Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 01 May 2017 14:31:45 +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/01/t1493645527539c3e5837ihd5i.htm/, Retrieved Wed, 15 May 2024 22:29:38 +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 22:29:38 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
101.68
101.25
101.24
101.11
101.08
101.09
101.09
101.62
101.66
101.96
102.04
102.02
102.02
101.51
101.62
101.83
102.06
102.14
102.14
102.59
102.92
103.31
103.54
103.58
103.58
102.83
102.86
103.03
103.2
103.28
103.28
103.79
103.92
104.26
104.41
104.45
99.92
99.18
99.18
99.35
99.62
99.67
99.72
100.08
100.39
100.77
101.03
101.07
101.29
101.1
101.2
101.15
101.24
101.16
100.81
101.02
101.15
101.06
101.17
101.22
101.84
101.79
101.88
101.9
101.91
101.96
101.26
101.06
100.98
101.12
101.24
101.25




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.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]'Gertrude Mary Cox' @ cox.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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0830728684730634
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0830728684730634 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0830728684730634[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

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

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0830728684730634
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3101.24100.820.420000000000002
4101.11100.8448906047590.265109395241325
5101.08100.7369140026810.343085997319463
6101.09100.7354151406110.354584859389206
7101.09100.7748715219970.31512847800262
8101.62100.8010501486030.818949851397392
9101.66101.3990826618940.260917338106211
10101.96101.4607578136050.499242186395378
11102.04101.8022312940910.237768705908763
12102.02101.9019834225240.118016577475771
13102.02101.8917873981420.128212601857498
14101.51101.902438386753-0.392438386753199
15101.62101.3598374042670.260162595733334
16101.83101.4914498573640.33855014263635
17102.06101.7295741888340.330425811165597
18102.14101.9870236087850.152976391214523
19102.14102.0797317964120.0602682035876825
20102.59102.0847384489620.505261551037933
21102.92102.5767119753360.343288024664062
22103.31102.9352298962570.374770103742776
23103.54103.3563631237930.183636876206918
24103.58103.601618365857-0.0216183658570372
25103.58103.639822466194-0.0598224661935802
26102.83103.634852842328-0.804852842327747
27102.86102.8179914080170.0420085919831195
28103.03102.8514811822530.178518817746564
29103.2103.036311252520.163688747479938
30103.28103.219909346310.0600906536900112
31103.28103.30490124928-0.0249012492804326
32103.79103.3028326310740.487167368925853
33103.92103.8533030218370.066696978162696
34104.26103.9888437311320.271156268868253
35104.41104.3513694601910.0586305398089024
36104.45104.506240067313-0.0562400673131407
3799.92104.541568043598-4.62156804359833
3899.1899.6276411293732-0.447641129373167
3999.1898.85045429670960.329545703290378
4099.3598.87783060357490.472169396425059
4199.6299.08705506974110.532944930258864
4299.6799.40132833383590.268671666164067
4399.7299.47364765982160.246352340178376
44100.0899.54411285537530.535887144624709
45100.3999.94863053765710.441369462342905
46100.77100.295296364950.474703635049664
47101.03100.7147313575890.315268642411496
48101.07101.0009216280530.0690783719467589
49101.29101.046660166560.243339833439705
50101.1101.286875104538-0.186875104537904
51101.2101.0813508535580.11864914644228
52101.15101.191207378495-0.0412073784945619
53101.24101.1377841633610.102215836639218
54101.16101.236275526114-0.0762755261137613
55100.81101.149939099365-0.339939099365196
56101.02100.7716993832750.248300616725203
57101.15101.002326427750.147673572250227
58101.06101.144594094994-0.084594094994273
59101.17101.0475666208670.122433379132787
60101.22101.1677375128690.0522624871313724
61101.84101.2220791075880.617920892411846
62101.79101.89341156861-0.103411568610241
63101.88101.8348208729730.0451791270274953
64101.9101.92857403265-0.0285740326497717
65101.91101.946200305794-0.0362003057937272
66101.96101.9531930425520.00680695744816262
67101.26102.003758516033-0.743758516032614
68101.06101.241972362655-0.181972362654534
69100.98101.026855396506-0.0468553965059897
70101.12100.9429629843150.177037015685201
71101.24101.0976699570340.142330042966307
72101.25101.2294937219730.0205062780272129

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 101.24 & 100.82 & 0.420000000000002 \tabularnewline
4 & 101.11 & 100.844890604759 & 0.265109395241325 \tabularnewline
5 & 101.08 & 100.736914002681 & 0.343085997319463 \tabularnewline
6 & 101.09 & 100.735415140611 & 0.354584859389206 \tabularnewline
7 & 101.09 & 100.774871521997 & 0.31512847800262 \tabularnewline
8 & 101.62 & 100.801050148603 & 0.818949851397392 \tabularnewline
9 & 101.66 & 101.399082661894 & 0.260917338106211 \tabularnewline
10 & 101.96 & 101.460757813605 & 0.499242186395378 \tabularnewline
11 & 102.04 & 101.802231294091 & 0.237768705908763 \tabularnewline
12 & 102.02 & 101.901983422524 & 0.118016577475771 \tabularnewline
13 & 102.02 & 101.891787398142 & 0.128212601857498 \tabularnewline
14 & 101.51 & 101.902438386753 & -0.392438386753199 \tabularnewline
15 & 101.62 & 101.359837404267 & 0.260162595733334 \tabularnewline
16 & 101.83 & 101.491449857364 & 0.33855014263635 \tabularnewline
17 & 102.06 & 101.729574188834 & 0.330425811165597 \tabularnewline
18 & 102.14 & 101.987023608785 & 0.152976391214523 \tabularnewline
19 & 102.14 & 102.079731796412 & 0.0602682035876825 \tabularnewline
20 & 102.59 & 102.084738448962 & 0.505261551037933 \tabularnewline
21 & 102.92 & 102.576711975336 & 0.343288024664062 \tabularnewline
22 & 103.31 & 102.935229896257 & 0.374770103742776 \tabularnewline
23 & 103.54 & 103.356363123793 & 0.183636876206918 \tabularnewline
24 & 103.58 & 103.601618365857 & -0.0216183658570372 \tabularnewline
25 & 103.58 & 103.639822466194 & -0.0598224661935802 \tabularnewline
26 & 102.83 & 103.634852842328 & -0.804852842327747 \tabularnewline
27 & 102.86 & 102.817991408017 & 0.0420085919831195 \tabularnewline
28 & 103.03 & 102.851481182253 & 0.178518817746564 \tabularnewline
29 & 103.2 & 103.03631125252 & 0.163688747479938 \tabularnewline
30 & 103.28 & 103.21990934631 & 0.0600906536900112 \tabularnewline
31 & 103.28 & 103.30490124928 & -0.0249012492804326 \tabularnewline
32 & 103.79 & 103.302832631074 & 0.487167368925853 \tabularnewline
33 & 103.92 & 103.853303021837 & 0.066696978162696 \tabularnewline
34 & 104.26 & 103.988843731132 & 0.271156268868253 \tabularnewline
35 & 104.41 & 104.351369460191 & 0.0586305398089024 \tabularnewline
36 & 104.45 & 104.506240067313 & -0.0562400673131407 \tabularnewline
37 & 99.92 & 104.541568043598 & -4.62156804359833 \tabularnewline
38 & 99.18 & 99.6276411293732 & -0.447641129373167 \tabularnewline
39 & 99.18 & 98.8504542967096 & 0.329545703290378 \tabularnewline
40 & 99.35 & 98.8778306035749 & 0.472169396425059 \tabularnewline
41 & 99.62 & 99.0870550697411 & 0.532944930258864 \tabularnewline
42 & 99.67 & 99.4013283338359 & 0.268671666164067 \tabularnewline
43 & 99.72 & 99.4736476598216 & 0.246352340178376 \tabularnewline
44 & 100.08 & 99.5441128553753 & 0.535887144624709 \tabularnewline
45 & 100.39 & 99.9486305376571 & 0.441369462342905 \tabularnewline
46 & 100.77 & 100.29529636495 & 0.474703635049664 \tabularnewline
47 & 101.03 & 100.714731357589 & 0.315268642411496 \tabularnewline
48 & 101.07 & 101.000921628053 & 0.0690783719467589 \tabularnewline
49 & 101.29 & 101.04666016656 & 0.243339833439705 \tabularnewline
50 & 101.1 & 101.286875104538 & -0.186875104537904 \tabularnewline
51 & 101.2 & 101.081350853558 & 0.11864914644228 \tabularnewline
52 & 101.15 & 101.191207378495 & -0.0412073784945619 \tabularnewline
53 & 101.24 & 101.137784163361 & 0.102215836639218 \tabularnewline
54 & 101.16 & 101.236275526114 & -0.0762755261137613 \tabularnewline
55 & 100.81 & 101.149939099365 & -0.339939099365196 \tabularnewline
56 & 101.02 & 100.771699383275 & 0.248300616725203 \tabularnewline
57 & 101.15 & 101.00232642775 & 0.147673572250227 \tabularnewline
58 & 101.06 & 101.144594094994 & -0.084594094994273 \tabularnewline
59 & 101.17 & 101.047566620867 & 0.122433379132787 \tabularnewline
60 & 101.22 & 101.167737512869 & 0.0522624871313724 \tabularnewline
61 & 101.84 & 101.222079107588 & 0.617920892411846 \tabularnewline
62 & 101.79 & 101.89341156861 & -0.103411568610241 \tabularnewline
63 & 101.88 & 101.834820872973 & 0.0451791270274953 \tabularnewline
64 & 101.9 & 101.92857403265 & -0.0285740326497717 \tabularnewline
65 & 101.91 & 101.946200305794 & -0.0362003057937272 \tabularnewline
66 & 101.96 & 101.953193042552 & 0.00680695744816262 \tabularnewline
67 & 101.26 & 102.003758516033 & -0.743758516032614 \tabularnewline
68 & 101.06 & 101.241972362655 & -0.181972362654534 \tabularnewline
69 & 100.98 & 101.026855396506 & -0.0468553965059897 \tabularnewline
70 & 101.12 & 100.942962984315 & 0.177037015685201 \tabularnewline
71 & 101.24 & 101.097669957034 & 0.142330042966307 \tabularnewline
72 & 101.25 & 101.229493721973 & 0.0205062780272129 \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]3[/C][C]101.24[/C][C]100.82[/C][C]0.420000000000002[/C][/ROW]
[ROW][C]4[/C][C]101.11[/C][C]100.844890604759[/C][C]0.265109395241325[/C][/ROW]
[ROW][C]5[/C][C]101.08[/C][C]100.736914002681[/C][C]0.343085997319463[/C][/ROW]
[ROW][C]6[/C][C]101.09[/C][C]100.735415140611[/C][C]0.354584859389206[/C][/ROW]
[ROW][C]7[/C][C]101.09[/C][C]100.774871521997[/C][C]0.31512847800262[/C][/ROW]
[ROW][C]8[/C][C]101.62[/C][C]100.801050148603[/C][C]0.818949851397392[/C][/ROW]
[ROW][C]9[/C][C]101.66[/C][C]101.399082661894[/C][C]0.260917338106211[/C][/ROW]
[ROW][C]10[/C][C]101.96[/C][C]101.460757813605[/C][C]0.499242186395378[/C][/ROW]
[ROW][C]11[/C][C]102.04[/C][C]101.802231294091[/C][C]0.237768705908763[/C][/ROW]
[ROW][C]12[/C][C]102.02[/C][C]101.901983422524[/C][C]0.118016577475771[/C][/ROW]
[ROW][C]13[/C][C]102.02[/C][C]101.891787398142[/C][C]0.128212601857498[/C][/ROW]
[ROW][C]14[/C][C]101.51[/C][C]101.902438386753[/C][C]-0.392438386753199[/C][/ROW]
[ROW][C]15[/C][C]101.62[/C][C]101.359837404267[/C][C]0.260162595733334[/C][/ROW]
[ROW][C]16[/C][C]101.83[/C][C]101.491449857364[/C][C]0.33855014263635[/C][/ROW]
[ROW][C]17[/C][C]102.06[/C][C]101.729574188834[/C][C]0.330425811165597[/C][/ROW]
[ROW][C]18[/C][C]102.14[/C][C]101.987023608785[/C][C]0.152976391214523[/C][/ROW]
[ROW][C]19[/C][C]102.14[/C][C]102.079731796412[/C][C]0.0602682035876825[/C][/ROW]
[ROW][C]20[/C][C]102.59[/C][C]102.084738448962[/C][C]0.505261551037933[/C][/ROW]
[ROW][C]21[/C][C]102.92[/C][C]102.576711975336[/C][C]0.343288024664062[/C][/ROW]
[ROW][C]22[/C][C]103.31[/C][C]102.935229896257[/C][C]0.374770103742776[/C][/ROW]
[ROW][C]23[/C][C]103.54[/C][C]103.356363123793[/C][C]0.183636876206918[/C][/ROW]
[ROW][C]24[/C][C]103.58[/C][C]103.601618365857[/C][C]-0.0216183658570372[/C][/ROW]
[ROW][C]25[/C][C]103.58[/C][C]103.639822466194[/C][C]-0.0598224661935802[/C][/ROW]
[ROW][C]26[/C][C]102.83[/C][C]103.634852842328[/C][C]-0.804852842327747[/C][/ROW]
[ROW][C]27[/C][C]102.86[/C][C]102.817991408017[/C][C]0.0420085919831195[/C][/ROW]
[ROW][C]28[/C][C]103.03[/C][C]102.851481182253[/C][C]0.178518817746564[/C][/ROW]
[ROW][C]29[/C][C]103.2[/C][C]103.03631125252[/C][C]0.163688747479938[/C][/ROW]
[ROW][C]30[/C][C]103.28[/C][C]103.21990934631[/C][C]0.0600906536900112[/C][/ROW]
[ROW][C]31[/C][C]103.28[/C][C]103.30490124928[/C][C]-0.0249012492804326[/C][/ROW]
[ROW][C]32[/C][C]103.79[/C][C]103.302832631074[/C][C]0.487167368925853[/C][/ROW]
[ROW][C]33[/C][C]103.92[/C][C]103.853303021837[/C][C]0.066696978162696[/C][/ROW]
[ROW][C]34[/C][C]104.26[/C][C]103.988843731132[/C][C]0.271156268868253[/C][/ROW]
[ROW][C]35[/C][C]104.41[/C][C]104.351369460191[/C][C]0.0586305398089024[/C][/ROW]
[ROW][C]36[/C][C]104.45[/C][C]104.506240067313[/C][C]-0.0562400673131407[/C][/ROW]
[ROW][C]37[/C][C]99.92[/C][C]104.541568043598[/C][C]-4.62156804359833[/C][/ROW]
[ROW][C]38[/C][C]99.18[/C][C]99.6276411293732[/C][C]-0.447641129373167[/C][/ROW]
[ROW][C]39[/C][C]99.18[/C][C]98.8504542967096[/C][C]0.329545703290378[/C][/ROW]
[ROW][C]40[/C][C]99.35[/C][C]98.8778306035749[/C][C]0.472169396425059[/C][/ROW]
[ROW][C]41[/C][C]99.62[/C][C]99.0870550697411[/C][C]0.532944930258864[/C][/ROW]
[ROW][C]42[/C][C]99.67[/C][C]99.4013283338359[/C][C]0.268671666164067[/C][/ROW]
[ROW][C]43[/C][C]99.72[/C][C]99.4736476598216[/C][C]0.246352340178376[/C][/ROW]
[ROW][C]44[/C][C]100.08[/C][C]99.5441128553753[/C][C]0.535887144624709[/C][/ROW]
[ROW][C]45[/C][C]100.39[/C][C]99.9486305376571[/C][C]0.441369462342905[/C][/ROW]
[ROW][C]46[/C][C]100.77[/C][C]100.29529636495[/C][C]0.474703635049664[/C][/ROW]
[ROW][C]47[/C][C]101.03[/C][C]100.714731357589[/C][C]0.315268642411496[/C][/ROW]
[ROW][C]48[/C][C]101.07[/C][C]101.000921628053[/C][C]0.0690783719467589[/C][/ROW]
[ROW][C]49[/C][C]101.29[/C][C]101.04666016656[/C][C]0.243339833439705[/C][/ROW]
[ROW][C]50[/C][C]101.1[/C][C]101.286875104538[/C][C]-0.186875104537904[/C][/ROW]
[ROW][C]51[/C][C]101.2[/C][C]101.081350853558[/C][C]0.11864914644228[/C][/ROW]
[ROW][C]52[/C][C]101.15[/C][C]101.191207378495[/C][C]-0.0412073784945619[/C][/ROW]
[ROW][C]53[/C][C]101.24[/C][C]101.137784163361[/C][C]0.102215836639218[/C][/ROW]
[ROW][C]54[/C][C]101.16[/C][C]101.236275526114[/C][C]-0.0762755261137613[/C][/ROW]
[ROW][C]55[/C][C]100.81[/C][C]101.149939099365[/C][C]-0.339939099365196[/C][/ROW]
[ROW][C]56[/C][C]101.02[/C][C]100.771699383275[/C][C]0.248300616725203[/C][/ROW]
[ROW][C]57[/C][C]101.15[/C][C]101.00232642775[/C][C]0.147673572250227[/C][/ROW]
[ROW][C]58[/C][C]101.06[/C][C]101.144594094994[/C][C]-0.084594094994273[/C][/ROW]
[ROW][C]59[/C][C]101.17[/C][C]101.047566620867[/C][C]0.122433379132787[/C][/ROW]
[ROW][C]60[/C][C]101.22[/C][C]101.167737512869[/C][C]0.0522624871313724[/C][/ROW]
[ROW][C]61[/C][C]101.84[/C][C]101.222079107588[/C][C]0.617920892411846[/C][/ROW]
[ROW][C]62[/C][C]101.79[/C][C]101.89341156861[/C][C]-0.103411568610241[/C][/ROW]
[ROW][C]63[/C][C]101.88[/C][C]101.834820872973[/C][C]0.0451791270274953[/C][/ROW]
[ROW][C]64[/C][C]101.9[/C][C]101.92857403265[/C][C]-0.0285740326497717[/C][/ROW]
[ROW][C]65[/C][C]101.91[/C][C]101.946200305794[/C][C]-0.0362003057937272[/C][/ROW]
[ROW][C]66[/C][C]101.96[/C][C]101.953193042552[/C][C]0.00680695744816262[/C][/ROW]
[ROW][C]67[/C][C]101.26[/C][C]102.003758516033[/C][C]-0.743758516032614[/C][/ROW]
[ROW][C]68[/C][C]101.06[/C][C]101.241972362655[/C][C]-0.181972362654534[/C][/ROW]
[ROW][C]69[/C][C]100.98[/C][C]101.026855396506[/C][C]-0.0468553965059897[/C][/ROW]
[ROW][C]70[/C][C]101.12[/C][C]100.942962984315[/C][C]0.177037015685201[/C][/ROW]
[ROW][C]71[/C][C]101.24[/C][C]101.097669957034[/C][C]0.142330042966307[/C][/ROW]
[ROW][C]72[/C][C]101.25[/C][C]101.229493721973[/C][C]0.0205062780272129[/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
3101.24100.820.420000000000002
4101.11100.8448906047590.265109395241325
5101.08100.7369140026810.343085997319463
6101.09100.7354151406110.354584859389206
7101.09100.7748715219970.31512847800262
8101.62100.8010501486030.818949851397392
9101.66101.3990826618940.260917338106211
10101.96101.4607578136050.499242186395378
11102.04101.8022312940910.237768705908763
12102.02101.9019834225240.118016577475771
13102.02101.8917873981420.128212601857498
14101.51101.902438386753-0.392438386753199
15101.62101.3598374042670.260162595733334
16101.83101.4914498573640.33855014263635
17102.06101.7295741888340.330425811165597
18102.14101.9870236087850.152976391214523
19102.14102.0797317964120.0602682035876825
20102.59102.0847384489620.505261551037933
21102.92102.5767119753360.343288024664062
22103.31102.9352298962570.374770103742776
23103.54103.3563631237930.183636876206918
24103.58103.601618365857-0.0216183658570372
25103.58103.639822466194-0.0598224661935802
26102.83103.634852842328-0.804852842327747
27102.86102.8179914080170.0420085919831195
28103.03102.8514811822530.178518817746564
29103.2103.036311252520.163688747479938
30103.28103.219909346310.0600906536900112
31103.28103.30490124928-0.0249012492804326
32103.79103.3028326310740.487167368925853
33103.92103.8533030218370.066696978162696
34104.26103.9888437311320.271156268868253
35104.41104.3513694601910.0586305398089024
36104.45104.506240067313-0.0562400673131407
3799.92104.541568043598-4.62156804359833
3899.1899.6276411293732-0.447641129373167
3999.1898.85045429670960.329545703290378
4099.3598.87783060357490.472169396425059
4199.6299.08705506974110.532944930258864
4299.6799.40132833383590.268671666164067
4399.7299.47364765982160.246352340178376
44100.0899.54411285537530.535887144624709
45100.3999.94863053765710.441369462342905
46100.77100.295296364950.474703635049664
47101.03100.7147313575890.315268642411496
48101.07101.0009216280530.0690783719467589
49101.29101.046660166560.243339833439705
50101.1101.286875104538-0.186875104537904
51101.2101.0813508535580.11864914644228
52101.15101.191207378495-0.0412073784945619
53101.24101.1377841633610.102215836639218
54101.16101.236275526114-0.0762755261137613
55100.81101.149939099365-0.339939099365196
56101.02100.7716993832750.248300616725203
57101.15101.002326427750.147673572250227
58101.06101.144594094994-0.084594094994273
59101.17101.0475666208670.122433379132787
60101.22101.1677375128690.0522624871313724
61101.84101.2220791075880.617920892411846
62101.79101.89341156861-0.103411568610241
63101.88101.8348208729730.0451791270274953
64101.9101.92857403265-0.0285740326497717
65101.91101.946200305794-0.0362003057937272
66101.96101.9531930425520.00680695744816262
67101.26102.003758516033-0.743758516032614
68101.06101.241972362655-0.181972362654534
69100.98101.026855396506-0.0468553965059897
70101.12100.9429629843150.177037015685201
71101.24101.0976699570340.142330042966307
72101.25101.2294937219730.0205062780272129







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73101.2411972373199.9957409048353102.486653569785
74101.2323944746299.3964351772704103.06835377197
75101.22359171193198.88261656431103.564566859551
76101.21478894924198.4039482880929104.025629610389
77101.20598618655197.9419185204653104.470053852637
78101.19718342386197.48753228035104.906834567373
79101.18838066117197.0357482067912105.341013115552
80101.17957789848296.5834837677935105.77567202917
81101.17077513579296.1287422200941106.21280805149
82101.16197237310295.6701776080748106.653767138129
83101.15316961041295.2068571263383107.099482094486
84101.14436684772394.7381220335037107.550611661941

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 101.24119723731 & 99.9957409048353 & 102.486653569785 \tabularnewline
74 & 101.23239447462 & 99.3964351772704 & 103.06835377197 \tabularnewline
75 & 101.223591711931 & 98.88261656431 & 103.564566859551 \tabularnewline
76 & 101.214788949241 & 98.4039482880929 & 104.025629610389 \tabularnewline
77 & 101.205986186551 & 97.9419185204653 & 104.470053852637 \tabularnewline
78 & 101.197183423861 & 97.48753228035 & 104.906834567373 \tabularnewline
79 & 101.188380661171 & 97.0357482067912 & 105.341013115552 \tabularnewline
80 & 101.179577898482 & 96.5834837677935 & 105.77567202917 \tabularnewline
81 & 101.170775135792 & 96.1287422200941 & 106.21280805149 \tabularnewline
82 & 101.161972373102 & 95.6701776080748 & 106.653767138129 \tabularnewline
83 & 101.153169610412 & 95.2068571263383 & 107.099482094486 \tabularnewline
84 & 101.144366847723 & 94.7381220335037 & 107.550611661941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]101.24119723731[/C][C]99.9957409048353[/C][C]102.486653569785[/C][/ROW]
[ROW][C]74[/C][C]101.23239447462[/C][C]99.3964351772704[/C][C]103.06835377197[/C][/ROW]
[ROW][C]75[/C][C]101.223591711931[/C][C]98.88261656431[/C][C]103.564566859551[/C][/ROW]
[ROW][C]76[/C][C]101.214788949241[/C][C]98.4039482880929[/C][C]104.025629610389[/C][/ROW]
[ROW][C]77[/C][C]101.205986186551[/C][C]97.9419185204653[/C][C]104.470053852637[/C][/ROW]
[ROW][C]78[/C][C]101.197183423861[/C][C]97.48753228035[/C][C]104.906834567373[/C][/ROW]
[ROW][C]79[/C][C]101.188380661171[/C][C]97.0357482067912[/C][C]105.341013115552[/C][/ROW]
[ROW][C]80[/C][C]101.179577898482[/C][C]96.5834837677935[/C][C]105.77567202917[/C][/ROW]
[ROW][C]81[/C][C]101.170775135792[/C][C]96.1287422200941[/C][C]106.21280805149[/C][/ROW]
[ROW][C]82[/C][C]101.161972373102[/C][C]95.6701776080748[/C][C]106.653767138129[/C][/ROW]
[ROW][C]83[/C][C]101.153169610412[/C][C]95.2068571263383[/C][C]107.099482094486[/C][/ROW]
[ROW][C]84[/C][C]101.144366847723[/C][C]94.7381220335037[/C][C]107.550611661941[/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
73101.2411972373199.9957409048353102.486653569785
74101.2323944746299.3964351772704103.06835377197
75101.22359171193198.88261656431103.564566859551
76101.21478894924198.4039482880929104.025629610389
77101.20598618655197.9419185204653104.470053852637
78101.19718342386197.48753228035104.906834567373
79101.18838066117197.0357482067912105.341013115552
80101.17957789848296.5834837677935105.77567202917
81101.17077513579296.1287422200941106.21280805149
82101.16197237310295.6701776080748106.653767138129
83101.15316961041295.2068571263383107.099482094486
84101.14436684772394.7381220335037107.550611661941



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