Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 26 Nov 2014 16:29:09 +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/2014/Nov/26/t1417019363ar4jgd00rkkoz6e.htm/, Retrieved Sun, 19 May 2024 15:41:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=259296, Retrieved Sun, 19 May 2024 15:41:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 11 oefening 2] [2014-11-26 16:29:09] [76c30f62b7052b57088120e90a652e05] [Current]
Feedback Forum

Post a new message
Dataseries X:
110,48
111,41
115,5
118,32
118,42
117,5
110,23
109,19
118,41
118,3
116,1
114,11
113,41
114,33
116,61
123,64
123,77
123,39
116,03
114,95
123,4
123,53
114,45
114,26
114,35
112,77
115,31
114,93
116,38
115,07
105
103,43
114,52
115,04
117,16
115
116,22
112,92
116,56
114,32
113,22
111,56
103,87
102,85
112,27
112,76
118,55
122,73
115,44
116,97
119,84
116,37
117,23
115,58
109,82
108,46
116,54
117,49
122,87
127,1
119,81
120,03
128,58
120,4
121,54
118,71
111,57
109,97
120,29
120,61
130,15
136,12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259296&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259296&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259296&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259296&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]0.999933893038648[/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=259296&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259296&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2111.41110.480.929999999999993
3115.5111.4099385205264.09006147947406
4118.32115.4997296184642.82027038153613
5118.42118.3198135604950.100186439505123
6117.5118.419993376979-0.919993376978923
7110.23117.500060817967-7.27006081796661
8109.19110.23048060163-1.04048060162953
9118.41109.1900687830119.21993121698908
10118.3118.409390498363-0.109390498363368
11116.1118.300007231473-2.20000723147345
12114.11116.100145435793-1.99014543579302
13113.41114.110131562467-0.700131562467419
14114.33113.410046283570.919953716429859
15116.61114.3299391846552.28006081534478
16123.64116.6098492721087.03015072789221
17123.77123.6395352580980.130464741902458
18123.39123.769991375372-0.379991375372342
19116.03123.390025120075-7.36002512007516
20114.95116.030486548896-1.08048654889616
21123.4114.9500714276838.44992857231748
22123.53123.3994414008980.130558599101548
23114.45123.529991369168-9.07999136916773
24114.26114.450600250639-0.190600250638511
25114.35114.2600126000030.0899873999965877
26112.77114.349994051206-1.57999405120643
27115.31112.7701044486062.53989555139432
28114.93115.309832095223-0.379832095222952
29116.38114.9300251095461.44997489045436
30115.07116.379904146566-1.30990414656596
31105115.070086593783-10.0700865937828
32103.43105.000665702825-1.57066570282527
33114.52103.43010383193711.0898961680631
34115.04114.5192668806630.520733119337393
35117.16115.0399655759162.1200344240842
36115117.159859850966-2.15985985096626
37116.22115.0001427817721.2198572182283
38112.92116.219919358946-3.29991935894601
39116.56112.9202181476423.63978185235848
40114.32116.559759385082-2.23975938508177
41113.22114.320148063687-1.1001480636871
42111.56113.220072727446-1.66007272744552
43103.87111.560109742364-7.69010974236365
44102.85103.870508369788-1.02050836978754
45112.27102.8500674627079.41993253729264
46112.76112.2693772768840.490622723116189
47118.55112.7599675664235.79003243357739
48122.73118.549617238554.18038276145032
49115.44122.729723647598-7.28972364759836
50116.97115.4404819014791.52951809852055
51119.84116.9698988882062.87010111179383
52116.37119.839810266337-3.46981026633672
53117.23116.3702293786130.859770621386815
54115.58117.229943163177-1.64994316317676
55109.82115.580109072729-5.76010907272894
56108.46109.820380783308-1.36038078330786
57116.54108.460089930648.07991006936014
58117.49116.5394658616970.950534138302672
59122.87117.4899371630765.38006283692356
60127.1122.8696443403944.23035565960603
61119.81127.099720344042-7.28972034404191
62120.03119.8104819012610.219518098738945
63128.58120.0299854883268.55001451167449
64120.4128.579434784521-8.17943478452113
65121.54120.4005407175791.13945928242082
66118.71121.539924673809-2.82992467380926
67111.57118.710187077721-7.14018707772105
68109.97111.570472016071-1.60047201607118
69120.29109.97010580234210.3198941976583
70120.61120.2893177831530.320682216846876
71130.15120.6099788006739.54002119932693
72136.12130.1493693381875.97063066181272

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 111.41 & 110.48 & 0.929999999999993 \tabularnewline
3 & 115.5 & 111.409938520526 & 4.09006147947406 \tabularnewline
4 & 118.32 & 115.499729618464 & 2.82027038153613 \tabularnewline
5 & 118.42 & 118.319813560495 & 0.100186439505123 \tabularnewline
6 & 117.5 & 118.419993376979 & -0.919993376978923 \tabularnewline
7 & 110.23 & 117.500060817967 & -7.27006081796661 \tabularnewline
8 & 109.19 & 110.23048060163 & -1.04048060162953 \tabularnewline
9 & 118.41 & 109.190068783011 & 9.21993121698908 \tabularnewline
10 & 118.3 & 118.409390498363 & -0.109390498363368 \tabularnewline
11 & 116.1 & 118.300007231473 & -2.20000723147345 \tabularnewline
12 & 114.11 & 116.100145435793 & -1.99014543579302 \tabularnewline
13 & 113.41 & 114.110131562467 & -0.700131562467419 \tabularnewline
14 & 114.33 & 113.41004628357 & 0.919953716429859 \tabularnewline
15 & 116.61 & 114.329939184655 & 2.28006081534478 \tabularnewline
16 & 123.64 & 116.609849272108 & 7.03015072789221 \tabularnewline
17 & 123.77 & 123.639535258098 & 0.130464741902458 \tabularnewline
18 & 123.39 & 123.769991375372 & -0.379991375372342 \tabularnewline
19 & 116.03 & 123.390025120075 & -7.36002512007516 \tabularnewline
20 & 114.95 & 116.030486548896 & -1.08048654889616 \tabularnewline
21 & 123.4 & 114.950071427683 & 8.44992857231748 \tabularnewline
22 & 123.53 & 123.399441400898 & 0.130558599101548 \tabularnewline
23 & 114.45 & 123.529991369168 & -9.07999136916773 \tabularnewline
24 & 114.26 & 114.450600250639 & -0.190600250638511 \tabularnewline
25 & 114.35 & 114.260012600003 & 0.0899873999965877 \tabularnewline
26 & 112.77 & 114.349994051206 & -1.57999405120643 \tabularnewline
27 & 115.31 & 112.770104448606 & 2.53989555139432 \tabularnewline
28 & 114.93 & 115.309832095223 & -0.379832095222952 \tabularnewline
29 & 116.38 & 114.930025109546 & 1.44997489045436 \tabularnewline
30 & 115.07 & 116.379904146566 & -1.30990414656596 \tabularnewline
31 & 105 & 115.070086593783 & -10.0700865937828 \tabularnewline
32 & 103.43 & 105.000665702825 & -1.57066570282527 \tabularnewline
33 & 114.52 & 103.430103831937 & 11.0898961680631 \tabularnewline
34 & 115.04 & 114.519266880663 & 0.520733119337393 \tabularnewline
35 & 117.16 & 115.039965575916 & 2.1200344240842 \tabularnewline
36 & 115 & 117.159859850966 & -2.15985985096626 \tabularnewline
37 & 116.22 & 115.000142781772 & 1.2198572182283 \tabularnewline
38 & 112.92 & 116.219919358946 & -3.29991935894601 \tabularnewline
39 & 116.56 & 112.920218147642 & 3.63978185235848 \tabularnewline
40 & 114.32 & 116.559759385082 & -2.23975938508177 \tabularnewline
41 & 113.22 & 114.320148063687 & -1.1001480636871 \tabularnewline
42 & 111.56 & 113.220072727446 & -1.66007272744552 \tabularnewline
43 & 103.87 & 111.560109742364 & -7.69010974236365 \tabularnewline
44 & 102.85 & 103.870508369788 & -1.02050836978754 \tabularnewline
45 & 112.27 & 102.850067462707 & 9.41993253729264 \tabularnewline
46 & 112.76 & 112.269377276884 & 0.490622723116189 \tabularnewline
47 & 118.55 & 112.759967566423 & 5.79003243357739 \tabularnewline
48 & 122.73 & 118.54961723855 & 4.18038276145032 \tabularnewline
49 & 115.44 & 122.729723647598 & -7.28972364759836 \tabularnewline
50 & 116.97 & 115.440481901479 & 1.52951809852055 \tabularnewline
51 & 119.84 & 116.969898888206 & 2.87010111179383 \tabularnewline
52 & 116.37 & 119.839810266337 & -3.46981026633672 \tabularnewline
53 & 117.23 & 116.370229378613 & 0.859770621386815 \tabularnewline
54 & 115.58 & 117.229943163177 & -1.64994316317676 \tabularnewline
55 & 109.82 & 115.580109072729 & -5.76010907272894 \tabularnewline
56 & 108.46 & 109.820380783308 & -1.36038078330786 \tabularnewline
57 & 116.54 & 108.46008993064 & 8.07991006936014 \tabularnewline
58 & 117.49 & 116.539465861697 & 0.950534138302672 \tabularnewline
59 & 122.87 & 117.489937163076 & 5.38006283692356 \tabularnewline
60 & 127.1 & 122.869644340394 & 4.23035565960603 \tabularnewline
61 & 119.81 & 127.099720344042 & -7.28972034404191 \tabularnewline
62 & 120.03 & 119.810481901261 & 0.219518098738945 \tabularnewline
63 & 128.58 & 120.029985488326 & 8.55001451167449 \tabularnewline
64 & 120.4 & 128.579434784521 & -8.17943478452113 \tabularnewline
65 & 121.54 & 120.400540717579 & 1.13945928242082 \tabularnewline
66 & 118.71 & 121.539924673809 & -2.82992467380926 \tabularnewline
67 & 111.57 & 118.710187077721 & -7.14018707772105 \tabularnewline
68 & 109.97 & 111.570472016071 & -1.60047201607118 \tabularnewline
69 & 120.29 & 109.970105802342 & 10.3198941976583 \tabularnewline
70 & 120.61 & 120.289317783153 & 0.320682216846876 \tabularnewline
71 & 130.15 & 120.609978800673 & 9.54002119932693 \tabularnewline
72 & 136.12 & 130.149369338187 & 5.97063066181272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259296&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]111.41[/C][C]110.48[/C][C]0.929999999999993[/C][/ROW]
[ROW][C]3[/C][C]115.5[/C][C]111.409938520526[/C][C]4.09006147947406[/C][/ROW]
[ROW][C]4[/C][C]118.32[/C][C]115.499729618464[/C][C]2.82027038153613[/C][/ROW]
[ROW][C]5[/C][C]118.42[/C][C]118.319813560495[/C][C]0.100186439505123[/C][/ROW]
[ROW][C]6[/C][C]117.5[/C][C]118.419993376979[/C][C]-0.919993376978923[/C][/ROW]
[ROW][C]7[/C][C]110.23[/C][C]117.500060817967[/C][C]-7.27006081796661[/C][/ROW]
[ROW][C]8[/C][C]109.19[/C][C]110.23048060163[/C][C]-1.04048060162953[/C][/ROW]
[ROW][C]9[/C][C]118.41[/C][C]109.190068783011[/C][C]9.21993121698908[/C][/ROW]
[ROW][C]10[/C][C]118.3[/C][C]118.409390498363[/C][C]-0.109390498363368[/C][/ROW]
[ROW][C]11[/C][C]116.1[/C][C]118.300007231473[/C][C]-2.20000723147345[/C][/ROW]
[ROW][C]12[/C][C]114.11[/C][C]116.100145435793[/C][C]-1.99014543579302[/C][/ROW]
[ROW][C]13[/C][C]113.41[/C][C]114.110131562467[/C][C]-0.700131562467419[/C][/ROW]
[ROW][C]14[/C][C]114.33[/C][C]113.41004628357[/C][C]0.919953716429859[/C][/ROW]
[ROW][C]15[/C][C]116.61[/C][C]114.329939184655[/C][C]2.28006081534478[/C][/ROW]
[ROW][C]16[/C][C]123.64[/C][C]116.609849272108[/C][C]7.03015072789221[/C][/ROW]
[ROW][C]17[/C][C]123.77[/C][C]123.639535258098[/C][C]0.130464741902458[/C][/ROW]
[ROW][C]18[/C][C]123.39[/C][C]123.769991375372[/C][C]-0.379991375372342[/C][/ROW]
[ROW][C]19[/C][C]116.03[/C][C]123.390025120075[/C][C]-7.36002512007516[/C][/ROW]
[ROW][C]20[/C][C]114.95[/C][C]116.030486548896[/C][C]-1.08048654889616[/C][/ROW]
[ROW][C]21[/C][C]123.4[/C][C]114.950071427683[/C][C]8.44992857231748[/C][/ROW]
[ROW][C]22[/C][C]123.53[/C][C]123.399441400898[/C][C]0.130558599101548[/C][/ROW]
[ROW][C]23[/C][C]114.45[/C][C]123.529991369168[/C][C]-9.07999136916773[/C][/ROW]
[ROW][C]24[/C][C]114.26[/C][C]114.450600250639[/C][C]-0.190600250638511[/C][/ROW]
[ROW][C]25[/C][C]114.35[/C][C]114.260012600003[/C][C]0.0899873999965877[/C][/ROW]
[ROW][C]26[/C][C]112.77[/C][C]114.349994051206[/C][C]-1.57999405120643[/C][/ROW]
[ROW][C]27[/C][C]115.31[/C][C]112.770104448606[/C][C]2.53989555139432[/C][/ROW]
[ROW][C]28[/C][C]114.93[/C][C]115.309832095223[/C][C]-0.379832095222952[/C][/ROW]
[ROW][C]29[/C][C]116.38[/C][C]114.930025109546[/C][C]1.44997489045436[/C][/ROW]
[ROW][C]30[/C][C]115.07[/C][C]116.379904146566[/C][C]-1.30990414656596[/C][/ROW]
[ROW][C]31[/C][C]105[/C][C]115.070086593783[/C][C]-10.0700865937828[/C][/ROW]
[ROW][C]32[/C][C]103.43[/C][C]105.000665702825[/C][C]-1.57066570282527[/C][/ROW]
[ROW][C]33[/C][C]114.52[/C][C]103.430103831937[/C][C]11.0898961680631[/C][/ROW]
[ROW][C]34[/C][C]115.04[/C][C]114.519266880663[/C][C]0.520733119337393[/C][/ROW]
[ROW][C]35[/C][C]117.16[/C][C]115.039965575916[/C][C]2.1200344240842[/C][/ROW]
[ROW][C]36[/C][C]115[/C][C]117.159859850966[/C][C]-2.15985985096626[/C][/ROW]
[ROW][C]37[/C][C]116.22[/C][C]115.000142781772[/C][C]1.2198572182283[/C][/ROW]
[ROW][C]38[/C][C]112.92[/C][C]116.219919358946[/C][C]-3.29991935894601[/C][/ROW]
[ROW][C]39[/C][C]116.56[/C][C]112.920218147642[/C][C]3.63978185235848[/C][/ROW]
[ROW][C]40[/C][C]114.32[/C][C]116.559759385082[/C][C]-2.23975938508177[/C][/ROW]
[ROW][C]41[/C][C]113.22[/C][C]114.320148063687[/C][C]-1.1001480636871[/C][/ROW]
[ROW][C]42[/C][C]111.56[/C][C]113.220072727446[/C][C]-1.66007272744552[/C][/ROW]
[ROW][C]43[/C][C]103.87[/C][C]111.560109742364[/C][C]-7.69010974236365[/C][/ROW]
[ROW][C]44[/C][C]102.85[/C][C]103.870508369788[/C][C]-1.02050836978754[/C][/ROW]
[ROW][C]45[/C][C]112.27[/C][C]102.850067462707[/C][C]9.41993253729264[/C][/ROW]
[ROW][C]46[/C][C]112.76[/C][C]112.269377276884[/C][C]0.490622723116189[/C][/ROW]
[ROW][C]47[/C][C]118.55[/C][C]112.759967566423[/C][C]5.79003243357739[/C][/ROW]
[ROW][C]48[/C][C]122.73[/C][C]118.54961723855[/C][C]4.18038276145032[/C][/ROW]
[ROW][C]49[/C][C]115.44[/C][C]122.729723647598[/C][C]-7.28972364759836[/C][/ROW]
[ROW][C]50[/C][C]116.97[/C][C]115.440481901479[/C][C]1.52951809852055[/C][/ROW]
[ROW][C]51[/C][C]119.84[/C][C]116.969898888206[/C][C]2.87010111179383[/C][/ROW]
[ROW][C]52[/C][C]116.37[/C][C]119.839810266337[/C][C]-3.46981026633672[/C][/ROW]
[ROW][C]53[/C][C]117.23[/C][C]116.370229378613[/C][C]0.859770621386815[/C][/ROW]
[ROW][C]54[/C][C]115.58[/C][C]117.229943163177[/C][C]-1.64994316317676[/C][/ROW]
[ROW][C]55[/C][C]109.82[/C][C]115.580109072729[/C][C]-5.76010907272894[/C][/ROW]
[ROW][C]56[/C][C]108.46[/C][C]109.820380783308[/C][C]-1.36038078330786[/C][/ROW]
[ROW][C]57[/C][C]116.54[/C][C]108.46008993064[/C][C]8.07991006936014[/C][/ROW]
[ROW][C]58[/C][C]117.49[/C][C]116.539465861697[/C][C]0.950534138302672[/C][/ROW]
[ROW][C]59[/C][C]122.87[/C][C]117.489937163076[/C][C]5.38006283692356[/C][/ROW]
[ROW][C]60[/C][C]127.1[/C][C]122.869644340394[/C][C]4.23035565960603[/C][/ROW]
[ROW][C]61[/C][C]119.81[/C][C]127.099720344042[/C][C]-7.28972034404191[/C][/ROW]
[ROW][C]62[/C][C]120.03[/C][C]119.810481901261[/C][C]0.219518098738945[/C][/ROW]
[ROW][C]63[/C][C]128.58[/C][C]120.029985488326[/C][C]8.55001451167449[/C][/ROW]
[ROW][C]64[/C][C]120.4[/C][C]128.579434784521[/C][C]-8.17943478452113[/C][/ROW]
[ROW][C]65[/C][C]121.54[/C][C]120.400540717579[/C][C]1.13945928242082[/C][/ROW]
[ROW][C]66[/C][C]118.71[/C][C]121.539924673809[/C][C]-2.82992467380926[/C][/ROW]
[ROW][C]67[/C][C]111.57[/C][C]118.710187077721[/C][C]-7.14018707772105[/C][/ROW]
[ROW][C]68[/C][C]109.97[/C][C]111.570472016071[/C][C]-1.60047201607118[/C][/ROW]
[ROW][C]69[/C][C]120.29[/C][C]109.970105802342[/C][C]10.3198941976583[/C][/ROW]
[ROW][C]70[/C][C]120.61[/C][C]120.289317783153[/C][C]0.320682216846876[/C][/ROW]
[ROW][C]71[/C][C]130.15[/C][C]120.609978800673[/C][C]9.54002119932693[/C][/ROW]
[ROW][C]72[/C][C]136.12[/C][C]130.149369338187[/C][C]5.97063066181272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259296&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259296&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
2111.41110.480.929999999999993
3115.5111.4099385205264.09006147947406
4118.32115.4997296184642.82027038153613
5118.42118.3198135604950.100186439505123
6117.5118.419993376979-0.919993376978923
7110.23117.500060817967-7.27006081796661
8109.19110.23048060163-1.04048060162953
9118.41109.1900687830119.21993121698908
10118.3118.409390498363-0.109390498363368
11116.1118.300007231473-2.20000723147345
12114.11116.100145435793-1.99014543579302
13113.41114.110131562467-0.700131562467419
14114.33113.410046283570.919953716429859
15116.61114.3299391846552.28006081534478
16123.64116.6098492721087.03015072789221
17123.77123.6395352580980.130464741902458
18123.39123.769991375372-0.379991375372342
19116.03123.390025120075-7.36002512007516
20114.95116.030486548896-1.08048654889616
21123.4114.9500714276838.44992857231748
22123.53123.3994414008980.130558599101548
23114.45123.529991369168-9.07999136916773
24114.26114.450600250639-0.190600250638511
25114.35114.2600126000030.0899873999965877
26112.77114.349994051206-1.57999405120643
27115.31112.7701044486062.53989555139432
28114.93115.309832095223-0.379832095222952
29116.38114.9300251095461.44997489045436
30115.07116.379904146566-1.30990414656596
31105115.070086593783-10.0700865937828
32103.43105.000665702825-1.57066570282527
33114.52103.43010383193711.0898961680631
34115.04114.5192668806630.520733119337393
35117.16115.0399655759162.1200344240842
36115117.159859850966-2.15985985096626
37116.22115.0001427817721.2198572182283
38112.92116.219919358946-3.29991935894601
39116.56112.9202181476423.63978185235848
40114.32116.559759385082-2.23975938508177
41113.22114.320148063687-1.1001480636871
42111.56113.220072727446-1.66007272744552
43103.87111.560109742364-7.69010974236365
44102.85103.870508369788-1.02050836978754
45112.27102.8500674627079.41993253729264
46112.76112.2693772768840.490622723116189
47118.55112.7599675664235.79003243357739
48122.73118.549617238554.18038276145032
49115.44122.729723647598-7.28972364759836
50116.97115.4404819014791.52951809852055
51119.84116.9698988882062.87010111179383
52116.37119.839810266337-3.46981026633672
53117.23116.3702293786130.859770621386815
54115.58117.229943163177-1.64994316317676
55109.82115.580109072729-5.76010907272894
56108.46109.820380783308-1.36038078330786
57116.54108.460089930648.07991006936014
58117.49116.5394658616970.950534138302672
59122.87117.4899371630765.38006283692356
60127.1122.8696443403944.23035565960603
61119.81127.099720344042-7.28972034404191
62120.03119.8104819012610.219518098738945
63128.58120.0299854883268.55001451167449
64120.4128.579434784521-8.17943478452113
65121.54120.4005407175791.13945928242082
66118.71121.539924673809-2.82992467380926
67111.57118.710187077721-7.14018707772105
68109.97111.570472016071-1.60047201607118
69120.29109.97010580234210.3198941976583
70120.61120.2893177831530.320682216846876
71130.15120.6099788006739.54002119932693
72136.12130.1493693381875.97063066181272







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73136.11960529975126.659382483476145.579828116023
74136.11960529975122.74127209769149.497938501809
75136.11960529975119.73474085731152.504469742189
76136.11960529975117.200097739326155.039112860173
77136.11960529975114.967022718402157.272187881097
78136.11960529975112.94816310483159.291047494669
79136.11960529975111.091626617397161.147583982102
80136.11960529975109.363602226494162.875608373006
81136.11960529975107.740604542361164.498606057138
82136.11960529975106.20553390317166.033676696329
83136.11960529975104.745481390842167.493729208657
84136.11960529975103.350418025982168.888792573517

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 136.11960529975 & 126.659382483476 & 145.579828116023 \tabularnewline
74 & 136.11960529975 & 122.74127209769 & 149.497938501809 \tabularnewline
75 & 136.11960529975 & 119.73474085731 & 152.504469742189 \tabularnewline
76 & 136.11960529975 & 117.200097739326 & 155.039112860173 \tabularnewline
77 & 136.11960529975 & 114.967022718402 & 157.272187881097 \tabularnewline
78 & 136.11960529975 & 112.94816310483 & 159.291047494669 \tabularnewline
79 & 136.11960529975 & 111.091626617397 & 161.147583982102 \tabularnewline
80 & 136.11960529975 & 109.363602226494 & 162.875608373006 \tabularnewline
81 & 136.11960529975 & 107.740604542361 & 164.498606057138 \tabularnewline
82 & 136.11960529975 & 106.20553390317 & 166.033676696329 \tabularnewline
83 & 136.11960529975 & 104.745481390842 & 167.493729208657 \tabularnewline
84 & 136.11960529975 & 103.350418025982 & 168.888792573517 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259296&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]136.11960529975[/C][C]126.659382483476[/C][C]145.579828116023[/C][/ROW]
[ROW][C]74[/C][C]136.11960529975[/C][C]122.74127209769[/C][C]149.497938501809[/C][/ROW]
[ROW][C]75[/C][C]136.11960529975[/C][C]119.73474085731[/C][C]152.504469742189[/C][/ROW]
[ROW][C]76[/C][C]136.11960529975[/C][C]117.200097739326[/C][C]155.039112860173[/C][/ROW]
[ROW][C]77[/C][C]136.11960529975[/C][C]114.967022718402[/C][C]157.272187881097[/C][/ROW]
[ROW][C]78[/C][C]136.11960529975[/C][C]112.94816310483[/C][C]159.291047494669[/C][/ROW]
[ROW][C]79[/C][C]136.11960529975[/C][C]111.091626617397[/C][C]161.147583982102[/C][/ROW]
[ROW][C]80[/C][C]136.11960529975[/C][C]109.363602226494[/C][C]162.875608373006[/C][/ROW]
[ROW][C]81[/C][C]136.11960529975[/C][C]107.740604542361[/C][C]164.498606057138[/C][/ROW]
[ROW][C]82[/C][C]136.11960529975[/C][C]106.20553390317[/C][C]166.033676696329[/C][/ROW]
[ROW][C]83[/C][C]136.11960529975[/C][C]104.745481390842[/C][C]167.493729208657[/C][/ROW]
[ROW][C]84[/C][C]136.11960529975[/C][C]103.350418025982[/C][C]168.888792573517[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259296&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259296&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
73136.11960529975126.659382483476145.579828116023
74136.11960529975122.74127209769149.497938501809
75136.11960529975119.73474085731152.504469742189
76136.11960529975117.200097739326155.039112860173
77136.11960529975114.967022718402157.272187881097
78136.11960529975112.94816310483159.291047494669
79136.11960529975111.091626617397161.147583982102
80136.11960529975109.363602226494162.875608373006
81136.11960529975107.740604542361164.498606057138
82136.11960529975106.20553390317166.033676696329
83136.11960529975104.745481390842167.493729208657
84136.11960529975103.350418025982168.888792573517



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')