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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 01 Apr 2015 20:41:15 +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/2015/Apr/01/t1427917303si29odt28kq4nb3.htm/, Retrieved Thu, 09 May 2024 12:25:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278535, Retrieved Thu, 09 May 2024 12:25:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-04-01 19:41:15] [70e23d918d09c907c02097a361cd6415] [Current]
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Dataseries X:
-23.5
5.9
8.4
7.8
4.8
3.5
8.7
6.8
6
3.6
8.7
8.9
8.1
7
7.9
8
7.5
6.3
7.6
8.4
6.8
8.8
8.7
8.7
7.4
2.8
4.8
-21.1
8.5
9.4
1.8
4.8
5.8
3.3
-9
-6
-0.9
-17.3
-9.2
-8.1
-20.9
-14.6
-13.9
-20.8
-16.1
-5
-7.2
-9.7
-1.4
0.2
2.6
-4.8
-6.2
-2
-0.8
-3.1
0.6
0.2
0.3
-0.1
4.3
-3.2
-1.3
1.5
2.5
-2.2
1.7
5.7
2.7
-4.8
-3.1
-0.5
-3.4
-4.7
-5.6
-1.7
-1.8
-5.4
-4.8
-2.8
-4.9
-6.8
-7.6
-6.6
-5.6
-1.4
0.1
-3.7
-5.6
-3.1
-3.8
-5.1
-4.1
-0.3
-0.3
-2.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278535&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278535&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278535&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.740910262823532
beta0.531124395641552
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.740910262823532 \tabularnewline
beta & 0.531124395641552 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278535&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]0.740910262823532[/C][/ROW]
[ROW][C]beta[/C][C]0.531124395641552[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278535&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278535&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
alpha0.740910262823532
beta0.531124395641552
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38.435.3-26.9
47.834.1839465613008-26.3839465613008
54.823.0677500777428-18.2677500777428
63.510.7762837738573-7.27628377385727
78.73.765177097319994.93482290268001
86.87.74333405664098-0.943334056640976
966.99508761066271-0.995087610662706
103.65.8169140112281-2.2169140112281
118.72.861086632130235.83891336786977
128.98.171607438047760.728392561952241
138.19.98232470503944-1.88232470503944
1479.11801077881871-2.11801077881871
157.97.245604518127510.654395481872487
1687.684817284132250.315182715867746
177.57.99673311945576-0.496733119455757
186.37.51161999023741-1.21161999023741
197.66.020048576569861.57995142343014
208.47.218516471654961.18148352834504
216.88.58668751365616-1.78668751365616
228.87.052620910729941.74737908927006
238.78.82460130661836-0.124601306618358
248.79.16057966797437-0.460579667974372
257.49.06638296781257-1.66638296781257
262.87.42304667514372-4.62304667514372
274.81.769847302136913.03015269786308
28-21.12.97939398917111-24.0793939891711
298.5-25.372415824896133.8724158248961
309.42.542186178302646.85781382169736
311.813.1400484529445-11.3400484529445
324.85.79244279334235-0.992442793342351
335.85.720942725097670.0790572749023317
343.36.47443831832408-3.17443831832408
35-93.56819490500769-12.5681949050077
36-6-11.24375886763655.24375886763652
37-0.9-10.79515281488459.89515281488448
38-17.3-3.00638508861991-14.2936149113801
39-9.2-18.7640828569649.56408285696403
40-8.1-13.08175250501844.98175250501838
41-20.9-8.83412083303867-12.0658791669613
42-14.6-21.96536508481747.36536508481738
43-13.9-17.80141561233313.90141561233307
44-20.8-14.668674277787-6.13132572221296
45-16.1-21.38206576494455.28206576494447
46-5-17.560583532894512.5605835328945
47-7.2-3.40358828366044-3.79641171633956
48-9.7-2.85960559739875-6.84039440260125
49-1.4-7.262742253265185.86274225326518
500.20.05308544967837660.146914550321623
512.63.19181090199407-0.591810901994071
52-4.85.55032031306388-10.3503203130639
53-6.2-3.39436168266452-2.80563831733548
54-2-7.853173566957985.85317356695798
55-0.8-3.593268248416782.79326824841678
56-3.1-0.501283788759041-2.59871621124096
570.6-2.426911101924933.02691110192493
580.21.00668307890293-0.806683078902933
590.31.28248567996138-0.982485679961383
60-0.11.04141097077758-1.14141097077758
614.30.2334239559667354.06657604403326
62-3.24.88434873764017-8.08434873764017
63-1.3-2.648788015739081.34878801573908
641.5-2.662047926517944.16204792651794
652.51.046895738206591.45310426179341
66-2.23.32057431307783-5.52057431307783
671.7-1.745048784841113.44504878484111
685.71.187730431815234.51226956818477
692.76.68687256504994-3.98687256504994
70-4.84.32001685364052-9.12001685364052
71-3.1-5.438906275877662.33890627587766
72-0.5-5.787399748815525.28739974881552
73-3.4-1.87065030962276-1.52934969037724
74-4.7-3.60632332091516-1.09367667908484
75-5.6-5.44958046913921-0.150419530860789
76-1.7-6.65316113500044.9531611350004
77-1.8-2.12630075065230.326300750652299
78-5.4-0.899124301596575-4.50087569840342
79-4.8-5.019616845065470.219616845065471
80-2.8-5.556225381483222.75622538148322
81-4.9-3.12881716849068-1.77118283150932
82-6.8-4.75280008960027-2.04719991039973
83-7.6-7.38689182538354-0.213108174616464
84-6.6-8.745947544370842.14594754437084
85-5.6-7.512691016285571.91269101628557
86-1.4-5.699583052335714.29958305233571
870.1-0.4260496410625040.526049641062504
88-3.72.25864283440732-5.95864283440732
89-5.6-2.20605830351303-3.39394169648696
90-3.1-6.106114763769643.00611476376964
91-3.8-4.081350908854380.281350908854383
92-5.1-3.96467660986344-1.13532339013656
93-4.1-5.344398207277821.24439820727782
94-0.3-4.471269648397784.17126964839778
95-0.30.21186732543042-0.51186732543042
96-2.41.22379231867243-3.62379231867243

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8.4 & 35.3 & -26.9 \tabularnewline
4 & 7.8 & 34.1839465613008 & -26.3839465613008 \tabularnewline
5 & 4.8 & 23.0677500777428 & -18.2677500777428 \tabularnewline
6 & 3.5 & 10.7762837738573 & -7.27628377385727 \tabularnewline
7 & 8.7 & 3.76517709731999 & 4.93482290268001 \tabularnewline
8 & 6.8 & 7.74333405664098 & -0.943334056640976 \tabularnewline
9 & 6 & 6.99508761066271 & -0.995087610662706 \tabularnewline
10 & 3.6 & 5.8169140112281 & -2.2169140112281 \tabularnewline
11 & 8.7 & 2.86108663213023 & 5.83891336786977 \tabularnewline
12 & 8.9 & 8.17160743804776 & 0.728392561952241 \tabularnewline
13 & 8.1 & 9.98232470503944 & -1.88232470503944 \tabularnewline
14 & 7 & 9.11801077881871 & -2.11801077881871 \tabularnewline
15 & 7.9 & 7.24560451812751 & 0.654395481872487 \tabularnewline
16 & 8 & 7.68481728413225 & 0.315182715867746 \tabularnewline
17 & 7.5 & 7.99673311945576 & -0.496733119455757 \tabularnewline
18 & 6.3 & 7.51161999023741 & -1.21161999023741 \tabularnewline
19 & 7.6 & 6.02004857656986 & 1.57995142343014 \tabularnewline
20 & 8.4 & 7.21851647165496 & 1.18148352834504 \tabularnewline
21 & 6.8 & 8.58668751365616 & -1.78668751365616 \tabularnewline
22 & 8.8 & 7.05262091072994 & 1.74737908927006 \tabularnewline
23 & 8.7 & 8.82460130661836 & -0.124601306618358 \tabularnewline
24 & 8.7 & 9.16057966797437 & -0.460579667974372 \tabularnewline
25 & 7.4 & 9.06638296781257 & -1.66638296781257 \tabularnewline
26 & 2.8 & 7.42304667514372 & -4.62304667514372 \tabularnewline
27 & 4.8 & 1.76984730213691 & 3.03015269786308 \tabularnewline
28 & -21.1 & 2.97939398917111 & -24.0793939891711 \tabularnewline
29 & 8.5 & -25.3724158248961 & 33.8724158248961 \tabularnewline
30 & 9.4 & 2.54218617830264 & 6.85781382169736 \tabularnewline
31 & 1.8 & 13.1400484529445 & -11.3400484529445 \tabularnewline
32 & 4.8 & 5.79244279334235 & -0.992442793342351 \tabularnewline
33 & 5.8 & 5.72094272509767 & 0.0790572749023317 \tabularnewline
34 & 3.3 & 6.47443831832408 & -3.17443831832408 \tabularnewline
35 & -9 & 3.56819490500769 & -12.5681949050077 \tabularnewline
36 & -6 & -11.2437588676365 & 5.24375886763652 \tabularnewline
37 & -0.9 & -10.7951528148845 & 9.89515281488448 \tabularnewline
38 & -17.3 & -3.00638508861991 & -14.2936149113801 \tabularnewline
39 & -9.2 & -18.764082856964 & 9.56408285696403 \tabularnewline
40 & -8.1 & -13.0817525050184 & 4.98175250501838 \tabularnewline
41 & -20.9 & -8.83412083303867 & -12.0658791669613 \tabularnewline
42 & -14.6 & -21.9653650848174 & 7.36536508481738 \tabularnewline
43 & -13.9 & -17.8014156123331 & 3.90141561233307 \tabularnewline
44 & -20.8 & -14.668674277787 & -6.13132572221296 \tabularnewline
45 & -16.1 & -21.3820657649445 & 5.28206576494447 \tabularnewline
46 & -5 & -17.5605835328945 & 12.5605835328945 \tabularnewline
47 & -7.2 & -3.40358828366044 & -3.79641171633956 \tabularnewline
48 & -9.7 & -2.85960559739875 & -6.84039440260125 \tabularnewline
49 & -1.4 & -7.26274225326518 & 5.86274225326518 \tabularnewline
50 & 0.2 & 0.0530854496783766 & 0.146914550321623 \tabularnewline
51 & 2.6 & 3.19181090199407 & -0.591810901994071 \tabularnewline
52 & -4.8 & 5.55032031306388 & -10.3503203130639 \tabularnewline
53 & -6.2 & -3.39436168266452 & -2.80563831733548 \tabularnewline
54 & -2 & -7.85317356695798 & 5.85317356695798 \tabularnewline
55 & -0.8 & -3.59326824841678 & 2.79326824841678 \tabularnewline
56 & -3.1 & -0.501283788759041 & -2.59871621124096 \tabularnewline
57 & 0.6 & -2.42691110192493 & 3.02691110192493 \tabularnewline
58 & 0.2 & 1.00668307890293 & -0.806683078902933 \tabularnewline
59 & 0.3 & 1.28248567996138 & -0.982485679961383 \tabularnewline
60 & -0.1 & 1.04141097077758 & -1.14141097077758 \tabularnewline
61 & 4.3 & 0.233423955966735 & 4.06657604403326 \tabularnewline
62 & -3.2 & 4.88434873764017 & -8.08434873764017 \tabularnewline
63 & -1.3 & -2.64878801573908 & 1.34878801573908 \tabularnewline
64 & 1.5 & -2.66204792651794 & 4.16204792651794 \tabularnewline
65 & 2.5 & 1.04689573820659 & 1.45310426179341 \tabularnewline
66 & -2.2 & 3.32057431307783 & -5.52057431307783 \tabularnewline
67 & 1.7 & -1.74504878484111 & 3.44504878484111 \tabularnewline
68 & 5.7 & 1.18773043181523 & 4.51226956818477 \tabularnewline
69 & 2.7 & 6.68687256504994 & -3.98687256504994 \tabularnewline
70 & -4.8 & 4.32001685364052 & -9.12001685364052 \tabularnewline
71 & -3.1 & -5.43890627587766 & 2.33890627587766 \tabularnewline
72 & -0.5 & -5.78739974881552 & 5.28739974881552 \tabularnewline
73 & -3.4 & -1.87065030962276 & -1.52934969037724 \tabularnewline
74 & -4.7 & -3.60632332091516 & -1.09367667908484 \tabularnewline
75 & -5.6 & -5.44958046913921 & -0.150419530860789 \tabularnewline
76 & -1.7 & -6.6531611350004 & 4.9531611350004 \tabularnewline
77 & -1.8 & -2.1263007506523 & 0.326300750652299 \tabularnewline
78 & -5.4 & -0.899124301596575 & -4.50087569840342 \tabularnewline
79 & -4.8 & -5.01961684506547 & 0.219616845065471 \tabularnewline
80 & -2.8 & -5.55622538148322 & 2.75622538148322 \tabularnewline
81 & -4.9 & -3.12881716849068 & -1.77118283150932 \tabularnewline
82 & -6.8 & -4.75280008960027 & -2.04719991039973 \tabularnewline
83 & -7.6 & -7.38689182538354 & -0.213108174616464 \tabularnewline
84 & -6.6 & -8.74594754437084 & 2.14594754437084 \tabularnewline
85 & -5.6 & -7.51269101628557 & 1.91269101628557 \tabularnewline
86 & -1.4 & -5.69958305233571 & 4.29958305233571 \tabularnewline
87 & 0.1 & -0.426049641062504 & 0.526049641062504 \tabularnewline
88 & -3.7 & 2.25864283440732 & -5.95864283440732 \tabularnewline
89 & -5.6 & -2.20605830351303 & -3.39394169648696 \tabularnewline
90 & -3.1 & -6.10611476376964 & 3.00611476376964 \tabularnewline
91 & -3.8 & -4.08135090885438 & 0.281350908854383 \tabularnewline
92 & -5.1 & -3.96467660986344 & -1.13532339013656 \tabularnewline
93 & -4.1 & -5.34439820727782 & 1.24439820727782 \tabularnewline
94 & -0.3 & -4.47126964839778 & 4.17126964839778 \tabularnewline
95 & -0.3 & 0.21186732543042 & -0.51186732543042 \tabularnewline
96 & -2.4 & 1.22379231867243 & -3.62379231867243 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278535&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]3[/C][C]8.4[/C][C]35.3[/C][C]-26.9[/C][/ROW]
[ROW][C]4[/C][C]7.8[/C][C]34.1839465613008[/C][C]-26.3839465613008[/C][/ROW]
[ROW][C]5[/C][C]4.8[/C][C]23.0677500777428[/C][C]-18.2677500777428[/C][/ROW]
[ROW][C]6[/C][C]3.5[/C][C]10.7762837738573[/C][C]-7.27628377385727[/C][/ROW]
[ROW][C]7[/C][C]8.7[/C][C]3.76517709731999[/C][C]4.93482290268001[/C][/ROW]
[ROW][C]8[/C][C]6.8[/C][C]7.74333405664098[/C][C]-0.943334056640976[/C][/ROW]
[ROW][C]9[/C][C]6[/C][C]6.99508761066271[/C][C]-0.995087610662706[/C][/ROW]
[ROW][C]10[/C][C]3.6[/C][C]5.8169140112281[/C][C]-2.2169140112281[/C][/ROW]
[ROW][C]11[/C][C]8.7[/C][C]2.86108663213023[/C][C]5.83891336786977[/C][/ROW]
[ROW][C]12[/C][C]8.9[/C][C]8.17160743804776[/C][C]0.728392561952241[/C][/ROW]
[ROW][C]13[/C][C]8.1[/C][C]9.98232470503944[/C][C]-1.88232470503944[/C][/ROW]
[ROW][C]14[/C][C]7[/C][C]9.11801077881871[/C][C]-2.11801077881871[/C][/ROW]
[ROW][C]15[/C][C]7.9[/C][C]7.24560451812751[/C][C]0.654395481872487[/C][/ROW]
[ROW][C]16[/C][C]8[/C][C]7.68481728413225[/C][C]0.315182715867746[/C][/ROW]
[ROW][C]17[/C][C]7.5[/C][C]7.99673311945576[/C][C]-0.496733119455757[/C][/ROW]
[ROW][C]18[/C][C]6.3[/C][C]7.51161999023741[/C][C]-1.21161999023741[/C][/ROW]
[ROW][C]19[/C][C]7.6[/C][C]6.02004857656986[/C][C]1.57995142343014[/C][/ROW]
[ROW][C]20[/C][C]8.4[/C][C]7.21851647165496[/C][C]1.18148352834504[/C][/ROW]
[ROW][C]21[/C][C]6.8[/C][C]8.58668751365616[/C][C]-1.78668751365616[/C][/ROW]
[ROW][C]22[/C][C]8.8[/C][C]7.05262091072994[/C][C]1.74737908927006[/C][/ROW]
[ROW][C]23[/C][C]8.7[/C][C]8.82460130661836[/C][C]-0.124601306618358[/C][/ROW]
[ROW][C]24[/C][C]8.7[/C][C]9.16057966797437[/C][C]-0.460579667974372[/C][/ROW]
[ROW][C]25[/C][C]7.4[/C][C]9.06638296781257[/C][C]-1.66638296781257[/C][/ROW]
[ROW][C]26[/C][C]2.8[/C][C]7.42304667514372[/C][C]-4.62304667514372[/C][/ROW]
[ROW][C]27[/C][C]4.8[/C][C]1.76984730213691[/C][C]3.03015269786308[/C][/ROW]
[ROW][C]28[/C][C]-21.1[/C][C]2.97939398917111[/C][C]-24.0793939891711[/C][/ROW]
[ROW][C]29[/C][C]8.5[/C][C]-25.3724158248961[/C][C]33.8724158248961[/C][/ROW]
[ROW][C]30[/C][C]9.4[/C][C]2.54218617830264[/C][C]6.85781382169736[/C][/ROW]
[ROW][C]31[/C][C]1.8[/C][C]13.1400484529445[/C][C]-11.3400484529445[/C][/ROW]
[ROW][C]32[/C][C]4.8[/C][C]5.79244279334235[/C][C]-0.992442793342351[/C][/ROW]
[ROW][C]33[/C][C]5.8[/C][C]5.72094272509767[/C][C]0.0790572749023317[/C][/ROW]
[ROW][C]34[/C][C]3.3[/C][C]6.47443831832408[/C][C]-3.17443831832408[/C][/ROW]
[ROW][C]35[/C][C]-9[/C][C]3.56819490500769[/C][C]-12.5681949050077[/C][/ROW]
[ROW][C]36[/C][C]-6[/C][C]-11.2437588676365[/C][C]5.24375886763652[/C][/ROW]
[ROW][C]37[/C][C]-0.9[/C][C]-10.7951528148845[/C][C]9.89515281488448[/C][/ROW]
[ROW][C]38[/C][C]-17.3[/C][C]-3.00638508861991[/C][C]-14.2936149113801[/C][/ROW]
[ROW][C]39[/C][C]-9.2[/C][C]-18.764082856964[/C][C]9.56408285696403[/C][/ROW]
[ROW][C]40[/C][C]-8.1[/C][C]-13.0817525050184[/C][C]4.98175250501838[/C][/ROW]
[ROW][C]41[/C][C]-20.9[/C][C]-8.83412083303867[/C][C]-12.0658791669613[/C][/ROW]
[ROW][C]42[/C][C]-14.6[/C][C]-21.9653650848174[/C][C]7.36536508481738[/C][/ROW]
[ROW][C]43[/C][C]-13.9[/C][C]-17.8014156123331[/C][C]3.90141561233307[/C][/ROW]
[ROW][C]44[/C][C]-20.8[/C][C]-14.668674277787[/C][C]-6.13132572221296[/C][/ROW]
[ROW][C]45[/C][C]-16.1[/C][C]-21.3820657649445[/C][C]5.28206576494447[/C][/ROW]
[ROW][C]46[/C][C]-5[/C][C]-17.5605835328945[/C][C]12.5605835328945[/C][/ROW]
[ROW][C]47[/C][C]-7.2[/C][C]-3.40358828366044[/C][C]-3.79641171633956[/C][/ROW]
[ROW][C]48[/C][C]-9.7[/C][C]-2.85960559739875[/C][C]-6.84039440260125[/C][/ROW]
[ROW][C]49[/C][C]-1.4[/C][C]-7.26274225326518[/C][C]5.86274225326518[/C][/ROW]
[ROW][C]50[/C][C]0.2[/C][C]0.0530854496783766[/C][C]0.146914550321623[/C][/ROW]
[ROW][C]51[/C][C]2.6[/C][C]3.19181090199407[/C][C]-0.591810901994071[/C][/ROW]
[ROW][C]52[/C][C]-4.8[/C][C]5.55032031306388[/C][C]-10.3503203130639[/C][/ROW]
[ROW][C]53[/C][C]-6.2[/C][C]-3.39436168266452[/C][C]-2.80563831733548[/C][/ROW]
[ROW][C]54[/C][C]-2[/C][C]-7.85317356695798[/C][C]5.85317356695798[/C][/ROW]
[ROW][C]55[/C][C]-0.8[/C][C]-3.59326824841678[/C][C]2.79326824841678[/C][/ROW]
[ROW][C]56[/C][C]-3.1[/C][C]-0.501283788759041[/C][C]-2.59871621124096[/C][/ROW]
[ROW][C]57[/C][C]0.6[/C][C]-2.42691110192493[/C][C]3.02691110192493[/C][/ROW]
[ROW][C]58[/C][C]0.2[/C][C]1.00668307890293[/C][C]-0.806683078902933[/C][/ROW]
[ROW][C]59[/C][C]0.3[/C][C]1.28248567996138[/C][C]-0.982485679961383[/C][/ROW]
[ROW][C]60[/C][C]-0.1[/C][C]1.04141097077758[/C][C]-1.14141097077758[/C][/ROW]
[ROW][C]61[/C][C]4.3[/C][C]0.233423955966735[/C][C]4.06657604403326[/C][/ROW]
[ROW][C]62[/C][C]-3.2[/C][C]4.88434873764017[/C][C]-8.08434873764017[/C][/ROW]
[ROW][C]63[/C][C]-1.3[/C][C]-2.64878801573908[/C][C]1.34878801573908[/C][/ROW]
[ROW][C]64[/C][C]1.5[/C][C]-2.66204792651794[/C][C]4.16204792651794[/C][/ROW]
[ROW][C]65[/C][C]2.5[/C][C]1.04689573820659[/C][C]1.45310426179341[/C][/ROW]
[ROW][C]66[/C][C]-2.2[/C][C]3.32057431307783[/C][C]-5.52057431307783[/C][/ROW]
[ROW][C]67[/C][C]1.7[/C][C]-1.74504878484111[/C][C]3.44504878484111[/C][/ROW]
[ROW][C]68[/C][C]5.7[/C][C]1.18773043181523[/C][C]4.51226956818477[/C][/ROW]
[ROW][C]69[/C][C]2.7[/C][C]6.68687256504994[/C][C]-3.98687256504994[/C][/ROW]
[ROW][C]70[/C][C]-4.8[/C][C]4.32001685364052[/C][C]-9.12001685364052[/C][/ROW]
[ROW][C]71[/C][C]-3.1[/C][C]-5.43890627587766[/C][C]2.33890627587766[/C][/ROW]
[ROW][C]72[/C][C]-0.5[/C][C]-5.78739974881552[/C][C]5.28739974881552[/C][/ROW]
[ROW][C]73[/C][C]-3.4[/C][C]-1.87065030962276[/C][C]-1.52934969037724[/C][/ROW]
[ROW][C]74[/C][C]-4.7[/C][C]-3.60632332091516[/C][C]-1.09367667908484[/C][/ROW]
[ROW][C]75[/C][C]-5.6[/C][C]-5.44958046913921[/C][C]-0.150419530860789[/C][/ROW]
[ROW][C]76[/C][C]-1.7[/C][C]-6.6531611350004[/C][C]4.9531611350004[/C][/ROW]
[ROW][C]77[/C][C]-1.8[/C][C]-2.1263007506523[/C][C]0.326300750652299[/C][/ROW]
[ROW][C]78[/C][C]-5.4[/C][C]-0.899124301596575[/C][C]-4.50087569840342[/C][/ROW]
[ROW][C]79[/C][C]-4.8[/C][C]-5.01961684506547[/C][C]0.219616845065471[/C][/ROW]
[ROW][C]80[/C][C]-2.8[/C][C]-5.55622538148322[/C][C]2.75622538148322[/C][/ROW]
[ROW][C]81[/C][C]-4.9[/C][C]-3.12881716849068[/C][C]-1.77118283150932[/C][/ROW]
[ROW][C]82[/C][C]-6.8[/C][C]-4.75280008960027[/C][C]-2.04719991039973[/C][/ROW]
[ROW][C]83[/C][C]-7.6[/C][C]-7.38689182538354[/C][C]-0.213108174616464[/C][/ROW]
[ROW][C]84[/C][C]-6.6[/C][C]-8.74594754437084[/C][C]2.14594754437084[/C][/ROW]
[ROW][C]85[/C][C]-5.6[/C][C]-7.51269101628557[/C][C]1.91269101628557[/C][/ROW]
[ROW][C]86[/C][C]-1.4[/C][C]-5.69958305233571[/C][C]4.29958305233571[/C][/ROW]
[ROW][C]87[/C][C]0.1[/C][C]-0.426049641062504[/C][C]0.526049641062504[/C][/ROW]
[ROW][C]88[/C][C]-3.7[/C][C]2.25864283440732[/C][C]-5.95864283440732[/C][/ROW]
[ROW][C]89[/C][C]-5.6[/C][C]-2.20605830351303[/C][C]-3.39394169648696[/C][/ROW]
[ROW][C]90[/C][C]-3.1[/C][C]-6.10611476376964[/C][C]3.00611476376964[/C][/ROW]
[ROW][C]91[/C][C]-3.8[/C][C]-4.08135090885438[/C][C]0.281350908854383[/C][/ROW]
[ROW][C]92[/C][C]-5.1[/C][C]-3.96467660986344[/C][C]-1.13532339013656[/C][/ROW]
[ROW][C]93[/C][C]-4.1[/C][C]-5.34439820727782[/C][C]1.24439820727782[/C][/ROW]
[ROW][C]94[/C][C]-0.3[/C][C]-4.47126964839778[/C][C]4.17126964839778[/C][/ROW]
[ROW][C]95[/C][C]-0.3[/C][C]0.21186732543042[/C][C]-0.51186732543042[/C][/ROW]
[ROW][C]96[/C][C]-2.4[/C][C]1.22379231867243[/C][C]-3.62379231867243[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278535&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278535&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
38.435.3-26.9
47.834.1839465613008-26.3839465613008
54.823.0677500777428-18.2677500777428
63.510.7762837738573-7.27628377385727
78.73.765177097319994.93482290268001
86.87.74333405664098-0.943334056640976
966.99508761066271-0.995087610662706
103.65.8169140112281-2.2169140112281
118.72.861086632130235.83891336786977
128.98.171607438047760.728392561952241
138.19.98232470503944-1.88232470503944
1479.11801077881871-2.11801077881871
157.97.245604518127510.654395481872487
1687.684817284132250.315182715867746
177.57.99673311945576-0.496733119455757
186.37.51161999023741-1.21161999023741
197.66.020048576569861.57995142343014
208.47.218516471654961.18148352834504
216.88.58668751365616-1.78668751365616
228.87.052620910729941.74737908927006
238.78.82460130661836-0.124601306618358
248.79.16057966797437-0.460579667974372
257.49.06638296781257-1.66638296781257
262.87.42304667514372-4.62304667514372
274.81.769847302136913.03015269786308
28-21.12.97939398917111-24.0793939891711
298.5-25.372415824896133.8724158248961
309.42.542186178302646.85781382169736
311.813.1400484529445-11.3400484529445
324.85.79244279334235-0.992442793342351
335.85.720942725097670.0790572749023317
343.36.47443831832408-3.17443831832408
35-93.56819490500769-12.5681949050077
36-6-11.24375886763655.24375886763652
37-0.9-10.79515281488459.89515281488448
38-17.3-3.00638508861991-14.2936149113801
39-9.2-18.7640828569649.56408285696403
40-8.1-13.08175250501844.98175250501838
41-20.9-8.83412083303867-12.0658791669613
42-14.6-21.96536508481747.36536508481738
43-13.9-17.80141561233313.90141561233307
44-20.8-14.668674277787-6.13132572221296
45-16.1-21.38206576494455.28206576494447
46-5-17.560583532894512.5605835328945
47-7.2-3.40358828366044-3.79641171633956
48-9.7-2.85960559739875-6.84039440260125
49-1.4-7.262742253265185.86274225326518
500.20.05308544967837660.146914550321623
512.63.19181090199407-0.591810901994071
52-4.85.55032031306388-10.3503203130639
53-6.2-3.39436168266452-2.80563831733548
54-2-7.853173566957985.85317356695798
55-0.8-3.593268248416782.79326824841678
56-3.1-0.501283788759041-2.59871621124096
570.6-2.426911101924933.02691110192493
580.21.00668307890293-0.806683078902933
590.31.28248567996138-0.982485679961383
60-0.11.04141097077758-1.14141097077758
614.30.2334239559667354.06657604403326
62-3.24.88434873764017-8.08434873764017
63-1.3-2.648788015739081.34878801573908
641.5-2.662047926517944.16204792651794
652.51.046895738206591.45310426179341
66-2.23.32057431307783-5.52057431307783
671.7-1.745048784841113.44504878484111
685.71.187730431815234.51226956818477
692.76.68687256504994-3.98687256504994
70-4.84.32001685364052-9.12001685364052
71-3.1-5.438906275877662.33890627587766
72-0.5-5.787399748815525.28739974881552
73-3.4-1.87065030962276-1.52934969037724
74-4.7-3.60632332091516-1.09367667908484
75-5.6-5.44958046913921-0.150419530860789
76-1.7-6.65316113500044.9531611350004
77-1.8-2.12630075065230.326300750652299
78-5.4-0.899124301596575-4.50087569840342
79-4.8-5.019616845065470.219616845065471
80-2.8-5.556225381483222.75622538148322
81-4.9-3.12881716849068-1.77118283150932
82-6.8-4.75280008960027-2.04719991039973
83-7.6-7.38689182538354-0.213108174616464
84-6.6-8.745947544370842.14594754437084
85-5.6-7.512691016285571.91269101628557
86-1.4-5.699583052335714.29958305233571
870.1-0.4260496410625040.526049641062504
88-3.72.25864283440732-5.95864283440732
89-5.6-2.20605830351303-3.39394169648696
90-3.1-6.106114763769643.00611476376964
91-3.8-4.081350908854380.281350908854383
92-5.1-3.96467660986344-1.13532339013656
93-4.1-5.344398207277821.24439820727782
94-0.3-4.471269648397784.17126964839778
95-0.30.21186732543042-0.51186732543042
96-2.41.22379231867243-3.62379231867243







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97-1.4959583553049-16.668517852240913.6766011416311
98-1.53080411003675-24.475616490457321.4140082703838
99-1.5656498647686-34.183217409400131.0519176798629
100-1.60049561950045-45.347809592014442.1468183530135
101-1.63534137423229-57.73816432522154.4674815767564
102-1.67018712896414-71.21370248707267.8733282291438
103-1.70503288369599-85.677920542415182.2678547750231
104-1.73987863842784-101.05885854290297.5791012660464
105-1.77472439315968-117.299783479844113.750334693524
106-1.80957014789153-134.354209462151130.735069166368
107-1.84441590262338-152.182977812785148.494146007538
108-1.87926165735523-170.752414235972166.993890921261

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & -1.4959583553049 & -16.6685178522409 & 13.6766011416311 \tabularnewline
98 & -1.53080411003675 & -24.4756164904573 & 21.4140082703838 \tabularnewline
99 & -1.5656498647686 & -34.1832174094001 & 31.0519176798629 \tabularnewline
100 & -1.60049561950045 & -45.3478095920144 & 42.1468183530135 \tabularnewline
101 & -1.63534137423229 & -57.738164325221 & 54.4674815767564 \tabularnewline
102 & -1.67018712896414 & -71.213702487072 & 67.8733282291438 \tabularnewline
103 & -1.70503288369599 & -85.6779205424151 & 82.2678547750231 \tabularnewline
104 & -1.73987863842784 & -101.058858542902 & 97.5791012660464 \tabularnewline
105 & -1.77472439315968 & -117.299783479844 & 113.750334693524 \tabularnewline
106 & -1.80957014789153 & -134.354209462151 & 130.735069166368 \tabularnewline
107 & -1.84441590262338 & -152.182977812785 & 148.494146007538 \tabularnewline
108 & -1.87926165735523 & -170.752414235972 & 166.993890921261 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278535&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]97[/C][C]-1.4959583553049[/C][C]-16.6685178522409[/C][C]13.6766011416311[/C][/ROW]
[ROW][C]98[/C][C]-1.53080411003675[/C][C]-24.4756164904573[/C][C]21.4140082703838[/C][/ROW]
[ROW][C]99[/C][C]-1.5656498647686[/C][C]-34.1832174094001[/C][C]31.0519176798629[/C][/ROW]
[ROW][C]100[/C][C]-1.60049561950045[/C][C]-45.3478095920144[/C][C]42.1468183530135[/C][/ROW]
[ROW][C]101[/C][C]-1.63534137423229[/C][C]-57.738164325221[/C][C]54.4674815767564[/C][/ROW]
[ROW][C]102[/C][C]-1.67018712896414[/C][C]-71.213702487072[/C][C]67.8733282291438[/C][/ROW]
[ROW][C]103[/C][C]-1.70503288369599[/C][C]-85.6779205424151[/C][C]82.2678547750231[/C][/ROW]
[ROW][C]104[/C][C]-1.73987863842784[/C][C]-101.058858542902[/C][C]97.5791012660464[/C][/ROW]
[ROW][C]105[/C][C]-1.77472439315968[/C][C]-117.299783479844[/C][C]113.750334693524[/C][/ROW]
[ROW][C]106[/C][C]-1.80957014789153[/C][C]-134.354209462151[/C][C]130.735069166368[/C][/ROW]
[ROW][C]107[/C][C]-1.84441590262338[/C][C]-152.182977812785[/C][C]148.494146007538[/C][/ROW]
[ROW][C]108[/C][C]-1.87926165735523[/C][C]-170.752414235972[/C][C]166.993890921261[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278535&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278535&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
97-1.4959583553049-16.668517852240913.6766011416311
98-1.53080411003675-24.475616490457321.4140082703838
99-1.5656498647686-34.183217409400131.0519176798629
100-1.60049561950045-45.347809592014442.1468183530135
101-1.63534137423229-57.73816432522154.4674815767564
102-1.67018712896414-71.21370248707267.8733282291438
103-1.70503288369599-85.677920542415182.2678547750231
104-1.73987863842784-101.05885854290297.5791012660464
105-1.77472439315968-117.299783479844113.750334693524
106-1.80957014789153-134.354209462151130.735069166368
107-1.84441590262338-152.182977812785148.494146007538
108-1.87926165735523-170.752414235972166.993890921261



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')