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 20:35:06 +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/t1493667342olgo56zp6p8q7y3.htm/, Retrieved Sat, 29 Aug 2026 15:36:01 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 29 Aug 2026 15:36:01 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
62.38
62.62
64.15
64.97
66.12
67.08
68.66
69.04
70.8
73.2
74.19
75.36
75.54
76.81
77.69
79.34
80.36
80.74
81.12
82.95
87.31
88.93
90.8
91.29
91.36
92.72
95.75
97.19
98.73
99.03
99.4
99.66
100.5
101.21
101.26
101.44
101.97
102.23
102.58
101.91
101.63
101.1
100.71
100.75
100.14
97.72
94.91
94.34
97.11
96.51
95.8
95.25
95.09
94.97
95.21
95.46
95.33
95.14
95.6
95.66
95.66
96.33
97.66
98.27
99.53
100.86
101.26
101.29
101.38
101.49
101.29
101.26




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 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]4 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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.26426505624659
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.26426505624659 \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]0.26426505624659[/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
beta0.26426505624659
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
364.1562.861.29000000000001
464.9764.73090192255810.239098077441895
566.1265.61408718944170.505912810558272
667.0866.89778226677980.182217733220213
768.6667.90593604629840.754063953701646
869.0469.6852087994368-0.64520879943683
970.869.89470265976290.905297340237112
1073.271.89394111230051.30605888769948
1174.1974.6390868377198-0.44908683771979
1275.3675.5104088792902-0.150408879290154
1375.5476.6406610683446-1.10066106834455
1476.8176.52979480921010.280205190789943
1577.6977.8738432497148-0.183843249714755
1679.3478.70525990298830.634740097011687
1780.3680.5229995304271-0.162999530427086
1880.7481.4999244503506-0.75992445035061
1981.1281.6791029727355-0.559102972735531
2082.9581.9113515941981.03864840580205
2187.3184.01583007357773.29416992642234
2288.9389.2463640744695-0.316364074469476
2390.890.78276010453540.0172398954645843
2491.2992.65731600648-1.36731600648002
2591.3692.7859821651207-1.42598216512074
2692.7292.47914490804850.240855091951531
2795.7593.90279449247031.84720550752968
2897.1997.4209463598167-0.230946359816656
2998.7398.7999153070498-0.0699153070497545
3099.03100.3214391345-1.29143913449977
3199.4100.280156898982-0.880156898982136
3299.66100.417562186567-0.757562186566801
33100.5100.4773649727230.0226350272765785
34101.21101.32334661948-0.113346619479827
35101.26102.003393068708-0.743393068707604
36101.44101.856940257592-0.416940257592287
37101.97101.9267575169680.0432424830318183
38102.23102.468184994179-0.238184994178823
39102.58102.665241023295-0.0852410232950689
40101.91102.992714799479-1.08271479947948
41101.63102.036591112096-0.406591112096024
42101.1101.649143288989-0.549143288988603
43100.71100.974023906837-0.264023906836584
44100.75100.5142516142460.235748385754036
45100.14100.616551674667-0.476551674667306
4697.7299.8806157195569-2.16061571955694
4794.9196.889640484901-1.97964048490097
4894.3493.55649068081060.78350931918942
4997.1193.19354481511593.9164551848841
5096.5196.9985270648366-0.488527064836546
5195.896.2694264325695-0.469426432569549
5295.2595.4353734299629-0.185373429962908
5395.0994.83638571006710.253614289932869
5494.9794.74340710466120.226592895338811
5595.2194.6832876888930.526712311107019
5695.4695.06247934741340.39752065258655
5795.3395.4175301650284-0.0875301650284115
5895.1495.2643990010439-0.124399001043898
5995.695.0415246920360.558475307963974
6095.6695.64911020070740.0108897992925563
6195.6695.71198799413-0.0519879941300161
6296.3395.69824938393710.631750616062902
6397.6696.53519899602481.12480100397522
6498.2798.16244459660650.107555403393491
6599.5398.80086773133390.729132268666092
66100.86100.2535519113240.606448088675833
67101.26101.743814949589-0.483814949588719
68101.29102.015959564723-0.725959564722714
69101.38101.854113819519-0.474113819518536
70101.49101.818822104336-0.328822104336169
71101.29101.841925912439-0.551925912438634
72101.26101.496071180144-0.236071180144108

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 64.15 & 62.86 & 1.29000000000001 \tabularnewline
4 & 64.97 & 64.7309019225581 & 0.239098077441895 \tabularnewline
5 & 66.12 & 65.6140871894417 & 0.505912810558272 \tabularnewline
6 & 67.08 & 66.8977822667798 & 0.182217733220213 \tabularnewline
7 & 68.66 & 67.9059360462984 & 0.754063953701646 \tabularnewline
8 & 69.04 & 69.6852087994368 & -0.64520879943683 \tabularnewline
9 & 70.8 & 69.8947026597629 & 0.905297340237112 \tabularnewline
10 & 73.2 & 71.8939411123005 & 1.30605888769948 \tabularnewline
11 & 74.19 & 74.6390868377198 & -0.44908683771979 \tabularnewline
12 & 75.36 & 75.5104088792902 & -0.150408879290154 \tabularnewline
13 & 75.54 & 76.6406610683446 & -1.10066106834455 \tabularnewline
14 & 76.81 & 76.5297948092101 & 0.280205190789943 \tabularnewline
15 & 77.69 & 77.8738432497148 & -0.183843249714755 \tabularnewline
16 & 79.34 & 78.7052599029883 & 0.634740097011687 \tabularnewline
17 & 80.36 & 80.5229995304271 & -0.162999530427086 \tabularnewline
18 & 80.74 & 81.4999244503506 & -0.75992445035061 \tabularnewline
19 & 81.12 & 81.6791029727355 & -0.559102972735531 \tabularnewline
20 & 82.95 & 81.911351594198 & 1.03864840580205 \tabularnewline
21 & 87.31 & 84.0158300735777 & 3.29416992642234 \tabularnewline
22 & 88.93 & 89.2463640744695 & -0.316364074469476 \tabularnewline
23 & 90.8 & 90.7827601045354 & 0.0172398954645843 \tabularnewline
24 & 91.29 & 92.65731600648 & -1.36731600648002 \tabularnewline
25 & 91.36 & 92.7859821651207 & -1.42598216512074 \tabularnewline
26 & 92.72 & 92.4791449080485 & 0.240855091951531 \tabularnewline
27 & 95.75 & 93.9027944924703 & 1.84720550752968 \tabularnewline
28 & 97.19 & 97.4209463598167 & -0.230946359816656 \tabularnewline
29 & 98.73 & 98.7999153070498 & -0.0699153070497545 \tabularnewline
30 & 99.03 & 100.3214391345 & -1.29143913449977 \tabularnewline
31 & 99.4 & 100.280156898982 & -0.880156898982136 \tabularnewline
32 & 99.66 & 100.417562186567 & -0.757562186566801 \tabularnewline
33 & 100.5 & 100.477364972723 & 0.0226350272765785 \tabularnewline
34 & 101.21 & 101.32334661948 & -0.113346619479827 \tabularnewline
35 & 101.26 & 102.003393068708 & -0.743393068707604 \tabularnewline
36 & 101.44 & 101.856940257592 & -0.416940257592287 \tabularnewline
37 & 101.97 & 101.926757516968 & 0.0432424830318183 \tabularnewline
38 & 102.23 & 102.468184994179 & -0.238184994178823 \tabularnewline
39 & 102.58 & 102.665241023295 & -0.0852410232950689 \tabularnewline
40 & 101.91 & 102.992714799479 & -1.08271479947948 \tabularnewline
41 & 101.63 & 102.036591112096 & -0.406591112096024 \tabularnewline
42 & 101.1 & 101.649143288989 & -0.549143288988603 \tabularnewline
43 & 100.71 & 100.974023906837 & -0.264023906836584 \tabularnewline
44 & 100.75 & 100.514251614246 & 0.235748385754036 \tabularnewline
45 & 100.14 & 100.616551674667 & -0.476551674667306 \tabularnewline
46 & 97.72 & 99.8806157195569 & -2.16061571955694 \tabularnewline
47 & 94.91 & 96.889640484901 & -1.97964048490097 \tabularnewline
48 & 94.34 & 93.5564906808106 & 0.78350931918942 \tabularnewline
49 & 97.11 & 93.1935448151159 & 3.9164551848841 \tabularnewline
50 & 96.51 & 96.9985270648366 & -0.488527064836546 \tabularnewline
51 & 95.8 & 96.2694264325695 & -0.469426432569549 \tabularnewline
52 & 95.25 & 95.4353734299629 & -0.185373429962908 \tabularnewline
53 & 95.09 & 94.8363857100671 & 0.253614289932869 \tabularnewline
54 & 94.97 & 94.7434071046612 & 0.226592895338811 \tabularnewline
55 & 95.21 & 94.683287688893 & 0.526712311107019 \tabularnewline
56 & 95.46 & 95.0624793474134 & 0.39752065258655 \tabularnewline
57 & 95.33 & 95.4175301650284 & -0.0875301650284115 \tabularnewline
58 & 95.14 & 95.2643990010439 & -0.124399001043898 \tabularnewline
59 & 95.6 & 95.041524692036 & 0.558475307963974 \tabularnewline
60 & 95.66 & 95.6491102007074 & 0.0108897992925563 \tabularnewline
61 & 95.66 & 95.71198799413 & -0.0519879941300161 \tabularnewline
62 & 96.33 & 95.6982493839371 & 0.631750616062902 \tabularnewline
63 & 97.66 & 96.5351989960248 & 1.12480100397522 \tabularnewline
64 & 98.27 & 98.1624445966065 & 0.107555403393491 \tabularnewline
65 & 99.53 & 98.8008677313339 & 0.729132268666092 \tabularnewline
66 & 100.86 & 100.253551911324 & 0.606448088675833 \tabularnewline
67 & 101.26 & 101.743814949589 & -0.483814949588719 \tabularnewline
68 & 101.29 & 102.015959564723 & -0.725959564722714 \tabularnewline
69 & 101.38 & 101.854113819519 & -0.474113819518536 \tabularnewline
70 & 101.49 & 101.818822104336 & -0.328822104336169 \tabularnewline
71 & 101.29 & 101.841925912439 & -0.551925912438634 \tabularnewline
72 & 101.26 & 101.496071180144 & -0.236071180144108 \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]64.15[/C][C]62.86[/C][C]1.29000000000001[/C][/ROW]
[ROW][C]4[/C][C]64.97[/C][C]64.7309019225581[/C][C]0.239098077441895[/C][/ROW]
[ROW][C]5[/C][C]66.12[/C][C]65.6140871894417[/C][C]0.505912810558272[/C][/ROW]
[ROW][C]6[/C][C]67.08[/C][C]66.8977822667798[/C][C]0.182217733220213[/C][/ROW]
[ROW][C]7[/C][C]68.66[/C][C]67.9059360462984[/C][C]0.754063953701646[/C][/ROW]
[ROW][C]8[/C][C]69.04[/C][C]69.6852087994368[/C][C]-0.64520879943683[/C][/ROW]
[ROW][C]9[/C][C]70.8[/C][C]69.8947026597629[/C][C]0.905297340237112[/C][/ROW]
[ROW][C]10[/C][C]73.2[/C][C]71.8939411123005[/C][C]1.30605888769948[/C][/ROW]
[ROW][C]11[/C][C]74.19[/C][C]74.6390868377198[/C][C]-0.44908683771979[/C][/ROW]
[ROW][C]12[/C][C]75.36[/C][C]75.5104088792902[/C][C]-0.150408879290154[/C][/ROW]
[ROW][C]13[/C][C]75.54[/C][C]76.6406610683446[/C][C]-1.10066106834455[/C][/ROW]
[ROW][C]14[/C][C]76.81[/C][C]76.5297948092101[/C][C]0.280205190789943[/C][/ROW]
[ROW][C]15[/C][C]77.69[/C][C]77.8738432497148[/C][C]-0.183843249714755[/C][/ROW]
[ROW][C]16[/C][C]79.34[/C][C]78.7052599029883[/C][C]0.634740097011687[/C][/ROW]
[ROW][C]17[/C][C]80.36[/C][C]80.5229995304271[/C][C]-0.162999530427086[/C][/ROW]
[ROW][C]18[/C][C]80.74[/C][C]81.4999244503506[/C][C]-0.75992445035061[/C][/ROW]
[ROW][C]19[/C][C]81.12[/C][C]81.6791029727355[/C][C]-0.559102972735531[/C][/ROW]
[ROW][C]20[/C][C]82.95[/C][C]81.911351594198[/C][C]1.03864840580205[/C][/ROW]
[ROW][C]21[/C][C]87.31[/C][C]84.0158300735777[/C][C]3.29416992642234[/C][/ROW]
[ROW][C]22[/C][C]88.93[/C][C]89.2463640744695[/C][C]-0.316364074469476[/C][/ROW]
[ROW][C]23[/C][C]90.8[/C][C]90.7827601045354[/C][C]0.0172398954645843[/C][/ROW]
[ROW][C]24[/C][C]91.29[/C][C]92.65731600648[/C][C]-1.36731600648002[/C][/ROW]
[ROW][C]25[/C][C]91.36[/C][C]92.7859821651207[/C][C]-1.42598216512074[/C][/ROW]
[ROW][C]26[/C][C]92.72[/C][C]92.4791449080485[/C][C]0.240855091951531[/C][/ROW]
[ROW][C]27[/C][C]95.75[/C][C]93.9027944924703[/C][C]1.84720550752968[/C][/ROW]
[ROW][C]28[/C][C]97.19[/C][C]97.4209463598167[/C][C]-0.230946359816656[/C][/ROW]
[ROW][C]29[/C][C]98.73[/C][C]98.7999153070498[/C][C]-0.0699153070497545[/C][/ROW]
[ROW][C]30[/C][C]99.03[/C][C]100.3214391345[/C][C]-1.29143913449977[/C][/ROW]
[ROW][C]31[/C][C]99.4[/C][C]100.280156898982[/C][C]-0.880156898982136[/C][/ROW]
[ROW][C]32[/C][C]99.66[/C][C]100.417562186567[/C][C]-0.757562186566801[/C][/ROW]
[ROW][C]33[/C][C]100.5[/C][C]100.477364972723[/C][C]0.0226350272765785[/C][/ROW]
[ROW][C]34[/C][C]101.21[/C][C]101.32334661948[/C][C]-0.113346619479827[/C][/ROW]
[ROW][C]35[/C][C]101.26[/C][C]102.003393068708[/C][C]-0.743393068707604[/C][/ROW]
[ROW][C]36[/C][C]101.44[/C][C]101.856940257592[/C][C]-0.416940257592287[/C][/ROW]
[ROW][C]37[/C][C]101.97[/C][C]101.926757516968[/C][C]0.0432424830318183[/C][/ROW]
[ROW][C]38[/C][C]102.23[/C][C]102.468184994179[/C][C]-0.238184994178823[/C][/ROW]
[ROW][C]39[/C][C]102.58[/C][C]102.665241023295[/C][C]-0.0852410232950689[/C][/ROW]
[ROW][C]40[/C][C]101.91[/C][C]102.992714799479[/C][C]-1.08271479947948[/C][/ROW]
[ROW][C]41[/C][C]101.63[/C][C]102.036591112096[/C][C]-0.406591112096024[/C][/ROW]
[ROW][C]42[/C][C]101.1[/C][C]101.649143288989[/C][C]-0.549143288988603[/C][/ROW]
[ROW][C]43[/C][C]100.71[/C][C]100.974023906837[/C][C]-0.264023906836584[/C][/ROW]
[ROW][C]44[/C][C]100.75[/C][C]100.514251614246[/C][C]0.235748385754036[/C][/ROW]
[ROW][C]45[/C][C]100.14[/C][C]100.616551674667[/C][C]-0.476551674667306[/C][/ROW]
[ROW][C]46[/C][C]97.72[/C][C]99.8806157195569[/C][C]-2.16061571955694[/C][/ROW]
[ROW][C]47[/C][C]94.91[/C][C]96.889640484901[/C][C]-1.97964048490097[/C][/ROW]
[ROW][C]48[/C][C]94.34[/C][C]93.5564906808106[/C][C]0.78350931918942[/C][/ROW]
[ROW][C]49[/C][C]97.11[/C][C]93.1935448151159[/C][C]3.9164551848841[/C][/ROW]
[ROW][C]50[/C][C]96.51[/C][C]96.9985270648366[/C][C]-0.488527064836546[/C][/ROW]
[ROW][C]51[/C][C]95.8[/C][C]96.2694264325695[/C][C]-0.469426432569549[/C][/ROW]
[ROW][C]52[/C][C]95.25[/C][C]95.4353734299629[/C][C]-0.185373429962908[/C][/ROW]
[ROW][C]53[/C][C]95.09[/C][C]94.8363857100671[/C][C]0.253614289932869[/C][/ROW]
[ROW][C]54[/C][C]94.97[/C][C]94.7434071046612[/C][C]0.226592895338811[/C][/ROW]
[ROW][C]55[/C][C]95.21[/C][C]94.683287688893[/C][C]0.526712311107019[/C][/ROW]
[ROW][C]56[/C][C]95.46[/C][C]95.0624793474134[/C][C]0.39752065258655[/C][/ROW]
[ROW][C]57[/C][C]95.33[/C][C]95.4175301650284[/C][C]-0.0875301650284115[/C][/ROW]
[ROW][C]58[/C][C]95.14[/C][C]95.2643990010439[/C][C]-0.124399001043898[/C][/ROW]
[ROW][C]59[/C][C]95.6[/C][C]95.041524692036[/C][C]0.558475307963974[/C][/ROW]
[ROW][C]60[/C][C]95.66[/C][C]95.6491102007074[/C][C]0.0108897992925563[/C][/ROW]
[ROW][C]61[/C][C]95.66[/C][C]95.71198799413[/C][C]-0.0519879941300161[/C][/ROW]
[ROW][C]62[/C][C]96.33[/C][C]95.6982493839371[/C][C]0.631750616062902[/C][/ROW]
[ROW][C]63[/C][C]97.66[/C][C]96.5351989960248[/C][C]1.12480100397522[/C][/ROW]
[ROW][C]64[/C][C]98.27[/C][C]98.1624445966065[/C][C]0.107555403393491[/C][/ROW]
[ROW][C]65[/C][C]99.53[/C][C]98.8008677313339[/C][C]0.729132268666092[/C][/ROW]
[ROW][C]66[/C][C]100.86[/C][C]100.253551911324[/C][C]0.606448088675833[/C][/ROW]
[ROW][C]67[/C][C]101.26[/C][C]101.743814949589[/C][C]-0.483814949588719[/C][/ROW]
[ROW][C]68[/C][C]101.29[/C][C]102.015959564723[/C][C]-0.725959564722714[/C][/ROW]
[ROW][C]69[/C][C]101.38[/C][C]101.854113819519[/C][C]-0.474113819518536[/C][/ROW]
[ROW][C]70[/C][C]101.49[/C][C]101.818822104336[/C][C]-0.328822104336169[/C][/ROW]
[ROW][C]71[/C][C]101.29[/C][C]101.841925912439[/C][C]-0.551925912438634[/C][/ROW]
[ROW][C]72[/C][C]101.26[/C][C]101.496071180144[/C][C]-0.236071180144108[/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
364.1562.861.29000000000001
464.9764.73090192255810.239098077441895
566.1265.61408718944170.505912810558272
667.0866.89778226677980.182217733220213
768.6667.90593604629840.754063953701646
869.0469.6852087994368-0.64520879943683
970.869.89470265976290.905297340237112
1073.271.89394111230051.30605888769948
1174.1974.6390868377198-0.44908683771979
1275.3675.5104088792902-0.150408879290154
1375.5476.6406610683446-1.10066106834455
1476.8176.52979480921010.280205190789943
1577.6977.8738432497148-0.183843249714755
1679.3478.70525990298830.634740097011687
1780.3680.5229995304271-0.162999530427086
1880.7481.4999244503506-0.75992445035061
1981.1281.6791029727355-0.559102972735531
2082.9581.9113515941981.03864840580205
2187.3184.01583007357773.29416992642234
2288.9389.2463640744695-0.316364074469476
2390.890.78276010453540.0172398954645843
2491.2992.65731600648-1.36731600648002
2591.3692.7859821651207-1.42598216512074
2692.7292.47914490804850.240855091951531
2795.7593.90279449247031.84720550752968
2897.1997.4209463598167-0.230946359816656
2998.7398.7999153070498-0.0699153070497545
3099.03100.3214391345-1.29143913449977
3199.4100.280156898982-0.880156898982136
3299.66100.417562186567-0.757562186566801
33100.5100.4773649727230.0226350272765785
34101.21101.32334661948-0.113346619479827
35101.26102.003393068708-0.743393068707604
36101.44101.856940257592-0.416940257592287
37101.97101.9267575169680.0432424830318183
38102.23102.468184994179-0.238184994178823
39102.58102.665241023295-0.0852410232950689
40101.91102.992714799479-1.08271479947948
41101.63102.036591112096-0.406591112096024
42101.1101.649143288989-0.549143288988603
43100.71100.974023906837-0.264023906836584
44100.75100.5142516142460.235748385754036
45100.14100.616551674667-0.476551674667306
4697.7299.8806157195569-2.16061571955694
4794.9196.889640484901-1.97964048490097
4894.3493.55649068081060.78350931918942
4997.1193.19354481511593.9164551848841
5096.5196.9985270648366-0.488527064836546
5195.896.2694264325695-0.469426432569549
5295.2595.4353734299629-0.185373429962908
5395.0994.83638571006710.253614289932869
5494.9794.74340710466120.226592895338811
5595.2194.6832876888930.526712311107019
5695.4695.06247934741340.39752065258655
5795.3395.4175301650284-0.0875301650284115
5895.1495.2643990010439-0.124399001043898
5995.695.0415246920360.558475307963974
6095.6695.64911020070740.0108897992925563
6195.6695.71198799413-0.0519879941300161
6296.3395.69824938393710.631750616062902
6397.6696.53519899602481.12480100397522
6498.2798.16244459660650.107555403393491
6599.5398.80086773133390.729132268666092
66100.86100.2535519113240.606448088675833
67101.26101.743814949589-0.483814949588719
68101.29102.015959564723-0.725959564722714
69101.38101.854113819519-0.474113819518536
70101.49101.818822104336-0.328822104336169
71101.29101.841925912439-0.551925912438634
72101.26101.496071180144-0.236071180144108







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73101.40368581644599.5217735211902103.2855981117
74101.5473716328998.5138328395103104.58091042627
75101.69105744933597.5105128897774105.871602008893
76101.8347432657896.4625890293241107.206897502237
77101.97842908222695.3567764009727108.600081763478
78102.12211489867194.1892501116111110.05497968573
79102.26580071511692.9595188969633111.572082533268
80102.40948653156191.6684177522828113.150555310839
81102.55317234800690.3173218626736114.789022833339
82102.69685816445188.9078053087877116.485911020115
83102.84054398089687.4414841123682118.239603849424
84102.98422979734185.9199426081024120.04851698658

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 101.403685816445 & 99.5217735211902 & 103.2855981117 \tabularnewline
74 & 101.54737163289 & 98.5138328395103 & 104.58091042627 \tabularnewline
75 & 101.691057449335 & 97.5105128897774 & 105.871602008893 \tabularnewline
76 & 101.83474326578 & 96.4625890293241 & 107.206897502237 \tabularnewline
77 & 101.978429082226 & 95.3567764009727 & 108.600081763478 \tabularnewline
78 & 102.122114898671 & 94.1892501116111 & 110.05497968573 \tabularnewline
79 & 102.265800715116 & 92.9595188969633 & 111.572082533268 \tabularnewline
80 & 102.409486531561 & 91.6684177522828 & 113.150555310839 \tabularnewline
81 & 102.553172348006 & 90.3173218626736 & 114.789022833339 \tabularnewline
82 & 102.696858164451 & 88.9078053087877 & 116.485911020115 \tabularnewline
83 & 102.840543980896 & 87.4414841123682 & 118.239603849424 \tabularnewline
84 & 102.984229797341 & 85.9199426081024 & 120.04851698658 \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]101.403685816445[/C][C]99.5217735211902[/C][C]103.2855981117[/C][/ROW]
[ROW][C]74[/C][C]101.54737163289[/C][C]98.5138328395103[/C][C]104.58091042627[/C][/ROW]
[ROW][C]75[/C][C]101.691057449335[/C][C]97.5105128897774[/C][C]105.871602008893[/C][/ROW]
[ROW][C]76[/C][C]101.83474326578[/C][C]96.4625890293241[/C][C]107.206897502237[/C][/ROW]
[ROW][C]77[/C][C]101.978429082226[/C][C]95.3567764009727[/C][C]108.600081763478[/C][/ROW]
[ROW][C]78[/C][C]102.122114898671[/C][C]94.1892501116111[/C][C]110.05497968573[/C][/ROW]
[ROW][C]79[/C][C]102.265800715116[/C][C]92.9595188969633[/C][C]111.572082533268[/C][/ROW]
[ROW][C]80[/C][C]102.409486531561[/C][C]91.6684177522828[/C][C]113.150555310839[/C][/ROW]
[ROW][C]81[/C][C]102.553172348006[/C][C]90.3173218626736[/C][C]114.789022833339[/C][/ROW]
[ROW][C]82[/C][C]102.696858164451[/C][C]88.9078053087877[/C][C]116.485911020115[/C][/ROW]
[ROW][C]83[/C][C]102.840543980896[/C][C]87.4414841123682[/C][C]118.239603849424[/C][/ROW]
[ROW][C]84[/C][C]102.984229797341[/C][C]85.9199426081024[/C][C]120.04851698658[/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
73101.40368581644599.5217735211902103.2855981117
74101.5473716328998.5138328395103104.58091042627
75101.69105744933597.5105128897774105.871602008893
76101.8347432657896.4625890293241107.206897502237
77101.97842908222695.3567764009727108.600081763478
78102.12211489867194.1892501116111110.05497968573
79102.26580071511692.9595188969633111.572082533268
80102.40948653156191.6684177522828113.150555310839
81102.55317234800690.3173218626736114.789022833339
82102.69685816445188.9078053087877116.485911020115
83102.84054398089687.4414841123682118.239603849424
84102.98422979734185.9199426081024120.04851698658



Parameters (Session):
par1 = multiplicative ; par2 = 12 ;
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')