Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 24 May 2016 18:48:56 +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/2016/May/24/t1464112157mrffvt25xre9w9g.htm/, Retrieved Wed, 08 May 2024 04:09:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295578, Retrieved Wed, 08 May 2024 04:09:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2016-04-25 16:29:08] [9dd841f4e56c9b98fc9b2251347c7b43]
- R PD    [Exponential Smoothing] [] [2016-05-24 17:48:56] [e1772292a6a44abe5991636299c33e7e] [Current]
Feedback Forum

Post a new message
Dataseries X:
92,8
92,9
93,06
93,28
93,41
93,49
93,49
93,5
93,56
94,12
94,3
94,36
94,36
94,5
94,85
95,16
95,73
95,76
95,76
95,81
96,09
96,48
96,71
96,69
96,69
96,66
96,73
96,84
97,87
98
97,98
98,03
98,11
98,18
98,32
98,34
98,28
98,52
98,56
99,6
100,16
100,46
100,46
100,68
100,83
100,64
100,9
100,92
100,75
100,96
101,05
101,33
101,38
101,44
101,51
101,4
101,26
100,83
100,75
100,81
100,82
100,85
100,79
100,84
101,04
101,11
101,15
101,11
101,28
101,62
102,07
102,14




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=295578&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=295578&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295578&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
alpha1
beta0.00307840933722774
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00307840933722774 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295578&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.00307840933722774[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295578&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295578&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.00307840933722774
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
393.06930.0599999999999881
493.2893.16018470456030.11981529543975
593.4193.38055354508450.0294464549155293
693.4993.5106441933262-0.020644193326234
793.4993.5905806420487-0.100580642048726
893.593.5902710136611-0.0902710136610949
993.5693.5999931225298-0.0399931225297649
1094.1293.6598700073280.460129992672051
1194.394.22128647579370.0787135242062647
1294.3694.4015287882416-0.0415287882416067
1394.3694.4614009456321-0.101400945632122
1494.594.46108879201430.0389112079857199
1594.8594.60120857664030.248791423359719
1695.1694.9519744584810.208025541519035
1795.7395.26261484625040.467385153749646
1895.7695.8340536490717-0.0740536490717432
1995.7695.863825681627-0.103825681626986
2095.8195.8635060636792-0.0535060636792224
2196.0995.91334135011320.176658649886804
2296.4896.19388517775050.286114822249488
2396.7196.58476595629080.125234043709156
2496.6996.8151514779403-0.125151477940335
2596.6996.7947662104621-0.104766210462074
2696.6696.7944436971816-0.134443697181567
2796.7396.7640298244488-0.0340298244488224
2896.8496.83392506671950.00607493328050168
2997.8796.94394376785080.926056232149165
309897.97679454800270.0232054519973133
3197.9898.1068659838828-0.12686598388278
3298.0398.0864754384534-0.0564754384534183
3398.1198.1363015839364-0.026301583936359
3498.1898.2162206168948-0.0362206168947807
3598.3298.28610911500950.0338908849904556
3698.3498.4262134450263-0.0862134450263312
3798.2898.4459480447522-0.165948044752184
3898.5298.38543718874170.134562811258277
3998.5698.6258514281563-0.0658514281563356
4099.698.6656487105050.934351289494955
41100.1699.70852502623890.451474973761137
42100.46100.2699148510140.190085148986384
43100.46100.570500010911-0.110500010911124
44100.68100.5701598466460.109840153354241
45100.83100.7904979795990.0395020204005334
46100.64100.940619582988-0.300619582987892
47100.9100.7496941528570.150305847143329
48100.92101.01015685578-0.0901568557799663
49100.75101.029879316073-0.27987931607332
50100.96100.8590177329730.100982267026581
51101.05101.069328597727-0.0193285977271245
52101.33101.1592690963910.1707309036086
53101.38101.439794675999-0.0597946759992283
54101.44101.48961060351-0.0496106035103168
55101.51101.549457881765-0.0394578817652302
56101.4101.619336414254-0.21933641425359
57101.26101.508661206988-0.248661206987961
58100.83101.367895726007-0.537895726006568
59100.75100.936239862781-0.186239862781164
60100.81100.855666540249-0.045666540248618
61100.82100.915525959945-0.0955259599447231
62100.85100.925231891938-0.0752318919376762
63100.79100.955000297379-0.165000297379066
64100.84100.894492358923-0.0544923589229853
65101.04100.9443246091360.0956753908635335
66101.11101.144619137153-0.0346191371530438
67101.15101.214512565278-0.0645125652779797
68101.11101.254313969195-0.14431396919467
69101.28101.2138697117240.0661302882756019
70101.62101.3840732878210.235926712178696
71102.07101.7247995668150.345200433185013
72102.14102.175862235052-0.0358622350516953

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 93.06 & 93 & 0.0599999999999881 \tabularnewline
4 & 93.28 & 93.1601847045603 & 0.11981529543975 \tabularnewline
5 & 93.41 & 93.3805535450845 & 0.0294464549155293 \tabularnewline
6 & 93.49 & 93.5106441933262 & -0.020644193326234 \tabularnewline
7 & 93.49 & 93.5905806420487 & -0.100580642048726 \tabularnewline
8 & 93.5 & 93.5902710136611 & -0.0902710136610949 \tabularnewline
9 & 93.56 & 93.5999931225298 & -0.0399931225297649 \tabularnewline
10 & 94.12 & 93.659870007328 & 0.460129992672051 \tabularnewline
11 & 94.3 & 94.2212864757937 & 0.0787135242062647 \tabularnewline
12 & 94.36 & 94.4015287882416 & -0.0415287882416067 \tabularnewline
13 & 94.36 & 94.4614009456321 & -0.101400945632122 \tabularnewline
14 & 94.5 & 94.4610887920143 & 0.0389112079857199 \tabularnewline
15 & 94.85 & 94.6012085766403 & 0.248791423359719 \tabularnewline
16 & 95.16 & 94.951974458481 & 0.208025541519035 \tabularnewline
17 & 95.73 & 95.2626148462504 & 0.467385153749646 \tabularnewline
18 & 95.76 & 95.8340536490717 & -0.0740536490717432 \tabularnewline
19 & 95.76 & 95.863825681627 & -0.103825681626986 \tabularnewline
20 & 95.81 & 95.8635060636792 & -0.0535060636792224 \tabularnewline
21 & 96.09 & 95.9133413501132 & 0.176658649886804 \tabularnewline
22 & 96.48 & 96.1938851777505 & 0.286114822249488 \tabularnewline
23 & 96.71 & 96.5847659562908 & 0.125234043709156 \tabularnewline
24 & 96.69 & 96.8151514779403 & -0.125151477940335 \tabularnewline
25 & 96.69 & 96.7947662104621 & -0.104766210462074 \tabularnewline
26 & 96.66 & 96.7944436971816 & -0.134443697181567 \tabularnewline
27 & 96.73 & 96.7640298244488 & -0.0340298244488224 \tabularnewline
28 & 96.84 & 96.8339250667195 & 0.00607493328050168 \tabularnewline
29 & 97.87 & 96.9439437678508 & 0.926056232149165 \tabularnewline
30 & 98 & 97.9767945480027 & 0.0232054519973133 \tabularnewline
31 & 97.98 & 98.1068659838828 & -0.12686598388278 \tabularnewline
32 & 98.03 & 98.0864754384534 & -0.0564754384534183 \tabularnewline
33 & 98.11 & 98.1363015839364 & -0.026301583936359 \tabularnewline
34 & 98.18 & 98.2162206168948 & -0.0362206168947807 \tabularnewline
35 & 98.32 & 98.2861091150095 & 0.0338908849904556 \tabularnewline
36 & 98.34 & 98.4262134450263 & -0.0862134450263312 \tabularnewline
37 & 98.28 & 98.4459480447522 & -0.165948044752184 \tabularnewline
38 & 98.52 & 98.3854371887417 & 0.134562811258277 \tabularnewline
39 & 98.56 & 98.6258514281563 & -0.0658514281563356 \tabularnewline
40 & 99.6 & 98.665648710505 & 0.934351289494955 \tabularnewline
41 & 100.16 & 99.7085250262389 & 0.451474973761137 \tabularnewline
42 & 100.46 & 100.269914851014 & 0.190085148986384 \tabularnewline
43 & 100.46 & 100.570500010911 & -0.110500010911124 \tabularnewline
44 & 100.68 & 100.570159846646 & 0.109840153354241 \tabularnewline
45 & 100.83 & 100.790497979599 & 0.0395020204005334 \tabularnewline
46 & 100.64 & 100.940619582988 & -0.300619582987892 \tabularnewline
47 & 100.9 & 100.749694152857 & 0.150305847143329 \tabularnewline
48 & 100.92 & 101.01015685578 & -0.0901568557799663 \tabularnewline
49 & 100.75 & 101.029879316073 & -0.27987931607332 \tabularnewline
50 & 100.96 & 100.859017732973 & 0.100982267026581 \tabularnewline
51 & 101.05 & 101.069328597727 & -0.0193285977271245 \tabularnewline
52 & 101.33 & 101.159269096391 & 0.1707309036086 \tabularnewline
53 & 101.38 & 101.439794675999 & -0.0597946759992283 \tabularnewline
54 & 101.44 & 101.48961060351 & -0.0496106035103168 \tabularnewline
55 & 101.51 & 101.549457881765 & -0.0394578817652302 \tabularnewline
56 & 101.4 & 101.619336414254 & -0.21933641425359 \tabularnewline
57 & 101.26 & 101.508661206988 & -0.248661206987961 \tabularnewline
58 & 100.83 & 101.367895726007 & -0.537895726006568 \tabularnewline
59 & 100.75 & 100.936239862781 & -0.186239862781164 \tabularnewline
60 & 100.81 & 100.855666540249 & -0.045666540248618 \tabularnewline
61 & 100.82 & 100.915525959945 & -0.0955259599447231 \tabularnewline
62 & 100.85 & 100.925231891938 & -0.0752318919376762 \tabularnewline
63 & 100.79 & 100.955000297379 & -0.165000297379066 \tabularnewline
64 & 100.84 & 100.894492358923 & -0.0544923589229853 \tabularnewline
65 & 101.04 & 100.944324609136 & 0.0956753908635335 \tabularnewline
66 & 101.11 & 101.144619137153 & -0.0346191371530438 \tabularnewline
67 & 101.15 & 101.214512565278 & -0.0645125652779797 \tabularnewline
68 & 101.11 & 101.254313969195 & -0.14431396919467 \tabularnewline
69 & 101.28 & 101.213869711724 & 0.0661302882756019 \tabularnewline
70 & 101.62 & 101.384073287821 & 0.235926712178696 \tabularnewline
71 & 102.07 & 101.724799566815 & 0.345200433185013 \tabularnewline
72 & 102.14 & 102.175862235052 & -0.0358622350516953 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295578&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]93.06[/C][C]93[/C][C]0.0599999999999881[/C][/ROW]
[ROW][C]4[/C][C]93.28[/C][C]93.1601847045603[/C][C]0.11981529543975[/C][/ROW]
[ROW][C]5[/C][C]93.41[/C][C]93.3805535450845[/C][C]0.0294464549155293[/C][/ROW]
[ROW][C]6[/C][C]93.49[/C][C]93.5106441933262[/C][C]-0.020644193326234[/C][/ROW]
[ROW][C]7[/C][C]93.49[/C][C]93.5905806420487[/C][C]-0.100580642048726[/C][/ROW]
[ROW][C]8[/C][C]93.5[/C][C]93.5902710136611[/C][C]-0.0902710136610949[/C][/ROW]
[ROW][C]9[/C][C]93.56[/C][C]93.5999931225298[/C][C]-0.0399931225297649[/C][/ROW]
[ROW][C]10[/C][C]94.12[/C][C]93.659870007328[/C][C]0.460129992672051[/C][/ROW]
[ROW][C]11[/C][C]94.3[/C][C]94.2212864757937[/C][C]0.0787135242062647[/C][/ROW]
[ROW][C]12[/C][C]94.36[/C][C]94.4015287882416[/C][C]-0.0415287882416067[/C][/ROW]
[ROW][C]13[/C][C]94.36[/C][C]94.4614009456321[/C][C]-0.101400945632122[/C][/ROW]
[ROW][C]14[/C][C]94.5[/C][C]94.4610887920143[/C][C]0.0389112079857199[/C][/ROW]
[ROW][C]15[/C][C]94.85[/C][C]94.6012085766403[/C][C]0.248791423359719[/C][/ROW]
[ROW][C]16[/C][C]95.16[/C][C]94.951974458481[/C][C]0.208025541519035[/C][/ROW]
[ROW][C]17[/C][C]95.73[/C][C]95.2626148462504[/C][C]0.467385153749646[/C][/ROW]
[ROW][C]18[/C][C]95.76[/C][C]95.8340536490717[/C][C]-0.0740536490717432[/C][/ROW]
[ROW][C]19[/C][C]95.76[/C][C]95.863825681627[/C][C]-0.103825681626986[/C][/ROW]
[ROW][C]20[/C][C]95.81[/C][C]95.8635060636792[/C][C]-0.0535060636792224[/C][/ROW]
[ROW][C]21[/C][C]96.09[/C][C]95.9133413501132[/C][C]0.176658649886804[/C][/ROW]
[ROW][C]22[/C][C]96.48[/C][C]96.1938851777505[/C][C]0.286114822249488[/C][/ROW]
[ROW][C]23[/C][C]96.71[/C][C]96.5847659562908[/C][C]0.125234043709156[/C][/ROW]
[ROW][C]24[/C][C]96.69[/C][C]96.8151514779403[/C][C]-0.125151477940335[/C][/ROW]
[ROW][C]25[/C][C]96.69[/C][C]96.7947662104621[/C][C]-0.104766210462074[/C][/ROW]
[ROW][C]26[/C][C]96.66[/C][C]96.7944436971816[/C][C]-0.134443697181567[/C][/ROW]
[ROW][C]27[/C][C]96.73[/C][C]96.7640298244488[/C][C]-0.0340298244488224[/C][/ROW]
[ROW][C]28[/C][C]96.84[/C][C]96.8339250667195[/C][C]0.00607493328050168[/C][/ROW]
[ROW][C]29[/C][C]97.87[/C][C]96.9439437678508[/C][C]0.926056232149165[/C][/ROW]
[ROW][C]30[/C][C]98[/C][C]97.9767945480027[/C][C]0.0232054519973133[/C][/ROW]
[ROW][C]31[/C][C]97.98[/C][C]98.1068659838828[/C][C]-0.12686598388278[/C][/ROW]
[ROW][C]32[/C][C]98.03[/C][C]98.0864754384534[/C][C]-0.0564754384534183[/C][/ROW]
[ROW][C]33[/C][C]98.11[/C][C]98.1363015839364[/C][C]-0.026301583936359[/C][/ROW]
[ROW][C]34[/C][C]98.18[/C][C]98.2162206168948[/C][C]-0.0362206168947807[/C][/ROW]
[ROW][C]35[/C][C]98.32[/C][C]98.2861091150095[/C][C]0.0338908849904556[/C][/ROW]
[ROW][C]36[/C][C]98.34[/C][C]98.4262134450263[/C][C]-0.0862134450263312[/C][/ROW]
[ROW][C]37[/C][C]98.28[/C][C]98.4459480447522[/C][C]-0.165948044752184[/C][/ROW]
[ROW][C]38[/C][C]98.52[/C][C]98.3854371887417[/C][C]0.134562811258277[/C][/ROW]
[ROW][C]39[/C][C]98.56[/C][C]98.6258514281563[/C][C]-0.0658514281563356[/C][/ROW]
[ROW][C]40[/C][C]99.6[/C][C]98.665648710505[/C][C]0.934351289494955[/C][/ROW]
[ROW][C]41[/C][C]100.16[/C][C]99.7085250262389[/C][C]0.451474973761137[/C][/ROW]
[ROW][C]42[/C][C]100.46[/C][C]100.269914851014[/C][C]0.190085148986384[/C][/ROW]
[ROW][C]43[/C][C]100.46[/C][C]100.570500010911[/C][C]-0.110500010911124[/C][/ROW]
[ROW][C]44[/C][C]100.68[/C][C]100.570159846646[/C][C]0.109840153354241[/C][/ROW]
[ROW][C]45[/C][C]100.83[/C][C]100.790497979599[/C][C]0.0395020204005334[/C][/ROW]
[ROW][C]46[/C][C]100.64[/C][C]100.940619582988[/C][C]-0.300619582987892[/C][/ROW]
[ROW][C]47[/C][C]100.9[/C][C]100.749694152857[/C][C]0.150305847143329[/C][/ROW]
[ROW][C]48[/C][C]100.92[/C][C]101.01015685578[/C][C]-0.0901568557799663[/C][/ROW]
[ROW][C]49[/C][C]100.75[/C][C]101.029879316073[/C][C]-0.27987931607332[/C][/ROW]
[ROW][C]50[/C][C]100.96[/C][C]100.859017732973[/C][C]0.100982267026581[/C][/ROW]
[ROW][C]51[/C][C]101.05[/C][C]101.069328597727[/C][C]-0.0193285977271245[/C][/ROW]
[ROW][C]52[/C][C]101.33[/C][C]101.159269096391[/C][C]0.1707309036086[/C][/ROW]
[ROW][C]53[/C][C]101.38[/C][C]101.439794675999[/C][C]-0.0597946759992283[/C][/ROW]
[ROW][C]54[/C][C]101.44[/C][C]101.48961060351[/C][C]-0.0496106035103168[/C][/ROW]
[ROW][C]55[/C][C]101.51[/C][C]101.549457881765[/C][C]-0.0394578817652302[/C][/ROW]
[ROW][C]56[/C][C]101.4[/C][C]101.619336414254[/C][C]-0.21933641425359[/C][/ROW]
[ROW][C]57[/C][C]101.26[/C][C]101.508661206988[/C][C]-0.248661206987961[/C][/ROW]
[ROW][C]58[/C][C]100.83[/C][C]101.367895726007[/C][C]-0.537895726006568[/C][/ROW]
[ROW][C]59[/C][C]100.75[/C][C]100.936239862781[/C][C]-0.186239862781164[/C][/ROW]
[ROW][C]60[/C][C]100.81[/C][C]100.855666540249[/C][C]-0.045666540248618[/C][/ROW]
[ROW][C]61[/C][C]100.82[/C][C]100.915525959945[/C][C]-0.0955259599447231[/C][/ROW]
[ROW][C]62[/C][C]100.85[/C][C]100.925231891938[/C][C]-0.0752318919376762[/C][/ROW]
[ROW][C]63[/C][C]100.79[/C][C]100.955000297379[/C][C]-0.165000297379066[/C][/ROW]
[ROW][C]64[/C][C]100.84[/C][C]100.894492358923[/C][C]-0.0544923589229853[/C][/ROW]
[ROW][C]65[/C][C]101.04[/C][C]100.944324609136[/C][C]0.0956753908635335[/C][/ROW]
[ROW][C]66[/C][C]101.11[/C][C]101.144619137153[/C][C]-0.0346191371530438[/C][/ROW]
[ROW][C]67[/C][C]101.15[/C][C]101.214512565278[/C][C]-0.0645125652779797[/C][/ROW]
[ROW][C]68[/C][C]101.11[/C][C]101.254313969195[/C][C]-0.14431396919467[/C][/ROW]
[ROW][C]69[/C][C]101.28[/C][C]101.213869711724[/C][C]0.0661302882756019[/C][/ROW]
[ROW][C]70[/C][C]101.62[/C][C]101.384073287821[/C][C]0.235926712178696[/C][/ROW]
[ROW][C]71[/C][C]102.07[/C][C]101.724799566815[/C][C]0.345200433185013[/C][/ROW]
[ROW][C]72[/C][C]102.14[/C][C]102.175862235052[/C][C]-0.0358622350516953[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295578&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295578&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
393.06930.0599999999999881
493.2893.16018470456030.11981529543975
593.4193.38055354508450.0294464549155293
693.4993.5106441933262-0.020644193326234
793.4993.5905806420487-0.100580642048726
893.593.5902710136611-0.0902710136610949
993.5693.5999931225298-0.0399931225297649
1094.1293.6598700073280.460129992672051
1194.394.22128647579370.0787135242062647
1294.3694.4015287882416-0.0415287882416067
1394.3694.4614009456321-0.101400945632122
1494.594.46108879201430.0389112079857199
1594.8594.60120857664030.248791423359719
1695.1694.9519744584810.208025541519035
1795.7395.26261484625040.467385153749646
1895.7695.8340536490717-0.0740536490717432
1995.7695.863825681627-0.103825681626986
2095.8195.8635060636792-0.0535060636792224
2196.0995.91334135011320.176658649886804
2296.4896.19388517775050.286114822249488
2396.7196.58476595629080.125234043709156
2496.6996.8151514779403-0.125151477940335
2596.6996.7947662104621-0.104766210462074
2696.6696.7944436971816-0.134443697181567
2796.7396.7640298244488-0.0340298244488224
2896.8496.83392506671950.00607493328050168
2997.8796.94394376785080.926056232149165
309897.97679454800270.0232054519973133
3197.9898.1068659838828-0.12686598388278
3298.0398.0864754384534-0.0564754384534183
3398.1198.1363015839364-0.026301583936359
3498.1898.2162206168948-0.0362206168947807
3598.3298.28610911500950.0338908849904556
3698.3498.4262134450263-0.0862134450263312
3798.2898.4459480447522-0.165948044752184
3898.5298.38543718874170.134562811258277
3998.5698.6258514281563-0.0658514281563356
4099.698.6656487105050.934351289494955
41100.1699.70852502623890.451474973761137
42100.46100.2699148510140.190085148986384
43100.46100.570500010911-0.110500010911124
44100.68100.5701598466460.109840153354241
45100.83100.7904979795990.0395020204005334
46100.64100.940619582988-0.300619582987892
47100.9100.7496941528570.150305847143329
48100.92101.01015685578-0.0901568557799663
49100.75101.029879316073-0.27987931607332
50100.96100.8590177329730.100982267026581
51101.05101.069328597727-0.0193285977271245
52101.33101.1592690963910.1707309036086
53101.38101.439794675999-0.0597946759992283
54101.44101.48961060351-0.0496106035103168
55101.51101.549457881765-0.0394578817652302
56101.4101.619336414254-0.21933641425359
57101.26101.508661206988-0.248661206987961
58100.83101.367895726007-0.537895726006568
59100.75100.936239862781-0.186239862781164
60100.81100.855666540249-0.045666540248618
61100.82100.915525959945-0.0955259599447231
62100.85100.925231891938-0.0752318919376762
63100.79100.955000297379-0.165000297379066
64100.84100.894492358923-0.0544923589229853
65101.04100.9443246091360.0956753908635335
66101.11101.144619137153-0.0346191371530438
67101.15101.214512565278-0.0645125652779797
68101.11101.254313969195-0.14431396919467
69101.28101.2138697117240.0661302882756019
70101.62101.3840732878210.235926712178696
71102.07101.7247995668150.345200433185013
72102.14102.175862235052-0.0358622350516953







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102.245751836412101.788318162579102.703185510246
74102.351503672825101.703598277061102.999409068589
75102.457255509237101.662515631301103.251995387174
76102.56300734565101.643910099979103.482104591321
77102.668759182062101.639599239202103.697919124922
78102.774511018475101.645393326461103.903628710489
79102.880262854887101.658807396768104.101718313007
80102.9860146913101.678224885897104.293804496703
81103.091766527712101.702524667873104.481008387551
82103.197518364125101.730891720399104.66414500785
83103.303270200537101.762711716785104.84382868429
84103.40902203695101.797508121301105.020535952598

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102.245751836412 & 101.788318162579 & 102.703185510246 \tabularnewline
74 & 102.351503672825 & 101.703598277061 & 102.999409068589 \tabularnewline
75 & 102.457255509237 & 101.662515631301 & 103.251995387174 \tabularnewline
76 & 102.56300734565 & 101.643910099979 & 103.482104591321 \tabularnewline
77 & 102.668759182062 & 101.639599239202 & 103.697919124922 \tabularnewline
78 & 102.774511018475 & 101.645393326461 & 103.903628710489 \tabularnewline
79 & 102.880262854887 & 101.658807396768 & 104.101718313007 \tabularnewline
80 & 102.9860146913 & 101.678224885897 & 104.293804496703 \tabularnewline
81 & 103.091766527712 & 101.702524667873 & 104.481008387551 \tabularnewline
82 & 103.197518364125 & 101.730891720399 & 104.66414500785 \tabularnewline
83 & 103.303270200537 & 101.762711716785 & 104.84382868429 \tabularnewline
84 & 103.40902203695 & 101.797508121301 & 105.020535952598 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295578&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]102.245751836412[/C][C]101.788318162579[/C][C]102.703185510246[/C][/ROW]
[ROW][C]74[/C][C]102.351503672825[/C][C]101.703598277061[/C][C]102.999409068589[/C][/ROW]
[ROW][C]75[/C][C]102.457255509237[/C][C]101.662515631301[/C][C]103.251995387174[/C][/ROW]
[ROW][C]76[/C][C]102.56300734565[/C][C]101.643910099979[/C][C]103.482104591321[/C][/ROW]
[ROW][C]77[/C][C]102.668759182062[/C][C]101.639599239202[/C][C]103.697919124922[/C][/ROW]
[ROW][C]78[/C][C]102.774511018475[/C][C]101.645393326461[/C][C]103.903628710489[/C][/ROW]
[ROW][C]79[/C][C]102.880262854887[/C][C]101.658807396768[/C][C]104.101718313007[/C][/ROW]
[ROW][C]80[/C][C]102.9860146913[/C][C]101.678224885897[/C][C]104.293804496703[/C][/ROW]
[ROW][C]81[/C][C]103.091766527712[/C][C]101.702524667873[/C][C]104.481008387551[/C][/ROW]
[ROW][C]82[/C][C]103.197518364125[/C][C]101.730891720399[/C][C]104.66414500785[/C][/ROW]
[ROW][C]83[/C][C]103.303270200537[/C][C]101.762711716785[/C][C]104.84382868429[/C][/ROW]
[ROW][C]84[/C][C]103.40902203695[/C][C]101.797508121301[/C][C]105.020535952598[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295578&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295578&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
73102.245751836412101.788318162579102.703185510246
74102.351503672825101.703598277061102.999409068589
75102.457255509237101.662515631301103.251995387174
76102.56300734565101.643910099979103.482104591321
77102.668759182062101.639599239202103.697919124922
78102.774511018475101.645393326461103.903628710489
79102.880262854887101.658807396768104.101718313007
80102.9860146913101.678224885897104.293804496703
81103.091766527712101.702524667873104.481008387551
82103.197518364125101.730891720399104.66414500785
83103.303270200537101.762711716785104.84382868429
84103.40902203695101.797508121301105.020535952598



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')