410.370010746415872
1694.0793.57998011951450.490019880485463
1794.5794.0699736714860.500026328513997
1895.0394.56997313384470.460026866155275
1995.2195.02997528299510.180024717004898
2095.8995.20999032736530.680009672634668
2196.4395.8899634634330.540036536566987
2296.3596.429970984117-0.0799709841170255
2396.7196.35000429679950.359995703200497
2496.3296.7099806576176-0.389980657617599
2597.2396.32002095345840.909979046541565
2697.8897.22995110729790.650048892702145
2798.297.87996507321020.32003492678983
2898.5698.19998280468940.360017195310618
2999.3198.55998065646280.750019343537161
3099.6999.30995970184970.380040298150277
3199.7799.68997958063190.0800204193680827
32101.0699.76999570054441.29000429945563
33101.77101.0599306887380.710069311261876
34101.91101.7699618483440.140038151655773
35102.52101.9099924758230.610007524177249
36102.09102.519967224612-0.429967224612128
37102.22102.0900231019160.129976898084038
38102.74102.2199930164090.520006983591315
39103.56102.7399720602940.820027939705511
40104.4103.5599559403240.840044059675847
41104.76104.3999548648680.3600451351316
42104.86104.7599806549620.100019345038348
43104.84104.859994626012-0.0199946260124619
44104.96104.8400010743010.119998925699107
45104.83104.95999355252-0.129993552519963
46104.58104.830006984486-0.250006984486149
47104.8104.5800134327460.219986567254409
48104.17104.799988180236-0.629988180235841
49104.63104.1700338489380.459966151061849
50105.32104.6299752862570.690024713742702
51106.16105.319962925330.840037074669965
52107.22106.1599548652441.06004513475629
53107.51107.2199430443250.29005695567524
54107.87107.509984415390.360015584609769
55107.79107.869980656549-0.079980656549381
56108.04107.7900042973190.249995702680806
57107.74108.039986567861-0.299986567860586
58107.71107.740016118123-0.0300161181226883
59111.19107.710001612753.47999838724955
60110.82111.189813021492-0.369813021491751
61113.65110.8200198698622.8299801301382
62114.72113.6498479466361.07015205336445
63114.32114.719942501285-0.399942501285267
64116.76114.3200214887032.43997851129687
65116.47116.75986890122-0.289868901220231
66117.34116.4700155745060.869984425494309
67116.92117.339953256188-0.419953256188094
68116.48116.920022563871-0.440022563870627
69115.07116.480023642184-1.41002364218413
70116.45115.0700757598391.3799242401611
71116.84116.4499258573860.390074142613642
72114.31116.839979041519-2.52997904151864

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 92.46 & 92.49 & -0.0300000000000011 \tabularnewline
3 & 92.55 & 92.4600016118844 & 0.0899983881155606 \tabularnewline
4 & 92.24 & 92.5499951644333 & -0.309995164433289 \tabularnewline
5 & 92.41 & 92.2400166558794 & 0.16998334412061 \tabularnewline
6 & 92.83 & 92.4099908668831 & 0.420009133116906 \tabularnewline
7 & 92.85 & 92.8299774331271 & 0.0200225668728535 \tabularnewline
8 & 93.04 & 92.8499989241979 & 0.190001075802144 \tabularnewline
9 & 93.04 & 93.0399897913408 & 1.02086592477235e-05 \tabularnewline
10 & 92.83 & 93.0399999994515 & -0.209999999451512 \tabularnewline
11 & 92.96 & 92.830011283191 & 0.129988716808953 \tabularnewline
12 & 92.83 & 92.9599930157737 & -0.129993015773678 \tabularnewline
13 & 93.01 & 92.8300069844573 & 0.179993015542692 \tabularnewline
14 & 93.21 & 93.0099903290686 & 0.200009670931351 \tabularnewline
15 & 93.58 & 93.2099892535841 & 0.370010746415872 \tabularnewline
16 & 94.07 & 93.5799801195145 & 0.490019880485463 \tabularnewline
17 & 94.57 & 94.069973671486 & 0.500026328513997 \tabularnewline
18 & 95.03 & 94.5699731338447 & 0.460026866155275 \tabularnewline
19 & 95.21 & 95.0299752829951 & 0.180024717004898 \tabularnewline
20 & 95.89 & 95.2099903273653 & 0.680009672634668 \tabularnewline
21 & 96.43 & 95.889963463433 & 0.540036536566987 \tabularnewline
22 & 96.35 & 96.429970984117 & -0.0799709841170255 \tabularnewline
23 & 96.71 & 96.3500042967995 & 0.359995703200497 \tabularnewline
24 & 96.32 & 96.7099806576176 & -0.389980657617599 \tabularnewline
25 & 97.23 & 96.3200209534584 & 0.909979046541565 \tabularnewline
26 & 97.88 & 97.2299511072979 & 0.650048892702145 \tabularnewline
27 & 98.2 & 97.8799650732102 & 0.32003492678983 \tabularnewline
28 & 98.56 & 98.1999828046894 & 0.360017195310618 \tabularnewline
29 & 99.31 & 98.5599806564628 & 0.750019343537161 \tabularnewline
30 & 99.69 & 99.3099597018497 & 0.380040298150277 \tabularnewline
31 & 99.77 & 99.6899795806319 & 0.0800204193680827 \tabularnewline
32 & 101.06 & 99.7699957005444 & 1.29000429945563 \tabularnewline
33 & 101.77 & 101.059930688738 & 0.710069311261876 \tabularnewline
34 & 101.91 & 101.769961848344 & 0.140038151655773 \tabularnewline
35 & 102.52 & 101.909992475823 & 0.610007524177249 \tabularnewline
36 & 102.09 & 102.519967224612 & -0.429967224612128 \tabularnewline
37 & 102.22 & 102.090023101916 & 0.129976898084038 \tabularnewline
38 & 102.74 & 102.219993016409 & 0.520006983591315 \tabularnewline
39 & 103.56 & 102.739972060294 & 0.820027939705511 \tabularnewline
40 & 104.4 & 103.559955940324 & 0.840044059675847 \tabularnewline
41 & 104.76 & 104.399954864868 & 0.3600451351316 \tabularnewline
42 & 104.86 & 104.759980654962 & 0.100019345038348 \tabularnewline
43 & 104.84 & 104.859994626012 & -0.0199946260124619 \tabularnewline
44 & 104.96 & 104.840001074301 & 0.119998925699107 \tabularnewline
45 & 104.83 & 104.95999355252 & -0.129993552519963 \tabularnewline
46 & 104.58 & 104.830006984486 & -0.250006984486149 \tabularnewline
47 & 104.8 & 104.580013432746 & 0.219986567254409 \tabularnewline
48 & 104.17 & 104.799988180236 & -0.629988180235841 \tabularnewline
49 & 104.63 & 104.170033848938 & 0.459966151061849 \tabularnewline
50 & 105.32 & 104.629975286257 & 0.690024713742702 \tabularnewline
51 & 106.16 & 105.31996292533 & 0.840037074669965 \tabularnewline
52 & 107.22 & 106.159954865244 & 1.06004513475629 \tabularnewline
53 & 107.51 & 107.219943044325 & 0.29005695567524 \tabularnewline
54 & 107.87 & 107.50998441539 & 0.360015584609769 \tabularnewline
55 & 107.79 & 107.869980656549 & -0.079980656549381 \tabularnewline
56 & 108.04 & 107.790004297319 & 0.249995702680806 \tabularnewline
57 & 107.74 & 108.039986567861 & -0.299986567860586 \tabularnewline
58 & 107.71 & 107.740016118123 & -0.0300161181226883 \tabularnewline
59 & 111.19 & 107.71000161275 & 3.47999838724955 \tabularnewline
60 & 110.82 & 111.189813021492 & -0.369813021491751 \tabularnewline
61 & 113.65 & 110.820019869862 & 2.8299801301382 \tabularnewline
62 & 114.72 & 113.649847946636 & 1.07015205336445 \tabularnewline
63 & 114.32 & 114.719942501285 & -0.399942501285267 \tabularnewline
64 & 116.76 & 114.320021488703 & 2.43997851129687 \tabularnewline
65 & 116.47 & 116.75986890122 & -0.289868901220231 \tabularnewline
66 & 117.34 & 116.470015574506 & 0.869984425494309 \tabularnewline
67 & 116.92 & 117.339953256188 & -0.419953256188094 \tabularnewline
68 & 116.48 & 116.920022563871 & -0.440022563870627 \tabularnewline
69 & 115.07 & 116.480023642184 & -1.41002364218413 \tabularnewline
70 & 116.45 & 115.070075759839 & 1.3799242401611 \tabularnewline
71 & 116.84 & 116.449925857386 & 0.390074142613642 \tabularnewline
72 & 114.31 & 116.839979041519 & -2.52997904151864 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]92.46[/C][C]92.49[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]3[/C][C]92.55[/C][C]92.4600016118844[/C][C]0.0899983881155606[/C][/ROW]
[ROW][C]4[/C][C]92.24[/C][C]92.5499951644333[/C][C]-0.309995164433289[/C][/ROW]
[ROW][C]5[/C][C]92.41[/C][C]92.2400166558794[/C][C]0.16998334412061[/C][/ROW]
[ROW][C]6[/C][C]92.83[/C][C]92.4099908668831[/C][C]0.420009133116906[/C][/ROW]
[ROW][C]7[/C][C]92.85[/C][C]92.8299774331271[/C][C]0.0200225668728535[/C][/ROW]
[ROW][C]8[/C][C]93.04[/C][C]92.8499989241979[/C][C]0.190001075802144[/C][/ROW]
[ROW][C]9[/C][C]93.04[/C][C]93.0399897913408[/C][C]1.02086592477235e-05[/C][/ROW]
[ROW][C]10[/C][C]92.83[/C][C]93.0399999994515[/C][C]-0.209999999451512[/C][/ROW]
[ROW][C]11[/C][C]92.96[/C][C]92.830011283191[/C][C]0.129988716808953[/C][/ROW]
[ROW][C]12[/C][C]92.83[/C][C]92.9599930157737[/C][C]-0.129993015773678[/C][/ROW]
[ROW][C]13[/C][C]93.01[/C][C]92.8300069844573[/C][C]0.179993015542692[/C][/ROW]
[ROW][C]14[/C][C]93.21[/C][C]93.0099903290686[/C][C]0.200009670931351[/C][/ROW]
[ROW][C]15[/C][C]93.58[/C][C]93.2099892535841[/C][C]0.370010746415872[/C][/ROW]
[ROW][C]16[/C][C]94.07[/C][C]93.5799801195145[/C][C]0.490019880485463[/C][/ROW]
[ROW][C]17[/C][C]94.57[/C][C]94.069973671486[/C][C]0.500026328513997[/C][/ROW]
[ROW][C]18[/C][C]95.03[/C][C]94.5699731338447[/C][C]0.460026866155275[/C][/ROW]
[ROW][C]19[/C][C]95.21[/C][C]95.0299752829951[/C][C]0.180024717004898[/C][/ROW]
[ROW][C]20[/C][C]95.89[/C][C]95.2099903273653[/C][C]0.680009672634668[/C][/ROW]
[ROW][C]21[/C][C]96.43[/C][C]95.889963463433[/C][C]0.540036536566987[/C][/ROW]
[ROW][C]22[/C][C]96.35[/C][C]96.429970984117[/C][C]-0.0799709841170255[/C][/ROW]
[ROW][C]23[/C][C]96.71[/C][C]96.3500042967995[/C][C]0.359995703200497[/C][/ROW]
[ROW][C]24[/C][C]96.32[/C][C]96.7099806576176[/C][C]-0.389980657617599[/C][/ROW]
[ROW][C]25[/C][C]97.23[/C][C]96.3200209534584[/C][C]0.909979046541565[/C][/ROW]
[ROW][C]26[/C][C]97.88[/C][C]97.2299511072979[/C][C]0.650048892702145[/C][/ROW]
[ROW][C]27[/C][C]98.2[/C][C]97.8799650732102[/C][C]0.32003492678983[/C][/ROW]
[ROW][C]28[/C][C]98.56[/C][C]98.1999828046894[/C][C]0.360017195310618[/C][/ROW]
[ROW][C]29[/C][C]99.31[/C][C]98.5599806564628[/C][C]0.750019343537161[/C][/ROW]
[ROW][C]30[/C][C]99.69[/C][C]99.3099597018497[/C][C]0.380040298150277[/C][/ROW]
[ROW][C]31[/C][C]99.77[/C][C]99.6899795806319[/C][C]0.0800204193680827[/C][/ROW]
[ROW][C]32[/C][C]101.06[/C][C]99.7699957005444[/C][C]1.29000429945563[/C][/ROW]
[ROW][C]33[/C][C]101.77[/C][C]101.059930688738[/C][C]0.710069311261876[/C][/ROW]
[ROW][C]34[/C][C]101.91[/C][C]101.769961848344[/C][C]0.140038151655773[/C][/ROW]
[ROW][C]35[/C][C]102.52[/C][C]101.909992475823[/C][C]0.610007524177249[/C][/ROW]
[ROW][C]36[/C][C]102.09[/C][C]102.519967224612[/C][C]-0.429967224612128[/C][/ROW]
[ROW][C]37[/C][C]102.22[/C][C]102.090023101916[/C][C]0.129976898084038[/C][/ROW]
[ROW][C]38[/C][C]102.74[/C][C]102.219993016409[/C][C]0.520006983591315[/C][/ROW]
[ROW][C]39[/C][C]103.56[/C][C]102.739972060294[/C][C]0.820027939705511[/C][/ROW]
[ROW][C]40[/C][C]104.4[/C][C]103.559955940324[/C][C]0.840044059675847[/C][/ROW]
[ROW][C]41[/C][C]104.76[/C][C]104.399954864868[/C][C]0.3600451351316[/C][/ROW]
[ROW][C]42[/C][C]104.86[/C][C]104.759980654962[/C][C]0.100019345038348[/C][/ROW]
[ROW][C]43[/C][C]104.84[/C][C]104.859994626012[/C][C]-0.0199946260124619[/C][/ROW]
[ROW][C]44[/C][C]104.96[/C][C]104.840001074301[/C][C]0.119998925699107[/C][/ROW]
[ROW][C]45[/C][C]104.83[/C][C]104.95999355252[/C][C]-0.129993552519963[/C][/ROW]
[ROW][C]46[/C][C]104.58[/C][C]104.830006984486[/C][C]-0.250006984486149[/C][/ROW]
[ROW][C]47[/C][C]104.8[/C][C]104.580013432746[/C][C]0.219986567254409[/C][/ROW]
[ROW][C]48[/C][C]104.17[/C][C]104.799988180236[/C][C]-0.629988180235841[/C][/ROW]
[ROW][C]49[/C][C]104.63[/C][C]104.170033848938[/C][C]0.459966151061849[/C][/ROW]
[ROW][C]50[/C][C]105.32[/C][C]104.629975286257[/C][C]0.690024713742702[/C][/ROW]
[ROW][C]51[/C][C]106.16[/C][C]105.31996292533[/C][C]0.840037074669965[/C][/ROW]
[ROW][C]52[/C][C]107.22[/C][C]106.159954865244[/C][C]1.06004513475629[/C][/ROW]
[ROW][C]53[/C][C]107.51[/C][C]107.219943044325[/C][C]0.29005695567524[/C][/ROW]
[ROW][C]54[/C][C]107.87[/C][C]107.50998441539[/C][C]0.360015584609769[/C][/ROW]
[ROW][C]55[/C][C]107.79[/C][C]107.869980656549[/C][C]-0.079980656549381[/C][/ROW]
[ROW][C]56[/C][C]108.04[/C][C]107.790004297319[/C][C]0.249995702680806[/C][/ROW]
[ROW][C]57[/C][C]107.74[/C][C]108.039986567861[/C][C]-0.299986567860586[/C][/ROW]
[ROW][C]58[/C][C]107.71[/C][C]107.740016118123[/C][C]-0.0300161181226883[/C][/ROW]
[ROW][C]59[/C][C]111.19[/C][C]107.71000161275[/C][C]3.47999838724955[/C][/ROW]
[ROW][C]60[/C][C]110.82[/C][C]111.189813021492[/C][C]-0.369813021491751[/C][/ROW]
[ROW][C]61[/C][C]113.65[/C][C]110.820019869862[/C][C]2.8299801301382[/C][/ROW]
[ROW][C]62[/C][C]114.72[/C][C]113.649847946636[/C][C]1.07015205336445[/C][/ROW]
[ROW][C]63[/C][C]114.32[/C][C]114.719942501285[/C][C]-0.399942501285267[/C][/ROW]
[ROW][C]64[/C][C]116.76[/C][C]114.320021488703[/C][C]2.43997851129687[/C][/ROW]
[ROW][C]65[/C][C]116.47[/C][C]116.75986890122[/C][C]-0.289868901220231[/C][/ROW]
[ROW][C]66[/C][C]117.34[/C][C]116.470015574506[/C][C]0.869984425494309[/C][/ROW]
[ROW][C]67[/C][C]116.92[/C][C]117.339953256188[/C][C]-0.419953256188094[/C][/ROW]
[ROW][C]68[/C][C]116.48[/C][C]116.920022563871[/C][C]-0.440022563870627[/C][/ROW]
[ROW][C]69[/C][C]115.07[/C][C]116.480023642184[/C][C]-1.41002364218413[/C][/ROW]
[ROW][C]70[/C][C]116.45[/C][C]115.070075759839[/C][C]1.3799242401611[/C][/ROW]
[ROW][C]71[/C][C]116.84[/C][C]116.449925857386[/C][C]0.390074142613642[/C][/ROW]
[ROW][C]72[/C][C]114.31[/C][C]116.839979041519[/C][C]-2.52997904151864[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

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

As an alternative you can also use a QR Code:  

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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
292.4692.49-0.0300000000000011
392.5592.46000161188440.0899983881155606
492.2492.5499951644333-0.309995164433289
592.4192.24001665587940.16998334412061
692.8392.40999086688310.420009133116906
792.8592.82997743312710.0200225668728535
893.0492.84999892419790.190001075802144
993.0493.03998979134081.02086592477235e-05
1092.8393.0399999994515-0.209999999451512
1192.9692.8300112831910.129988716808953
1292.8392.9599930157737-0.129993015773678
1393.0192.83000698445730.179993015542692
1493.2193.00999032906860.200009670931351
1593.5893.20998925358410.370010746415872
1694.0793.57998011951450.490019880485463
1794.5794.0699736714860.500026328513997
1895.0394.56997313384470.460026866155275
1995.2195.02997528299510.180024717004898
2095.8995.20999032736530.680009672634668
2196.4395.8899634634330.540036536566987
2296.3596.429970984117-0.0799709841170255
2396.7196.35000429679950.359995703200497
2496.3296.7099806576176-0.389980657617599
2597.2396.32002095345840.909979046541565
2697.8897.22995110729790.650048892702145
2798.297.87996507321020.32003492678983
2898.5698.19998280468940.360017195310618
2999.3198.55998065646280.750019343537161
3099.6999.30995970184970.380040298150277
3199.7799.68997958063190.0800204193680827
32101.0699.76999570054441.29000429945563
33101.77101.0599306887380.710069311261876
34101.91101.7699618483440.140038151655773
35102.52101.9099924758230.610007524177249
36102.09102.519967224612-0.429967224612128
37102.22102.0900231019160.129976898084038
38102.74102.2199930164090.520006983591315
39103.56102.7399720602940.820027939705511
40104.4103.5599559403240.840044059675847
41104.76104.3999548648680.3600451351316
42104.86104.7599806549620.100019345038348
43104.84104.859994626012-0.0199946260124619
44104.96104.8400010743010.119998925699107
45104.83104.95999355252-0.129993552519963
46104.58104.830006984486-0.250006984486149
47104.8104.5800134327460.219986567254409
48104.17104.799988180236-0.629988180235841
49104.63104.1700338489380.459966151061849
50105.32104.6299752862570.690024713742702
51106.16105.319962925330.840037074669965
52107.22106.1599548652441.06004513475629
53107.51107.2199430443250.29005695567524
54107.87107.509984415390.360015584609769
55107.79107.869980656549-0.079980656549381
56108.04107.7900042973190.249995702680806
57107.74108.039986567861-0.299986567860586
58107.71107.740016118123-0.0300161181226883
59111.19107.710001612753.47999838724955
60110.82111.189813021492-0.369813021491751
61113.65110.8200198698622.8299801301382
62114.72113.6498479466361.07015205336445
63114.32114.719942501285-0.399942501285267
64116.76114.3200214887032.43997851129687
65116.47116.75986890122-0.289868901220231
66117.34116.4700155745060.869984425494309
67116.92117.339953256188-0.419953256188094
68116.48116.920022563871-0.440022563870627
69115.07116.480023642184-1.41002364218413
70116.45115.0700757598391.3799242401611
71116.84116.4499258573860.390074142613642
72114.31116.839979041519-2.52997904151864







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73114.310135934462112.737784471534115.882487397389
74114.310135934462112.086554907502116.533716961421
75114.310135934462111.586840863424117.033431005499
76114.310135934462111.165559730198117.454712138725
77114.310135934462110.794402303353117.82586956557
78114.310135934462110.4588496006118.161422268323
79114.310135934462110.150276575556118.469995293367
80114.310135934462109.863063487744118.757208381179
81114.310135934462109.593306829349119.026965039575
82114.310135934462109.338164467596119.282107401327
83114.310135934462109.095490814436119.524781054487
84114.310135934462108.863618956769119.756652912154

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 114.310135934462 & 112.737784471534 & 115.882487397389 \tabularnewline
74 & 114.310135934462 & 112.086554907502 & 116.533716961421 \tabularnewline
75 & 114.310135934462 & 111.586840863424 & 117.033431005499 \tabularnewline
76 & 114.310135934462 & 111.165559730198 & 117.454712138725 \tabularnewline
77 & 114.310135934462 & 110.794402303353 & 117.82586956557 \tabularnewline
78 & 114.310135934462 & 110.4588496006 & 118.161422268323 \tabularnewline
79 & 114.310135934462 & 110.150276575556 & 118.469995293367 \tabularnewline
80 & 114.310135934462 & 109.863063487744 & 118.757208381179 \tabularnewline
81 & 114.310135934462 & 109.593306829349 & 119.026965039575 \tabularnewline
82 & 114.310135934462 & 109.338164467596 & 119.282107401327 \tabularnewline
83 & 114.310135934462 & 109.095490814436 & 119.524781054487 \tabularnewline
84 & 114.310135934462 & 108.863618956769 & 119.756652912154 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]114.310135934462[/C][C]112.737784471534[/C][C]115.882487397389[/C][/ROW]
[ROW][C]74[/C][C]114.310135934462[/C][C]112.086554907502[/C][C]116.533716961421[/C][/ROW]
[ROW][C]75[/C][C]114.310135934462[/C][C]111.586840863424[/C][C]117.033431005499[/C][/ROW]
[ROW][C]76[/C][C]114.310135934462[/C][C]111.165559730198[/C][C]117.454712138725[/C][/ROW]
[ROW][C]77[/C][C]114.310135934462[/C][C]110.794402303353[/C][C]117.82586956557[/C][/ROW]
[ROW][C]78[/C][C]114.310135934462[/C][C]110.4588496006[/C][C]118.161422268323[/C][/ROW]
[ROW][C]79[/C][C]114.310135934462[/C][C]110.150276575556[/C][C]118.469995293367[/C][/ROW]
[ROW][C]80[/C][C]114.310135934462[/C][C]109.863063487744[/C][C]118.757208381179[/C][/ROW]
[ROW][C]81[/C][C]114.310135934462[/C][C]109.593306829349[/C][C]119.026965039575[/C][/ROW]
[ROW][C]82[/C][C]114.310135934462[/C][C]109.338164467596[/C][C]119.282107401327[/C][/ROW]
[ROW][C]83[/C][C]114.310135934462[/C][C]109.095490814436[/C][C]119.524781054487[/C][/ROW]
[ROW][C]84[/C][C]114.310135934462[/C][C]108.863618956769[/C][C]119.756652912154[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

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

As an alternative you can also use a QR Code:  

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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73114.310135934462112.737784471534115.882487397389
74114.310135934462112.086554907502116.533716961421
75114.310135934462111.586840863424117.033431005499
76114.310135934462111.165559730198117.454712138725
77114.310135934462110.794402303353117.82586956557
78114.310135934462110.4588496006118.161422268323
79114.310135934462110.150276575556118.469995293367
80114.310135934462109.863063487744118.757208381179
81114.310135934462109.593306829349119.026965039575
82114.310135934462109.338164467596119.282107401327
83114.310135934462109.095490814436119.524781054487
84114.310135934462108.863618956769119.756652912154



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