Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Apr 2017 20:22:54 +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/Apr/30/t1493580236a5ki0neopbpkf4g.htm/, Retrieved Mon, 13 May 2024 19:58:37 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 13 May 2024 19:58:37 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
101.16
100.81
100.94
101.13
101.29
101.34
101.35
101.7
102.05
102.48
102.66
102.72
102.73
102.18
102.22
102.37
102.53
102.61
102.62
103
103.17
103.52
103.69
103.73
99.57
99.09
99.14
99.36
99.6
99.65
99.8
100.15
100.45
100.89
101.13
101.17
101.21
101.1
101.17
101.11
101.2
101.15
100.92
101.1
101.22
101.25
101.39
101.43
101.95
101.92
102.05
102.07
102.1
102.16
101.63
101.43
101.4
101.6
101.72
101.73
102.67
102.59
102.69
102.93
103.02
103.06
102.47
102.4
102.42
102.51
102.61
102.78




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.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 time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.064127696335847
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.064127696335847 \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]0.064127696335847[/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
beta0.064127696335847
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3100.94100.460.47999999999999
4101.13100.6207812942410.509218705758784
5101.29100.8434363167730.446563683227367
6101.34101.0320734170450.307926582954735
7101.35101.1018200394510.248179960549265
8101.7101.1277352485970.572264751402543
9102.05101.5144332687990.535566731200873
10102.48101.8987779295050.58122207049486
11102.66102.3660503619460.293949638054457
12102.72102.5649006750730.155099324927278
13102.73102.6348468374840.0951531625164534
14102.18102.650948790595-0.470948790594804
15102.22102.0707479295620.14925207043818
16102.37102.1203191210120.249680878987647
17102.53102.2863305806010.243669419399041
18102.61102.4619565391350.148043460865495
19102.62102.5514502252370.0685497747626016
20103102.5658461643770.434153835622737
21103.17102.9736874497110.19631255028888
22103.52103.1562765213230.363723478677031
23103.69103.5296012701140.160398729886225
24103.73103.7098872711570.0201127288434293
2599.57103.751177054124-4.18117705412435
2699.0999.323047801671-0.233047801671034
2799.1498.82810298301370.311897016986251
2899.3698.89810422020710.461895779792911
2999.699.14772453251250.452275467487539
3099.6599.41672791635160.233272083648359
3199.899.48168711769550.318312882304497
32100.1599.65209978955170.497900210448307
33100.45100.0340289830530.415971016947111
34100.89100.3607042461120.529295753887823
35101.13100.8346467634890.29535323651065
36101.17101.0935870861520.0764129138478893
37101.21101.1384872702870.0715127297124951
38101.1101.183073216903-0.0830732169026476
39101.17101.0677459228750.102254077124542
40101.11101.144303241282-0.0343032412824158
41101.2101.0821034534420.117896546557887
42101.15101.179663887379-0.0296638873788311
43100.92101.127761610617-0.207761610616856
44101.1100.8844383371410.215561662859017
45101.22101.0782618099980.141738190001561
46101.25101.2073511536060.042648846393945
47101.39101.2400861258770.149913874123314
48101.43101.3896997572730.0403002427270138
49101.95101.4322841190010.517715880999148
50101.92101.985484045806-0.0654840458058175
51102.05101.9512847048020.0987152951984598
52102.07102.087615089276-0.0176150892757221
53102.1102.10648547418-0.00648547417972622
54102.16102.1360695756610.0239304243390706
55101.63102.197604178646-0.567604178646135
56101.43101.631205030239-0.201205030238953
57101.4101.418302215159-0.0183022151585561
58101.6101.3871285362630.2128714637374
59101.72101.6007794928480.119220507152292
60101.73101.7284248293270.00157517067262347
61102.67101.7385258413940.931474158606051
62102.59102.738259133382-0.148259133381728
63102.69102.6487516166970.0412483833027864
64102.93102.7513967804960.178603219504012
65103.02103.0028501935210.0171498064790399
66103.06103.093949971103-0.0339499711030555
67102.47103.131772837666-0.661772837665552
68102.4102.499334870088-0.0993348700884127
69102.42102.422964753704-0.00296475370383575
70102.51102.4427746308790.0672253691214024
71102.61102.5370856389360.0729143610643064
72102.78102.6417614689410.138238531059471

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 100.94 & 100.46 & 0.47999999999999 \tabularnewline
4 & 101.13 & 100.620781294241 & 0.509218705758784 \tabularnewline
5 & 101.29 & 100.843436316773 & 0.446563683227367 \tabularnewline
6 & 101.34 & 101.032073417045 & 0.307926582954735 \tabularnewline
7 & 101.35 & 101.101820039451 & 0.248179960549265 \tabularnewline
8 & 101.7 & 101.127735248597 & 0.572264751402543 \tabularnewline
9 & 102.05 & 101.514433268799 & 0.535566731200873 \tabularnewline
10 & 102.48 & 101.898777929505 & 0.58122207049486 \tabularnewline
11 & 102.66 & 102.366050361946 & 0.293949638054457 \tabularnewline
12 & 102.72 & 102.564900675073 & 0.155099324927278 \tabularnewline
13 & 102.73 & 102.634846837484 & 0.0951531625164534 \tabularnewline
14 & 102.18 & 102.650948790595 & -0.470948790594804 \tabularnewline
15 & 102.22 & 102.070747929562 & 0.14925207043818 \tabularnewline
16 & 102.37 & 102.120319121012 & 0.249680878987647 \tabularnewline
17 & 102.53 & 102.286330580601 & 0.243669419399041 \tabularnewline
18 & 102.61 & 102.461956539135 & 0.148043460865495 \tabularnewline
19 & 102.62 & 102.551450225237 & 0.0685497747626016 \tabularnewline
20 & 103 & 102.565846164377 & 0.434153835622737 \tabularnewline
21 & 103.17 & 102.973687449711 & 0.19631255028888 \tabularnewline
22 & 103.52 & 103.156276521323 & 0.363723478677031 \tabularnewline
23 & 103.69 & 103.529601270114 & 0.160398729886225 \tabularnewline
24 & 103.73 & 103.709887271157 & 0.0201127288434293 \tabularnewline
25 & 99.57 & 103.751177054124 & -4.18117705412435 \tabularnewline
26 & 99.09 & 99.323047801671 & -0.233047801671034 \tabularnewline
27 & 99.14 & 98.8281029830137 & 0.311897016986251 \tabularnewline
28 & 99.36 & 98.8981042202071 & 0.461895779792911 \tabularnewline
29 & 99.6 & 99.1477245325125 & 0.452275467487539 \tabularnewline
30 & 99.65 & 99.4167279163516 & 0.233272083648359 \tabularnewline
31 & 99.8 & 99.4816871176955 & 0.318312882304497 \tabularnewline
32 & 100.15 & 99.6520997895517 & 0.497900210448307 \tabularnewline
33 & 100.45 & 100.034028983053 & 0.415971016947111 \tabularnewline
34 & 100.89 & 100.360704246112 & 0.529295753887823 \tabularnewline
35 & 101.13 & 100.834646763489 & 0.29535323651065 \tabularnewline
36 & 101.17 & 101.093587086152 & 0.0764129138478893 \tabularnewline
37 & 101.21 & 101.138487270287 & 0.0715127297124951 \tabularnewline
38 & 101.1 & 101.183073216903 & -0.0830732169026476 \tabularnewline
39 & 101.17 & 101.067745922875 & 0.102254077124542 \tabularnewline
40 & 101.11 & 101.144303241282 & -0.0343032412824158 \tabularnewline
41 & 101.2 & 101.082103453442 & 0.117896546557887 \tabularnewline
42 & 101.15 & 101.179663887379 & -0.0296638873788311 \tabularnewline
43 & 100.92 & 101.127761610617 & -0.207761610616856 \tabularnewline
44 & 101.1 & 100.884438337141 & 0.215561662859017 \tabularnewline
45 & 101.22 & 101.078261809998 & 0.141738190001561 \tabularnewline
46 & 101.25 & 101.207351153606 & 0.042648846393945 \tabularnewline
47 & 101.39 & 101.240086125877 & 0.149913874123314 \tabularnewline
48 & 101.43 & 101.389699757273 & 0.0403002427270138 \tabularnewline
49 & 101.95 & 101.432284119001 & 0.517715880999148 \tabularnewline
50 & 101.92 & 101.985484045806 & -0.0654840458058175 \tabularnewline
51 & 102.05 & 101.951284704802 & 0.0987152951984598 \tabularnewline
52 & 102.07 & 102.087615089276 & -0.0176150892757221 \tabularnewline
53 & 102.1 & 102.10648547418 & -0.00648547417972622 \tabularnewline
54 & 102.16 & 102.136069575661 & 0.0239304243390706 \tabularnewline
55 & 101.63 & 102.197604178646 & -0.567604178646135 \tabularnewline
56 & 101.43 & 101.631205030239 & -0.201205030238953 \tabularnewline
57 & 101.4 & 101.418302215159 & -0.0183022151585561 \tabularnewline
58 & 101.6 & 101.387128536263 & 0.2128714637374 \tabularnewline
59 & 101.72 & 101.600779492848 & 0.119220507152292 \tabularnewline
60 & 101.73 & 101.728424829327 & 0.00157517067262347 \tabularnewline
61 & 102.67 & 101.738525841394 & 0.931474158606051 \tabularnewline
62 & 102.59 & 102.738259133382 & -0.148259133381728 \tabularnewline
63 & 102.69 & 102.648751616697 & 0.0412483833027864 \tabularnewline
64 & 102.93 & 102.751396780496 & 0.178603219504012 \tabularnewline
65 & 103.02 & 103.002850193521 & 0.0171498064790399 \tabularnewline
66 & 103.06 & 103.093949971103 & -0.0339499711030555 \tabularnewline
67 & 102.47 & 103.131772837666 & -0.661772837665552 \tabularnewline
68 & 102.4 & 102.499334870088 & -0.0993348700884127 \tabularnewline
69 & 102.42 & 102.422964753704 & -0.00296475370383575 \tabularnewline
70 & 102.51 & 102.442774630879 & 0.0672253691214024 \tabularnewline
71 & 102.61 & 102.537085638936 & 0.0729143610643064 \tabularnewline
72 & 102.78 & 102.641761468941 & 0.138238531059471 \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]100.94[/C][C]100.46[/C][C]0.47999999999999[/C][/ROW]
[ROW][C]4[/C][C]101.13[/C][C]100.620781294241[/C][C]0.509218705758784[/C][/ROW]
[ROW][C]5[/C][C]101.29[/C][C]100.843436316773[/C][C]0.446563683227367[/C][/ROW]
[ROW][C]6[/C][C]101.34[/C][C]101.032073417045[/C][C]0.307926582954735[/C][/ROW]
[ROW][C]7[/C][C]101.35[/C][C]101.101820039451[/C][C]0.248179960549265[/C][/ROW]
[ROW][C]8[/C][C]101.7[/C][C]101.127735248597[/C][C]0.572264751402543[/C][/ROW]
[ROW][C]9[/C][C]102.05[/C][C]101.514433268799[/C][C]0.535566731200873[/C][/ROW]
[ROW][C]10[/C][C]102.48[/C][C]101.898777929505[/C][C]0.58122207049486[/C][/ROW]
[ROW][C]11[/C][C]102.66[/C][C]102.366050361946[/C][C]0.293949638054457[/C][/ROW]
[ROW][C]12[/C][C]102.72[/C][C]102.564900675073[/C][C]0.155099324927278[/C][/ROW]
[ROW][C]13[/C][C]102.73[/C][C]102.634846837484[/C][C]0.0951531625164534[/C][/ROW]
[ROW][C]14[/C][C]102.18[/C][C]102.650948790595[/C][C]-0.470948790594804[/C][/ROW]
[ROW][C]15[/C][C]102.22[/C][C]102.070747929562[/C][C]0.14925207043818[/C][/ROW]
[ROW][C]16[/C][C]102.37[/C][C]102.120319121012[/C][C]0.249680878987647[/C][/ROW]
[ROW][C]17[/C][C]102.53[/C][C]102.286330580601[/C][C]0.243669419399041[/C][/ROW]
[ROW][C]18[/C][C]102.61[/C][C]102.461956539135[/C][C]0.148043460865495[/C][/ROW]
[ROW][C]19[/C][C]102.62[/C][C]102.551450225237[/C][C]0.0685497747626016[/C][/ROW]
[ROW][C]20[/C][C]103[/C][C]102.565846164377[/C][C]0.434153835622737[/C][/ROW]
[ROW][C]21[/C][C]103.17[/C][C]102.973687449711[/C][C]0.19631255028888[/C][/ROW]
[ROW][C]22[/C][C]103.52[/C][C]103.156276521323[/C][C]0.363723478677031[/C][/ROW]
[ROW][C]23[/C][C]103.69[/C][C]103.529601270114[/C][C]0.160398729886225[/C][/ROW]
[ROW][C]24[/C][C]103.73[/C][C]103.709887271157[/C][C]0.0201127288434293[/C][/ROW]
[ROW][C]25[/C][C]99.57[/C][C]103.751177054124[/C][C]-4.18117705412435[/C][/ROW]
[ROW][C]26[/C][C]99.09[/C][C]99.323047801671[/C][C]-0.233047801671034[/C][/ROW]
[ROW][C]27[/C][C]99.14[/C][C]98.8281029830137[/C][C]0.311897016986251[/C][/ROW]
[ROW][C]28[/C][C]99.36[/C][C]98.8981042202071[/C][C]0.461895779792911[/C][/ROW]
[ROW][C]29[/C][C]99.6[/C][C]99.1477245325125[/C][C]0.452275467487539[/C][/ROW]
[ROW][C]30[/C][C]99.65[/C][C]99.4167279163516[/C][C]0.233272083648359[/C][/ROW]
[ROW][C]31[/C][C]99.8[/C][C]99.4816871176955[/C][C]0.318312882304497[/C][/ROW]
[ROW][C]32[/C][C]100.15[/C][C]99.6520997895517[/C][C]0.497900210448307[/C][/ROW]
[ROW][C]33[/C][C]100.45[/C][C]100.034028983053[/C][C]0.415971016947111[/C][/ROW]
[ROW][C]34[/C][C]100.89[/C][C]100.360704246112[/C][C]0.529295753887823[/C][/ROW]
[ROW][C]35[/C][C]101.13[/C][C]100.834646763489[/C][C]0.29535323651065[/C][/ROW]
[ROW][C]36[/C][C]101.17[/C][C]101.093587086152[/C][C]0.0764129138478893[/C][/ROW]
[ROW][C]37[/C][C]101.21[/C][C]101.138487270287[/C][C]0.0715127297124951[/C][/ROW]
[ROW][C]38[/C][C]101.1[/C][C]101.183073216903[/C][C]-0.0830732169026476[/C][/ROW]
[ROW][C]39[/C][C]101.17[/C][C]101.067745922875[/C][C]0.102254077124542[/C][/ROW]
[ROW][C]40[/C][C]101.11[/C][C]101.144303241282[/C][C]-0.0343032412824158[/C][/ROW]
[ROW][C]41[/C][C]101.2[/C][C]101.082103453442[/C][C]0.117896546557887[/C][/ROW]
[ROW][C]42[/C][C]101.15[/C][C]101.179663887379[/C][C]-0.0296638873788311[/C][/ROW]
[ROW][C]43[/C][C]100.92[/C][C]101.127761610617[/C][C]-0.207761610616856[/C][/ROW]
[ROW][C]44[/C][C]101.1[/C][C]100.884438337141[/C][C]0.215561662859017[/C][/ROW]
[ROW][C]45[/C][C]101.22[/C][C]101.078261809998[/C][C]0.141738190001561[/C][/ROW]
[ROW][C]46[/C][C]101.25[/C][C]101.207351153606[/C][C]0.042648846393945[/C][/ROW]
[ROW][C]47[/C][C]101.39[/C][C]101.240086125877[/C][C]0.149913874123314[/C][/ROW]
[ROW][C]48[/C][C]101.43[/C][C]101.389699757273[/C][C]0.0403002427270138[/C][/ROW]
[ROW][C]49[/C][C]101.95[/C][C]101.432284119001[/C][C]0.517715880999148[/C][/ROW]
[ROW][C]50[/C][C]101.92[/C][C]101.985484045806[/C][C]-0.0654840458058175[/C][/ROW]
[ROW][C]51[/C][C]102.05[/C][C]101.951284704802[/C][C]0.0987152951984598[/C][/ROW]
[ROW][C]52[/C][C]102.07[/C][C]102.087615089276[/C][C]-0.0176150892757221[/C][/ROW]
[ROW][C]53[/C][C]102.1[/C][C]102.10648547418[/C][C]-0.00648547417972622[/C][/ROW]
[ROW][C]54[/C][C]102.16[/C][C]102.136069575661[/C][C]0.0239304243390706[/C][/ROW]
[ROW][C]55[/C][C]101.63[/C][C]102.197604178646[/C][C]-0.567604178646135[/C][/ROW]
[ROW][C]56[/C][C]101.43[/C][C]101.631205030239[/C][C]-0.201205030238953[/C][/ROW]
[ROW][C]57[/C][C]101.4[/C][C]101.418302215159[/C][C]-0.0183022151585561[/C][/ROW]
[ROW][C]58[/C][C]101.6[/C][C]101.387128536263[/C][C]0.2128714637374[/C][/ROW]
[ROW][C]59[/C][C]101.72[/C][C]101.600779492848[/C][C]0.119220507152292[/C][/ROW]
[ROW][C]60[/C][C]101.73[/C][C]101.728424829327[/C][C]0.00157517067262347[/C][/ROW]
[ROW][C]61[/C][C]102.67[/C][C]101.738525841394[/C][C]0.931474158606051[/C][/ROW]
[ROW][C]62[/C][C]102.59[/C][C]102.738259133382[/C][C]-0.148259133381728[/C][/ROW]
[ROW][C]63[/C][C]102.69[/C][C]102.648751616697[/C][C]0.0412483833027864[/C][/ROW]
[ROW][C]64[/C][C]102.93[/C][C]102.751396780496[/C][C]0.178603219504012[/C][/ROW]
[ROW][C]65[/C][C]103.02[/C][C]103.002850193521[/C][C]0.0171498064790399[/C][/ROW]
[ROW][C]66[/C][C]103.06[/C][C]103.093949971103[/C][C]-0.0339499711030555[/C][/ROW]
[ROW][C]67[/C][C]102.47[/C][C]103.131772837666[/C][C]-0.661772837665552[/C][/ROW]
[ROW][C]68[/C][C]102.4[/C][C]102.499334870088[/C][C]-0.0993348700884127[/C][/ROW]
[ROW][C]69[/C][C]102.42[/C][C]102.422964753704[/C][C]-0.00296475370383575[/C][/ROW]
[ROW][C]70[/C][C]102.51[/C][C]102.442774630879[/C][C]0.0672253691214024[/C][/ROW]
[ROW][C]71[/C][C]102.61[/C][C]102.537085638936[/C][C]0.0729143610643064[/C][/ROW]
[ROW][C]72[/C][C]102.78[/C][C]102.641761468941[/C][C]0.138238531059471[/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
3100.94100.460.47999999999999
4101.13100.6207812942410.509218705758784
5101.29100.8434363167730.446563683227367
6101.34101.0320734170450.307926582954735
7101.35101.1018200394510.248179960549265
8101.7101.1277352485970.572264751402543
9102.05101.5144332687990.535566731200873
10102.48101.8987779295050.58122207049486
11102.66102.3660503619460.293949638054457
12102.72102.5649006750730.155099324927278
13102.73102.6348468374840.0951531625164534
14102.18102.650948790595-0.470948790594804
15102.22102.0707479295620.14925207043818
16102.37102.1203191210120.249680878987647
17102.53102.2863305806010.243669419399041
18102.61102.4619565391350.148043460865495
19102.62102.5514502252370.0685497747626016
20103102.5658461643770.434153835622737
21103.17102.9736874497110.19631255028888
22103.52103.1562765213230.363723478677031
23103.69103.5296012701140.160398729886225
24103.73103.7098872711570.0201127288434293
2599.57103.751177054124-4.18117705412435
2699.0999.323047801671-0.233047801671034
2799.1498.82810298301370.311897016986251
2899.3698.89810422020710.461895779792911
2999.699.14772453251250.452275467487539
3099.6599.41672791635160.233272083648359
3199.899.48168711769550.318312882304497
32100.1599.65209978955170.497900210448307
33100.45100.0340289830530.415971016947111
34100.89100.3607042461120.529295753887823
35101.13100.8346467634890.29535323651065
36101.17101.0935870861520.0764129138478893
37101.21101.1384872702870.0715127297124951
38101.1101.183073216903-0.0830732169026476
39101.17101.0677459228750.102254077124542
40101.11101.144303241282-0.0343032412824158
41101.2101.0821034534420.117896546557887
42101.15101.179663887379-0.0296638873788311
43100.92101.127761610617-0.207761610616856
44101.1100.8844383371410.215561662859017
45101.22101.0782618099980.141738190001561
46101.25101.2073511536060.042648846393945
47101.39101.2400861258770.149913874123314
48101.43101.3896997572730.0403002427270138
49101.95101.4322841190010.517715880999148
50101.92101.985484045806-0.0654840458058175
51102.05101.9512847048020.0987152951984598
52102.07102.087615089276-0.0176150892757221
53102.1102.10648547418-0.00648547417972622
54102.16102.1360695756610.0239304243390706
55101.63102.197604178646-0.567604178646135
56101.43101.631205030239-0.201205030238953
57101.4101.418302215159-0.0183022151585561
58101.6101.3871285362630.2128714637374
59101.72101.6007794928480.119220507152292
60101.73101.7284248293270.00157517067262347
61102.67101.7385258413940.931474158606051
62102.59102.738259133382-0.148259133381728
63102.69102.6487516166970.0412483833027864
64102.93102.7513967804960.178603219504012
65103.02103.0028501935210.0171498064790399
66103.06103.093949971103-0.0339499711030555
67102.47103.131772837666-0.661772837665552
68102.4102.499334870088-0.0993348700884127
69102.42102.422964753704-0.00296475370383575
70102.51102.4427746308790.0672253691214024
71102.61102.5370856389360.0729143610643064
72102.78102.6417614689410.138238531059471







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102.820626387482101.678082324833103.963170450131
74102.861252774964101.192838062015104.529667487914
75102.901879162447100.793481958845105.010276366048
76102.942505549929100.432259170252105.452751929606
77102.983131937411100.091361092368105.874902782454
78103.02375832489399.7619979751557106.285518674631
79103.06438471237699.4391537716499106.689615653101
80103.10501109985899.1196966061265107.090325593589
81103.1456374873498.8015479497671107.489727024913
82103.18626387482298.4832666524765107.889261097168
83103.22689026230598.1638205301115108.289959994498
84103.26751664978797.8424519276196108.692581371954

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102.820626387482 & 101.678082324833 & 103.963170450131 \tabularnewline
74 & 102.861252774964 & 101.192838062015 & 104.529667487914 \tabularnewline
75 & 102.901879162447 & 100.793481958845 & 105.010276366048 \tabularnewline
76 & 102.942505549929 & 100.432259170252 & 105.452751929606 \tabularnewline
77 & 102.983131937411 & 100.091361092368 & 105.874902782454 \tabularnewline
78 & 103.023758324893 & 99.7619979751557 & 106.285518674631 \tabularnewline
79 & 103.064384712376 & 99.4391537716499 & 106.689615653101 \tabularnewline
80 & 103.105011099858 & 99.1196966061265 & 107.090325593589 \tabularnewline
81 & 103.14563748734 & 98.8015479497671 & 107.489727024913 \tabularnewline
82 & 103.186263874822 & 98.4832666524765 & 107.889261097168 \tabularnewline
83 & 103.226890262305 & 98.1638205301115 & 108.289959994498 \tabularnewline
84 & 103.267516649787 & 97.8424519276196 & 108.692581371954 \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]102.820626387482[/C][C]101.678082324833[/C][C]103.963170450131[/C][/ROW]
[ROW][C]74[/C][C]102.861252774964[/C][C]101.192838062015[/C][C]104.529667487914[/C][/ROW]
[ROW][C]75[/C][C]102.901879162447[/C][C]100.793481958845[/C][C]105.010276366048[/C][/ROW]
[ROW][C]76[/C][C]102.942505549929[/C][C]100.432259170252[/C][C]105.452751929606[/C][/ROW]
[ROW][C]77[/C][C]102.983131937411[/C][C]100.091361092368[/C][C]105.874902782454[/C][/ROW]
[ROW][C]78[/C][C]103.023758324893[/C][C]99.7619979751557[/C][C]106.285518674631[/C][/ROW]
[ROW][C]79[/C][C]103.064384712376[/C][C]99.4391537716499[/C][C]106.689615653101[/C][/ROW]
[ROW][C]80[/C][C]103.105011099858[/C][C]99.1196966061265[/C][C]107.090325593589[/C][/ROW]
[ROW][C]81[/C][C]103.14563748734[/C][C]98.8015479497671[/C][C]107.489727024913[/C][/ROW]
[ROW][C]82[/C][C]103.186263874822[/C][C]98.4832666524765[/C][C]107.889261097168[/C][/ROW]
[ROW][C]83[/C][C]103.226890262305[/C][C]98.1638205301115[/C][C]108.289959994498[/C][/ROW]
[ROW][C]84[/C][C]103.267516649787[/C][C]97.8424519276196[/C][C]108.692581371954[/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
73102.820626387482101.678082324833103.963170450131
74102.861252774964101.192838062015104.529667487914
75102.901879162447100.793481958845105.010276366048
76102.942505549929100.432259170252105.452751929606
77102.983131937411100.091361092368105.874902782454
78103.02375832489399.7619979751557106.285518674631
79103.06438471237699.4391537716499106.689615653101
80103.10501109985899.1196966061265107.090325593589
81103.1456374873498.8015479497671107.489727024913
82103.18626387482298.4832666524765107.889261097168
83103.22689026230598.1638205301115108.289959994498
84103.26751664978797.8424519276196108.692581371954



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')