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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 15:54:08 +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/Apr/25/t1461596144ubyclqjpn4q8adk.htm/, Retrieved Sun, 05 May 2024 23:31:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294729, Retrieved Sun, 05 May 2024 23:31:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 14:54:08] [a1d1814f81d637d5e936c79e282724ec] [Current]
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Dataseries X:
89,65
90,65
89,34
89,15
88,82
88,82
91,97
93,01
93,24
93,2
93,19
92,2
93,39
94,75
94,25
94,37
94,02
92,77
92,64
93,19
92,74
92,52
92,25
91,6
93,73
96,21
96,36
95,69
95,07
95,5
95,22
97,41
98,31
98,54
98,45
98,03
101,45
102,44
102,42
100,98
100,69
100,28
98,06
97,37
97,25
98,93
100,04
100,09
100,79
99,76
99,63
99,26
99,69
99,17
98,79
97,97
98,1
97,91
97,16
96,8
97,46
96,59
96,35
96,12
96,16
95,95
96,06
95,89
95,9
95,82
95,54
95,51




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=294729&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=294729&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294729&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
alpha1
beta0.0892728687927934
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0892728687927934 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294729&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]0.0892728687927934[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294729&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294729&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
beta0.0892728687927934
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
389.3491.65-2.31
489.1590.1337796730887-0.983779673088648
588.8289.855954839412-1.035954839412
688.8289.4334721789579-0.613472178957906
791.9789.37870575761782.59129424238225
893.0192.76003802852150.249961971478527
993.2493.8223528508045-0.582352850804469
1093.294.0003645411635-0.800364541163475
1193.1993.8889137024938-0.698913702493797
1292.293.8165196712336-1.61651967123358
1393.3992.68220832272260.707791677277427
1494.7593.93539491626080.81460508373921
1594.2595.3681170490194-1.11811704901939
1694.3794.7682995324073-0.398299532407293
1794.0294.8527421905105-0.832742190510473
1892.7794.4284009061988-1.65840090619881
1992.6493.0303506996939-0.390350699693869
2093.1992.86550297289690.324497027103078
2192.7493.4444717534211-0.704471753421146
2292.5292.9315815390097-0.411581539009745
2392.2592.6748384742802-0.424838474280193
2491.692.3669119249077-0.76691192490766
2593.7391.64844749725972.08155250274027
2696.2193.96427366072222.24572633927781
2796.3696.644756093553-0.284756093553042
2895.6996.7693351001753-1.07933510017534
2995.0796.0029797593939-0.93297975939393
3095.595.29968997974720.200310020252786
3195.2295.7475722299031-0.527572229903129
3297.4195.42047434344431.98952565655573
3398.3197.78808500634190.521914993658143
3498.5498.7346778550917-0.194677855091697
3598.4598.9472984044772-0.497298404477235
3698.0398.8129031492635-0.782903149263475
37101.4598.32301113914183.12698886085819
38102.44102.0221664054340.417833594566261
39102.42103.049467609099-0.629467609098668
40100.98102.973273229822-1.99327322982229
41100.69101.355328010308-0.665328010308187
42100.28101.00593227014-0.725932270139765
4398.06100.531126213835-2.47112621383512
4497.3798.090521687577-0.720521687576991
4597.2597.3361986494996-0.0861986494995648
4698.9397.20850344877271.72149655122733
47100.0499.04218638451760.997813615482357
48100.09100.241264068492-0.151264068492253
49100.79100.2777602911530.512239708847318
5099.76101.023489399471-1.26348939947107
5199.6399.880694076091-0.250694076091008
5299.2699.728313896729-0.468313896728986
5399.6999.31650617167250.373493828327526
5499.1799.7798490372037-0.609849037203674
5598.7999.205406064122-0.415406064121967
5697.9798.7883215730639-0.818321573063898
5798.197.89526765864140.20473234135855
5897.9198.0435447020892-0.133544702089182
5997.1697.8416227834216-0.681622783421602
6096.897.030772362111-0.230772362111026
6197.4696.65017065130730.809829348692716
6296.5997.3824664404977-0.792466440497677
6396.3596.4417206879324-0.091720687932451
6496.1296.1935325189931-0.073532518993062
6596.1695.9569680600730.203031939927001
6695.9596.0150933038068-0.0650933038068331
6796.0695.79928223783680.260717762163196
6895.8995.9325572604103-0.0425572604103479
6995.995.75875805168560.141241948314445
7095.8295.78136712560550.0386328743945086
7195.5495.7048159931324-0.164815993132365
7295.5195.41010239660250.0998976033974799

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 89.34 & 91.65 & -2.31 \tabularnewline
4 & 89.15 & 90.1337796730887 & -0.983779673088648 \tabularnewline
5 & 88.82 & 89.855954839412 & -1.035954839412 \tabularnewline
6 & 88.82 & 89.4334721789579 & -0.613472178957906 \tabularnewline
7 & 91.97 & 89.3787057576178 & 2.59129424238225 \tabularnewline
8 & 93.01 & 92.7600380285215 & 0.249961971478527 \tabularnewline
9 & 93.24 & 93.8223528508045 & -0.582352850804469 \tabularnewline
10 & 93.2 & 94.0003645411635 & -0.800364541163475 \tabularnewline
11 & 93.19 & 93.8889137024938 & -0.698913702493797 \tabularnewline
12 & 92.2 & 93.8165196712336 & -1.61651967123358 \tabularnewline
13 & 93.39 & 92.6822083227226 & 0.707791677277427 \tabularnewline
14 & 94.75 & 93.9353949162608 & 0.81460508373921 \tabularnewline
15 & 94.25 & 95.3681170490194 & -1.11811704901939 \tabularnewline
16 & 94.37 & 94.7682995324073 & -0.398299532407293 \tabularnewline
17 & 94.02 & 94.8527421905105 & -0.832742190510473 \tabularnewline
18 & 92.77 & 94.4284009061988 & -1.65840090619881 \tabularnewline
19 & 92.64 & 93.0303506996939 & -0.390350699693869 \tabularnewline
20 & 93.19 & 92.8655029728969 & 0.324497027103078 \tabularnewline
21 & 92.74 & 93.4444717534211 & -0.704471753421146 \tabularnewline
22 & 92.52 & 92.9315815390097 & -0.411581539009745 \tabularnewline
23 & 92.25 & 92.6748384742802 & -0.424838474280193 \tabularnewline
24 & 91.6 & 92.3669119249077 & -0.76691192490766 \tabularnewline
25 & 93.73 & 91.6484474972597 & 2.08155250274027 \tabularnewline
26 & 96.21 & 93.9642736607222 & 2.24572633927781 \tabularnewline
27 & 96.36 & 96.644756093553 & -0.284756093553042 \tabularnewline
28 & 95.69 & 96.7693351001753 & -1.07933510017534 \tabularnewline
29 & 95.07 & 96.0029797593939 & -0.93297975939393 \tabularnewline
30 & 95.5 & 95.2996899797472 & 0.200310020252786 \tabularnewline
31 & 95.22 & 95.7475722299031 & -0.527572229903129 \tabularnewline
32 & 97.41 & 95.4204743434443 & 1.98952565655573 \tabularnewline
33 & 98.31 & 97.7880850063419 & 0.521914993658143 \tabularnewline
34 & 98.54 & 98.7346778550917 & -0.194677855091697 \tabularnewline
35 & 98.45 & 98.9472984044772 & -0.497298404477235 \tabularnewline
36 & 98.03 & 98.8129031492635 & -0.782903149263475 \tabularnewline
37 & 101.45 & 98.3230111391418 & 3.12698886085819 \tabularnewline
38 & 102.44 & 102.022166405434 & 0.417833594566261 \tabularnewline
39 & 102.42 & 103.049467609099 & -0.629467609098668 \tabularnewline
40 & 100.98 & 102.973273229822 & -1.99327322982229 \tabularnewline
41 & 100.69 & 101.355328010308 & -0.665328010308187 \tabularnewline
42 & 100.28 & 101.00593227014 & -0.725932270139765 \tabularnewline
43 & 98.06 & 100.531126213835 & -2.47112621383512 \tabularnewline
44 & 97.37 & 98.090521687577 & -0.720521687576991 \tabularnewline
45 & 97.25 & 97.3361986494996 & -0.0861986494995648 \tabularnewline
46 & 98.93 & 97.2085034487727 & 1.72149655122733 \tabularnewline
47 & 100.04 & 99.0421863845176 & 0.997813615482357 \tabularnewline
48 & 100.09 & 100.241264068492 & -0.151264068492253 \tabularnewline
49 & 100.79 & 100.277760291153 & 0.512239708847318 \tabularnewline
50 & 99.76 & 101.023489399471 & -1.26348939947107 \tabularnewline
51 & 99.63 & 99.880694076091 & -0.250694076091008 \tabularnewline
52 & 99.26 & 99.728313896729 & -0.468313896728986 \tabularnewline
53 & 99.69 & 99.3165061716725 & 0.373493828327526 \tabularnewline
54 & 99.17 & 99.7798490372037 & -0.609849037203674 \tabularnewline
55 & 98.79 & 99.205406064122 & -0.415406064121967 \tabularnewline
56 & 97.97 & 98.7883215730639 & -0.818321573063898 \tabularnewline
57 & 98.1 & 97.8952676586414 & 0.20473234135855 \tabularnewline
58 & 97.91 & 98.0435447020892 & -0.133544702089182 \tabularnewline
59 & 97.16 & 97.8416227834216 & -0.681622783421602 \tabularnewline
60 & 96.8 & 97.030772362111 & -0.230772362111026 \tabularnewline
61 & 97.46 & 96.6501706513073 & 0.809829348692716 \tabularnewline
62 & 96.59 & 97.3824664404977 & -0.792466440497677 \tabularnewline
63 & 96.35 & 96.4417206879324 & -0.091720687932451 \tabularnewline
64 & 96.12 & 96.1935325189931 & -0.073532518993062 \tabularnewline
65 & 96.16 & 95.956968060073 & 0.203031939927001 \tabularnewline
66 & 95.95 & 96.0150933038068 & -0.0650933038068331 \tabularnewline
67 & 96.06 & 95.7992822378368 & 0.260717762163196 \tabularnewline
68 & 95.89 & 95.9325572604103 & -0.0425572604103479 \tabularnewline
69 & 95.9 & 95.7587580516856 & 0.141241948314445 \tabularnewline
70 & 95.82 & 95.7813671256055 & 0.0386328743945086 \tabularnewline
71 & 95.54 & 95.7048159931324 & -0.164815993132365 \tabularnewline
72 & 95.51 & 95.4101023966025 & 0.0998976033974799 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294729&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]89.34[/C][C]91.65[/C][C]-2.31[/C][/ROW]
[ROW][C]4[/C][C]89.15[/C][C]90.1337796730887[/C][C]-0.983779673088648[/C][/ROW]
[ROW][C]5[/C][C]88.82[/C][C]89.855954839412[/C][C]-1.035954839412[/C][/ROW]
[ROW][C]6[/C][C]88.82[/C][C]89.4334721789579[/C][C]-0.613472178957906[/C][/ROW]
[ROW][C]7[/C][C]91.97[/C][C]89.3787057576178[/C][C]2.59129424238225[/C][/ROW]
[ROW][C]8[/C][C]93.01[/C][C]92.7600380285215[/C][C]0.249961971478527[/C][/ROW]
[ROW][C]9[/C][C]93.24[/C][C]93.8223528508045[/C][C]-0.582352850804469[/C][/ROW]
[ROW][C]10[/C][C]93.2[/C][C]94.0003645411635[/C][C]-0.800364541163475[/C][/ROW]
[ROW][C]11[/C][C]93.19[/C][C]93.8889137024938[/C][C]-0.698913702493797[/C][/ROW]
[ROW][C]12[/C][C]92.2[/C][C]93.8165196712336[/C][C]-1.61651967123358[/C][/ROW]
[ROW][C]13[/C][C]93.39[/C][C]92.6822083227226[/C][C]0.707791677277427[/C][/ROW]
[ROW][C]14[/C][C]94.75[/C][C]93.9353949162608[/C][C]0.81460508373921[/C][/ROW]
[ROW][C]15[/C][C]94.25[/C][C]95.3681170490194[/C][C]-1.11811704901939[/C][/ROW]
[ROW][C]16[/C][C]94.37[/C][C]94.7682995324073[/C][C]-0.398299532407293[/C][/ROW]
[ROW][C]17[/C][C]94.02[/C][C]94.8527421905105[/C][C]-0.832742190510473[/C][/ROW]
[ROW][C]18[/C][C]92.77[/C][C]94.4284009061988[/C][C]-1.65840090619881[/C][/ROW]
[ROW][C]19[/C][C]92.64[/C][C]93.0303506996939[/C][C]-0.390350699693869[/C][/ROW]
[ROW][C]20[/C][C]93.19[/C][C]92.8655029728969[/C][C]0.324497027103078[/C][/ROW]
[ROW][C]21[/C][C]92.74[/C][C]93.4444717534211[/C][C]-0.704471753421146[/C][/ROW]
[ROW][C]22[/C][C]92.52[/C][C]92.9315815390097[/C][C]-0.411581539009745[/C][/ROW]
[ROW][C]23[/C][C]92.25[/C][C]92.6748384742802[/C][C]-0.424838474280193[/C][/ROW]
[ROW][C]24[/C][C]91.6[/C][C]92.3669119249077[/C][C]-0.76691192490766[/C][/ROW]
[ROW][C]25[/C][C]93.73[/C][C]91.6484474972597[/C][C]2.08155250274027[/C][/ROW]
[ROW][C]26[/C][C]96.21[/C][C]93.9642736607222[/C][C]2.24572633927781[/C][/ROW]
[ROW][C]27[/C][C]96.36[/C][C]96.644756093553[/C][C]-0.284756093553042[/C][/ROW]
[ROW][C]28[/C][C]95.69[/C][C]96.7693351001753[/C][C]-1.07933510017534[/C][/ROW]
[ROW][C]29[/C][C]95.07[/C][C]96.0029797593939[/C][C]-0.93297975939393[/C][/ROW]
[ROW][C]30[/C][C]95.5[/C][C]95.2996899797472[/C][C]0.200310020252786[/C][/ROW]
[ROW][C]31[/C][C]95.22[/C][C]95.7475722299031[/C][C]-0.527572229903129[/C][/ROW]
[ROW][C]32[/C][C]97.41[/C][C]95.4204743434443[/C][C]1.98952565655573[/C][/ROW]
[ROW][C]33[/C][C]98.31[/C][C]97.7880850063419[/C][C]0.521914993658143[/C][/ROW]
[ROW][C]34[/C][C]98.54[/C][C]98.7346778550917[/C][C]-0.194677855091697[/C][/ROW]
[ROW][C]35[/C][C]98.45[/C][C]98.9472984044772[/C][C]-0.497298404477235[/C][/ROW]
[ROW][C]36[/C][C]98.03[/C][C]98.8129031492635[/C][C]-0.782903149263475[/C][/ROW]
[ROW][C]37[/C][C]101.45[/C][C]98.3230111391418[/C][C]3.12698886085819[/C][/ROW]
[ROW][C]38[/C][C]102.44[/C][C]102.022166405434[/C][C]0.417833594566261[/C][/ROW]
[ROW][C]39[/C][C]102.42[/C][C]103.049467609099[/C][C]-0.629467609098668[/C][/ROW]
[ROW][C]40[/C][C]100.98[/C][C]102.973273229822[/C][C]-1.99327322982229[/C][/ROW]
[ROW][C]41[/C][C]100.69[/C][C]101.355328010308[/C][C]-0.665328010308187[/C][/ROW]
[ROW][C]42[/C][C]100.28[/C][C]101.00593227014[/C][C]-0.725932270139765[/C][/ROW]
[ROW][C]43[/C][C]98.06[/C][C]100.531126213835[/C][C]-2.47112621383512[/C][/ROW]
[ROW][C]44[/C][C]97.37[/C][C]98.090521687577[/C][C]-0.720521687576991[/C][/ROW]
[ROW][C]45[/C][C]97.25[/C][C]97.3361986494996[/C][C]-0.0861986494995648[/C][/ROW]
[ROW][C]46[/C][C]98.93[/C][C]97.2085034487727[/C][C]1.72149655122733[/C][/ROW]
[ROW][C]47[/C][C]100.04[/C][C]99.0421863845176[/C][C]0.997813615482357[/C][/ROW]
[ROW][C]48[/C][C]100.09[/C][C]100.241264068492[/C][C]-0.151264068492253[/C][/ROW]
[ROW][C]49[/C][C]100.79[/C][C]100.277760291153[/C][C]0.512239708847318[/C][/ROW]
[ROW][C]50[/C][C]99.76[/C][C]101.023489399471[/C][C]-1.26348939947107[/C][/ROW]
[ROW][C]51[/C][C]99.63[/C][C]99.880694076091[/C][C]-0.250694076091008[/C][/ROW]
[ROW][C]52[/C][C]99.26[/C][C]99.728313896729[/C][C]-0.468313896728986[/C][/ROW]
[ROW][C]53[/C][C]99.69[/C][C]99.3165061716725[/C][C]0.373493828327526[/C][/ROW]
[ROW][C]54[/C][C]99.17[/C][C]99.7798490372037[/C][C]-0.609849037203674[/C][/ROW]
[ROW][C]55[/C][C]98.79[/C][C]99.205406064122[/C][C]-0.415406064121967[/C][/ROW]
[ROW][C]56[/C][C]97.97[/C][C]98.7883215730639[/C][C]-0.818321573063898[/C][/ROW]
[ROW][C]57[/C][C]98.1[/C][C]97.8952676586414[/C][C]0.20473234135855[/C][/ROW]
[ROW][C]58[/C][C]97.91[/C][C]98.0435447020892[/C][C]-0.133544702089182[/C][/ROW]
[ROW][C]59[/C][C]97.16[/C][C]97.8416227834216[/C][C]-0.681622783421602[/C][/ROW]
[ROW][C]60[/C][C]96.8[/C][C]97.030772362111[/C][C]-0.230772362111026[/C][/ROW]
[ROW][C]61[/C][C]97.46[/C][C]96.6501706513073[/C][C]0.809829348692716[/C][/ROW]
[ROW][C]62[/C][C]96.59[/C][C]97.3824664404977[/C][C]-0.792466440497677[/C][/ROW]
[ROW][C]63[/C][C]96.35[/C][C]96.4417206879324[/C][C]-0.091720687932451[/C][/ROW]
[ROW][C]64[/C][C]96.12[/C][C]96.1935325189931[/C][C]-0.073532518993062[/C][/ROW]
[ROW][C]65[/C][C]96.16[/C][C]95.956968060073[/C][C]0.203031939927001[/C][/ROW]
[ROW][C]66[/C][C]95.95[/C][C]96.0150933038068[/C][C]-0.0650933038068331[/C][/ROW]
[ROW][C]67[/C][C]96.06[/C][C]95.7992822378368[/C][C]0.260717762163196[/C][/ROW]
[ROW][C]68[/C][C]95.89[/C][C]95.9325572604103[/C][C]-0.0425572604103479[/C][/ROW]
[ROW][C]69[/C][C]95.9[/C][C]95.7587580516856[/C][C]0.141241948314445[/C][/ROW]
[ROW][C]70[/C][C]95.82[/C][C]95.7813671256055[/C][C]0.0386328743945086[/C][/ROW]
[ROW][C]71[/C][C]95.54[/C][C]95.7048159931324[/C][C]-0.164815993132365[/C][/ROW]
[ROW][C]72[/C][C]95.51[/C][C]95.4101023966025[/C][C]0.0998976033974799[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294729&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294729&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
389.3491.65-2.31
489.1590.1337796730887-0.983779673088648
588.8289.855954839412-1.035954839412
688.8289.4334721789579-0.613472178957906
791.9789.37870575761782.59129424238225
893.0192.76003802852150.249961971478527
993.2493.8223528508045-0.582352850804469
1093.294.0003645411635-0.800364541163475
1193.1993.8889137024938-0.698913702493797
1292.293.8165196712336-1.61651967123358
1393.3992.68220832272260.707791677277427
1494.7593.93539491626080.81460508373921
1594.2595.3681170490194-1.11811704901939
1694.3794.7682995324073-0.398299532407293
1794.0294.8527421905105-0.832742190510473
1892.7794.4284009061988-1.65840090619881
1992.6493.0303506996939-0.390350699693869
2093.1992.86550297289690.324497027103078
2192.7493.4444717534211-0.704471753421146
2292.5292.9315815390097-0.411581539009745
2392.2592.6748384742802-0.424838474280193
2491.692.3669119249077-0.76691192490766
2593.7391.64844749725972.08155250274027
2696.2193.96427366072222.24572633927781
2796.3696.644756093553-0.284756093553042
2895.6996.7693351001753-1.07933510017534
2995.0796.0029797593939-0.93297975939393
3095.595.29968997974720.200310020252786
3195.2295.7475722299031-0.527572229903129
3297.4195.42047434344431.98952565655573
3398.3197.78808500634190.521914993658143
3498.5498.7346778550917-0.194677855091697
3598.4598.9472984044772-0.497298404477235
3698.0398.8129031492635-0.782903149263475
37101.4598.32301113914183.12698886085819
38102.44102.0221664054340.417833594566261
39102.42103.049467609099-0.629467609098668
40100.98102.973273229822-1.99327322982229
41100.69101.355328010308-0.665328010308187
42100.28101.00593227014-0.725932270139765
4398.06100.531126213835-2.47112621383512
4497.3798.090521687577-0.720521687576991
4597.2597.3361986494996-0.0861986494995648
4698.9397.20850344877271.72149655122733
47100.0499.04218638451760.997813615482357
48100.09100.241264068492-0.151264068492253
49100.79100.2777602911530.512239708847318
5099.76101.023489399471-1.26348939947107
5199.6399.880694076091-0.250694076091008
5299.2699.728313896729-0.468313896728986
5399.6999.31650617167250.373493828327526
5499.1799.7798490372037-0.609849037203674
5598.7999.205406064122-0.415406064121967
5697.9798.7883215730639-0.818321573063898
5798.197.89526765864140.20473234135855
5897.9198.0435447020892-0.133544702089182
5997.1697.8416227834216-0.681622783421602
6096.897.030772362111-0.230772362111026
6197.4696.65017065130730.809829348692716
6296.5997.3824664404977-0.792466440497677
6396.3596.4417206879324-0.091720687932451
6496.1296.1935325189931-0.073532518993062
6596.1695.9569680600730.203031939927001
6695.9596.0150933038068-0.0650933038068331
6796.0695.79928223783680.260717762163196
6895.8995.9325572604103-0.0425572604103479
6995.995.75875805168560.141241948314445
7095.8295.78136712560550.0386328743945086
7195.5495.7048159931324-0.164815993132365
7295.5195.41010239660250.0998976033974799







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7395.389020542243393.380529705729497.3975113787573
7495.268041084486792.298111700703898.2379704682696
7595.1470616267391.349215529996998.9449077234631
7695.026082168973490.453577560841999.5985867771048
7794.905102711216789.5818264214704100.228379000963
7894.7841232534688.7197724363629100.848474070557
7994.663143795703487.8595168820256101.466770709381
8094.542164337946786.996269085451102.088059590442
8194.421184880190186.1269556551349102.715414105245
8294.300205422433485.2495287256077103.350882119259
8394.179225964676784.3625887848001103.995863144553
8494.058246506920183.465164393958104.651328619882

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 95.3890205422433 & 93.3805297057294 & 97.3975113787573 \tabularnewline
74 & 95.2680410844867 & 92.2981117007038 & 98.2379704682696 \tabularnewline
75 & 95.14706162673 & 91.3492155299969 & 98.9449077234631 \tabularnewline
76 & 95.0260821689734 & 90.4535775608419 & 99.5985867771048 \tabularnewline
77 & 94.9051027112167 & 89.5818264214704 & 100.228379000963 \tabularnewline
78 & 94.78412325346 & 88.7197724363629 & 100.848474070557 \tabularnewline
79 & 94.6631437957034 & 87.8595168820256 & 101.466770709381 \tabularnewline
80 & 94.5421643379467 & 86.996269085451 & 102.088059590442 \tabularnewline
81 & 94.4211848801901 & 86.1269556551349 & 102.715414105245 \tabularnewline
82 & 94.3002054224334 & 85.2495287256077 & 103.350882119259 \tabularnewline
83 & 94.1792259646767 & 84.3625887848001 & 103.995863144553 \tabularnewline
84 & 94.0582465069201 & 83.465164393958 & 104.651328619882 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294729&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]95.3890205422433[/C][C]93.3805297057294[/C][C]97.3975113787573[/C][/ROW]
[ROW][C]74[/C][C]95.2680410844867[/C][C]92.2981117007038[/C][C]98.2379704682696[/C][/ROW]
[ROW][C]75[/C][C]95.14706162673[/C][C]91.3492155299969[/C][C]98.9449077234631[/C][/ROW]
[ROW][C]76[/C][C]95.0260821689734[/C][C]90.4535775608419[/C][C]99.5985867771048[/C][/ROW]
[ROW][C]77[/C][C]94.9051027112167[/C][C]89.5818264214704[/C][C]100.228379000963[/C][/ROW]
[ROW][C]78[/C][C]94.78412325346[/C][C]88.7197724363629[/C][C]100.848474070557[/C][/ROW]
[ROW][C]79[/C][C]94.6631437957034[/C][C]87.8595168820256[/C][C]101.466770709381[/C][/ROW]
[ROW][C]80[/C][C]94.5421643379467[/C][C]86.996269085451[/C][C]102.088059590442[/C][/ROW]
[ROW][C]81[/C][C]94.4211848801901[/C][C]86.1269556551349[/C][C]102.715414105245[/C][/ROW]
[ROW][C]82[/C][C]94.3002054224334[/C][C]85.2495287256077[/C][C]103.350882119259[/C][/ROW]
[ROW][C]83[/C][C]94.1792259646767[/C][C]84.3625887848001[/C][C]103.995863144553[/C][/ROW]
[ROW][C]84[/C][C]94.0582465069201[/C][C]83.465164393958[/C][C]104.651328619882[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294729&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294729&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
7395.389020542243393.380529705729497.3975113787573
7495.268041084486792.298111700703898.2379704682696
7595.1470616267391.349215529996998.9449077234631
7695.026082168973490.453577560841999.5985867771048
7794.905102711216789.5818264214704100.228379000963
7894.7841232534688.7197724363629100.848474070557
7994.663143795703487.8595168820256101.466770709381
8094.542164337946786.996269085451102.088059590442
8194.421184880190186.1269556551349102.715414105245
8294.300205422433485.2495287256077103.350882119259
8394.179225964676784.3625887848001103.995863144553
8494.058246506920183.465164393958104.651328619882



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')