Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 26 Nov 2016 17:22:52 +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/Nov/26/t1480180988qvdhv4u710xz1ge.htm/, Retrieved Fri, 03 May 2024 22:05:36 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 03 May 2024 22:05:36 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
91.16
91.17
91.17
91.38
92.68
92.72
92.79
92.81
92.81
92.81
92.81
92.81
92.81
92.82
92.82
92.88
93.38
93.89
94.1
94.18
94.3
94.31
94.36
94.38
94.38
94.5
94.57
94.89
96.71
97.57
97.88
97.97
98.4
98.51
98.46
98.46
98.48
98.6
98.6
98.71
99.13
99.2
99.3
100.18
101.37
101.77
102.28
102.38
102.35
103.23
105.37
106.62
107
107.24
107.31
107.35
107.42
107.58
107.64
107.64
107.68
108.51
110.37
111.31
111.57
111.66
111.69
111.9
111.95
112.04
112.13
112.14




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 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]1 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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999922413518761
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999922413518761 \tabularnewline
beta & FALSE \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]0.999922413518761[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/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
alpha0.999922413518761
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
291.1791.160.0100000000000051
391.1791.16999922413527.75864819502203e-07
491.3891.16999999993980.210000000060191
592.6891.37998370683891.30001629316108
692.7292.67989913631030.0401008636897302
792.7992.71999688871510.0700031112849189
892.8192.78999456870490.0200054312950755
992.8192.8099984478491.55215101926842e-06
1092.8192.80999999987961.20436993711337e-10
1192.8192.811.4210854715202e-14
1292.8192.810
1392.8192.810
1492.8292.810.00999999999999091
1592.8292.81999922413527.75864805291349e-07
1692.8892.81999999993980.0600000000601995
1793.3892.87999534481110.500004655188874
1893.8993.37996120639820.510038793601808
1994.193.88996042788470.210039572115292
2094.1894.09998370376870.0800162962313351
2194.394.17999379181710.120006208182858
2294.3194.29999068914060.0100093108594166
2394.3694.30999922341280.0500007765872112
2494.3894.35999612061570.0200038793843049
2594.3894.37999844796941.55203061069642e-06
2694.594.37999999987960.120000000120413
2794.5794.49999068962220.0700093103777562
2894.8994.56999456822390.320005431776053
2996.7194.88997517190461.82002482809543
3097.5796.70985879067780.860141209322165
3197.8897.56993326467020.310066735329798
3297.9797.87997594301310.0900240569869482
3398.497.96999301535020.430006984649808
3498.5198.39996663727120.110033362728842
3598.4698.5099914628986-0.0499914628985891
3698.4698.4600038786617-3.87866170115103e-06
3798.4898.46000000030090.0199999996990812
3898.698.47999844827040.120001551729601
3998.698.59999068950199.31049814312246e-06
4098.7198.59999999927760.110000000722366
4199.1398.7099914654870.420008534512988
4299.299.12996741301570.0700325869842828
4399.399.1999945664180.100005433581998
44100.1899.29999224093030.880007759069713
45101.37100.1799317232951.19006827670549
46101.77101.369907666790.400092333210011
47102.28101.7699689582440.510031041756307
48102.38102.2799604284860.100039571513847
49102.35102.379992238282-0.0299922382816504
50103.23102.3500023269920.879997673007779
51105.37103.2299317240772.14006827592294
52106.62105.3698339596331.25016604036713
53107106.6199030040160.380096995984033
54107.24106.9999705096120.240029490388437
55107.31107.2399813769560.070018623043552
56107.35107.3099945675010.0400054324985746
57107.42107.3499968961190.0700031038807509
58107.58107.4199945687060.160005431294493
59107.64107.5799875857420.0600124142583951
60107.64107.6399953438484.65615204348069e-06
61107.68107.6399999996390.0400000003612604
62108.51107.6799968965410.830003103459276
63110.37108.509935602981.86006439702022
64111.31110.3698556841490.940144315851441
65111.57111.3099270575110.260072942489316
66111.66111.5699798218560.0900201781444849
67111.69111.6599930156510.0300069843488586
68111.9111.6899976718640.210002328136341
69111.95111.8999837066580.0500162933416846
70112.04111.9499961194120.0900038805882133
71112.13112.0399930169160.090006983084379
72112.14112.1299930166750.0100069833250984

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 91.17 & 91.16 & 0.0100000000000051 \tabularnewline
3 & 91.17 & 91.1699992241352 & 7.75864819502203e-07 \tabularnewline
4 & 91.38 & 91.1699999999398 & 0.210000000060191 \tabularnewline
5 & 92.68 & 91.3799837068389 & 1.30001629316108 \tabularnewline
6 & 92.72 & 92.6798991363103 & 0.0401008636897302 \tabularnewline
7 & 92.79 & 92.7199968887151 & 0.0700031112849189 \tabularnewline
8 & 92.81 & 92.7899945687049 & 0.0200054312950755 \tabularnewline
9 & 92.81 & 92.809998447849 & 1.55215101926842e-06 \tabularnewline
10 & 92.81 & 92.8099999998796 & 1.20436993711337e-10 \tabularnewline
11 & 92.81 & 92.81 & 1.4210854715202e-14 \tabularnewline
12 & 92.81 & 92.81 & 0 \tabularnewline
13 & 92.81 & 92.81 & 0 \tabularnewline
14 & 92.82 & 92.81 & 0.00999999999999091 \tabularnewline
15 & 92.82 & 92.8199992241352 & 7.75864805291349e-07 \tabularnewline
16 & 92.88 & 92.8199999999398 & 0.0600000000601995 \tabularnewline
17 & 93.38 & 92.8799953448111 & 0.500004655188874 \tabularnewline
18 & 93.89 & 93.3799612063982 & 0.510038793601808 \tabularnewline
19 & 94.1 & 93.8899604278847 & 0.210039572115292 \tabularnewline
20 & 94.18 & 94.0999837037687 & 0.0800162962313351 \tabularnewline
21 & 94.3 & 94.1799937918171 & 0.120006208182858 \tabularnewline
22 & 94.31 & 94.2999906891406 & 0.0100093108594166 \tabularnewline
23 & 94.36 & 94.3099992234128 & 0.0500007765872112 \tabularnewline
24 & 94.38 & 94.3599961206157 & 0.0200038793843049 \tabularnewline
25 & 94.38 & 94.3799984479694 & 1.55203061069642e-06 \tabularnewline
26 & 94.5 & 94.3799999998796 & 0.120000000120413 \tabularnewline
27 & 94.57 & 94.4999906896222 & 0.0700093103777562 \tabularnewline
28 & 94.89 & 94.5699945682239 & 0.320005431776053 \tabularnewline
29 & 96.71 & 94.8899751719046 & 1.82002482809543 \tabularnewline
30 & 97.57 & 96.7098587906778 & 0.860141209322165 \tabularnewline
31 & 97.88 & 97.5699332646702 & 0.310066735329798 \tabularnewline
32 & 97.97 & 97.8799759430131 & 0.0900240569869482 \tabularnewline
33 & 98.4 & 97.9699930153502 & 0.430006984649808 \tabularnewline
34 & 98.51 & 98.3999666372712 & 0.110033362728842 \tabularnewline
35 & 98.46 & 98.5099914628986 & -0.0499914628985891 \tabularnewline
36 & 98.46 & 98.4600038786617 & -3.87866170115103e-06 \tabularnewline
37 & 98.48 & 98.4600000003009 & 0.0199999996990812 \tabularnewline
38 & 98.6 & 98.4799984482704 & 0.120001551729601 \tabularnewline
39 & 98.6 & 98.5999906895019 & 9.31049814312246e-06 \tabularnewline
40 & 98.71 & 98.5999999992776 & 0.110000000722366 \tabularnewline
41 & 99.13 & 98.709991465487 & 0.420008534512988 \tabularnewline
42 & 99.2 & 99.1299674130157 & 0.0700325869842828 \tabularnewline
43 & 99.3 & 99.199994566418 & 0.100005433581998 \tabularnewline
44 & 100.18 & 99.2999922409303 & 0.880007759069713 \tabularnewline
45 & 101.37 & 100.179931723295 & 1.19006827670549 \tabularnewline
46 & 101.77 & 101.36990766679 & 0.400092333210011 \tabularnewline
47 & 102.28 & 101.769968958244 & 0.510031041756307 \tabularnewline
48 & 102.38 & 102.279960428486 & 0.100039571513847 \tabularnewline
49 & 102.35 & 102.379992238282 & -0.0299922382816504 \tabularnewline
50 & 103.23 & 102.350002326992 & 0.879997673007779 \tabularnewline
51 & 105.37 & 103.229931724077 & 2.14006827592294 \tabularnewline
52 & 106.62 & 105.369833959633 & 1.25016604036713 \tabularnewline
53 & 107 & 106.619903004016 & 0.380096995984033 \tabularnewline
54 & 107.24 & 106.999970509612 & 0.240029490388437 \tabularnewline
55 & 107.31 & 107.239981376956 & 0.070018623043552 \tabularnewline
56 & 107.35 & 107.309994567501 & 0.0400054324985746 \tabularnewline
57 & 107.42 & 107.349996896119 & 0.0700031038807509 \tabularnewline
58 & 107.58 & 107.419994568706 & 0.160005431294493 \tabularnewline
59 & 107.64 & 107.579987585742 & 0.0600124142583951 \tabularnewline
60 & 107.64 & 107.639995343848 & 4.65615204348069e-06 \tabularnewline
61 & 107.68 & 107.639999999639 & 0.0400000003612604 \tabularnewline
62 & 108.51 & 107.679996896541 & 0.830003103459276 \tabularnewline
63 & 110.37 & 108.50993560298 & 1.86006439702022 \tabularnewline
64 & 111.31 & 110.369855684149 & 0.940144315851441 \tabularnewline
65 & 111.57 & 111.309927057511 & 0.260072942489316 \tabularnewline
66 & 111.66 & 111.569979821856 & 0.0900201781444849 \tabularnewline
67 & 111.69 & 111.659993015651 & 0.0300069843488586 \tabularnewline
68 & 111.9 & 111.689997671864 & 0.210002328136341 \tabularnewline
69 & 111.95 & 111.899983706658 & 0.0500162933416846 \tabularnewline
70 & 112.04 & 111.949996119412 & 0.0900038805882133 \tabularnewline
71 & 112.13 & 112.039993016916 & 0.090006983084379 \tabularnewline
72 & 112.14 & 112.129993016675 & 0.0100069833250984 \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]2[/C][C]91.17[/C][C]91.16[/C][C]0.0100000000000051[/C][/ROW]
[ROW][C]3[/C][C]91.17[/C][C]91.1699992241352[/C][C]7.75864819502203e-07[/C][/ROW]
[ROW][C]4[/C][C]91.38[/C][C]91.1699999999398[/C][C]0.210000000060191[/C][/ROW]
[ROW][C]5[/C][C]92.68[/C][C]91.3799837068389[/C][C]1.30001629316108[/C][/ROW]
[ROW][C]6[/C][C]92.72[/C][C]92.6798991363103[/C][C]0.0401008636897302[/C][/ROW]
[ROW][C]7[/C][C]92.79[/C][C]92.7199968887151[/C][C]0.0700031112849189[/C][/ROW]
[ROW][C]8[/C][C]92.81[/C][C]92.7899945687049[/C][C]0.0200054312950755[/C][/ROW]
[ROW][C]9[/C][C]92.81[/C][C]92.809998447849[/C][C]1.55215101926842e-06[/C][/ROW]
[ROW][C]10[/C][C]92.81[/C][C]92.8099999998796[/C][C]1.20436993711337e-10[/C][/ROW]
[ROW][C]11[/C][C]92.81[/C][C]92.81[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]12[/C][C]92.81[/C][C]92.81[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]92.81[/C][C]92.81[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]92.82[/C][C]92.81[/C][C]0.00999999999999091[/C][/ROW]
[ROW][C]15[/C][C]92.82[/C][C]92.8199992241352[/C][C]7.75864805291349e-07[/C][/ROW]
[ROW][C]16[/C][C]92.88[/C][C]92.8199999999398[/C][C]0.0600000000601995[/C][/ROW]
[ROW][C]17[/C][C]93.38[/C][C]92.8799953448111[/C][C]0.500004655188874[/C][/ROW]
[ROW][C]18[/C][C]93.89[/C][C]93.3799612063982[/C][C]0.510038793601808[/C][/ROW]
[ROW][C]19[/C][C]94.1[/C][C]93.8899604278847[/C][C]0.210039572115292[/C][/ROW]
[ROW][C]20[/C][C]94.18[/C][C]94.0999837037687[/C][C]0.0800162962313351[/C][/ROW]
[ROW][C]21[/C][C]94.3[/C][C]94.1799937918171[/C][C]0.120006208182858[/C][/ROW]
[ROW][C]22[/C][C]94.31[/C][C]94.2999906891406[/C][C]0.0100093108594166[/C][/ROW]
[ROW][C]23[/C][C]94.36[/C][C]94.3099992234128[/C][C]0.0500007765872112[/C][/ROW]
[ROW][C]24[/C][C]94.38[/C][C]94.3599961206157[/C][C]0.0200038793843049[/C][/ROW]
[ROW][C]25[/C][C]94.38[/C][C]94.3799984479694[/C][C]1.55203061069642e-06[/C][/ROW]
[ROW][C]26[/C][C]94.5[/C][C]94.3799999998796[/C][C]0.120000000120413[/C][/ROW]
[ROW][C]27[/C][C]94.57[/C][C]94.4999906896222[/C][C]0.0700093103777562[/C][/ROW]
[ROW][C]28[/C][C]94.89[/C][C]94.5699945682239[/C][C]0.320005431776053[/C][/ROW]
[ROW][C]29[/C][C]96.71[/C][C]94.8899751719046[/C][C]1.82002482809543[/C][/ROW]
[ROW][C]30[/C][C]97.57[/C][C]96.7098587906778[/C][C]0.860141209322165[/C][/ROW]
[ROW][C]31[/C][C]97.88[/C][C]97.5699332646702[/C][C]0.310066735329798[/C][/ROW]
[ROW][C]32[/C][C]97.97[/C][C]97.8799759430131[/C][C]0.0900240569869482[/C][/ROW]
[ROW][C]33[/C][C]98.4[/C][C]97.9699930153502[/C][C]0.430006984649808[/C][/ROW]
[ROW][C]34[/C][C]98.51[/C][C]98.3999666372712[/C][C]0.110033362728842[/C][/ROW]
[ROW][C]35[/C][C]98.46[/C][C]98.5099914628986[/C][C]-0.0499914628985891[/C][/ROW]
[ROW][C]36[/C][C]98.46[/C][C]98.4600038786617[/C][C]-3.87866170115103e-06[/C][/ROW]
[ROW][C]37[/C][C]98.48[/C][C]98.4600000003009[/C][C]0.0199999996990812[/C][/ROW]
[ROW][C]38[/C][C]98.6[/C][C]98.4799984482704[/C][C]0.120001551729601[/C][/ROW]
[ROW][C]39[/C][C]98.6[/C][C]98.5999906895019[/C][C]9.31049814312246e-06[/C][/ROW]
[ROW][C]40[/C][C]98.71[/C][C]98.5999999992776[/C][C]0.110000000722366[/C][/ROW]
[ROW][C]41[/C][C]99.13[/C][C]98.709991465487[/C][C]0.420008534512988[/C][/ROW]
[ROW][C]42[/C][C]99.2[/C][C]99.1299674130157[/C][C]0.0700325869842828[/C][/ROW]
[ROW][C]43[/C][C]99.3[/C][C]99.199994566418[/C][C]0.100005433581998[/C][/ROW]
[ROW][C]44[/C][C]100.18[/C][C]99.2999922409303[/C][C]0.880007759069713[/C][/ROW]
[ROW][C]45[/C][C]101.37[/C][C]100.179931723295[/C][C]1.19006827670549[/C][/ROW]
[ROW][C]46[/C][C]101.77[/C][C]101.36990766679[/C][C]0.400092333210011[/C][/ROW]
[ROW][C]47[/C][C]102.28[/C][C]101.769968958244[/C][C]0.510031041756307[/C][/ROW]
[ROW][C]48[/C][C]102.38[/C][C]102.279960428486[/C][C]0.100039571513847[/C][/ROW]
[ROW][C]49[/C][C]102.35[/C][C]102.379992238282[/C][C]-0.0299922382816504[/C][/ROW]
[ROW][C]50[/C][C]103.23[/C][C]102.350002326992[/C][C]0.879997673007779[/C][/ROW]
[ROW][C]51[/C][C]105.37[/C][C]103.229931724077[/C][C]2.14006827592294[/C][/ROW]
[ROW][C]52[/C][C]106.62[/C][C]105.369833959633[/C][C]1.25016604036713[/C][/ROW]
[ROW][C]53[/C][C]107[/C][C]106.619903004016[/C][C]0.380096995984033[/C][/ROW]
[ROW][C]54[/C][C]107.24[/C][C]106.999970509612[/C][C]0.240029490388437[/C][/ROW]
[ROW][C]55[/C][C]107.31[/C][C]107.239981376956[/C][C]0.070018623043552[/C][/ROW]
[ROW][C]56[/C][C]107.35[/C][C]107.309994567501[/C][C]0.0400054324985746[/C][/ROW]
[ROW][C]57[/C][C]107.42[/C][C]107.349996896119[/C][C]0.0700031038807509[/C][/ROW]
[ROW][C]58[/C][C]107.58[/C][C]107.419994568706[/C][C]0.160005431294493[/C][/ROW]
[ROW][C]59[/C][C]107.64[/C][C]107.579987585742[/C][C]0.0600124142583951[/C][/ROW]
[ROW][C]60[/C][C]107.64[/C][C]107.639995343848[/C][C]4.65615204348069e-06[/C][/ROW]
[ROW][C]61[/C][C]107.68[/C][C]107.639999999639[/C][C]0.0400000003612604[/C][/ROW]
[ROW][C]62[/C][C]108.51[/C][C]107.679996896541[/C][C]0.830003103459276[/C][/ROW]
[ROW][C]63[/C][C]110.37[/C][C]108.50993560298[/C][C]1.86006439702022[/C][/ROW]
[ROW][C]64[/C][C]111.31[/C][C]110.369855684149[/C][C]0.940144315851441[/C][/ROW]
[ROW][C]65[/C][C]111.57[/C][C]111.309927057511[/C][C]0.260072942489316[/C][/ROW]
[ROW][C]66[/C][C]111.66[/C][C]111.569979821856[/C][C]0.0900201781444849[/C][/ROW]
[ROW][C]67[/C][C]111.69[/C][C]111.659993015651[/C][C]0.0300069843488586[/C][/ROW]
[ROW][C]68[/C][C]111.9[/C][C]111.689997671864[/C][C]0.210002328136341[/C][/ROW]
[ROW][C]69[/C][C]111.95[/C][C]111.899983706658[/C][C]0.0500162933416846[/C][/ROW]
[ROW][C]70[/C][C]112.04[/C][C]111.949996119412[/C][C]0.0900038805882133[/C][/ROW]
[ROW][C]71[/C][C]112.13[/C][C]112.039993016916[/C][C]0.090006983084379[/C][/ROW]
[ROW][C]72[/C][C]112.14[/C][C]112.129993016675[/C][C]0.0100069833250984[/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
291.1791.160.0100000000000051
391.1791.16999922413527.75864819502203e-07
491.3891.16999999993980.210000000060191
592.6891.37998370683891.30001629316108
692.7292.67989913631030.0401008636897302
792.7992.71999688871510.0700031112849189
892.8192.78999456870490.0200054312950755
992.8192.8099984478491.55215101926842e-06
1092.8192.80999999987961.20436993711337e-10
1192.8192.811.4210854715202e-14
1292.8192.810
1392.8192.810
1492.8292.810.00999999999999091
1592.8292.81999922413527.75864805291349e-07
1692.8892.81999999993980.0600000000601995
1793.3892.87999534481110.500004655188874
1893.8993.37996120639820.510038793601808
1994.193.88996042788470.210039572115292
2094.1894.09998370376870.0800162962313351
2194.394.17999379181710.120006208182858
2294.3194.29999068914060.0100093108594166
2394.3694.30999922341280.0500007765872112
2494.3894.35999612061570.0200038793843049
2594.3894.37999844796941.55203061069642e-06
2694.594.37999999987960.120000000120413
2794.5794.49999068962220.0700093103777562
2894.8994.56999456822390.320005431776053
2996.7194.88997517190461.82002482809543
3097.5796.70985879067780.860141209322165
3197.8897.56993326467020.310066735329798
3297.9797.87997594301310.0900240569869482
3398.497.96999301535020.430006984649808
3498.5198.39996663727120.110033362728842
3598.4698.5099914628986-0.0499914628985891
3698.4698.4600038786617-3.87866170115103e-06
3798.4898.46000000030090.0199999996990812
3898.698.47999844827040.120001551729601
3998.698.59999068950199.31049814312246e-06
4098.7198.59999999927760.110000000722366
4199.1398.7099914654870.420008534512988
4299.299.12996741301570.0700325869842828
4399.399.1999945664180.100005433581998
44100.1899.29999224093030.880007759069713
45101.37100.1799317232951.19006827670549
46101.77101.369907666790.400092333210011
47102.28101.7699689582440.510031041756307
48102.38102.2799604284860.100039571513847
49102.35102.379992238282-0.0299922382816504
50103.23102.3500023269920.879997673007779
51105.37103.2299317240772.14006827592294
52106.62105.3698339596331.25016604036713
53107106.6199030040160.380096995984033
54107.24106.9999705096120.240029490388437
55107.31107.2399813769560.070018623043552
56107.35107.3099945675010.0400054324985746
57107.42107.3499968961190.0700031038807509
58107.58107.4199945687060.160005431294493
59107.64107.5799875857420.0600124142583951
60107.64107.6399953438484.65615204348069e-06
61107.68107.6399999996390.0400000003612604
62108.51107.6799968965410.830003103459276
63110.37108.509935602981.86006439702022
64111.31110.3698556841490.940144315851441
65111.57111.3099270575110.260072942489316
66111.66111.5699798218560.0900201781444849
67111.69111.6599930156510.0300069843488586
68111.9111.6899976718640.210002328136341
69111.95111.8999837066580.0500162933416846
70112.04111.9499961194120.0900038805882133
71112.13112.0399930169160.090006983084379
72112.14112.1299930166750.0100069833250984







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73112.139999223593111.209599440729113.070399006458
74112.139999223593110.824266274772113.455732172415
75112.139999223593110.52858288097113.751415566217
76112.139999223593110.279307936482114.000690510705
77112.139999223593110.059691192894114.220307254293
78112.139999223593109.86114184779114.418856599396
79112.139999223593109.678556480828114.601441966358
80112.139999223593109.508609892352114.771388554835
81112.139999223593109.348992371357114.93100607583
82112.139999223593109.198022220643115.081976226544
83112.139999223593109.054429888357115.225568558829
84112.139999223593108.917229055057115.36276939213

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 112.139999223593 & 111.209599440729 & 113.070399006458 \tabularnewline
74 & 112.139999223593 & 110.824266274772 & 113.455732172415 \tabularnewline
75 & 112.139999223593 & 110.52858288097 & 113.751415566217 \tabularnewline
76 & 112.139999223593 & 110.279307936482 & 114.000690510705 \tabularnewline
77 & 112.139999223593 & 110.059691192894 & 114.220307254293 \tabularnewline
78 & 112.139999223593 & 109.86114184779 & 114.418856599396 \tabularnewline
79 & 112.139999223593 & 109.678556480828 & 114.601441966358 \tabularnewline
80 & 112.139999223593 & 109.508609892352 & 114.771388554835 \tabularnewline
81 & 112.139999223593 & 109.348992371357 & 114.93100607583 \tabularnewline
82 & 112.139999223593 & 109.198022220643 & 115.081976226544 \tabularnewline
83 & 112.139999223593 & 109.054429888357 & 115.225568558829 \tabularnewline
84 & 112.139999223593 & 108.917229055057 & 115.36276939213 \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]112.139999223593[/C][C]111.209599440729[/C][C]113.070399006458[/C][/ROW]
[ROW][C]74[/C][C]112.139999223593[/C][C]110.824266274772[/C][C]113.455732172415[/C][/ROW]
[ROW][C]75[/C][C]112.139999223593[/C][C]110.52858288097[/C][C]113.751415566217[/C][/ROW]
[ROW][C]76[/C][C]112.139999223593[/C][C]110.279307936482[/C][C]114.000690510705[/C][/ROW]
[ROW][C]77[/C][C]112.139999223593[/C][C]110.059691192894[/C][C]114.220307254293[/C][/ROW]
[ROW][C]78[/C][C]112.139999223593[/C][C]109.86114184779[/C][C]114.418856599396[/C][/ROW]
[ROW][C]79[/C][C]112.139999223593[/C][C]109.678556480828[/C][C]114.601441966358[/C][/ROW]
[ROW][C]80[/C][C]112.139999223593[/C][C]109.508609892352[/C][C]114.771388554835[/C][/ROW]
[ROW][C]81[/C][C]112.139999223593[/C][C]109.348992371357[/C][C]114.93100607583[/C][/ROW]
[ROW][C]82[/C][C]112.139999223593[/C][C]109.198022220643[/C][C]115.081976226544[/C][/ROW]
[ROW][C]83[/C][C]112.139999223593[/C][C]109.054429888357[/C][C]115.225568558829[/C][/ROW]
[ROW][C]84[/C][C]112.139999223593[/C][C]108.917229055057[/C][C]115.36276939213[/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
73112.139999223593111.209599440729113.070399006458
74112.139999223593110.824266274772113.455732172415
75112.139999223593110.52858288097113.751415566217
76112.139999223593110.279307936482114.000690510705
77112.139999223593110.059691192894114.220307254293
78112.139999223593109.86114184779114.418856599396
79112.139999223593109.678556480828114.601441966358
80112.139999223593109.508609892352114.771388554835
81112.139999223593109.348992371357114.93100607583
82112.139999223593109.198022220643115.081976226544
83112.139999223593109.054429888357115.225568558829
84112.139999223593108.917229055057115.36276939213



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')