Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 29 Dec 2016 16:24:39 +0000
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/Dec/29/t14830293025jjbz0pagwrro28.htm/, Retrieved Thu, 02 May 2024 03:39:43 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Thu, 02 May 2024 03:39:43 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
102.59
102.91
101.94
101.8
102.25
102.6
102.49
102.13
100.76
100.86
101.12
100.74
99.99
99.39
99.52
99.21
99.38
99.37
99.38
99.26
99.36
99.2
98.53
98.65
99.15
100.17
99.98
100.07
99.94
100.05
99.13
98.74
98.64
98.44
98.81
98.88
99.63
100.08
100.07
100.55
99.98
99.89
99.86
99.61
100.12
100.24
100.1
99.86
97.99
97.57
98.28
97.97
97.99
97.84
97.33
96.7
96.79
96.76
96.23
96.29
96.46
97.23
97.59
97.13
97.37
96.12
96.96
96.7
97
97.15
96.51
96.68




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.083185237678146
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.083185237678146 \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]0.083185237678146[/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
beta0.083185237678146
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3101.94103.23-1.28999999999999
4101.8102.152691043395-0.352691043395183
5102.25101.9833523551230.266647644876599
6102.6102.4555335028390.144466497161218
7102.49102.817550982742-0.32755098274167
8102.13102.680303576391-0.55030357639059
9100.76102.274526442593-1.51452644259339
10100.86100.7785402004960.0814597995035626
11101.12100.8853164532790.234683546720646
12100.74101.164838659892-0.424838659892472
1399.99100.749498354994-0.759498354994449
1499.3999.9363193038181-0.546319303818066
1599.5299.29087360268180.229126397318197
1699.2199.439933536501-0.229933536501051
1799.3899.1108064606170.269193539382968
1899.3799.3031993891720.0668006108279826
1999.3899.29875621386080.0812437861391828
2099.2699.3155144975207-0.0555144975206474
2199.3699.19089651084980.169103489150174
2299.299.304963424787-0.104963424786988
2398.5399.1362320173486-0.606232017348574
2498.6598.41580246289730.234197537102673
2599.1598.55528424068490.59471575931515
26100.1799.10475581247441.06524418752558
2799.98100.213368403399-0.233368403398998
28100.07100.0039555972960.066044402704307
2999.94100.099449516632-0.159449516631952
30100.0599.95618567069330.0938143293067384
3199.13100.073989637974-0.943989637974255
3298.7499.0754636355737-0.33546363557366
3398.6498.6575580133161-0.0175580133160764
3498.4498.5560974458052-0.116097445805238
3598.8198.34643985218210.463560147817901
3698.8898.75500121325640.124998786743546
3799.6398.83539926704120.794600732958813
38100.0899.65149831787160.428501682128399
39100.07100.137143332145-0.0671433321449371
40100.55100.1215579981020.428442001898048
4199.98100.637198047861-0.657198047861144
4299.89100.012528872048-0.122528872048207
4399.8699.9123362787044-0.0523362787044448
4499.6199.8779826729212-0.267982672921221
45100.1299.60569047058060.514309529419364
46100.24100.1584734310260.0815265689744678
47100.1100.285255238043-0.185255238042757
4899.86100.129844737035-0.269844737035044
4997.9999.8673976384486-1.8773976384486
5097.5797.8412258696778-0.271225869677849
5198.2897.39866388124420.881336118755769
5297.9798.1819780357573-0.211978035757269
5397.9997.85434459247030.13565540752974
5497.8497.8856291197879-0.0456291197879324
5597.3397.7318334506133-0.401833450613339
5696.797.188406839517-0.48840683951704
5796.7996.51777860048820.272221399511821
5896.7696.63042340230770.129576597692349
5996.2396.6112022623842-0.381202262384221
6096.2996.04949186158430.240508138415663
6196.4696.1294985882420.330501411758021
6297.2396.3269914267320.903008573267982
6397.5997.17210840952470.417891590475278
6497.1397.5668708208021-0.436870820802113
6597.3797.0705296177390.299470382260964
6696.1297.335441132665-1.21544113266498
6796.9695.98433437316050.975665626839543
6896.796.9054953502235-0.205495350223487
699796.62840117067340.371598829326601
7097.1596.95931270761190.190687292388148
7196.5197.1251750753514-0.61517507535136
7296.6896.43400159049460.245998409505418

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 101.94 & 103.23 & -1.28999999999999 \tabularnewline
4 & 101.8 & 102.152691043395 & -0.352691043395183 \tabularnewline
5 & 102.25 & 101.983352355123 & 0.266647644876599 \tabularnewline
6 & 102.6 & 102.455533502839 & 0.144466497161218 \tabularnewline
7 & 102.49 & 102.817550982742 & -0.32755098274167 \tabularnewline
8 & 102.13 & 102.680303576391 & -0.55030357639059 \tabularnewline
9 & 100.76 & 102.274526442593 & -1.51452644259339 \tabularnewline
10 & 100.86 & 100.778540200496 & 0.0814597995035626 \tabularnewline
11 & 101.12 & 100.885316453279 & 0.234683546720646 \tabularnewline
12 & 100.74 & 101.164838659892 & -0.424838659892472 \tabularnewline
13 & 99.99 & 100.749498354994 & -0.759498354994449 \tabularnewline
14 & 99.39 & 99.9363193038181 & -0.546319303818066 \tabularnewline
15 & 99.52 & 99.2908736026818 & 0.229126397318197 \tabularnewline
16 & 99.21 & 99.439933536501 & -0.229933536501051 \tabularnewline
17 & 99.38 & 99.110806460617 & 0.269193539382968 \tabularnewline
18 & 99.37 & 99.303199389172 & 0.0668006108279826 \tabularnewline
19 & 99.38 & 99.2987562138608 & 0.0812437861391828 \tabularnewline
20 & 99.26 & 99.3155144975207 & -0.0555144975206474 \tabularnewline
21 & 99.36 & 99.1908965108498 & 0.169103489150174 \tabularnewline
22 & 99.2 & 99.304963424787 & -0.104963424786988 \tabularnewline
23 & 98.53 & 99.1362320173486 & -0.606232017348574 \tabularnewline
24 & 98.65 & 98.4158024628973 & 0.234197537102673 \tabularnewline
25 & 99.15 & 98.5552842406849 & 0.59471575931515 \tabularnewline
26 & 100.17 & 99.1047558124744 & 1.06524418752558 \tabularnewline
27 & 99.98 & 100.213368403399 & -0.233368403398998 \tabularnewline
28 & 100.07 & 100.003955597296 & 0.066044402704307 \tabularnewline
29 & 99.94 & 100.099449516632 & -0.159449516631952 \tabularnewline
30 & 100.05 & 99.9561856706933 & 0.0938143293067384 \tabularnewline
31 & 99.13 & 100.073989637974 & -0.943989637974255 \tabularnewline
32 & 98.74 & 99.0754636355737 & -0.33546363557366 \tabularnewline
33 & 98.64 & 98.6575580133161 & -0.0175580133160764 \tabularnewline
34 & 98.44 & 98.5560974458052 & -0.116097445805238 \tabularnewline
35 & 98.81 & 98.3464398521821 & 0.463560147817901 \tabularnewline
36 & 98.88 & 98.7550012132564 & 0.124998786743546 \tabularnewline
37 & 99.63 & 98.8353992670412 & 0.794600732958813 \tabularnewline
38 & 100.08 & 99.6514983178716 & 0.428501682128399 \tabularnewline
39 & 100.07 & 100.137143332145 & -0.0671433321449371 \tabularnewline
40 & 100.55 & 100.121557998102 & 0.428442001898048 \tabularnewline
41 & 99.98 & 100.637198047861 & -0.657198047861144 \tabularnewline
42 & 99.89 & 100.012528872048 & -0.122528872048207 \tabularnewline
43 & 99.86 & 99.9123362787044 & -0.0523362787044448 \tabularnewline
44 & 99.61 & 99.8779826729212 & -0.267982672921221 \tabularnewline
45 & 100.12 & 99.6056904705806 & 0.514309529419364 \tabularnewline
46 & 100.24 & 100.158473431026 & 0.0815265689744678 \tabularnewline
47 & 100.1 & 100.285255238043 & -0.185255238042757 \tabularnewline
48 & 99.86 & 100.129844737035 & -0.269844737035044 \tabularnewline
49 & 97.99 & 99.8673976384486 & -1.8773976384486 \tabularnewline
50 & 97.57 & 97.8412258696778 & -0.271225869677849 \tabularnewline
51 & 98.28 & 97.3986638812442 & 0.881336118755769 \tabularnewline
52 & 97.97 & 98.1819780357573 & -0.211978035757269 \tabularnewline
53 & 97.99 & 97.8543445924703 & 0.13565540752974 \tabularnewline
54 & 97.84 & 97.8856291197879 & -0.0456291197879324 \tabularnewline
55 & 97.33 & 97.7318334506133 & -0.401833450613339 \tabularnewline
56 & 96.7 & 97.188406839517 & -0.48840683951704 \tabularnewline
57 & 96.79 & 96.5177786004882 & 0.272221399511821 \tabularnewline
58 & 96.76 & 96.6304234023077 & 0.129576597692349 \tabularnewline
59 & 96.23 & 96.6112022623842 & -0.381202262384221 \tabularnewline
60 & 96.29 & 96.0494918615843 & 0.240508138415663 \tabularnewline
61 & 96.46 & 96.129498588242 & 0.330501411758021 \tabularnewline
62 & 97.23 & 96.326991426732 & 0.903008573267982 \tabularnewline
63 & 97.59 & 97.1721084095247 & 0.417891590475278 \tabularnewline
64 & 97.13 & 97.5668708208021 & -0.436870820802113 \tabularnewline
65 & 97.37 & 97.070529617739 & 0.299470382260964 \tabularnewline
66 & 96.12 & 97.335441132665 & -1.21544113266498 \tabularnewline
67 & 96.96 & 95.9843343731605 & 0.975665626839543 \tabularnewline
68 & 96.7 & 96.9054953502235 & -0.205495350223487 \tabularnewline
69 & 97 & 96.6284011706734 & 0.371598829326601 \tabularnewline
70 & 97.15 & 96.9593127076119 & 0.190687292388148 \tabularnewline
71 & 96.51 & 97.1251750753514 & -0.61517507535136 \tabularnewline
72 & 96.68 & 96.4340015904946 & 0.245998409505418 \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]101.94[/C][C]103.23[/C][C]-1.28999999999999[/C][/ROW]
[ROW][C]4[/C][C]101.8[/C][C]102.152691043395[/C][C]-0.352691043395183[/C][/ROW]
[ROW][C]5[/C][C]102.25[/C][C]101.983352355123[/C][C]0.266647644876599[/C][/ROW]
[ROW][C]6[/C][C]102.6[/C][C]102.455533502839[/C][C]0.144466497161218[/C][/ROW]
[ROW][C]7[/C][C]102.49[/C][C]102.817550982742[/C][C]-0.32755098274167[/C][/ROW]
[ROW][C]8[/C][C]102.13[/C][C]102.680303576391[/C][C]-0.55030357639059[/C][/ROW]
[ROW][C]9[/C][C]100.76[/C][C]102.274526442593[/C][C]-1.51452644259339[/C][/ROW]
[ROW][C]10[/C][C]100.86[/C][C]100.778540200496[/C][C]0.0814597995035626[/C][/ROW]
[ROW][C]11[/C][C]101.12[/C][C]100.885316453279[/C][C]0.234683546720646[/C][/ROW]
[ROW][C]12[/C][C]100.74[/C][C]101.164838659892[/C][C]-0.424838659892472[/C][/ROW]
[ROW][C]13[/C][C]99.99[/C][C]100.749498354994[/C][C]-0.759498354994449[/C][/ROW]
[ROW][C]14[/C][C]99.39[/C][C]99.9363193038181[/C][C]-0.546319303818066[/C][/ROW]
[ROW][C]15[/C][C]99.52[/C][C]99.2908736026818[/C][C]0.229126397318197[/C][/ROW]
[ROW][C]16[/C][C]99.21[/C][C]99.439933536501[/C][C]-0.229933536501051[/C][/ROW]
[ROW][C]17[/C][C]99.38[/C][C]99.110806460617[/C][C]0.269193539382968[/C][/ROW]
[ROW][C]18[/C][C]99.37[/C][C]99.303199389172[/C][C]0.0668006108279826[/C][/ROW]
[ROW][C]19[/C][C]99.38[/C][C]99.2987562138608[/C][C]0.0812437861391828[/C][/ROW]
[ROW][C]20[/C][C]99.26[/C][C]99.3155144975207[/C][C]-0.0555144975206474[/C][/ROW]
[ROW][C]21[/C][C]99.36[/C][C]99.1908965108498[/C][C]0.169103489150174[/C][/ROW]
[ROW][C]22[/C][C]99.2[/C][C]99.304963424787[/C][C]-0.104963424786988[/C][/ROW]
[ROW][C]23[/C][C]98.53[/C][C]99.1362320173486[/C][C]-0.606232017348574[/C][/ROW]
[ROW][C]24[/C][C]98.65[/C][C]98.4158024628973[/C][C]0.234197537102673[/C][/ROW]
[ROW][C]25[/C][C]99.15[/C][C]98.5552842406849[/C][C]0.59471575931515[/C][/ROW]
[ROW][C]26[/C][C]100.17[/C][C]99.1047558124744[/C][C]1.06524418752558[/C][/ROW]
[ROW][C]27[/C][C]99.98[/C][C]100.213368403399[/C][C]-0.233368403398998[/C][/ROW]
[ROW][C]28[/C][C]100.07[/C][C]100.003955597296[/C][C]0.066044402704307[/C][/ROW]
[ROW][C]29[/C][C]99.94[/C][C]100.099449516632[/C][C]-0.159449516631952[/C][/ROW]
[ROW][C]30[/C][C]100.05[/C][C]99.9561856706933[/C][C]0.0938143293067384[/C][/ROW]
[ROW][C]31[/C][C]99.13[/C][C]100.073989637974[/C][C]-0.943989637974255[/C][/ROW]
[ROW][C]32[/C][C]98.74[/C][C]99.0754636355737[/C][C]-0.33546363557366[/C][/ROW]
[ROW][C]33[/C][C]98.64[/C][C]98.6575580133161[/C][C]-0.0175580133160764[/C][/ROW]
[ROW][C]34[/C][C]98.44[/C][C]98.5560974458052[/C][C]-0.116097445805238[/C][/ROW]
[ROW][C]35[/C][C]98.81[/C][C]98.3464398521821[/C][C]0.463560147817901[/C][/ROW]
[ROW][C]36[/C][C]98.88[/C][C]98.7550012132564[/C][C]0.124998786743546[/C][/ROW]
[ROW][C]37[/C][C]99.63[/C][C]98.8353992670412[/C][C]0.794600732958813[/C][/ROW]
[ROW][C]38[/C][C]100.08[/C][C]99.6514983178716[/C][C]0.428501682128399[/C][/ROW]
[ROW][C]39[/C][C]100.07[/C][C]100.137143332145[/C][C]-0.0671433321449371[/C][/ROW]
[ROW][C]40[/C][C]100.55[/C][C]100.121557998102[/C][C]0.428442001898048[/C][/ROW]
[ROW][C]41[/C][C]99.98[/C][C]100.637198047861[/C][C]-0.657198047861144[/C][/ROW]
[ROW][C]42[/C][C]99.89[/C][C]100.012528872048[/C][C]-0.122528872048207[/C][/ROW]
[ROW][C]43[/C][C]99.86[/C][C]99.9123362787044[/C][C]-0.0523362787044448[/C][/ROW]
[ROW][C]44[/C][C]99.61[/C][C]99.8779826729212[/C][C]-0.267982672921221[/C][/ROW]
[ROW][C]45[/C][C]100.12[/C][C]99.6056904705806[/C][C]0.514309529419364[/C][/ROW]
[ROW][C]46[/C][C]100.24[/C][C]100.158473431026[/C][C]0.0815265689744678[/C][/ROW]
[ROW][C]47[/C][C]100.1[/C][C]100.285255238043[/C][C]-0.185255238042757[/C][/ROW]
[ROW][C]48[/C][C]99.86[/C][C]100.129844737035[/C][C]-0.269844737035044[/C][/ROW]
[ROW][C]49[/C][C]97.99[/C][C]99.8673976384486[/C][C]-1.8773976384486[/C][/ROW]
[ROW][C]50[/C][C]97.57[/C][C]97.8412258696778[/C][C]-0.271225869677849[/C][/ROW]
[ROW][C]51[/C][C]98.28[/C][C]97.3986638812442[/C][C]0.881336118755769[/C][/ROW]
[ROW][C]52[/C][C]97.97[/C][C]98.1819780357573[/C][C]-0.211978035757269[/C][/ROW]
[ROW][C]53[/C][C]97.99[/C][C]97.8543445924703[/C][C]0.13565540752974[/C][/ROW]
[ROW][C]54[/C][C]97.84[/C][C]97.8856291197879[/C][C]-0.0456291197879324[/C][/ROW]
[ROW][C]55[/C][C]97.33[/C][C]97.7318334506133[/C][C]-0.401833450613339[/C][/ROW]
[ROW][C]56[/C][C]96.7[/C][C]97.188406839517[/C][C]-0.48840683951704[/C][/ROW]
[ROW][C]57[/C][C]96.79[/C][C]96.5177786004882[/C][C]0.272221399511821[/C][/ROW]
[ROW][C]58[/C][C]96.76[/C][C]96.6304234023077[/C][C]0.129576597692349[/C][/ROW]
[ROW][C]59[/C][C]96.23[/C][C]96.6112022623842[/C][C]-0.381202262384221[/C][/ROW]
[ROW][C]60[/C][C]96.29[/C][C]96.0494918615843[/C][C]0.240508138415663[/C][/ROW]
[ROW][C]61[/C][C]96.46[/C][C]96.129498588242[/C][C]0.330501411758021[/C][/ROW]
[ROW][C]62[/C][C]97.23[/C][C]96.326991426732[/C][C]0.903008573267982[/C][/ROW]
[ROW][C]63[/C][C]97.59[/C][C]97.1721084095247[/C][C]0.417891590475278[/C][/ROW]
[ROW][C]64[/C][C]97.13[/C][C]97.5668708208021[/C][C]-0.436870820802113[/C][/ROW]
[ROW][C]65[/C][C]97.37[/C][C]97.070529617739[/C][C]0.299470382260964[/C][/ROW]
[ROW][C]66[/C][C]96.12[/C][C]97.335441132665[/C][C]-1.21544113266498[/C][/ROW]
[ROW][C]67[/C][C]96.96[/C][C]95.9843343731605[/C][C]0.975665626839543[/C][/ROW]
[ROW][C]68[/C][C]96.7[/C][C]96.9054953502235[/C][C]-0.205495350223487[/C][/ROW]
[ROW][C]69[/C][C]97[/C][C]96.6284011706734[/C][C]0.371598829326601[/C][/ROW]
[ROW][C]70[/C][C]97.15[/C][C]96.9593127076119[/C][C]0.190687292388148[/C][/ROW]
[ROW][C]71[/C][C]96.51[/C][C]97.1251750753514[/C][C]-0.61517507535136[/C][/ROW]
[ROW][C]72[/C][C]96.68[/C][C]96.4340015904946[/C][C]0.245998409505418[/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
3101.94103.23-1.28999999999999
4101.8102.152691043395-0.352691043395183
5102.25101.9833523551230.266647644876599
6102.6102.4555335028390.144466497161218
7102.49102.817550982742-0.32755098274167
8102.13102.680303576391-0.55030357639059
9100.76102.274526442593-1.51452644259339
10100.86100.7785402004960.0814597995035626
11101.12100.8853164532790.234683546720646
12100.74101.164838659892-0.424838659892472
1399.99100.749498354994-0.759498354994449
1499.3999.9363193038181-0.546319303818066
1599.5299.29087360268180.229126397318197
1699.2199.439933536501-0.229933536501051
1799.3899.1108064606170.269193539382968
1899.3799.3031993891720.0668006108279826
1999.3899.29875621386080.0812437861391828
2099.2699.3155144975207-0.0555144975206474
2199.3699.19089651084980.169103489150174
2299.299.304963424787-0.104963424786988
2398.5399.1362320173486-0.606232017348574
2498.6598.41580246289730.234197537102673
2599.1598.55528424068490.59471575931515
26100.1799.10475581247441.06524418752558
2799.98100.213368403399-0.233368403398998
28100.07100.0039555972960.066044402704307
2999.94100.099449516632-0.159449516631952
30100.0599.95618567069330.0938143293067384
3199.13100.073989637974-0.943989637974255
3298.7499.0754636355737-0.33546363557366
3398.6498.6575580133161-0.0175580133160764
3498.4498.5560974458052-0.116097445805238
3598.8198.34643985218210.463560147817901
3698.8898.75500121325640.124998786743546
3799.6398.83539926704120.794600732958813
38100.0899.65149831787160.428501682128399
39100.07100.137143332145-0.0671433321449371
40100.55100.1215579981020.428442001898048
4199.98100.637198047861-0.657198047861144
4299.89100.012528872048-0.122528872048207
4399.8699.9123362787044-0.0523362787044448
4499.6199.8779826729212-0.267982672921221
45100.1299.60569047058060.514309529419364
46100.24100.1584734310260.0815265689744678
47100.1100.285255238043-0.185255238042757
4899.86100.129844737035-0.269844737035044
4997.9999.8673976384486-1.8773976384486
5097.5797.8412258696778-0.271225869677849
5198.2897.39866388124420.881336118755769
5297.9798.1819780357573-0.211978035757269
5397.9997.85434459247030.13565540752974
5497.8497.8856291197879-0.0456291197879324
5597.3397.7318334506133-0.401833450613339
5696.797.188406839517-0.48840683951704
5796.7996.51777860048820.272221399511821
5896.7696.63042340230770.129576597692349
5996.2396.6112022623842-0.381202262384221
6096.2996.04949186158430.240508138415663
6196.4696.1294985882420.330501411758021
6297.2396.3269914267320.903008573267982
6397.5997.17210840952470.417891590475278
6497.1397.5668708208021-0.436870820802113
6597.3797.0705296177390.299470382260964
6696.1297.335441132665-1.21544113266498
6796.9695.98433437316050.975665626839543
6896.796.9054953502235-0.205495350223487
699796.62840117067340.371598829326601
7097.1596.95931270761190.190687292388148
7196.5197.1251750753514-0.61517507535136
7296.6896.43400159049460.245998409505418







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7396.624465026657795.558858618484697.6900714348309
7496.568930053315594.998004188604198.1398559180269
7596.513395079973294.510250494506698.5165396654399
7696.45786010663194.05253839110598.863181822157
7796.402325133288793.609033864631799.1956164019457
7896.346790159946593.172043876563599.5215364433294
7996.291255186604292.737257272068999.8452531011396
8096.23572021326292.3020383738137100.16940205271
8196.180185239919791.8646801778498100.49569030199
8296.124650266577491.4240322623993100.825268270756
8396.069115293235290.9792975244137101.158933062057
8496.013580319892990.5299132164833101.497247423303

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 96.6244650266577 & 95.5588586184846 & 97.6900714348309 \tabularnewline
74 & 96.5689300533155 & 94.9980041886041 & 98.1398559180269 \tabularnewline
75 & 96.5133950799732 & 94.5102504945066 & 98.5165396654399 \tabularnewline
76 & 96.457860106631 & 94.052538391105 & 98.863181822157 \tabularnewline
77 & 96.4023251332887 & 93.6090338646317 & 99.1956164019457 \tabularnewline
78 & 96.3467901599465 & 93.1720438765635 & 99.5215364433294 \tabularnewline
79 & 96.2912551866042 & 92.7372572720689 & 99.8452531011396 \tabularnewline
80 & 96.235720213262 & 92.3020383738137 & 100.16940205271 \tabularnewline
81 & 96.1801852399197 & 91.8646801778498 & 100.49569030199 \tabularnewline
82 & 96.1246502665774 & 91.4240322623993 & 100.825268270756 \tabularnewline
83 & 96.0691152932352 & 90.9792975244137 & 101.158933062057 \tabularnewline
84 & 96.0135803198929 & 90.5299132164833 & 101.497247423303 \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]96.6244650266577[/C][C]95.5588586184846[/C][C]97.6900714348309[/C][/ROW]
[ROW][C]74[/C][C]96.5689300533155[/C][C]94.9980041886041[/C][C]98.1398559180269[/C][/ROW]
[ROW][C]75[/C][C]96.5133950799732[/C][C]94.5102504945066[/C][C]98.5165396654399[/C][/ROW]
[ROW][C]76[/C][C]96.457860106631[/C][C]94.052538391105[/C][C]98.863181822157[/C][/ROW]
[ROW][C]77[/C][C]96.4023251332887[/C][C]93.6090338646317[/C][C]99.1956164019457[/C][/ROW]
[ROW][C]78[/C][C]96.3467901599465[/C][C]93.1720438765635[/C][C]99.5215364433294[/C][/ROW]
[ROW][C]79[/C][C]96.2912551866042[/C][C]92.7372572720689[/C][C]99.8452531011396[/C][/ROW]
[ROW][C]80[/C][C]96.235720213262[/C][C]92.3020383738137[/C][C]100.16940205271[/C][/ROW]
[ROW][C]81[/C][C]96.1801852399197[/C][C]91.8646801778498[/C][C]100.49569030199[/C][/ROW]
[ROW][C]82[/C][C]96.1246502665774[/C][C]91.4240322623993[/C][C]100.825268270756[/C][/ROW]
[ROW][C]83[/C][C]96.0691152932352[/C][C]90.9792975244137[/C][C]101.158933062057[/C][/ROW]
[ROW][C]84[/C][C]96.0135803198929[/C][C]90.5299132164833[/C][C]101.497247423303[/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
7396.624465026657795.558858618484697.6900714348309
7496.568930053315594.998004188604198.1398559180269
7596.513395079973294.510250494506698.5165396654399
7696.45786010663194.05253839110598.863181822157
7796.402325133288793.609033864631799.1956164019457
7896.346790159946593.172043876563599.5215364433294
7996.291255186604292.737257272068999.8452531011396
8096.23572021326292.3020383738137100.16940205271
8196.180185239919791.8646801778498100.49569030199
8296.124650266577491.4240322623993100.825268270756
8396.069115293235290.9792975244137101.158933062057
8496.013580319892990.5299132164833101.497247423303



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')