Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 May 2017 11:36:51 +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/02/t14937221575rfnhkom0v457jf.htm/, Retrieved Fri, 17 May 2024 06:48:32 +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 06:48:32 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
93.55
94.11
94.34
94.38
94.39
94.42
94.42
94.47
94.59
94.63
94.84
94.98
95.19
95.76
96.04
96.08
96.2
96.29
96.3
96.31
96.46
96.66
96.83
97
97.1
97.16
97.31
97.33
97.4
97.4
97.52
97.77
98
98.2
98.48
98.53
98.71
99.03
99.52
99.65
99.94
99.98
100.12
100.17
100.38
100.75
100.84
100.9
100.91
101.15
101.25
101.39
101.4
101.53
101.55
101.58
101.58
101.65
101.7
101.71
101.71
101.73
101.73
101.75
101.84
101.95
101.95
101.98
101.99
102.03
102.11
102.14
102.18
102.2
102.28
102.29
102.32
102.33
102.33
102.36
102.54
102.58
102.79
103.01




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 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]4 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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.907834293674592
beta0.496259020053144
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.907834293674592 \tabularnewline
beta & 0.496259020053144 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.907834293674592[/C][/ROW]
[ROW][C]beta[/C][C]0.496259020053144[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

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

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.907834293674592
beta0.496259020053144
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1395.1994.3025320512820.887467948717955
1495.7696.0759775171325-0.315977517132467
1596.0496.3249560917903-0.284956091790264
1696.0896.2258016223838-0.145801622383772
1796.296.2622896659814-0.0622896659814387
1896.2996.3169465942736-0.0269465942736389
1996.396.27946583633390.0205341636660563
2096.3196.3964241431399-0.0864241431398796
2196.4696.44484614336310.015153856636914
2296.6696.51022793192670.149772068073247
2396.8396.9307128714848-0.100712871484788
249797.0013424002913-0.00134240029126431
2597.197.3104565148301-0.210456514830071
2697.1697.5034540827227-0.343454082722673
2797.3197.24517081511930.0648291848806792
2897.3397.14879749750720.181202502492823
2997.497.3095790618040.0904209381960186
3097.497.3946596837890.0053403162110186
3197.5297.293942468870.226057531129996
3297.7797.5832929139560.186707086044009
339898.007755026586-0.00775502658602534
3498.298.17314580366280.0268541963371547
3598.4898.5119777611658-0.0319777611657912
3698.5398.7381547362324-0.208154736232402
3798.7198.8310598845502-0.121059884550235
3899.0399.1240475345576-0.0940475345575891
3999.5299.2732672471260.246732752873996
4099.6599.5781626721610.0718373278389919
4199.9499.80742534670250.132574653297482
4299.98100.118057686633-0.138057686632933
43100.12100.0380222450230.0819777549766059
44100.17100.258555248022-0.0885552480215779
45100.38100.3568004672050.0231995327947487
46100.75100.5090267471630.240973252836852
47100.84101.088830269257-0.248830269256928
48100.9101.056216257091-0.156216257090563
49100.91101.18201210141-0.272012101409544
50101.15101.250154632322-0.100154632321562
51101.25101.332191860228-0.0821918602282778
52101.39101.0811249418450.308875058154783
53101.4101.396733021230.003266978770327
54101.53101.3723331076220.157666892377762
55101.55101.521577131140.0284228688595363
56101.58101.594177107639-0.0141771076386163
57101.58101.720157453036-0.140157453036323
58101.65101.6204703236570.0295296763432873
59101.7101.74423166162-0.0442316616197189
60101.71101.779127711616-0.0691277116164315
61101.71101.885780927033-0.175780927033216
62101.73102.01294675267-0.282946752670185
63101.73101.804164865186-0.0741648651859208
64101.75101.4735147049160.276485295083887
65101.84101.5940460130570.245953986943107
66101.95101.7760259992850.173974000715262
67101.95101.9073389364120.0426610635876585
68101.98101.9745298107010.00547018929873389
69101.99102.101178330798-0.111178330797657
70102.03102.050937230681-0.0209372306806728
71102.11102.1068467688520.00315323114776334
72102.14102.188575829621-0.0485758296206882
73102.18102.319425975074-0.139425975073848
74102.2102.501466722269-0.301466722269112
75102.28102.318518330405-0.0385183304051253
76102.29102.0920107765280.197989223472192
77102.32102.1425661340350.177433865964929
78102.33102.2289367825610.101063217439034
79102.33102.2223380889990.107661911001074
80102.36102.3147773108160.0452226891835892
81102.54102.4543389269370.0856610730632497
82102.58102.667368205932-0.0873682059315541
83102.79102.7115168777060.0784831222943723
84103.01102.9371301828860.0728698171138547

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 95.19 & 94.302532051282 & 0.887467948717955 \tabularnewline
14 & 95.76 & 96.0759775171325 & -0.315977517132467 \tabularnewline
15 & 96.04 & 96.3249560917903 & -0.284956091790264 \tabularnewline
16 & 96.08 & 96.2258016223838 & -0.145801622383772 \tabularnewline
17 & 96.2 & 96.2622896659814 & -0.0622896659814387 \tabularnewline
18 & 96.29 & 96.3169465942736 & -0.0269465942736389 \tabularnewline
19 & 96.3 & 96.2794658363339 & 0.0205341636660563 \tabularnewline
20 & 96.31 & 96.3964241431399 & -0.0864241431398796 \tabularnewline
21 & 96.46 & 96.4448461433631 & 0.015153856636914 \tabularnewline
22 & 96.66 & 96.5102279319267 & 0.149772068073247 \tabularnewline
23 & 96.83 & 96.9307128714848 & -0.100712871484788 \tabularnewline
24 & 97 & 97.0013424002913 & -0.00134240029126431 \tabularnewline
25 & 97.1 & 97.3104565148301 & -0.210456514830071 \tabularnewline
26 & 97.16 & 97.5034540827227 & -0.343454082722673 \tabularnewline
27 & 97.31 & 97.2451708151193 & 0.0648291848806792 \tabularnewline
28 & 97.33 & 97.1487974975072 & 0.181202502492823 \tabularnewline
29 & 97.4 & 97.309579061804 & 0.0904209381960186 \tabularnewline
30 & 97.4 & 97.394659683789 & 0.0053403162110186 \tabularnewline
31 & 97.52 & 97.29394246887 & 0.226057531129996 \tabularnewline
32 & 97.77 & 97.583292913956 & 0.186707086044009 \tabularnewline
33 & 98 & 98.007755026586 & -0.00775502658602534 \tabularnewline
34 & 98.2 & 98.1731458036628 & 0.0268541963371547 \tabularnewline
35 & 98.48 & 98.5119777611658 & -0.0319777611657912 \tabularnewline
36 & 98.53 & 98.7381547362324 & -0.208154736232402 \tabularnewline
37 & 98.71 & 98.8310598845502 & -0.121059884550235 \tabularnewline
38 & 99.03 & 99.1240475345576 & -0.0940475345575891 \tabularnewline
39 & 99.52 & 99.273267247126 & 0.246732752873996 \tabularnewline
40 & 99.65 & 99.578162672161 & 0.0718373278389919 \tabularnewline
41 & 99.94 & 99.8074253467025 & 0.132574653297482 \tabularnewline
42 & 99.98 & 100.118057686633 & -0.138057686632933 \tabularnewline
43 & 100.12 & 100.038022245023 & 0.0819777549766059 \tabularnewline
44 & 100.17 & 100.258555248022 & -0.0885552480215779 \tabularnewline
45 & 100.38 & 100.356800467205 & 0.0231995327947487 \tabularnewline
46 & 100.75 & 100.509026747163 & 0.240973252836852 \tabularnewline
47 & 100.84 & 101.088830269257 & -0.248830269256928 \tabularnewline
48 & 100.9 & 101.056216257091 & -0.156216257090563 \tabularnewline
49 & 100.91 & 101.18201210141 & -0.272012101409544 \tabularnewline
50 & 101.15 & 101.250154632322 & -0.100154632321562 \tabularnewline
51 & 101.25 & 101.332191860228 & -0.0821918602282778 \tabularnewline
52 & 101.39 & 101.081124941845 & 0.308875058154783 \tabularnewline
53 & 101.4 & 101.39673302123 & 0.003266978770327 \tabularnewline
54 & 101.53 & 101.372333107622 & 0.157666892377762 \tabularnewline
55 & 101.55 & 101.52157713114 & 0.0284228688595363 \tabularnewline
56 & 101.58 & 101.594177107639 & -0.0141771076386163 \tabularnewline
57 & 101.58 & 101.720157453036 & -0.140157453036323 \tabularnewline
58 & 101.65 & 101.620470323657 & 0.0295296763432873 \tabularnewline
59 & 101.7 & 101.74423166162 & -0.0442316616197189 \tabularnewline
60 & 101.71 & 101.779127711616 & -0.0691277116164315 \tabularnewline
61 & 101.71 & 101.885780927033 & -0.175780927033216 \tabularnewline
62 & 101.73 & 102.01294675267 & -0.282946752670185 \tabularnewline
63 & 101.73 & 101.804164865186 & -0.0741648651859208 \tabularnewline
64 & 101.75 & 101.473514704916 & 0.276485295083887 \tabularnewline
65 & 101.84 & 101.594046013057 & 0.245953986943107 \tabularnewline
66 & 101.95 & 101.776025999285 & 0.173974000715262 \tabularnewline
67 & 101.95 & 101.907338936412 & 0.0426610635876585 \tabularnewline
68 & 101.98 & 101.974529810701 & 0.00547018929873389 \tabularnewline
69 & 101.99 & 102.101178330798 & -0.111178330797657 \tabularnewline
70 & 102.03 & 102.050937230681 & -0.0209372306806728 \tabularnewline
71 & 102.11 & 102.106846768852 & 0.00315323114776334 \tabularnewline
72 & 102.14 & 102.188575829621 & -0.0485758296206882 \tabularnewline
73 & 102.18 & 102.319425975074 & -0.139425975073848 \tabularnewline
74 & 102.2 & 102.501466722269 & -0.301466722269112 \tabularnewline
75 & 102.28 & 102.318518330405 & -0.0385183304051253 \tabularnewline
76 & 102.29 & 102.092010776528 & 0.197989223472192 \tabularnewline
77 & 102.32 & 102.142566134035 & 0.177433865964929 \tabularnewline
78 & 102.33 & 102.228936782561 & 0.101063217439034 \tabularnewline
79 & 102.33 & 102.222338088999 & 0.107661911001074 \tabularnewline
80 & 102.36 & 102.314777310816 & 0.0452226891835892 \tabularnewline
81 & 102.54 & 102.454338926937 & 0.0856610730632497 \tabularnewline
82 & 102.58 & 102.667368205932 & -0.0873682059315541 \tabularnewline
83 & 102.79 & 102.711516877706 & 0.0784831222943723 \tabularnewline
84 & 103.01 & 102.937130182886 & 0.0728698171138547 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]95.19[/C][C]94.302532051282[/C][C]0.887467948717955[/C][/ROW]
[ROW][C]14[/C][C]95.76[/C][C]96.0759775171325[/C][C]-0.315977517132467[/C][/ROW]
[ROW][C]15[/C][C]96.04[/C][C]96.3249560917903[/C][C]-0.284956091790264[/C][/ROW]
[ROW][C]16[/C][C]96.08[/C][C]96.2258016223838[/C][C]-0.145801622383772[/C][/ROW]
[ROW][C]17[/C][C]96.2[/C][C]96.2622896659814[/C][C]-0.0622896659814387[/C][/ROW]
[ROW][C]18[/C][C]96.29[/C][C]96.3169465942736[/C][C]-0.0269465942736389[/C][/ROW]
[ROW][C]19[/C][C]96.3[/C][C]96.2794658363339[/C][C]0.0205341636660563[/C][/ROW]
[ROW][C]20[/C][C]96.31[/C][C]96.3964241431399[/C][C]-0.0864241431398796[/C][/ROW]
[ROW][C]21[/C][C]96.46[/C][C]96.4448461433631[/C][C]0.015153856636914[/C][/ROW]
[ROW][C]22[/C][C]96.66[/C][C]96.5102279319267[/C][C]0.149772068073247[/C][/ROW]
[ROW][C]23[/C][C]96.83[/C][C]96.9307128714848[/C][C]-0.100712871484788[/C][/ROW]
[ROW][C]24[/C][C]97[/C][C]97.0013424002913[/C][C]-0.00134240029126431[/C][/ROW]
[ROW][C]25[/C][C]97.1[/C][C]97.3104565148301[/C][C]-0.210456514830071[/C][/ROW]
[ROW][C]26[/C][C]97.16[/C][C]97.5034540827227[/C][C]-0.343454082722673[/C][/ROW]
[ROW][C]27[/C][C]97.31[/C][C]97.2451708151193[/C][C]0.0648291848806792[/C][/ROW]
[ROW][C]28[/C][C]97.33[/C][C]97.1487974975072[/C][C]0.181202502492823[/C][/ROW]
[ROW][C]29[/C][C]97.4[/C][C]97.309579061804[/C][C]0.0904209381960186[/C][/ROW]
[ROW][C]30[/C][C]97.4[/C][C]97.394659683789[/C][C]0.0053403162110186[/C][/ROW]
[ROW][C]31[/C][C]97.52[/C][C]97.29394246887[/C][C]0.226057531129996[/C][/ROW]
[ROW][C]32[/C][C]97.77[/C][C]97.583292913956[/C][C]0.186707086044009[/C][/ROW]
[ROW][C]33[/C][C]98[/C][C]98.007755026586[/C][C]-0.00775502658602534[/C][/ROW]
[ROW][C]34[/C][C]98.2[/C][C]98.1731458036628[/C][C]0.0268541963371547[/C][/ROW]
[ROW][C]35[/C][C]98.48[/C][C]98.5119777611658[/C][C]-0.0319777611657912[/C][/ROW]
[ROW][C]36[/C][C]98.53[/C][C]98.7381547362324[/C][C]-0.208154736232402[/C][/ROW]
[ROW][C]37[/C][C]98.71[/C][C]98.8310598845502[/C][C]-0.121059884550235[/C][/ROW]
[ROW][C]38[/C][C]99.03[/C][C]99.1240475345576[/C][C]-0.0940475345575891[/C][/ROW]
[ROW][C]39[/C][C]99.52[/C][C]99.273267247126[/C][C]0.246732752873996[/C][/ROW]
[ROW][C]40[/C][C]99.65[/C][C]99.578162672161[/C][C]0.0718373278389919[/C][/ROW]
[ROW][C]41[/C][C]99.94[/C][C]99.8074253467025[/C][C]0.132574653297482[/C][/ROW]
[ROW][C]42[/C][C]99.98[/C][C]100.118057686633[/C][C]-0.138057686632933[/C][/ROW]
[ROW][C]43[/C][C]100.12[/C][C]100.038022245023[/C][C]0.0819777549766059[/C][/ROW]
[ROW][C]44[/C][C]100.17[/C][C]100.258555248022[/C][C]-0.0885552480215779[/C][/ROW]
[ROW][C]45[/C][C]100.38[/C][C]100.356800467205[/C][C]0.0231995327947487[/C][/ROW]
[ROW][C]46[/C][C]100.75[/C][C]100.509026747163[/C][C]0.240973252836852[/C][/ROW]
[ROW][C]47[/C][C]100.84[/C][C]101.088830269257[/C][C]-0.248830269256928[/C][/ROW]
[ROW][C]48[/C][C]100.9[/C][C]101.056216257091[/C][C]-0.156216257090563[/C][/ROW]
[ROW][C]49[/C][C]100.91[/C][C]101.18201210141[/C][C]-0.272012101409544[/C][/ROW]
[ROW][C]50[/C][C]101.15[/C][C]101.250154632322[/C][C]-0.100154632321562[/C][/ROW]
[ROW][C]51[/C][C]101.25[/C][C]101.332191860228[/C][C]-0.0821918602282778[/C][/ROW]
[ROW][C]52[/C][C]101.39[/C][C]101.081124941845[/C][C]0.308875058154783[/C][/ROW]
[ROW][C]53[/C][C]101.4[/C][C]101.39673302123[/C][C]0.003266978770327[/C][/ROW]
[ROW][C]54[/C][C]101.53[/C][C]101.372333107622[/C][C]0.157666892377762[/C][/ROW]
[ROW][C]55[/C][C]101.55[/C][C]101.52157713114[/C][C]0.0284228688595363[/C][/ROW]
[ROW][C]56[/C][C]101.58[/C][C]101.594177107639[/C][C]-0.0141771076386163[/C][/ROW]
[ROW][C]57[/C][C]101.58[/C][C]101.720157453036[/C][C]-0.140157453036323[/C][/ROW]
[ROW][C]58[/C][C]101.65[/C][C]101.620470323657[/C][C]0.0295296763432873[/C][/ROW]
[ROW][C]59[/C][C]101.7[/C][C]101.74423166162[/C][C]-0.0442316616197189[/C][/ROW]
[ROW][C]60[/C][C]101.71[/C][C]101.779127711616[/C][C]-0.0691277116164315[/C][/ROW]
[ROW][C]61[/C][C]101.71[/C][C]101.885780927033[/C][C]-0.175780927033216[/C][/ROW]
[ROW][C]62[/C][C]101.73[/C][C]102.01294675267[/C][C]-0.282946752670185[/C][/ROW]
[ROW][C]63[/C][C]101.73[/C][C]101.804164865186[/C][C]-0.0741648651859208[/C][/ROW]
[ROW][C]64[/C][C]101.75[/C][C]101.473514704916[/C][C]0.276485295083887[/C][/ROW]
[ROW][C]65[/C][C]101.84[/C][C]101.594046013057[/C][C]0.245953986943107[/C][/ROW]
[ROW][C]66[/C][C]101.95[/C][C]101.776025999285[/C][C]0.173974000715262[/C][/ROW]
[ROW][C]67[/C][C]101.95[/C][C]101.907338936412[/C][C]0.0426610635876585[/C][/ROW]
[ROW][C]68[/C][C]101.98[/C][C]101.974529810701[/C][C]0.00547018929873389[/C][/ROW]
[ROW][C]69[/C][C]101.99[/C][C]102.101178330798[/C][C]-0.111178330797657[/C][/ROW]
[ROW][C]70[/C][C]102.03[/C][C]102.050937230681[/C][C]-0.0209372306806728[/C][/ROW]
[ROW][C]71[/C][C]102.11[/C][C]102.106846768852[/C][C]0.00315323114776334[/C][/ROW]
[ROW][C]72[/C][C]102.14[/C][C]102.188575829621[/C][C]-0.0485758296206882[/C][/ROW]
[ROW][C]73[/C][C]102.18[/C][C]102.319425975074[/C][C]-0.139425975073848[/C][/ROW]
[ROW][C]74[/C][C]102.2[/C][C]102.501466722269[/C][C]-0.301466722269112[/C][/ROW]
[ROW][C]75[/C][C]102.28[/C][C]102.318518330405[/C][C]-0.0385183304051253[/C][/ROW]
[ROW][C]76[/C][C]102.29[/C][C]102.092010776528[/C][C]0.197989223472192[/C][/ROW]
[ROW][C]77[/C][C]102.32[/C][C]102.142566134035[/C][C]0.177433865964929[/C][/ROW]
[ROW][C]78[/C][C]102.33[/C][C]102.228936782561[/C][C]0.101063217439034[/C][/ROW]
[ROW][C]79[/C][C]102.33[/C][C]102.222338088999[/C][C]0.107661911001074[/C][/ROW]
[ROW][C]80[/C][C]102.36[/C][C]102.314777310816[/C][C]0.0452226891835892[/C][/ROW]
[ROW][C]81[/C][C]102.54[/C][C]102.454338926937[/C][C]0.0856610730632497[/C][/ROW]
[ROW][C]82[/C][C]102.58[/C][C]102.667368205932[/C][C]-0.0873682059315541[/C][/ROW]
[ROW][C]83[/C][C]102.79[/C][C]102.711516877706[/C][C]0.0784831222943723[/C][/ROW]
[ROW][C]84[/C][C]103.01[/C][C]102.937130182886[/C][C]0.0728698171138547[/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
1395.1994.3025320512820.887467948717955
1495.7696.0759775171325-0.315977517132467
1596.0496.3249560917903-0.284956091790264
1696.0896.2258016223838-0.145801622383772
1796.296.2622896659814-0.0622896659814387
1896.2996.3169465942736-0.0269465942736389
1996.396.27946583633390.0205341636660563
2096.3196.3964241431399-0.0864241431398796
2196.4696.44484614336310.015153856636914
2296.6696.51022793192670.149772068073247
2396.8396.9307128714848-0.100712871484788
249797.0013424002913-0.00134240029126431
2597.197.3104565148301-0.210456514830071
2697.1697.5034540827227-0.343454082722673
2797.3197.24517081511930.0648291848806792
2897.3397.14879749750720.181202502492823
2997.497.3095790618040.0904209381960186
3097.497.3946596837890.0053403162110186
3197.5297.293942468870.226057531129996
3297.7797.5832929139560.186707086044009
339898.007755026586-0.00775502658602534
3498.298.17314580366280.0268541963371547
3598.4898.5119777611658-0.0319777611657912
3698.5398.7381547362324-0.208154736232402
3798.7198.8310598845502-0.121059884550235
3899.0399.1240475345576-0.0940475345575891
3999.5299.2732672471260.246732752873996
4099.6599.5781626721610.0718373278389919
4199.9499.80742534670250.132574653297482
4299.98100.118057686633-0.138057686632933
43100.12100.0380222450230.0819777549766059
44100.17100.258555248022-0.0885552480215779
45100.38100.3568004672050.0231995327947487
46100.75100.5090267471630.240973252836852
47100.84101.088830269257-0.248830269256928
48100.9101.056216257091-0.156216257090563
49100.91101.18201210141-0.272012101409544
50101.15101.250154632322-0.100154632321562
51101.25101.332191860228-0.0821918602282778
52101.39101.0811249418450.308875058154783
53101.4101.396733021230.003266978770327
54101.53101.3723331076220.157666892377762
55101.55101.521577131140.0284228688595363
56101.58101.594177107639-0.0141771076386163
57101.58101.720157453036-0.140157453036323
58101.65101.6204703236570.0295296763432873
59101.7101.74423166162-0.0442316616197189
60101.71101.779127711616-0.0691277116164315
61101.71101.885780927033-0.175780927033216
62101.73102.01294675267-0.282946752670185
63101.73101.804164865186-0.0741648651859208
64101.75101.4735147049160.276485295083887
65101.84101.5940460130570.245953986943107
66101.95101.7760259992850.173974000715262
67101.95101.9073389364120.0426610635876585
68101.98101.9745298107010.00547018929873389
69101.99102.101178330798-0.111178330797657
70102.03102.050937230681-0.0209372306806728
71102.11102.1068467688520.00315323114776334
72102.14102.188575829621-0.0485758296206882
73102.18102.319425975074-0.139425975073848
74102.2102.501466722269-0.301466722269112
75102.28102.318518330405-0.0385183304051253
76102.29102.0920107765280.197989223472192
77102.32102.1425661340350.177433865964929
78102.33102.2289367825610.101063217439034
79102.33102.2223380889990.107661911001074
80102.36102.3147773108160.0452226891835892
81102.54102.4543389269370.0856610730632497
82102.58102.667368205932-0.0873682059315541
83102.79102.7115168777060.0784831222943723
84103.01102.9371301828860.0728698171138547







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85103.304838223735102.942091620207103.667584827262
86103.796313016624103.184449814905104.408176218344
87104.244891318118103.347713866623105.142068769613
88104.426113266563103.210937176237105.641289356889
89104.556797779048102.993797888683106.119797669412
90104.656876510204102.718503484603106.595249535805
91104.695433623619102.355982332317107.03488491492
92104.772171256698102.007463106128107.536879407269
93104.941823768905101.728968052672108.154679485137
94105.089966085782101.407176401666108.772755769898
95105.296904086988101.123353967878109.470454206098
96105.483579747777100.799286898503110.167872597051

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 103.304838223735 & 102.942091620207 & 103.667584827262 \tabularnewline
86 & 103.796313016624 & 103.184449814905 & 104.408176218344 \tabularnewline
87 & 104.244891318118 & 103.347713866623 & 105.142068769613 \tabularnewline
88 & 104.426113266563 & 103.210937176237 & 105.641289356889 \tabularnewline
89 & 104.556797779048 & 102.993797888683 & 106.119797669412 \tabularnewline
90 & 104.656876510204 & 102.718503484603 & 106.595249535805 \tabularnewline
91 & 104.695433623619 & 102.355982332317 & 107.03488491492 \tabularnewline
92 & 104.772171256698 & 102.007463106128 & 107.536879407269 \tabularnewline
93 & 104.941823768905 & 101.728968052672 & 108.154679485137 \tabularnewline
94 & 105.089966085782 & 101.407176401666 & 108.772755769898 \tabularnewline
95 & 105.296904086988 & 101.123353967878 & 109.470454206098 \tabularnewline
96 & 105.483579747777 & 100.799286898503 & 110.167872597051 \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]85[/C][C]103.304838223735[/C][C]102.942091620207[/C][C]103.667584827262[/C][/ROW]
[ROW][C]86[/C][C]103.796313016624[/C][C]103.184449814905[/C][C]104.408176218344[/C][/ROW]
[ROW][C]87[/C][C]104.244891318118[/C][C]103.347713866623[/C][C]105.142068769613[/C][/ROW]
[ROW][C]88[/C][C]104.426113266563[/C][C]103.210937176237[/C][C]105.641289356889[/C][/ROW]
[ROW][C]89[/C][C]104.556797779048[/C][C]102.993797888683[/C][C]106.119797669412[/C][/ROW]
[ROW][C]90[/C][C]104.656876510204[/C][C]102.718503484603[/C][C]106.595249535805[/C][/ROW]
[ROW][C]91[/C][C]104.695433623619[/C][C]102.355982332317[/C][C]107.03488491492[/C][/ROW]
[ROW][C]92[/C][C]104.772171256698[/C][C]102.007463106128[/C][C]107.536879407269[/C][/ROW]
[ROW][C]93[/C][C]104.941823768905[/C][C]101.728968052672[/C][C]108.154679485137[/C][/ROW]
[ROW][C]94[/C][C]105.089966085782[/C][C]101.407176401666[/C][C]108.772755769898[/C][/ROW]
[ROW][C]95[/C][C]105.296904086988[/C][C]101.123353967878[/C][C]109.470454206098[/C][/ROW]
[ROW][C]96[/C][C]105.483579747777[/C][C]100.799286898503[/C][C]110.167872597051[/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
85103.304838223735102.942091620207103.667584827262
86103.796313016624103.184449814905104.408176218344
87104.244891318118103.347713866623105.142068769613
88104.426113266563103.210937176237105.641289356889
89104.556797779048102.993797888683106.119797669412
90104.656876510204102.718503484603106.595249535805
91104.695433623619102.355982332317107.03488491492
92104.772171256698102.007463106128107.536879407269
93104.941823768905101.728968052672108.154679485137
94105.089966085782101.407176401666108.772755769898
95105.296904086988101.123353967878109.470454206098
96105.483579747777100.799286898503110.167872597051



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
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')