Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 May 2017 14:45:57 +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/02/t1493732854otrsci31z69l47i.htm/, Retrieved Fri, 17 May 2024 06:19:48 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 06:19:48 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
90,36
90,67
91,21
91,35
91,62
91,28
91,17
91,13
91,55
91,62
91,73
91,91
92,5
92,93
92,77
93,42
93,82
94,02
94,13
93,7
93,84
94,22
95,03
95,03
95,25
96,11
96,16
96,1
96,52
96,35
96,35
96,66
96,86
97,84
98,04
98,06
98,79
99,38
99,75
100,4
100,97
101,16
100,42
99,88
99,8
99,78
99,78
99,89
100,38
100,1
100,02
101,15
100,02
99,99
100,14
98,93
98,52
98,42
98,78
99,04
99,53
99,97
99,95
101,68
101,29
101,45
100,98
100,64
100,6
101,59
101,15
101,03




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.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]'George Udny Yule' @ yule.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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.883700397177305
beta0
gamma0.531325836948658

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.883700397177305 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.531325836948658 \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]0.883700397177305[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.531325836948658[/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
alpha0.883700397177305
beta0
gamma0.531325836948658







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1392.591.3655088177561.13449118224402
1492.9392.772459127080.157540872919995
1592.7792.75439857978420.0156014202157593
1693.4293.41958494657670.000415053423324707
1793.8293.77908344983370.0409165501662727
1894.0293.95265525452260.0673447454774134
1994.1393.62644706496170.503552935038329
2093.794.0460728404516-0.346072840451583
2193.8494.2136243982062-0.373624398206204
2294.2294.00514212863290.214857871367059
2395.0394.33026060925250.699739390747467
2495.0395.1270652525844-0.0970652525844429
2595.2595.6835185344909-0.433518534490929
2696.1195.64872046895890.461279531041114
2796.1695.87779173586080.282208264139243
2896.196.7937370968326-0.693737096832649
2996.5296.5469107187621-0.0269107187621529
3096.3596.6602442514917-0.310244251491724
3196.3596.01296088868570.337039111314297
3296.6696.2262489319640.433751068035974
3396.8697.0893796964741-0.229379696474112
3497.8497.04320234229850.796797657701518
3598.0497.91077503216360.129224967836421
3698.0698.1517740864763-0.0917740864763346
3798.7998.70529472514430.0847052748556791
3899.3899.19090268266560.189097317334443
3999.7599.15489722117640.595102778823588
40100.4100.3014907247130.0985092752868866
41100.97100.804879197660.165120802340454
42101.16101.0663849585080.0936150414917165
43100.42100.789229089377-0.369229089377356
4499.88100.372126743905-0.492126743904535
4599.8100.384050496016-0.584050496016218
4699.78100.087966489471-0.307966489470786
4799.7899.9362978464608-0.15629784646076
4899.8999.9096773175874-0.0196773175873659
49100.38100.546014838342-0.16601483834188
50100.1100.819947664923-0.719947664923367
51100.02100.002374583130.0176254168696062
52101.15100.6091175578170.540882442182792
53100.02101.509010928748-1.48901092874783
5499.99100.305057281271-0.315057281270569
55100.1499.6447002537940.495299746206044
5698.9399.9849337637116-1.05493376371155
5798.5299.4916172826425-0.971617282642541
5898.4298.8696595630217-0.449659563021655
5998.7898.60312634992640.176873650073617
6099.0498.88024189038550.159758109614458
6199.5399.6622632125999-0.132263212599852
6299.9799.92999353915440.0400064608456461
6399.9599.83016049345010.119839506549951
64101.68100.5590592452141.12094075478608
65101.29101.845287934782-0.555287934782356
66101.45101.538684098641-0.0886840986407975
67100.98101.120513909335-0.140513909334913
68100.64100.798961201795-0.158961201794511
69100.6101.106077706934-0.50607770693442
70101.59100.929017230890.660982769110447
71101.15101.681566158323-0.531566158323372
72101.03101.329469939476-0.299469939475827

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 92.5 & 91.365508817756 & 1.13449118224402 \tabularnewline
14 & 92.93 & 92.77245912708 & 0.157540872919995 \tabularnewline
15 & 92.77 & 92.7543985797842 & 0.0156014202157593 \tabularnewline
16 & 93.42 & 93.4195849465767 & 0.000415053423324707 \tabularnewline
17 & 93.82 & 93.7790834498337 & 0.0409165501662727 \tabularnewline
18 & 94.02 & 93.9526552545226 & 0.0673447454774134 \tabularnewline
19 & 94.13 & 93.6264470649617 & 0.503552935038329 \tabularnewline
20 & 93.7 & 94.0460728404516 & -0.346072840451583 \tabularnewline
21 & 93.84 & 94.2136243982062 & -0.373624398206204 \tabularnewline
22 & 94.22 & 94.0051421286329 & 0.214857871367059 \tabularnewline
23 & 95.03 & 94.3302606092525 & 0.699739390747467 \tabularnewline
24 & 95.03 & 95.1270652525844 & -0.0970652525844429 \tabularnewline
25 & 95.25 & 95.6835185344909 & -0.433518534490929 \tabularnewline
26 & 96.11 & 95.6487204689589 & 0.461279531041114 \tabularnewline
27 & 96.16 & 95.8777917358608 & 0.282208264139243 \tabularnewline
28 & 96.1 & 96.7937370968326 & -0.693737096832649 \tabularnewline
29 & 96.52 & 96.5469107187621 & -0.0269107187621529 \tabularnewline
30 & 96.35 & 96.6602442514917 & -0.310244251491724 \tabularnewline
31 & 96.35 & 96.0129608886857 & 0.337039111314297 \tabularnewline
32 & 96.66 & 96.226248931964 & 0.433751068035974 \tabularnewline
33 & 96.86 & 97.0893796964741 & -0.229379696474112 \tabularnewline
34 & 97.84 & 97.0432023422985 & 0.796797657701518 \tabularnewline
35 & 98.04 & 97.9107750321636 & 0.129224967836421 \tabularnewline
36 & 98.06 & 98.1517740864763 & -0.0917740864763346 \tabularnewline
37 & 98.79 & 98.7052947251443 & 0.0847052748556791 \tabularnewline
38 & 99.38 & 99.1909026826656 & 0.189097317334443 \tabularnewline
39 & 99.75 & 99.1548972211764 & 0.595102778823588 \tabularnewline
40 & 100.4 & 100.301490724713 & 0.0985092752868866 \tabularnewline
41 & 100.97 & 100.80487919766 & 0.165120802340454 \tabularnewline
42 & 101.16 & 101.066384958508 & 0.0936150414917165 \tabularnewline
43 & 100.42 & 100.789229089377 & -0.369229089377356 \tabularnewline
44 & 99.88 & 100.372126743905 & -0.492126743904535 \tabularnewline
45 & 99.8 & 100.384050496016 & -0.584050496016218 \tabularnewline
46 & 99.78 & 100.087966489471 & -0.307966489470786 \tabularnewline
47 & 99.78 & 99.9362978464608 & -0.15629784646076 \tabularnewline
48 & 99.89 & 99.9096773175874 & -0.0196773175873659 \tabularnewline
49 & 100.38 & 100.546014838342 & -0.16601483834188 \tabularnewline
50 & 100.1 & 100.819947664923 & -0.719947664923367 \tabularnewline
51 & 100.02 & 100.00237458313 & 0.0176254168696062 \tabularnewline
52 & 101.15 & 100.609117557817 & 0.540882442182792 \tabularnewline
53 & 100.02 & 101.509010928748 & -1.48901092874783 \tabularnewline
54 & 99.99 & 100.305057281271 & -0.315057281270569 \tabularnewline
55 & 100.14 & 99.644700253794 & 0.495299746206044 \tabularnewline
56 & 98.93 & 99.9849337637116 & -1.05493376371155 \tabularnewline
57 & 98.52 & 99.4916172826425 & -0.971617282642541 \tabularnewline
58 & 98.42 & 98.8696595630217 & -0.449659563021655 \tabularnewline
59 & 98.78 & 98.6031263499264 & 0.176873650073617 \tabularnewline
60 & 99.04 & 98.8802418903855 & 0.159758109614458 \tabularnewline
61 & 99.53 & 99.6622632125999 & -0.132263212599852 \tabularnewline
62 & 99.97 & 99.9299935391544 & 0.0400064608456461 \tabularnewline
63 & 99.95 & 99.8301604934501 & 0.119839506549951 \tabularnewline
64 & 101.68 & 100.559059245214 & 1.12094075478608 \tabularnewline
65 & 101.29 & 101.845287934782 & -0.555287934782356 \tabularnewline
66 & 101.45 & 101.538684098641 & -0.0886840986407975 \tabularnewline
67 & 100.98 & 101.120513909335 & -0.140513909334913 \tabularnewline
68 & 100.64 & 100.798961201795 & -0.158961201794511 \tabularnewline
69 & 100.6 & 101.106077706934 & -0.50607770693442 \tabularnewline
70 & 101.59 & 100.92901723089 & 0.660982769110447 \tabularnewline
71 & 101.15 & 101.681566158323 & -0.531566158323372 \tabularnewline
72 & 101.03 & 101.329469939476 & -0.299469939475827 \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]13[/C][C]92.5[/C][C]91.365508817756[/C][C]1.13449118224402[/C][/ROW]
[ROW][C]14[/C][C]92.93[/C][C]92.77245912708[/C][C]0.157540872919995[/C][/ROW]
[ROW][C]15[/C][C]92.77[/C][C]92.7543985797842[/C][C]0.0156014202157593[/C][/ROW]
[ROW][C]16[/C][C]93.42[/C][C]93.4195849465767[/C][C]0.000415053423324707[/C][/ROW]
[ROW][C]17[/C][C]93.82[/C][C]93.7790834498337[/C][C]0.0409165501662727[/C][/ROW]
[ROW][C]18[/C][C]94.02[/C][C]93.9526552545226[/C][C]0.0673447454774134[/C][/ROW]
[ROW][C]19[/C][C]94.13[/C][C]93.6264470649617[/C][C]0.503552935038329[/C][/ROW]
[ROW][C]20[/C][C]93.7[/C][C]94.0460728404516[/C][C]-0.346072840451583[/C][/ROW]
[ROW][C]21[/C][C]93.84[/C][C]94.2136243982062[/C][C]-0.373624398206204[/C][/ROW]
[ROW][C]22[/C][C]94.22[/C][C]94.0051421286329[/C][C]0.214857871367059[/C][/ROW]
[ROW][C]23[/C][C]95.03[/C][C]94.3302606092525[/C][C]0.699739390747467[/C][/ROW]
[ROW][C]24[/C][C]95.03[/C][C]95.1270652525844[/C][C]-0.0970652525844429[/C][/ROW]
[ROW][C]25[/C][C]95.25[/C][C]95.6835185344909[/C][C]-0.433518534490929[/C][/ROW]
[ROW][C]26[/C][C]96.11[/C][C]95.6487204689589[/C][C]0.461279531041114[/C][/ROW]
[ROW][C]27[/C][C]96.16[/C][C]95.8777917358608[/C][C]0.282208264139243[/C][/ROW]
[ROW][C]28[/C][C]96.1[/C][C]96.7937370968326[/C][C]-0.693737096832649[/C][/ROW]
[ROW][C]29[/C][C]96.52[/C][C]96.5469107187621[/C][C]-0.0269107187621529[/C][/ROW]
[ROW][C]30[/C][C]96.35[/C][C]96.6602442514917[/C][C]-0.310244251491724[/C][/ROW]
[ROW][C]31[/C][C]96.35[/C][C]96.0129608886857[/C][C]0.337039111314297[/C][/ROW]
[ROW][C]32[/C][C]96.66[/C][C]96.226248931964[/C][C]0.433751068035974[/C][/ROW]
[ROW][C]33[/C][C]96.86[/C][C]97.0893796964741[/C][C]-0.229379696474112[/C][/ROW]
[ROW][C]34[/C][C]97.84[/C][C]97.0432023422985[/C][C]0.796797657701518[/C][/ROW]
[ROW][C]35[/C][C]98.04[/C][C]97.9107750321636[/C][C]0.129224967836421[/C][/ROW]
[ROW][C]36[/C][C]98.06[/C][C]98.1517740864763[/C][C]-0.0917740864763346[/C][/ROW]
[ROW][C]37[/C][C]98.79[/C][C]98.7052947251443[/C][C]0.0847052748556791[/C][/ROW]
[ROW][C]38[/C][C]99.38[/C][C]99.1909026826656[/C][C]0.189097317334443[/C][/ROW]
[ROW][C]39[/C][C]99.75[/C][C]99.1548972211764[/C][C]0.595102778823588[/C][/ROW]
[ROW][C]40[/C][C]100.4[/C][C]100.301490724713[/C][C]0.0985092752868866[/C][/ROW]
[ROW][C]41[/C][C]100.97[/C][C]100.80487919766[/C][C]0.165120802340454[/C][/ROW]
[ROW][C]42[/C][C]101.16[/C][C]101.066384958508[/C][C]0.0936150414917165[/C][/ROW]
[ROW][C]43[/C][C]100.42[/C][C]100.789229089377[/C][C]-0.369229089377356[/C][/ROW]
[ROW][C]44[/C][C]99.88[/C][C]100.372126743905[/C][C]-0.492126743904535[/C][/ROW]
[ROW][C]45[/C][C]99.8[/C][C]100.384050496016[/C][C]-0.584050496016218[/C][/ROW]
[ROW][C]46[/C][C]99.78[/C][C]100.087966489471[/C][C]-0.307966489470786[/C][/ROW]
[ROW][C]47[/C][C]99.78[/C][C]99.9362978464608[/C][C]-0.15629784646076[/C][/ROW]
[ROW][C]48[/C][C]99.89[/C][C]99.9096773175874[/C][C]-0.0196773175873659[/C][/ROW]
[ROW][C]49[/C][C]100.38[/C][C]100.546014838342[/C][C]-0.16601483834188[/C][/ROW]
[ROW][C]50[/C][C]100.1[/C][C]100.819947664923[/C][C]-0.719947664923367[/C][/ROW]
[ROW][C]51[/C][C]100.02[/C][C]100.00237458313[/C][C]0.0176254168696062[/C][/ROW]
[ROW][C]52[/C][C]101.15[/C][C]100.609117557817[/C][C]0.540882442182792[/C][/ROW]
[ROW][C]53[/C][C]100.02[/C][C]101.509010928748[/C][C]-1.48901092874783[/C][/ROW]
[ROW][C]54[/C][C]99.99[/C][C]100.305057281271[/C][C]-0.315057281270569[/C][/ROW]
[ROW][C]55[/C][C]100.14[/C][C]99.644700253794[/C][C]0.495299746206044[/C][/ROW]
[ROW][C]56[/C][C]98.93[/C][C]99.9849337637116[/C][C]-1.05493376371155[/C][/ROW]
[ROW][C]57[/C][C]98.52[/C][C]99.4916172826425[/C][C]-0.971617282642541[/C][/ROW]
[ROW][C]58[/C][C]98.42[/C][C]98.8696595630217[/C][C]-0.449659563021655[/C][/ROW]
[ROW][C]59[/C][C]98.78[/C][C]98.6031263499264[/C][C]0.176873650073617[/C][/ROW]
[ROW][C]60[/C][C]99.04[/C][C]98.8802418903855[/C][C]0.159758109614458[/C][/ROW]
[ROW][C]61[/C][C]99.53[/C][C]99.6622632125999[/C][C]-0.132263212599852[/C][/ROW]
[ROW][C]62[/C][C]99.97[/C][C]99.9299935391544[/C][C]0.0400064608456461[/C][/ROW]
[ROW][C]63[/C][C]99.95[/C][C]99.8301604934501[/C][C]0.119839506549951[/C][/ROW]
[ROW][C]64[/C][C]101.68[/C][C]100.559059245214[/C][C]1.12094075478608[/C][/ROW]
[ROW][C]65[/C][C]101.29[/C][C]101.845287934782[/C][C]-0.555287934782356[/C][/ROW]
[ROW][C]66[/C][C]101.45[/C][C]101.538684098641[/C][C]-0.0886840986407975[/C][/ROW]
[ROW][C]67[/C][C]100.98[/C][C]101.120513909335[/C][C]-0.140513909334913[/C][/ROW]
[ROW][C]68[/C][C]100.64[/C][C]100.798961201795[/C][C]-0.158961201794511[/C][/ROW]
[ROW][C]69[/C][C]100.6[/C][C]101.106077706934[/C][C]-0.50607770693442[/C][/ROW]
[ROW][C]70[/C][C]101.59[/C][C]100.92901723089[/C][C]0.660982769110447[/C][/ROW]
[ROW][C]71[/C][C]101.15[/C][C]101.681566158323[/C][C]-0.531566158323372[/C][/ROW]
[ROW][C]72[/C][C]101.03[/C][C]101.329469939476[/C][C]-0.299469939475827[/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
1392.591.3655088177561.13449118224402
1492.9392.772459127080.157540872919995
1592.7792.75439857978420.0156014202157593
1693.4293.41958494657670.000415053423324707
1793.8293.77908344983370.0409165501662727
1894.0293.95265525452260.0673447454774134
1994.1393.62644706496170.503552935038329
2093.794.0460728404516-0.346072840451583
2193.8494.2136243982062-0.373624398206204
2294.2294.00514212863290.214857871367059
2395.0394.33026060925250.699739390747467
2495.0395.1270652525844-0.0970652525844429
2595.2595.6835185344909-0.433518534490929
2696.1195.64872046895890.461279531041114
2796.1695.87779173586080.282208264139243
2896.196.7937370968326-0.693737096832649
2996.5296.5469107187621-0.0269107187621529
3096.3596.6602442514917-0.310244251491724
3196.3596.01296088868570.337039111314297
3296.6696.2262489319640.433751068035974
3396.8697.0893796964741-0.229379696474112
3497.8497.04320234229850.796797657701518
3598.0497.91077503216360.129224967836421
3698.0698.1517740864763-0.0917740864763346
3798.7998.70529472514430.0847052748556791
3899.3899.19090268266560.189097317334443
3999.7599.15489722117640.595102778823588
40100.4100.3014907247130.0985092752868866
41100.97100.804879197660.165120802340454
42101.16101.0663849585080.0936150414917165
43100.42100.789229089377-0.369229089377356
4499.88100.372126743905-0.492126743904535
4599.8100.384050496016-0.584050496016218
4699.78100.087966489471-0.307966489470786
4799.7899.9362978464608-0.15629784646076
4899.8999.9096773175874-0.0196773175873659
49100.38100.546014838342-0.16601483834188
50100.1100.819947664923-0.719947664923367
51100.02100.002374583130.0176254168696062
52101.15100.6091175578170.540882442182792
53100.02101.509010928748-1.48901092874783
5499.99100.305057281271-0.315057281270569
55100.1499.6447002537940.495299746206044
5698.9399.9849337637116-1.05493376371155
5798.5299.4916172826425-0.971617282642541
5898.4298.8696595630217-0.449659563021655
5998.7898.60312634992640.176873650073617
6099.0498.88024189038550.159758109614458
6199.5399.6622632125999-0.132263212599852
6299.9799.92999353915440.0400064608456461
6399.9599.83016049345010.119839506549951
64101.68100.5590592452141.12094075478608
65101.29101.845287934782-0.555287934782356
66101.45101.538684098641-0.0886840986407975
67100.98101.120513909335-0.140513909334913
68100.64100.798961201795-0.158961201794511
69100.6101.106077706934-0.50607770693442
70101.59100.929017230890.660982769110447
71101.15101.681566158323-0.531566158323372
72101.03101.329469939476-0.299469939475827







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73101.696191344509100.790979128496102.601403560522
74102.095560429635100.855422096449103.335698762822
75101.958164900321100.460117970688103.456211829953
76102.65198822358100.92558021942104.37839622774
77102.843753882356100.921386127241104.76612163747
78103.05679281556100.956363986369105.157221644751
79102.705129937751100.450976438086104.959283437416
80102.499750756814100.100289592679104.89921192095
81102.92982854998100.38068343572105.47897366424
82103.27501285575100.585884077054105.964141634446
83103.367745497289100.551399837137106.184091157442
84103.49812231927298.2849564525581108.711288185986

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 101.696191344509 & 100.790979128496 & 102.601403560522 \tabularnewline
74 & 102.095560429635 & 100.855422096449 & 103.335698762822 \tabularnewline
75 & 101.958164900321 & 100.460117970688 & 103.456211829953 \tabularnewline
76 & 102.65198822358 & 100.92558021942 & 104.37839622774 \tabularnewline
77 & 102.843753882356 & 100.921386127241 & 104.76612163747 \tabularnewline
78 & 103.05679281556 & 100.956363986369 & 105.157221644751 \tabularnewline
79 & 102.705129937751 & 100.450976438086 & 104.959283437416 \tabularnewline
80 & 102.499750756814 & 100.100289592679 & 104.89921192095 \tabularnewline
81 & 102.92982854998 & 100.38068343572 & 105.47897366424 \tabularnewline
82 & 103.27501285575 & 100.585884077054 & 105.964141634446 \tabularnewline
83 & 103.367745497289 & 100.551399837137 & 106.184091157442 \tabularnewline
84 & 103.498122319272 & 98.2849564525581 & 108.711288185986 \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]101.696191344509[/C][C]100.790979128496[/C][C]102.601403560522[/C][/ROW]
[ROW][C]74[/C][C]102.095560429635[/C][C]100.855422096449[/C][C]103.335698762822[/C][/ROW]
[ROW][C]75[/C][C]101.958164900321[/C][C]100.460117970688[/C][C]103.456211829953[/C][/ROW]
[ROW][C]76[/C][C]102.65198822358[/C][C]100.92558021942[/C][C]104.37839622774[/C][/ROW]
[ROW][C]77[/C][C]102.843753882356[/C][C]100.921386127241[/C][C]104.76612163747[/C][/ROW]
[ROW][C]78[/C][C]103.05679281556[/C][C]100.956363986369[/C][C]105.157221644751[/C][/ROW]
[ROW][C]79[/C][C]102.705129937751[/C][C]100.450976438086[/C][C]104.959283437416[/C][/ROW]
[ROW][C]80[/C][C]102.499750756814[/C][C]100.100289592679[/C][C]104.89921192095[/C][/ROW]
[ROW][C]81[/C][C]102.92982854998[/C][C]100.38068343572[/C][C]105.47897366424[/C][/ROW]
[ROW][C]82[/C][C]103.27501285575[/C][C]100.585884077054[/C][C]105.964141634446[/C][/ROW]
[ROW][C]83[/C][C]103.367745497289[/C][C]100.551399837137[/C][C]106.184091157442[/C][/ROW]
[ROW][C]84[/C][C]103.498122319272[/C][C]98.2849564525581[/C][C]108.711288185986[/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
73101.696191344509100.790979128496102.601403560522
74102.095560429635100.855422096449103.335698762822
75101.958164900321100.460117970688103.456211829953
76102.65198822358100.92558021942104.37839622774
77102.843753882356100.921386127241104.76612163747
78103.05679281556100.956363986369105.157221644751
79102.705129937751100.450976438086104.959283437416
80102.499750756814100.100289592679104.89921192095
81102.92982854998100.38068343572105.47897366424
82103.27501285575100.585884077054105.964141634446
83103.367745497289100.551399837137106.184091157442
84103.49812231927298.2849564525581108.711288185986



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