Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 10 Jan 2017 03:46:53 +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/2017/Jan/10/t1484020029t0h7j4yboctblt3.htm/, Retrieved Wed, 15 May 2024 07:55:29 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 07:55:29 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
2.32
1.93
0.62
0.6
-0.37
-1.1
-1.68
-0.77
-1.2
-0.97
-0.12
0.26
0.62
0.7
1.65
1.79
2.28
2.46
2.57
2.32
2.91
3.01
2.87
3.11
3.22
3.38
3.52
3.41
3.35
3.68
3.75
3.6
3.56
3.57
3.85
3.48
3.65
3.66
3.36
3.19
2.81
2.25
2.32
2.85
2.75
2.78
2.26
2.23
1.46
1.19
1.11
1
1.18
1.59
1.51
1.01
0.9
0.63
0.81
0.97
1.14
0.97
0.89
0.62
0.36
0.27
0.34
0.02
-0.12
0.09
-0.11
-0.38
-0.65
-0.4
-0.4
0.29
0.56
0.63
0.46
0.91
1.06
1.28
1.52
1.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.708939147935893
beta0.0699089185460378
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.708939147935893 \tabularnewline
beta & 0.0699089185460378 \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]0.708939147935893[/C][/ROW]
[ROW][C]beta[/C][C]0.0699089185460378[/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
alpha0.708939147935893
beta0.0699089185460378
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
130.62-0.3585550213675220.978555021367522
140.70.3843130138816860.315686986118314
151.651.548727098477280.101272901522722
161.791.719070514703270.070929485296727
172.282.268084310169520.0119156898304751
182.462.512934804614-0.0529348046139959
192.570.8154367339785361.75456326602146
202.323.47546967890848-1.15546967890848
212.912.561449919193630.348550080806374
223.013.29012986258753-0.280129862587532
232.874.11173041908451-1.24173041908451
243.113.62132308506843-0.511323085068433
253.223.8215407258121-0.601540725812097
263.383.189815827414090.190184172585913
273.524.13516217615472-0.615162176154724
283.413.68557124620289-0.275571246202891
293.353.85139382928871-0.501393829288713
303.683.567656777109770.112343222890233
313.752.375807177944621.37419282205538
323.63.76271683096689-0.162716830966892
333.563.88299456900826-0.322994569008259
343.573.81205842942422-0.242058429424222
353.854.24210423159044-0.39210423159044
363.484.47007080478434-0.990070804784339
373.654.18434698572596-0.534346985725958
383.663.71374904809304-0.0537490480930374
393.364.12271774152414-0.76271774152414
403.193.53100844266029-0.341008442660286
412.813.44511670048502-0.63511670048502
422.253.09899041593995-0.848990415939947
432.321.399021283058080.920978716941917
442.851.800966158058971.04903384194103
452.752.577377267369850.172622732630145
462.782.749650806689160.030349193310844
472.263.21093524767603-0.950935247676031
482.232.72277432756826-0.492774327568257
491.462.80098775862546-1.34098775862546
501.191.7371767304093-0.547176730409304
511.111.40429022476793-0.29429022476793
5211.10493444733839-0.104934447338387
531.180.9500253543330520.229974645666948
541.591.047044816493770.542955183506228
551.510.8101344768304690.699865523169531
561.011.04272210006749-0.0327221000674871
570.90.6936587337570630.206341266242937
580.630.746611158348065-0.116611158348065
590.810.7089973948551830.101002605144817
600.971.04298560496928-0.0729856049692794
611.141.135763688622460.004236311377535
620.971.28719457556109-0.317194575561093
630.891.23286756403655-0.342867564036549
640.620.993690692701398-0.373690692701398
650.360.771912058026897-0.411912058026897
660.270.499339989874218-0.229339989874218
670.34-0.2833153260680750.623315326068075
680.02-0.365923780703990.38592378070399
69-0.12-0.375561195142630.25556119514263
700.09-0.4062247359768770.496224735976877
71-0.110.0598254761154579-0.169825476115458
72-0.380.143611115448572-0.523611115448572
73-0.65-0.0904949016428576-0.559505098357142
74-0.4-0.4901123126500770.0901123126500773
75-0.4-0.300803317657328-0.0991966823426717
760.29-0.4017745439150980.691774543915098
770.560.1479070219912860.412092978008714
780.630.580717543406630.0492824565933697
790.460.3256456039380370.134354396061963
800.91-0.1150528227112181.02505282271122
811.060.3797948571844550.680205142815545
821.280.8305965616668850.449403438333115
831.521.177642454022440.342357545977563
841.51.65499620175443-0.15499620175443

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.62 & -0.358555021367522 & 0.978555021367522 \tabularnewline
14 & 0.7 & 0.384313013881686 & 0.315686986118314 \tabularnewline
15 & 1.65 & 1.54872709847728 & 0.101272901522722 \tabularnewline
16 & 1.79 & 1.71907051470327 & 0.070929485296727 \tabularnewline
17 & 2.28 & 2.26808431016952 & 0.0119156898304751 \tabularnewline
18 & 2.46 & 2.512934804614 & -0.0529348046139959 \tabularnewline
19 & 2.57 & 0.815436733978536 & 1.75456326602146 \tabularnewline
20 & 2.32 & 3.47546967890848 & -1.15546967890848 \tabularnewline
21 & 2.91 & 2.56144991919363 & 0.348550080806374 \tabularnewline
22 & 3.01 & 3.29012986258753 & -0.280129862587532 \tabularnewline
23 & 2.87 & 4.11173041908451 & -1.24173041908451 \tabularnewline
24 & 3.11 & 3.62132308506843 & -0.511323085068433 \tabularnewline
25 & 3.22 & 3.8215407258121 & -0.601540725812097 \tabularnewline
26 & 3.38 & 3.18981582741409 & 0.190184172585913 \tabularnewline
27 & 3.52 & 4.13516217615472 & -0.615162176154724 \tabularnewline
28 & 3.41 & 3.68557124620289 & -0.275571246202891 \tabularnewline
29 & 3.35 & 3.85139382928871 & -0.501393829288713 \tabularnewline
30 & 3.68 & 3.56765677710977 & 0.112343222890233 \tabularnewline
31 & 3.75 & 2.37580717794462 & 1.37419282205538 \tabularnewline
32 & 3.6 & 3.76271683096689 & -0.162716830966892 \tabularnewline
33 & 3.56 & 3.88299456900826 & -0.322994569008259 \tabularnewline
34 & 3.57 & 3.81205842942422 & -0.242058429424222 \tabularnewline
35 & 3.85 & 4.24210423159044 & -0.39210423159044 \tabularnewline
36 & 3.48 & 4.47007080478434 & -0.990070804784339 \tabularnewline
37 & 3.65 & 4.18434698572596 & -0.534346985725958 \tabularnewline
38 & 3.66 & 3.71374904809304 & -0.0537490480930374 \tabularnewline
39 & 3.36 & 4.12271774152414 & -0.76271774152414 \tabularnewline
40 & 3.19 & 3.53100844266029 & -0.341008442660286 \tabularnewline
41 & 2.81 & 3.44511670048502 & -0.63511670048502 \tabularnewline
42 & 2.25 & 3.09899041593995 & -0.848990415939947 \tabularnewline
43 & 2.32 & 1.39902128305808 & 0.920978716941917 \tabularnewline
44 & 2.85 & 1.80096615805897 & 1.04903384194103 \tabularnewline
45 & 2.75 & 2.57737726736985 & 0.172622732630145 \tabularnewline
46 & 2.78 & 2.74965080668916 & 0.030349193310844 \tabularnewline
47 & 2.26 & 3.21093524767603 & -0.950935247676031 \tabularnewline
48 & 2.23 & 2.72277432756826 & -0.492774327568257 \tabularnewline
49 & 1.46 & 2.80098775862546 & -1.34098775862546 \tabularnewline
50 & 1.19 & 1.7371767304093 & -0.547176730409304 \tabularnewline
51 & 1.11 & 1.40429022476793 & -0.29429022476793 \tabularnewline
52 & 1 & 1.10493444733839 & -0.104934447338387 \tabularnewline
53 & 1.18 & 0.950025354333052 & 0.229974645666948 \tabularnewline
54 & 1.59 & 1.04704481649377 & 0.542955183506228 \tabularnewline
55 & 1.51 & 0.810134476830469 & 0.699865523169531 \tabularnewline
56 & 1.01 & 1.04272210006749 & -0.0327221000674871 \tabularnewline
57 & 0.9 & 0.693658733757063 & 0.206341266242937 \tabularnewline
58 & 0.63 & 0.746611158348065 & -0.116611158348065 \tabularnewline
59 & 0.81 & 0.708997394855183 & 0.101002605144817 \tabularnewline
60 & 0.97 & 1.04298560496928 & -0.0729856049692794 \tabularnewline
61 & 1.14 & 1.13576368862246 & 0.004236311377535 \tabularnewline
62 & 0.97 & 1.28719457556109 & -0.317194575561093 \tabularnewline
63 & 0.89 & 1.23286756403655 & -0.342867564036549 \tabularnewline
64 & 0.62 & 0.993690692701398 & -0.373690692701398 \tabularnewline
65 & 0.36 & 0.771912058026897 & -0.411912058026897 \tabularnewline
66 & 0.27 & 0.499339989874218 & -0.229339989874218 \tabularnewline
67 & 0.34 & -0.283315326068075 & 0.623315326068075 \tabularnewline
68 & 0.02 & -0.36592378070399 & 0.38592378070399 \tabularnewline
69 & -0.12 & -0.37556119514263 & 0.25556119514263 \tabularnewline
70 & 0.09 & -0.406224735976877 & 0.496224735976877 \tabularnewline
71 & -0.11 & 0.0598254761154579 & -0.169825476115458 \tabularnewline
72 & -0.38 & 0.143611115448572 & -0.523611115448572 \tabularnewline
73 & -0.65 & -0.0904949016428576 & -0.559505098357142 \tabularnewline
74 & -0.4 & -0.490112312650077 & 0.0901123126500773 \tabularnewline
75 & -0.4 & -0.300803317657328 & -0.0991966823426717 \tabularnewline
76 & 0.29 & -0.401774543915098 & 0.691774543915098 \tabularnewline
77 & 0.56 & 0.147907021991286 & 0.412092978008714 \tabularnewline
78 & 0.63 & 0.58071754340663 & 0.0492824565933697 \tabularnewline
79 & 0.46 & 0.325645603938037 & 0.134354396061963 \tabularnewline
80 & 0.91 & -0.115052822711218 & 1.02505282271122 \tabularnewline
81 & 1.06 & 0.379794857184455 & 0.680205142815545 \tabularnewline
82 & 1.28 & 0.830596561666885 & 0.449403438333115 \tabularnewline
83 & 1.52 & 1.17764245402244 & 0.342357545977563 \tabularnewline
84 & 1.5 & 1.65499620175443 & -0.15499620175443 \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]0.62[/C][C]-0.358555021367522[/C][C]0.978555021367522[/C][/ROW]
[ROW][C]14[/C][C]0.7[/C][C]0.384313013881686[/C][C]0.315686986118314[/C][/ROW]
[ROW][C]15[/C][C]1.65[/C][C]1.54872709847728[/C][C]0.101272901522722[/C][/ROW]
[ROW][C]16[/C][C]1.79[/C][C]1.71907051470327[/C][C]0.070929485296727[/C][/ROW]
[ROW][C]17[/C][C]2.28[/C][C]2.26808431016952[/C][C]0.0119156898304751[/C][/ROW]
[ROW][C]18[/C][C]2.46[/C][C]2.512934804614[/C][C]-0.0529348046139959[/C][/ROW]
[ROW][C]19[/C][C]2.57[/C][C]0.815436733978536[/C][C]1.75456326602146[/C][/ROW]
[ROW][C]20[/C][C]2.32[/C][C]3.47546967890848[/C][C]-1.15546967890848[/C][/ROW]
[ROW][C]21[/C][C]2.91[/C][C]2.56144991919363[/C][C]0.348550080806374[/C][/ROW]
[ROW][C]22[/C][C]3.01[/C][C]3.29012986258753[/C][C]-0.280129862587532[/C][/ROW]
[ROW][C]23[/C][C]2.87[/C][C]4.11173041908451[/C][C]-1.24173041908451[/C][/ROW]
[ROW][C]24[/C][C]3.11[/C][C]3.62132308506843[/C][C]-0.511323085068433[/C][/ROW]
[ROW][C]25[/C][C]3.22[/C][C]3.8215407258121[/C][C]-0.601540725812097[/C][/ROW]
[ROW][C]26[/C][C]3.38[/C][C]3.18981582741409[/C][C]0.190184172585913[/C][/ROW]
[ROW][C]27[/C][C]3.52[/C][C]4.13516217615472[/C][C]-0.615162176154724[/C][/ROW]
[ROW][C]28[/C][C]3.41[/C][C]3.68557124620289[/C][C]-0.275571246202891[/C][/ROW]
[ROW][C]29[/C][C]3.35[/C][C]3.85139382928871[/C][C]-0.501393829288713[/C][/ROW]
[ROW][C]30[/C][C]3.68[/C][C]3.56765677710977[/C][C]0.112343222890233[/C][/ROW]
[ROW][C]31[/C][C]3.75[/C][C]2.37580717794462[/C][C]1.37419282205538[/C][/ROW]
[ROW][C]32[/C][C]3.6[/C][C]3.76271683096689[/C][C]-0.162716830966892[/C][/ROW]
[ROW][C]33[/C][C]3.56[/C][C]3.88299456900826[/C][C]-0.322994569008259[/C][/ROW]
[ROW][C]34[/C][C]3.57[/C][C]3.81205842942422[/C][C]-0.242058429424222[/C][/ROW]
[ROW][C]35[/C][C]3.85[/C][C]4.24210423159044[/C][C]-0.39210423159044[/C][/ROW]
[ROW][C]36[/C][C]3.48[/C][C]4.47007080478434[/C][C]-0.990070804784339[/C][/ROW]
[ROW][C]37[/C][C]3.65[/C][C]4.18434698572596[/C][C]-0.534346985725958[/C][/ROW]
[ROW][C]38[/C][C]3.66[/C][C]3.71374904809304[/C][C]-0.0537490480930374[/C][/ROW]
[ROW][C]39[/C][C]3.36[/C][C]4.12271774152414[/C][C]-0.76271774152414[/C][/ROW]
[ROW][C]40[/C][C]3.19[/C][C]3.53100844266029[/C][C]-0.341008442660286[/C][/ROW]
[ROW][C]41[/C][C]2.81[/C][C]3.44511670048502[/C][C]-0.63511670048502[/C][/ROW]
[ROW][C]42[/C][C]2.25[/C][C]3.09899041593995[/C][C]-0.848990415939947[/C][/ROW]
[ROW][C]43[/C][C]2.32[/C][C]1.39902128305808[/C][C]0.920978716941917[/C][/ROW]
[ROW][C]44[/C][C]2.85[/C][C]1.80096615805897[/C][C]1.04903384194103[/C][/ROW]
[ROW][C]45[/C][C]2.75[/C][C]2.57737726736985[/C][C]0.172622732630145[/C][/ROW]
[ROW][C]46[/C][C]2.78[/C][C]2.74965080668916[/C][C]0.030349193310844[/C][/ROW]
[ROW][C]47[/C][C]2.26[/C][C]3.21093524767603[/C][C]-0.950935247676031[/C][/ROW]
[ROW][C]48[/C][C]2.23[/C][C]2.72277432756826[/C][C]-0.492774327568257[/C][/ROW]
[ROW][C]49[/C][C]1.46[/C][C]2.80098775862546[/C][C]-1.34098775862546[/C][/ROW]
[ROW][C]50[/C][C]1.19[/C][C]1.7371767304093[/C][C]-0.547176730409304[/C][/ROW]
[ROW][C]51[/C][C]1.11[/C][C]1.40429022476793[/C][C]-0.29429022476793[/C][/ROW]
[ROW][C]52[/C][C]1[/C][C]1.10493444733839[/C][C]-0.104934447338387[/C][/ROW]
[ROW][C]53[/C][C]1.18[/C][C]0.950025354333052[/C][C]0.229974645666948[/C][/ROW]
[ROW][C]54[/C][C]1.59[/C][C]1.04704481649377[/C][C]0.542955183506228[/C][/ROW]
[ROW][C]55[/C][C]1.51[/C][C]0.810134476830469[/C][C]0.699865523169531[/C][/ROW]
[ROW][C]56[/C][C]1.01[/C][C]1.04272210006749[/C][C]-0.0327221000674871[/C][/ROW]
[ROW][C]57[/C][C]0.9[/C][C]0.693658733757063[/C][C]0.206341266242937[/C][/ROW]
[ROW][C]58[/C][C]0.63[/C][C]0.746611158348065[/C][C]-0.116611158348065[/C][/ROW]
[ROW][C]59[/C][C]0.81[/C][C]0.708997394855183[/C][C]0.101002605144817[/C][/ROW]
[ROW][C]60[/C][C]0.97[/C][C]1.04298560496928[/C][C]-0.0729856049692794[/C][/ROW]
[ROW][C]61[/C][C]1.14[/C][C]1.13576368862246[/C][C]0.004236311377535[/C][/ROW]
[ROW][C]62[/C][C]0.97[/C][C]1.28719457556109[/C][C]-0.317194575561093[/C][/ROW]
[ROW][C]63[/C][C]0.89[/C][C]1.23286756403655[/C][C]-0.342867564036549[/C][/ROW]
[ROW][C]64[/C][C]0.62[/C][C]0.993690692701398[/C][C]-0.373690692701398[/C][/ROW]
[ROW][C]65[/C][C]0.36[/C][C]0.771912058026897[/C][C]-0.411912058026897[/C][/ROW]
[ROW][C]66[/C][C]0.27[/C][C]0.499339989874218[/C][C]-0.229339989874218[/C][/ROW]
[ROW][C]67[/C][C]0.34[/C][C]-0.283315326068075[/C][C]0.623315326068075[/C][/ROW]
[ROW][C]68[/C][C]0.02[/C][C]-0.36592378070399[/C][C]0.38592378070399[/C][/ROW]
[ROW][C]69[/C][C]-0.12[/C][C]-0.37556119514263[/C][C]0.25556119514263[/C][/ROW]
[ROW][C]70[/C][C]0.09[/C][C]-0.406224735976877[/C][C]0.496224735976877[/C][/ROW]
[ROW][C]71[/C][C]-0.11[/C][C]0.0598254761154579[/C][C]-0.169825476115458[/C][/ROW]
[ROW][C]72[/C][C]-0.38[/C][C]0.143611115448572[/C][C]-0.523611115448572[/C][/ROW]
[ROW][C]73[/C][C]-0.65[/C][C]-0.0904949016428576[/C][C]-0.559505098357142[/C][/ROW]
[ROW][C]74[/C][C]-0.4[/C][C]-0.490112312650077[/C][C]0.0901123126500773[/C][/ROW]
[ROW][C]75[/C][C]-0.4[/C][C]-0.300803317657328[/C][C]-0.0991966823426717[/C][/ROW]
[ROW][C]76[/C][C]0.29[/C][C]-0.401774543915098[/C][C]0.691774543915098[/C][/ROW]
[ROW][C]77[/C][C]0.56[/C][C]0.147907021991286[/C][C]0.412092978008714[/C][/ROW]
[ROW][C]78[/C][C]0.63[/C][C]0.58071754340663[/C][C]0.0492824565933697[/C][/ROW]
[ROW][C]79[/C][C]0.46[/C][C]0.325645603938037[/C][C]0.134354396061963[/C][/ROW]
[ROW][C]80[/C][C]0.91[/C][C]-0.115052822711218[/C][C]1.02505282271122[/C][/ROW]
[ROW][C]81[/C][C]1.06[/C][C]0.379794857184455[/C][C]0.680205142815545[/C][/ROW]
[ROW][C]82[/C][C]1.28[/C][C]0.830596561666885[/C][C]0.449403438333115[/C][/ROW]
[ROW][C]83[/C][C]1.52[/C][C]1.17764245402244[/C][C]0.342357545977563[/C][/ROW]
[ROW][C]84[/C][C]1.5[/C][C]1.65499620175443[/C][C]-0.15499620175443[/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
130.62-0.3585550213675220.978555021367522
140.70.3843130138816860.315686986118314
151.651.548727098477280.101272901522722
161.791.719070514703270.070929485296727
172.282.268084310169520.0119156898304751
182.462.512934804614-0.0529348046139959
192.570.8154367339785361.75456326602146
202.323.47546967890848-1.15546967890848
212.912.561449919193630.348550080806374
223.013.29012986258753-0.280129862587532
232.874.11173041908451-1.24173041908451
243.113.62132308506843-0.511323085068433
253.223.8215407258121-0.601540725812097
263.383.189815827414090.190184172585913
273.524.13516217615472-0.615162176154724
283.413.68557124620289-0.275571246202891
293.353.85139382928871-0.501393829288713
303.683.567656777109770.112343222890233
313.752.375807177944621.37419282205538
323.63.76271683096689-0.162716830966892
333.563.88299456900826-0.322994569008259
343.573.81205842942422-0.242058429424222
353.854.24210423159044-0.39210423159044
363.484.47007080478434-0.990070804784339
373.654.18434698572596-0.534346985725958
383.663.71374904809304-0.0537490480930374
393.364.12271774152414-0.76271774152414
403.193.53100844266029-0.341008442660286
412.813.44511670048502-0.63511670048502
422.253.09899041593995-0.848990415939947
432.321.399021283058080.920978716941917
442.851.800966158058971.04903384194103
452.752.577377267369850.172622732630145
462.782.749650806689160.030349193310844
472.263.21093524767603-0.950935247676031
482.232.72277432756826-0.492774327568257
491.462.80098775862546-1.34098775862546
501.191.7371767304093-0.547176730409304
511.111.40429022476793-0.29429022476793
5211.10493444733839-0.104934447338387
531.180.9500253543330520.229974645666948
541.591.047044816493770.542955183506228
551.510.8101344768304690.699865523169531
561.011.04272210006749-0.0327221000674871
570.90.6936587337570630.206341266242937
580.630.746611158348065-0.116611158348065
590.810.7089973948551830.101002605144817
600.971.04298560496928-0.0729856049692794
611.141.135763688622460.004236311377535
620.971.28719457556109-0.317194575561093
630.891.23286756403655-0.342867564036549
640.620.993690692701398-0.373690692701398
650.360.771912058026897-0.411912058026897
660.270.499339989874218-0.229339989874218
670.34-0.2833153260680750.623315326068075
680.02-0.365923780703990.38592378070399
69-0.12-0.375561195142630.25556119514263
700.09-0.4062247359768770.496224735976877
71-0.110.0598254761154579-0.169825476115458
72-0.380.143611115448572-0.523611115448572
73-0.65-0.0904949016428576-0.559505098357142
74-0.4-0.4901123126500770.0901123126500773
75-0.4-0.300803317657328-0.0991966823426717
760.29-0.4017745439150980.691774543915098
770.560.1479070219912860.412092978008714
780.630.580717543406630.0492824565933697
790.460.3256456039380370.134354396061963
800.91-0.1150528227112181.02505282271122
811.060.3797948571844550.680205142815545
821.280.8305965616668850.449403438333115
831.521.177642454022440.342357545977563
841.51.65499620175443-0.15499620175443







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
851.823472043093560.6687937054536012.97815038073353
862.189021272612380.7397629997871653.63827954543759
872.434312988168460.7106732680765214.15795270826039
882.813770540091960.8259111385856864.80162994159824
892.937220147859850.6902549067957535.18418538892396
903.097456527754670.5936020642081785.60131099130117
912.954939583202160.1946066237325435.71527254267179
922.7943128940442-0.2232780853383785.81190387342678
932.527359408908-0.7490851422076115.8038039600236
942.46031852535187-1.077150723553265.99778777425701
952.4668937056898-1.334185693225356.26797310460494
962.54909478792257-1.5184826892776.61667226512213

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.82347204309356 & 0.668793705453601 & 2.97815038073353 \tabularnewline
86 & 2.18902127261238 & 0.739762999787165 & 3.63827954543759 \tabularnewline
87 & 2.43431298816846 & 0.710673268076521 & 4.15795270826039 \tabularnewline
88 & 2.81377054009196 & 0.825911138585686 & 4.80162994159824 \tabularnewline
89 & 2.93722014785985 & 0.690254906795753 & 5.18418538892396 \tabularnewline
90 & 3.09745652775467 & 0.593602064208178 & 5.60131099130117 \tabularnewline
91 & 2.95493958320216 & 0.194606623732543 & 5.71527254267179 \tabularnewline
92 & 2.7943128940442 & -0.223278085338378 & 5.81190387342678 \tabularnewline
93 & 2.527359408908 & -0.749085142207611 & 5.8038039600236 \tabularnewline
94 & 2.46031852535187 & -1.07715072355326 & 5.99778777425701 \tabularnewline
95 & 2.4668937056898 & -1.33418569322535 & 6.26797310460494 \tabularnewline
96 & 2.54909478792257 & -1.518482689277 & 6.61667226512213 \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]1.82347204309356[/C][C]0.668793705453601[/C][C]2.97815038073353[/C][/ROW]
[ROW][C]86[/C][C]2.18902127261238[/C][C]0.739762999787165[/C][C]3.63827954543759[/C][/ROW]
[ROW][C]87[/C][C]2.43431298816846[/C][C]0.710673268076521[/C][C]4.15795270826039[/C][/ROW]
[ROW][C]88[/C][C]2.81377054009196[/C][C]0.825911138585686[/C][C]4.80162994159824[/C][/ROW]
[ROW][C]89[/C][C]2.93722014785985[/C][C]0.690254906795753[/C][C]5.18418538892396[/C][/ROW]
[ROW][C]90[/C][C]3.09745652775467[/C][C]0.593602064208178[/C][C]5.60131099130117[/C][/ROW]
[ROW][C]91[/C][C]2.95493958320216[/C][C]0.194606623732543[/C][C]5.71527254267179[/C][/ROW]
[ROW][C]92[/C][C]2.7943128940442[/C][C]-0.223278085338378[/C][C]5.81190387342678[/C][/ROW]
[ROW][C]93[/C][C]2.527359408908[/C][C]-0.749085142207611[/C][C]5.8038039600236[/C][/ROW]
[ROW][C]94[/C][C]2.46031852535187[/C][C]-1.07715072355326[/C][C]5.99778777425701[/C][/ROW]
[ROW][C]95[/C][C]2.4668937056898[/C][C]-1.33418569322535[/C][C]6.26797310460494[/C][/ROW]
[ROW][C]96[/C][C]2.54909478792257[/C][C]-1.518482689277[/C][C]6.61667226512213[/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
851.823472043093560.6687937054536012.97815038073353
862.189021272612380.7397629997871653.63827954543759
872.434312988168460.7106732680765214.15795270826039
882.813770540091960.8259111385856864.80162994159824
892.937220147859850.6902549067957535.18418538892396
903.097456527754670.5936020642081785.60131099130117
912.954939583202160.1946066237325435.71527254267179
922.7943128940442-0.2232780853383785.81190387342678
932.527359408908-0.7490851422076115.8038039600236
942.46031852535187-1.077150723553265.99778777425701
952.4668937056898-1.334185693225356.26797310460494
962.54909478792257-1.5184826892776.61667226512213



Parameters (Session):
par1 = 12 ;
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')