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 16:33:03 +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/t1493653384zddd9sbqgqk1tu3.htm/, Retrieved Fri, 28 Aug 2026 23:17:53 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 28 Aug 2026 23:17:53 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
93.55
94.11
94.47
94.38
94.42
94.39
94.42
94.34
94.59
94.63
94.84
94.98
95.19
95.76
96.08
96.04
96.2
96.31
96.3
96.29
96.46
96.66
96.83
97
97.1
97.33
97.31
97.16
97.4
97.4
97.52
97.77
98
98.2
98.48
98.53
98.71
99.03
99.52
99.65
99.98
99.94
100.12
100.17
100.38
100.75
100.84
100.91
100.9
101.15
101.4
101.39
101.55
101.73
101.7
101.65
101.73
101.53
101.58
101.58
101.71
101.71
101.98
101.99
101.95
102.11
102.28
102.32
102.18
102.14
102.29
102.33




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 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]3 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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.418130155331003
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.418130155331003 \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]0.418130155331003[/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
beta0.418130155331003
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
394.4794.67-0.200000000000003
494.3894.9463739689338-0.566373968933803
594.4294.6195559333281-0.199555933328071
694.3994.5761155799284-0.186115579928384
794.4294.4682950435834-0.0482950435834084
894.3494.4781014295082-0.138101429508154
994.5994.34035705733650.249642942663513
1094.6394.6947402997297-0.064740299729678
1194.8494.70767042814750.13232957185248
1294.9894.97300141258110.00699858741892001
1395.1995.11592773302570.0740722669743406
1495.7695.35689958152130.403100418478658
1596.0896.0954480221138-0.01544802211383
1696.0496.4089887382278-0.368988738227799
1796.296.2147034197972-0.0147034197972289
1896.3196.3685554765935-0.0585554765935115
1996.396.45407166607-0.154071666069996
2096.2996.379649656404-0.0896496564040206
2196.4696.33216443164650.127835568353532
2296.6696.55561633769890.104383662301061
2396.8396.79926229463090.0307377053691056
249796.98211465615140.0178853438486044
2597.197.159593057753-0.0595930577529771
2697.3397.23467540325810.0953245967419321
2797.3197.5045334917006-0.194533491700639
2897.1697.4031931725988-0.243193172598779
2997.497.15150677356460.2484932264354
3097.497.4954092849327-0.0954092849327424
3197.5297.45551578580380.0644842141961988
3297.7797.6024785803020.167521419697948
339897.92252433754160.077475662458383
3498.298.18491924831970.0150807516802871
3598.4898.39122496536230.0887750346376919
3698.5398.7083444843849-0.17834448438488
3798.7198.68377327742660.0262267225733979
3899.0398.874739461010.155260538989978
3999.5299.25965857429470.260341425705306
4099.6599.8585151750639-0.208515175063937
4199.9899.90132869252560.0786713074744085
4299.94100.26422353854-0.324223538539968
43100.12100.0886559000080.0313440999917276
44100.17100.281761813407-0.111761813406531
45100.38100.2850308290070.0949691709932097
46100.75100.5347403032260.215259696774169
47100.84100.994746873675-0.154746873674512
48100.91101.020042539348-0.110042539348015
49100.9101.044030435277-0.144030435277401
50101.15100.9738069670020.176193032997531
51101.4101.2974785872580.102521412742036
52101.39101.590345881493-0.200345881492552
53101.55101.4965752269440.0534247730558519
54101.73101.6789137356010.0510862643995011
55101.7101.880274443269-0.180274443269155
56101.65101.774896262303-0.124896262302812
57101.73101.6726733687460.0573266312541278
58101.53101.776643361977-0.246643361976766
59101.58101.4735143347220.106485665277944
60101.58101.5680392024850.011960797514746
61101.71101.5730403726080.136959627392017
62101.71101.760307322883-0.0503073228834694
63101.98101.7392723141520.240727685848086
64101.99102.109927818828-0.11992781882806
65101.95102.069782381313-0.119782381312959
66102.11101.9796977556090.130302244391331
67102.28102.1941810532960.0858189467040091
68102.32102.400064542812-0.0800645428116837
69102.18102.406587143089-0.226587143089304
70102.14102.171844225753-0.0318442257533889
71102.29102.1185291946930.17147080530728
72102.33102.340226309151-0.0102263091505961

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 94.47 & 94.67 & -0.200000000000003 \tabularnewline
4 & 94.38 & 94.9463739689338 & -0.566373968933803 \tabularnewline
5 & 94.42 & 94.6195559333281 & -0.199555933328071 \tabularnewline
6 & 94.39 & 94.5761155799284 & -0.186115579928384 \tabularnewline
7 & 94.42 & 94.4682950435834 & -0.0482950435834084 \tabularnewline
8 & 94.34 & 94.4781014295082 & -0.138101429508154 \tabularnewline
9 & 94.59 & 94.3403570573365 & 0.249642942663513 \tabularnewline
10 & 94.63 & 94.6947402997297 & -0.064740299729678 \tabularnewline
11 & 94.84 & 94.7076704281475 & 0.13232957185248 \tabularnewline
12 & 94.98 & 94.9730014125811 & 0.00699858741892001 \tabularnewline
13 & 95.19 & 95.1159277330257 & 0.0740722669743406 \tabularnewline
14 & 95.76 & 95.3568995815213 & 0.403100418478658 \tabularnewline
15 & 96.08 & 96.0954480221138 & -0.01544802211383 \tabularnewline
16 & 96.04 & 96.4089887382278 & -0.368988738227799 \tabularnewline
17 & 96.2 & 96.2147034197972 & -0.0147034197972289 \tabularnewline
18 & 96.31 & 96.3685554765935 & -0.0585554765935115 \tabularnewline
19 & 96.3 & 96.45407166607 & -0.154071666069996 \tabularnewline
20 & 96.29 & 96.379649656404 & -0.0896496564040206 \tabularnewline
21 & 96.46 & 96.3321644316465 & 0.127835568353532 \tabularnewline
22 & 96.66 & 96.5556163376989 & 0.104383662301061 \tabularnewline
23 & 96.83 & 96.7992622946309 & 0.0307377053691056 \tabularnewline
24 & 97 & 96.9821146561514 & 0.0178853438486044 \tabularnewline
25 & 97.1 & 97.159593057753 & -0.0595930577529771 \tabularnewline
26 & 97.33 & 97.2346754032581 & 0.0953245967419321 \tabularnewline
27 & 97.31 & 97.5045334917006 & -0.194533491700639 \tabularnewline
28 & 97.16 & 97.4031931725988 & -0.243193172598779 \tabularnewline
29 & 97.4 & 97.1515067735646 & 0.2484932264354 \tabularnewline
30 & 97.4 & 97.4954092849327 & -0.0954092849327424 \tabularnewline
31 & 97.52 & 97.4555157858038 & 0.0644842141961988 \tabularnewline
32 & 97.77 & 97.602478580302 & 0.167521419697948 \tabularnewline
33 & 98 & 97.9225243375416 & 0.077475662458383 \tabularnewline
34 & 98.2 & 98.1849192483197 & 0.0150807516802871 \tabularnewline
35 & 98.48 & 98.3912249653623 & 0.0887750346376919 \tabularnewline
36 & 98.53 & 98.7083444843849 & -0.17834448438488 \tabularnewline
37 & 98.71 & 98.6837732774266 & 0.0262267225733979 \tabularnewline
38 & 99.03 & 98.87473946101 & 0.155260538989978 \tabularnewline
39 & 99.52 & 99.2596585742947 & 0.260341425705306 \tabularnewline
40 & 99.65 & 99.8585151750639 & -0.208515175063937 \tabularnewline
41 & 99.98 & 99.9013286925256 & 0.0786713074744085 \tabularnewline
42 & 99.94 & 100.26422353854 & -0.324223538539968 \tabularnewline
43 & 100.12 & 100.088655900008 & 0.0313440999917276 \tabularnewline
44 & 100.17 & 100.281761813407 & -0.111761813406531 \tabularnewline
45 & 100.38 & 100.285030829007 & 0.0949691709932097 \tabularnewline
46 & 100.75 & 100.534740303226 & 0.215259696774169 \tabularnewline
47 & 100.84 & 100.994746873675 & -0.154746873674512 \tabularnewline
48 & 100.91 & 101.020042539348 & -0.110042539348015 \tabularnewline
49 & 100.9 & 101.044030435277 & -0.144030435277401 \tabularnewline
50 & 101.15 & 100.973806967002 & 0.176193032997531 \tabularnewline
51 & 101.4 & 101.297478587258 & 0.102521412742036 \tabularnewline
52 & 101.39 & 101.590345881493 & -0.200345881492552 \tabularnewline
53 & 101.55 & 101.496575226944 & 0.0534247730558519 \tabularnewline
54 & 101.73 & 101.678913735601 & 0.0510862643995011 \tabularnewline
55 & 101.7 & 101.880274443269 & -0.180274443269155 \tabularnewline
56 & 101.65 & 101.774896262303 & -0.124896262302812 \tabularnewline
57 & 101.73 & 101.672673368746 & 0.0573266312541278 \tabularnewline
58 & 101.53 & 101.776643361977 & -0.246643361976766 \tabularnewline
59 & 101.58 & 101.473514334722 & 0.106485665277944 \tabularnewline
60 & 101.58 & 101.568039202485 & 0.011960797514746 \tabularnewline
61 & 101.71 & 101.573040372608 & 0.136959627392017 \tabularnewline
62 & 101.71 & 101.760307322883 & -0.0503073228834694 \tabularnewline
63 & 101.98 & 101.739272314152 & 0.240727685848086 \tabularnewline
64 & 101.99 & 102.109927818828 & -0.11992781882806 \tabularnewline
65 & 101.95 & 102.069782381313 & -0.119782381312959 \tabularnewline
66 & 102.11 & 101.979697755609 & 0.130302244391331 \tabularnewline
67 & 102.28 & 102.194181053296 & 0.0858189467040091 \tabularnewline
68 & 102.32 & 102.400064542812 & -0.0800645428116837 \tabularnewline
69 & 102.18 & 102.406587143089 & -0.226587143089304 \tabularnewline
70 & 102.14 & 102.171844225753 & -0.0318442257533889 \tabularnewline
71 & 102.29 & 102.118529194693 & 0.17147080530728 \tabularnewline
72 & 102.33 & 102.340226309151 & -0.0102263091505961 \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]94.47[/C][C]94.67[/C][C]-0.200000000000003[/C][/ROW]
[ROW][C]4[/C][C]94.38[/C][C]94.9463739689338[/C][C]-0.566373968933803[/C][/ROW]
[ROW][C]5[/C][C]94.42[/C][C]94.6195559333281[/C][C]-0.199555933328071[/C][/ROW]
[ROW][C]6[/C][C]94.39[/C][C]94.5761155799284[/C][C]-0.186115579928384[/C][/ROW]
[ROW][C]7[/C][C]94.42[/C][C]94.4682950435834[/C][C]-0.0482950435834084[/C][/ROW]
[ROW][C]8[/C][C]94.34[/C][C]94.4781014295082[/C][C]-0.138101429508154[/C][/ROW]
[ROW][C]9[/C][C]94.59[/C][C]94.3403570573365[/C][C]0.249642942663513[/C][/ROW]
[ROW][C]10[/C][C]94.63[/C][C]94.6947402997297[/C][C]-0.064740299729678[/C][/ROW]
[ROW][C]11[/C][C]94.84[/C][C]94.7076704281475[/C][C]0.13232957185248[/C][/ROW]
[ROW][C]12[/C][C]94.98[/C][C]94.9730014125811[/C][C]0.00699858741892001[/C][/ROW]
[ROW][C]13[/C][C]95.19[/C][C]95.1159277330257[/C][C]0.0740722669743406[/C][/ROW]
[ROW][C]14[/C][C]95.76[/C][C]95.3568995815213[/C][C]0.403100418478658[/C][/ROW]
[ROW][C]15[/C][C]96.08[/C][C]96.0954480221138[/C][C]-0.01544802211383[/C][/ROW]
[ROW][C]16[/C][C]96.04[/C][C]96.4089887382278[/C][C]-0.368988738227799[/C][/ROW]
[ROW][C]17[/C][C]96.2[/C][C]96.2147034197972[/C][C]-0.0147034197972289[/C][/ROW]
[ROW][C]18[/C][C]96.31[/C][C]96.3685554765935[/C][C]-0.0585554765935115[/C][/ROW]
[ROW][C]19[/C][C]96.3[/C][C]96.45407166607[/C][C]-0.154071666069996[/C][/ROW]
[ROW][C]20[/C][C]96.29[/C][C]96.379649656404[/C][C]-0.0896496564040206[/C][/ROW]
[ROW][C]21[/C][C]96.46[/C][C]96.3321644316465[/C][C]0.127835568353532[/C][/ROW]
[ROW][C]22[/C][C]96.66[/C][C]96.5556163376989[/C][C]0.104383662301061[/C][/ROW]
[ROW][C]23[/C][C]96.83[/C][C]96.7992622946309[/C][C]0.0307377053691056[/C][/ROW]
[ROW][C]24[/C][C]97[/C][C]96.9821146561514[/C][C]0.0178853438486044[/C][/ROW]
[ROW][C]25[/C][C]97.1[/C][C]97.159593057753[/C][C]-0.0595930577529771[/C][/ROW]
[ROW][C]26[/C][C]97.33[/C][C]97.2346754032581[/C][C]0.0953245967419321[/C][/ROW]
[ROW][C]27[/C][C]97.31[/C][C]97.5045334917006[/C][C]-0.194533491700639[/C][/ROW]
[ROW][C]28[/C][C]97.16[/C][C]97.4031931725988[/C][C]-0.243193172598779[/C][/ROW]
[ROW][C]29[/C][C]97.4[/C][C]97.1515067735646[/C][C]0.2484932264354[/C][/ROW]
[ROW][C]30[/C][C]97.4[/C][C]97.4954092849327[/C][C]-0.0954092849327424[/C][/ROW]
[ROW][C]31[/C][C]97.52[/C][C]97.4555157858038[/C][C]0.0644842141961988[/C][/ROW]
[ROW][C]32[/C][C]97.77[/C][C]97.602478580302[/C][C]0.167521419697948[/C][/ROW]
[ROW][C]33[/C][C]98[/C][C]97.9225243375416[/C][C]0.077475662458383[/C][/ROW]
[ROW][C]34[/C][C]98.2[/C][C]98.1849192483197[/C][C]0.0150807516802871[/C][/ROW]
[ROW][C]35[/C][C]98.48[/C][C]98.3912249653623[/C][C]0.0887750346376919[/C][/ROW]
[ROW][C]36[/C][C]98.53[/C][C]98.7083444843849[/C][C]-0.17834448438488[/C][/ROW]
[ROW][C]37[/C][C]98.71[/C][C]98.6837732774266[/C][C]0.0262267225733979[/C][/ROW]
[ROW][C]38[/C][C]99.03[/C][C]98.87473946101[/C][C]0.155260538989978[/C][/ROW]
[ROW][C]39[/C][C]99.52[/C][C]99.2596585742947[/C][C]0.260341425705306[/C][/ROW]
[ROW][C]40[/C][C]99.65[/C][C]99.8585151750639[/C][C]-0.208515175063937[/C][/ROW]
[ROW][C]41[/C][C]99.98[/C][C]99.9013286925256[/C][C]0.0786713074744085[/C][/ROW]
[ROW][C]42[/C][C]99.94[/C][C]100.26422353854[/C][C]-0.324223538539968[/C][/ROW]
[ROW][C]43[/C][C]100.12[/C][C]100.088655900008[/C][C]0.0313440999917276[/C][/ROW]
[ROW][C]44[/C][C]100.17[/C][C]100.281761813407[/C][C]-0.111761813406531[/C][/ROW]
[ROW][C]45[/C][C]100.38[/C][C]100.285030829007[/C][C]0.0949691709932097[/C][/ROW]
[ROW][C]46[/C][C]100.75[/C][C]100.534740303226[/C][C]0.215259696774169[/C][/ROW]
[ROW][C]47[/C][C]100.84[/C][C]100.994746873675[/C][C]-0.154746873674512[/C][/ROW]
[ROW][C]48[/C][C]100.91[/C][C]101.020042539348[/C][C]-0.110042539348015[/C][/ROW]
[ROW][C]49[/C][C]100.9[/C][C]101.044030435277[/C][C]-0.144030435277401[/C][/ROW]
[ROW][C]50[/C][C]101.15[/C][C]100.973806967002[/C][C]0.176193032997531[/C][/ROW]
[ROW][C]51[/C][C]101.4[/C][C]101.297478587258[/C][C]0.102521412742036[/C][/ROW]
[ROW][C]52[/C][C]101.39[/C][C]101.590345881493[/C][C]-0.200345881492552[/C][/ROW]
[ROW][C]53[/C][C]101.55[/C][C]101.496575226944[/C][C]0.0534247730558519[/C][/ROW]
[ROW][C]54[/C][C]101.73[/C][C]101.678913735601[/C][C]0.0510862643995011[/C][/ROW]
[ROW][C]55[/C][C]101.7[/C][C]101.880274443269[/C][C]-0.180274443269155[/C][/ROW]
[ROW][C]56[/C][C]101.65[/C][C]101.774896262303[/C][C]-0.124896262302812[/C][/ROW]
[ROW][C]57[/C][C]101.73[/C][C]101.672673368746[/C][C]0.0573266312541278[/C][/ROW]
[ROW][C]58[/C][C]101.53[/C][C]101.776643361977[/C][C]-0.246643361976766[/C][/ROW]
[ROW][C]59[/C][C]101.58[/C][C]101.473514334722[/C][C]0.106485665277944[/C][/ROW]
[ROW][C]60[/C][C]101.58[/C][C]101.568039202485[/C][C]0.011960797514746[/C][/ROW]
[ROW][C]61[/C][C]101.71[/C][C]101.573040372608[/C][C]0.136959627392017[/C][/ROW]
[ROW][C]62[/C][C]101.71[/C][C]101.760307322883[/C][C]-0.0503073228834694[/C][/ROW]
[ROW][C]63[/C][C]101.98[/C][C]101.739272314152[/C][C]0.240727685848086[/C][/ROW]
[ROW][C]64[/C][C]101.99[/C][C]102.109927818828[/C][C]-0.11992781882806[/C][/ROW]
[ROW][C]65[/C][C]101.95[/C][C]102.069782381313[/C][C]-0.119782381312959[/C][/ROW]
[ROW][C]66[/C][C]102.11[/C][C]101.979697755609[/C][C]0.130302244391331[/C][/ROW]
[ROW][C]67[/C][C]102.28[/C][C]102.194181053296[/C][C]0.0858189467040091[/C][/ROW]
[ROW][C]68[/C][C]102.32[/C][C]102.400064542812[/C][C]-0.0800645428116837[/C][/ROW]
[ROW][C]69[/C][C]102.18[/C][C]102.406587143089[/C][C]-0.226587143089304[/C][/ROW]
[ROW][C]70[/C][C]102.14[/C][C]102.171844225753[/C][C]-0.0318442257533889[/C][/ROW]
[ROW][C]71[/C][C]102.29[/C][C]102.118529194693[/C][C]0.17147080530728[/C][/ROW]
[ROW][C]72[/C][C]102.33[/C][C]102.340226309151[/C][C]-0.0102263091505961[/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
394.4794.67-0.200000000000003
494.3894.9463739689338-0.566373968933803
594.4294.6195559333281-0.199555933328071
694.3994.5761155799284-0.186115579928384
794.4294.4682950435834-0.0482950435834084
894.3494.4781014295082-0.138101429508154
994.5994.34035705733650.249642942663513
1094.6394.6947402997297-0.064740299729678
1194.8494.70767042814750.13232957185248
1294.9894.97300141258110.00699858741892001
1395.1995.11592773302570.0740722669743406
1495.7695.35689958152130.403100418478658
1596.0896.0954480221138-0.01544802211383
1696.0496.4089887382278-0.368988738227799
1796.296.2147034197972-0.0147034197972289
1896.3196.3685554765935-0.0585554765935115
1996.396.45407166607-0.154071666069996
2096.2996.379649656404-0.0896496564040206
2196.4696.33216443164650.127835568353532
2296.6696.55561633769890.104383662301061
2396.8396.79926229463090.0307377053691056
249796.98211465615140.0178853438486044
2597.197.159593057753-0.0595930577529771
2697.3397.23467540325810.0953245967419321
2797.3197.5045334917006-0.194533491700639
2897.1697.4031931725988-0.243193172598779
2997.497.15150677356460.2484932264354
3097.497.4954092849327-0.0954092849327424
3197.5297.45551578580380.0644842141961988
3297.7797.6024785803020.167521419697948
339897.92252433754160.077475662458383
3498.298.18491924831970.0150807516802871
3598.4898.39122496536230.0887750346376919
3698.5398.7083444843849-0.17834448438488
3798.7198.68377327742660.0262267225733979
3899.0398.874739461010.155260538989978
3999.5299.25965857429470.260341425705306
4099.6599.8585151750639-0.208515175063937
4199.9899.90132869252560.0786713074744085
4299.94100.26422353854-0.324223538539968
43100.12100.0886559000080.0313440999917276
44100.17100.281761813407-0.111761813406531
45100.38100.2850308290070.0949691709932097
46100.75100.5347403032260.215259696774169
47100.84100.994746873675-0.154746873674512
48100.91101.020042539348-0.110042539348015
49100.9101.044030435277-0.144030435277401
50101.15100.9738069670020.176193032997531
51101.4101.2974785872580.102521412742036
52101.39101.590345881493-0.200345881492552
53101.55101.4965752269440.0534247730558519
54101.73101.6789137356010.0510862643995011
55101.7101.880274443269-0.180274443269155
56101.65101.774896262303-0.124896262302812
57101.73101.6726733687460.0573266312541278
58101.53101.776643361977-0.246643361976766
59101.58101.4735143347220.106485665277944
60101.58101.5680392024850.011960797514746
61101.71101.5730403726080.136959627392017
62101.71101.760307322883-0.0503073228834694
63101.98101.7392723141520.240727685848086
64101.99102.109927818828-0.11992781882806
65101.95102.069782381313-0.119782381312959
66102.11101.9796977556090.130302244391331
67102.28102.1941810532960.0858189467040091
68102.32102.400064542812-0.0800645428116837
69102.18102.406587143089-0.226587143089304
70102.14102.171844225753-0.0318442257533889
71102.29102.1185291946930.17147080530728
72102.33102.340226309151-0.0102263091505961







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102.375950380917102.046422178943102.705478582891
74102.421900761834101.850086894765102.993714628903
75102.467851142751101.635314912726103.300387372776
76102.513801523668101.39800806188103.629594985456
77102.559751904585101.138282133522103.981221675647
78102.605702285502100.857037039491104.354367531513
79102.651652666419100.55529240794104.748012924898
80102.697603047336100.234021372519105.161184722153
81102.74355342825399.8941105117555105.59299634475
82102.7895038091799.5363565765269106.042651041813
83102.83545419008799.1614740045935106.50943437558
84102.88140457100498.7701048763707106.992704265637

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102.375950380917 & 102.046422178943 & 102.705478582891 \tabularnewline
74 & 102.421900761834 & 101.850086894765 & 102.993714628903 \tabularnewline
75 & 102.467851142751 & 101.635314912726 & 103.300387372776 \tabularnewline
76 & 102.513801523668 & 101.39800806188 & 103.629594985456 \tabularnewline
77 & 102.559751904585 & 101.138282133522 & 103.981221675647 \tabularnewline
78 & 102.605702285502 & 100.857037039491 & 104.354367531513 \tabularnewline
79 & 102.651652666419 & 100.55529240794 & 104.748012924898 \tabularnewline
80 & 102.697603047336 & 100.234021372519 & 105.161184722153 \tabularnewline
81 & 102.743553428253 & 99.8941105117555 & 105.59299634475 \tabularnewline
82 & 102.78950380917 & 99.5363565765269 & 106.042651041813 \tabularnewline
83 & 102.835454190087 & 99.1614740045935 & 106.50943437558 \tabularnewline
84 & 102.881404571004 & 98.7701048763707 & 106.992704265637 \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]102.375950380917[/C][C]102.046422178943[/C][C]102.705478582891[/C][/ROW]
[ROW][C]74[/C][C]102.421900761834[/C][C]101.850086894765[/C][C]102.993714628903[/C][/ROW]
[ROW][C]75[/C][C]102.467851142751[/C][C]101.635314912726[/C][C]103.300387372776[/C][/ROW]
[ROW][C]76[/C][C]102.513801523668[/C][C]101.39800806188[/C][C]103.629594985456[/C][/ROW]
[ROW][C]77[/C][C]102.559751904585[/C][C]101.138282133522[/C][C]103.981221675647[/C][/ROW]
[ROW][C]78[/C][C]102.605702285502[/C][C]100.857037039491[/C][C]104.354367531513[/C][/ROW]
[ROW][C]79[/C][C]102.651652666419[/C][C]100.55529240794[/C][C]104.748012924898[/C][/ROW]
[ROW][C]80[/C][C]102.697603047336[/C][C]100.234021372519[/C][C]105.161184722153[/C][/ROW]
[ROW][C]81[/C][C]102.743553428253[/C][C]99.8941105117555[/C][C]105.59299634475[/C][/ROW]
[ROW][C]82[/C][C]102.78950380917[/C][C]99.5363565765269[/C][C]106.042651041813[/C][/ROW]
[ROW][C]83[/C][C]102.835454190087[/C][C]99.1614740045935[/C][C]106.50943437558[/C][/ROW]
[ROW][C]84[/C][C]102.881404571004[/C][C]98.7701048763707[/C][C]106.992704265637[/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
73102.375950380917102.046422178943102.705478582891
74102.421900761834101.850086894765102.993714628903
75102.467851142751101.635314912726103.300387372776
76102.513801523668101.39800806188103.629594985456
77102.559751904585101.138282133522103.981221675647
78102.605702285502100.857037039491104.354367531513
79102.651652666419100.55529240794104.748012924898
80102.697603047336100.234021372519105.161184722153
81102.74355342825399.8941105117555105.59299634475
82102.7895038091799.5363565765269106.042651041813
83102.83545419008799.1614740045935106.50943437558
84102.88140457100498.7701048763707106.992704265637



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')