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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Dec 2013 05:18:21 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/16/t1387189181wvy8x6qul7msxon.htm/, Retrieved Thu, 28 Mar 2024 15:11:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232379, Retrieved Thu, 28 Mar 2024 15:11:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-16 10:18:21] [160234dce973f424b6ed2b48d1c7832a] [Current]
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Dataseries X:
125326
122716
116615
113719
110737
112093
143565
149946
149147
134339
122683
115614
116566
111272
104609
101802
94542
93051
124129
130374
123946
114971
105531
104919
104782
101281
94545
93248
84031
87486
115867
120327
117008
108811
104519
106758
109337
109078
108293
106534
99197
103493
130676
137448
134704
123725
118277
121225
120528
118240
112514
107304
100001
102082
130455
135574
132540
119920
112454
109415
109843
106365
102304
97968
92462
92286
120092
126656
124144
114045
108120
105698
111203
110030
104009
99772
96301
97680
121563
134210
133111
124527
117589
115699




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232379&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]3 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=232379&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232379&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0187104010472294
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0187104010472294 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232379&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]0.0187104010472294[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232379&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232379&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
beta0.0187104010472294
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3116615120106-3491
4113719113939.681989944-220.681989944118
5110737111039.552941408-302.552941408372
6112093108051.8920545374041.1079454634
7143565109483.50280487134081.4971951286
8149946141593.1812856828352.81871431775
9149147148130.4658737021016.53412629807
10134339147350.485634883-13011.4856348832
11122683132299.035520434-9616.03552043423
12115614120463.115639363-4849.11563936251
13116566113303.3867410263262.61325897436
14111272114316.431543563-3044.43154356306
15104609108965.469008422-4356.46900842217
16101802102220.957726125-418.957726124761
179454299406.1188590471-4864.11885904713
189305192055.109244453995.890755547036
1912412990582.742759888533546.2572401115
20130374122288.4066864848085.59331351552
21123946128684.691380085-4738.69138008516
22114971122168.028563925-7197.02856392472
23105531113058.369273145-7527.36927314532
24104919103477.5291752141441.47082478582
25104782102892.4996724441889.5003275562
26101281102790.852981351-1509.85298135124
279454599261.6030265478-4716.6030265478
289324892437.3534923405810.646507659476
298403191155.5210136064-7124.52101360637
308748681805.21836817245680.78163182762
3111586785366.508070765630500.4919292344
32120327114318.1845068996008.81549310063
33117008118890.611854594-1882.61185459408
34108811115536.387431778-6725.38743177836
35104519107213.552735732-2694.55273573179
36106758102871.1365734033886.86342659665
37109337105182.8613469314154.13865306923
38109078107839.5869471351238.4130528645
39108293107603.758152017689.241847983285
40106534106831.654143411-297.654143411011
4199197105067.084915014-5870.08491501442
4210349397620.25327207325872.74672792679
43130676102026.13471860228649.8652813985
44137448129745.1851879667702.81481203441
45134704136661.307942291-1957.30794229129
46123725133880.685925718-10155.6859257181
47118277122711.668969138-4434.66896913821
48121225117180.6945342144044.30546578608
49120528120204.365111436323.634888563713
50118240119513.420449994-1273.42044999418
51112514117201.594242673-4687.59424267305
52107304111387.887474446-4083.88747444596
53100001106101.476301967-6100.47630196731
5410208298684.33394377843397.66605622161
55130455100828.90563831529626.0943616851
56135574129756.2217452855817.77825471495
57132540134984.074709635-2444.07470963462
58119920131904.345091628-11984.345091628
59112454119060.113188675-6606.1131886752
60109415111470.510161552-2055.51016155169
61109843108393.0507420721449.94925792758
62106365108848.179874186-2483.17987418637
63102304105323.718582868-3019.71858286794
6497968101206.218437133-3238.2184371327
659246296809.6300714954-4347.63007149541
669228691222.28416925271063.71583074726
6712009291066.186719046329025.8132809537
68126656119415.2713262557240.72867374505
69124144126114.748263615-1970.74826361489
70114045123565.87477324-9520.87477323953
71108120113288.735387912-5168.73538791177
72105698107267.026275897-1569.02627589693
73111203104815.6691650216387.33083497874
74110030110440.178686565-410.17868656505
75104009109259.504078838-5250.50407883839
7699772103140.265041823-3368.26504182321
779630198840.2434520573-2539.24345205733
789768095321.73318871282358.26681128721
7912156396744.857306528324818.1426934717
80134210121092.21470957113117.7852904294
81133111133984.653733206-873.653733205952
82124527132869.307321481-8342.30732148126
83117589124129.219405837-6540.2194058371
84115699117068.849277817-1369.84927781702

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 116615 & 120106 & -3491 \tabularnewline
4 & 113719 & 113939.681989944 & -220.681989944118 \tabularnewline
5 & 110737 & 111039.552941408 & -302.552941408372 \tabularnewline
6 & 112093 & 108051.892054537 & 4041.1079454634 \tabularnewline
7 & 143565 & 109483.502804871 & 34081.4971951286 \tabularnewline
8 & 149946 & 141593.181285682 & 8352.81871431775 \tabularnewline
9 & 149147 & 148130.465873702 & 1016.53412629807 \tabularnewline
10 & 134339 & 147350.485634883 & -13011.4856348832 \tabularnewline
11 & 122683 & 132299.035520434 & -9616.03552043423 \tabularnewline
12 & 115614 & 120463.115639363 & -4849.11563936251 \tabularnewline
13 & 116566 & 113303.386741026 & 3262.61325897436 \tabularnewline
14 & 111272 & 114316.431543563 & -3044.43154356306 \tabularnewline
15 & 104609 & 108965.469008422 & -4356.46900842217 \tabularnewline
16 & 101802 & 102220.957726125 & -418.957726124761 \tabularnewline
17 & 94542 & 99406.1188590471 & -4864.11885904713 \tabularnewline
18 & 93051 & 92055.109244453 & 995.890755547036 \tabularnewline
19 & 124129 & 90582.7427598885 & 33546.2572401115 \tabularnewline
20 & 130374 & 122288.406686484 & 8085.59331351552 \tabularnewline
21 & 123946 & 128684.691380085 & -4738.69138008516 \tabularnewline
22 & 114971 & 122168.028563925 & -7197.02856392472 \tabularnewline
23 & 105531 & 113058.369273145 & -7527.36927314532 \tabularnewline
24 & 104919 & 103477.529175214 & 1441.47082478582 \tabularnewline
25 & 104782 & 102892.499672444 & 1889.5003275562 \tabularnewline
26 & 101281 & 102790.852981351 & -1509.85298135124 \tabularnewline
27 & 94545 & 99261.6030265478 & -4716.6030265478 \tabularnewline
28 & 93248 & 92437.3534923405 & 810.646507659476 \tabularnewline
29 & 84031 & 91155.5210136064 & -7124.52101360637 \tabularnewline
30 & 87486 & 81805.2183681724 & 5680.78163182762 \tabularnewline
31 & 115867 & 85366.5080707656 & 30500.4919292344 \tabularnewline
32 & 120327 & 114318.184506899 & 6008.81549310063 \tabularnewline
33 & 117008 & 118890.611854594 & -1882.61185459408 \tabularnewline
34 & 108811 & 115536.387431778 & -6725.38743177836 \tabularnewline
35 & 104519 & 107213.552735732 & -2694.55273573179 \tabularnewline
36 & 106758 & 102871.136573403 & 3886.86342659665 \tabularnewline
37 & 109337 & 105182.861346931 & 4154.13865306923 \tabularnewline
38 & 109078 & 107839.586947135 & 1238.4130528645 \tabularnewline
39 & 108293 & 107603.758152017 & 689.241847983285 \tabularnewline
40 & 106534 & 106831.654143411 & -297.654143411011 \tabularnewline
41 & 99197 & 105067.084915014 & -5870.08491501442 \tabularnewline
42 & 103493 & 97620.2532720732 & 5872.74672792679 \tabularnewline
43 & 130676 & 102026.134718602 & 28649.8652813985 \tabularnewline
44 & 137448 & 129745.185187966 & 7702.81481203441 \tabularnewline
45 & 134704 & 136661.307942291 & -1957.30794229129 \tabularnewline
46 & 123725 & 133880.685925718 & -10155.6859257181 \tabularnewline
47 & 118277 & 122711.668969138 & -4434.66896913821 \tabularnewline
48 & 121225 & 117180.694534214 & 4044.30546578608 \tabularnewline
49 & 120528 & 120204.365111436 & 323.634888563713 \tabularnewline
50 & 118240 & 119513.420449994 & -1273.42044999418 \tabularnewline
51 & 112514 & 117201.594242673 & -4687.59424267305 \tabularnewline
52 & 107304 & 111387.887474446 & -4083.88747444596 \tabularnewline
53 & 100001 & 106101.476301967 & -6100.47630196731 \tabularnewline
54 & 102082 & 98684.3339437784 & 3397.66605622161 \tabularnewline
55 & 130455 & 100828.905638315 & 29626.0943616851 \tabularnewline
56 & 135574 & 129756.221745285 & 5817.77825471495 \tabularnewline
57 & 132540 & 134984.074709635 & -2444.07470963462 \tabularnewline
58 & 119920 & 131904.345091628 & -11984.345091628 \tabularnewline
59 & 112454 & 119060.113188675 & -6606.1131886752 \tabularnewline
60 & 109415 & 111470.510161552 & -2055.51016155169 \tabularnewline
61 & 109843 & 108393.050742072 & 1449.94925792758 \tabularnewline
62 & 106365 & 108848.179874186 & -2483.17987418637 \tabularnewline
63 & 102304 & 105323.718582868 & -3019.71858286794 \tabularnewline
64 & 97968 & 101206.218437133 & -3238.2184371327 \tabularnewline
65 & 92462 & 96809.6300714954 & -4347.63007149541 \tabularnewline
66 & 92286 & 91222.2841692527 & 1063.71583074726 \tabularnewline
67 & 120092 & 91066.1867190463 & 29025.8132809537 \tabularnewline
68 & 126656 & 119415.271326255 & 7240.72867374505 \tabularnewline
69 & 124144 & 126114.748263615 & -1970.74826361489 \tabularnewline
70 & 114045 & 123565.87477324 & -9520.87477323953 \tabularnewline
71 & 108120 & 113288.735387912 & -5168.73538791177 \tabularnewline
72 & 105698 & 107267.026275897 & -1569.02627589693 \tabularnewline
73 & 111203 & 104815.669165021 & 6387.33083497874 \tabularnewline
74 & 110030 & 110440.178686565 & -410.17868656505 \tabularnewline
75 & 104009 & 109259.504078838 & -5250.50407883839 \tabularnewline
76 & 99772 & 103140.265041823 & -3368.26504182321 \tabularnewline
77 & 96301 & 98840.2434520573 & -2539.24345205733 \tabularnewline
78 & 97680 & 95321.7331887128 & 2358.26681128721 \tabularnewline
79 & 121563 & 96744.8573065283 & 24818.1426934717 \tabularnewline
80 & 134210 & 121092.214709571 & 13117.7852904294 \tabularnewline
81 & 133111 & 133984.653733206 & -873.653733205952 \tabularnewline
82 & 124527 & 132869.307321481 & -8342.30732148126 \tabularnewline
83 & 117589 & 124129.219405837 & -6540.2194058371 \tabularnewline
84 & 115699 & 117068.849277817 & -1369.84927781702 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232379&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]116615[/C][C]120106[/C][C]-3491[/C][/ROW]
[ROW][C]4[/C][C]113719[/C][C]113939.681989944[/C][C]-220.681989944118[/C][/ROW]
[ROW][C]5[/C][C]110737[/C][C]111039.552941408[/C][C]-302.552941408372[/C][/ROW]
[ROW][C]6[/C][C]112093[/C][C]108051.892054537[/C][C]4041.1079454634[/C][/ROW]
[ROW][C]7[/C][C]143565[/C][C]109483.502804871[/C][C]34081.4971951286[/C][/ROW]
[ROW][C]8[/C][C]149946[/C][C]141593.181285682[/C][C]8352.81871431775[/C][/ROW]
[ROW][C]9[/C][C]149147[/C][C]148130.465873702[/C][C]1016.53412629807[/C][/ROW]
[ROW][C]10[/C][C]134339[/C][C]147350.485634883[/C][C]-13011.4856348832[/C][/ROW]
[ROW][C]11[/C][C]122683[/C][C]132299.035520434[/C][C]-9616.03552043423[/C][/ROW]
[ROW][C]12[/C][C]115614[/C][C]120463.115639363[/C][C]-4849.11563936251[/C][/ROW]
[ROW][C]13[/C][C]116566[/C][C]113303.386741026[/C][C]3262.61325897436[/C][/ROW]
[ROW][C]14[/C][C]111272[/C][C]114316.431543563[/C][C]-3044.43154356306[/C][/ROW]
[ROW][C]15[/C][C]104609[/C][C]108965.469008422[/C][C]-4356.46900842217[/C][/ROW]
[ROW][C]16[/C][C]101802[/C][C]102220.957726125[/C][C]-418.957726124761[/C][/ROW]
[ROW][C]17[/C][C]94542[/C][C]99406.1188590471[/C][C]-4864.11885904713[/C][/ROW]
[ROW][C]18[/C][C]93051[/C][C]92055.109244453[/C][C]995.890755547036[/C][/ROW]
[ROW][C]19[/C][C]124129[/C][C]90582.7427598885[/C][C]33546.2572401115[/C][/ROW]
[ROW][C]20[/C][C]130374[/C][C]122288.406686484[/C][C]8085.59331351552[/C][/ROW]
[ROW][C]21[/C][C]123946[/C][C]128684.691380085[/C][C]-4738.69138008516[/C][/ROW]
[ROW][C]22[/C][C]114971[/C][C]122168.028563925[/C][C]-7197.02856392472[/C][/ROW]
[ROW][C]23[/C][C]105531[/C][C]113058.369273145[/C][C]-7527.36927314532[/C][/ROW]
[ROW][C]24[/C][C]104919[/C][C]103477.529175214[/C][C]1441.47082478582[/C][/ROW]
[ROW][C]25[/C][C]104782[/C][C]102892.499672444[/C][C]1889.5003275562[/C][/ROW]
[ROW][C]26[/C][C]101281[/C][C]102790.852981351[/C][C]-1509.85298135124[/C][/ROW]
[ROW][C]27[/C][C]94545[/C][C]99261.6030265478[/C][C]-4716.6030265478[/C][/ROW]
[ROW][C]28[/C][C]93248[/C][C]92437.3534923405[/C][C]810.646507659476[/C][/ROW]
[ROW][C]29[/C][C]84031[/C][C]91155.5210136064[/C][C]-7124.52101360637[/C][/ROW]
[ROW][C]30[/C][C]87486[/C][C]81805.2183681724[/C][C]5680.78163182762[/C][/ROW]
[ROW][C]31[/C][C]115867[/C][C]85366.5080707656[/C][C]30500.4919292344[/C][/ROW]
[ROW][C]32[/C][C]120327[/C][C]114318.184506899[/C][C]6008.81549310063[/C][/ROW]
[ROW][C]33[/C][C]117008[/C][C]118890.611854594[/C][C]-1882.61185459408[/C][/ROW]
[ROW][C]34[/C][C]108811[/C][C]115536.387431778[/C][C]-6725.38743177836[/C][/ROW]
[ROW][C]35[/C][C]104519[/C][C]107213.552735732[/C][C]-2694.55273573179[/C][/ROW]
[ROW][C]36[/C][C]106758[/C][C]102871.136573403[/C][C]3886.86342659665[/C][/ROW]
[ROW][C]37[/C][C]109337[/C][C]105182.861346931[/C][C]4154.13865306923[/C][/ROW]
[ROW][C]38[/C][C]109078[/C][C]107839.586947135[/C][C]1238.4130528645[/C][/ROW]
[ROW][C]39[/C][C]108293[/C][C]107603.758152017[/C][C]689.241847983285[/C][/ROW]
[ROW][C]40[/C][C]106534[/C][C]106831.654143411[/C][C]-297.654143411011[/C][/ROW]
[ROW][C]41[/C][C]99197[/C][C]105067.084915014[/C][C]-5870.08491501442[/C][/ROW]
[ROW][C]42[/C][C]103493[/C][C]97620.2532720732[/C][C]5872.74672792679[/C][/ROW]
[ROW][C]43[/C][C]130676[/C][C]102026.134718602[/C][C]28649.8652813985[/C][/ROW]
[ROW][C]44[/C][C]137448[/C][C]129745.185187966[/C][C]7702.81481203441[/C][/ROW]
[ROW][C]45[/C][C]134704[/C][C]136661.307942291[/C][C]-1957.30794229129[/C][/ROW]
[ROW][C]46[/C][C]123725[/C][C]133880.685925718[/C][C]-10155.6859257181[/C][/ROW]
[ROW][C]47[/C][C]118277[/C][C]122711.668969138[/C][C]-4434.66896913821[/C][/ROW]
[ROW][C]48[/C][C]121225[/C][C]117180.694534214[/C][C]4044.30546578608[/C][/ROW]
[ROW][C]49[/C][C]120528[/C][C]120204.365111436[/C][C]323.634888563713[/C][/ROW]
[ROW][C]50[/C][C]118240[/C][C]119513.420449994[/C][C]-1273.42044999418[/C][/ROW]
[ROW][C]51[/C][C]112514[/C][C]117201.594242673[/C][C]-4687.59424267305[/C][/ROW]
[ROW][C]52[/C][C]107304[/C][C]111387.887474446[/C][C]-4083.88747444596[/C][/ROW]
[ROW][C]53[/C][C]100001[/C][C]106101.476301967[/C][C]-6100.47630196731[/C][/ROW]
[ROW][C]54[/C][C]102082[/C][C]98684.3339437784[/C][C]3397.66605622161[/C][/ROW]
[ROW][C]55[/C][C]130455[/C][C]100828.905638315[/C][C]29626.0943616851[/C][/ROW]
[ROW][C]56[/C][C]135574[/C][C]129756.221745285[/C][C]5817.77825471495[/C][/ROW]
[ROW][C]57[/C][C]132540[/C][C]134984.074709635[/C][C]-2444.07470963462[/C][/ROW]
[ROW][C]58[/C][C]119920[/C][C]131904.345091628[/C][C]-11984.345091628[/C][/ROW]
[ROW][C]59[/C][C]112454[/C][C]119060.113188675[/C][C]-6606.1131886752[/C][/ROW]
[ROW][C]60[/C][C]109415[/C][C]111470.510161552[/C][C]-2055.51016155169[/C][/ROW]
[ROW][C]61[/C][C]109843[/C][C]108393.050742072[/C][C]1449.94925792758[/C][/ROW]
[ROW][C]62[/C][C]106365[/C][C]108848.179874186[/C][C]-2483.17987418637[/C][/ROW]
[ROW][C]63[/C][C]102304[/C][C]105323.718582868[/C][C]-3019.71858286794[/C][/ROW]
[ROW][C]64[/C][C]97968[/C][C]101206.218437133[/C][C]-3238.2184371327[/C][/ROW]
[ROW][C]65[/C][C]92462[/C][C]96809.6300714954[/C][C]-4347.63007149541[/C][/ROW]
[ROW][C]66[/C][C]92286[/C][C]91222.2841692527[/C][C]1063.71583074726[/C][/ROW]
[ROW][C]67[/C][C]120092[/C][C]91066.1867190463[/C][C]29025.8132809537[/C][/ROW]
[ROW][C]68[/C][C]126656[/C][C]119415.271326255[/C][C]7240.72867374505[/C][/ROW]
[ROW][C]69[/C][C]124144[/C][C]126114.748263615[/C][C]-1970.74826361489[/C][/ROW]
[ROW][C]70[/C][C]114045[/C][C]123565.87477324[/C][C]-9520.87477323953[/C][/ROW]
[ROW][C]71[/C][C]108120[/C][C]113288.735387912[/C][C]-5168.73538791177[/C][/ROW]
[ROW][C]72[/C][C]105698[/C][C]107267.026275897[/C][C]-1569.02627589693[/C][/ROW]
[ROW][C]73[/C][C]111203[/C][C]104815.669165021[/C][C]6387.33083497874[/C][/ROW]
[ROW][C]74[/C][C]110030[/C][C]110440.178686565[/C][C]-410.17868656505[/C][/ROW]
[ROW][C]75[/C][C]104009[/C][C]109259.504078838[/C][C]-5250.50407883839[/C][/ROW]
[ROW][C]76[/C][C]99772[/C][C]103140.265041823[/C][C]-3368.26504182321[/C][/ROW]
[ROW][C]77[/C][C]96301[/C][C]98840.2434520573[/C][C]-2539.24345205733[/C][/ROW]
[ROW][C]78[/C][C]97680[/C][C]95321.7331887128[/C][C]2358.26681128721[/C][/ROW]
[ROW][C]79[/C][C]121563[/C][C]96744.8573065283[/C][C]24818.1426934717[/C][/ROW]
[ROW][C]80[/C][C]134210[/C][C]121092.214709571[/C][C]13117.7852904294[/C][/ROW]
[ROW][C]81[/C][C]133111[/C][C]133984.653733206[/C][C]-873.653733205952[/C][/ROW]
[ROW][C]82[/C][C]124527[/C][C]132869.307321481[/C][C]-8342.30732148126[/C][/ROW]
[ROW][C]83[/C][C]117589[/C][C]124129.219405837[/C][C]-6540.2194058371[/C][/ROW]
[ROW][C]84[/C][C]115699[/C][C]117068.849277817[/C][C]-1369.84927781702[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232379&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232379&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
3116615120106-3491
4113719113939.681989944-220.681989944118
5110737111039.552941408-302.552941408372
6112093108051.8920545374041.1079454634
7143565109483.50280487134081.4971951286
8149946141593.1812856828352.81871431775
9149147148130.4658737021016.53412629807
10134339147350.485634883-13011.4856348832
11122683132299.035520434-9616.03552043423
12115614120463.115639363-4849.11563936251
13116566113303.3867410263262.61325897436
14111272114316.431543563-3044.43154356306
15104609108965.469008422-4356.46900842217
16101802102220.957726125-418.957726124761
179454299406.1188590471-4864.11885904713
189305192055.109244453995.890755547036
1912412990582.742759888533546.2572401115
20130374122288.4066864848085.59331351552
21123946128684.691380085-4738.69138008516
22114971122168.028563925-7197.02856392472
23105531113058.369273145-7527.36927314532
24104919103477.5291752141441.47082478582
25104782102892.4996724441889.5003275562
26101281102790.852981351-1509.85298135124
279454599261.6030265478-4716.6030265478
289324892437.3534923405810.646507659476
298403191155.5210136064-7124.52101360637
308748681805.21836817245680.78163182762
3111586785366.508070765630500.4919292344
32120327114318.1845068996008.81549310063
33117008118890.611854594-1882.61185459408
34108811115536.387431778-6725.38743177836
35104519107213.552735732-2694.55273573179
36106758102871.1365734033886.86342659665
37109337105182.8613469314154.13865306923
38109078107839.5869471351238.4130528645
39108293107603.758152017689.241847983285
40106534106831.654143411-297.654143411011
4199197105067.084915014-5870.08491501442
4210349397620.25327207325872.74672792679
43130676102026.13471860228649.8652813985
44137448129745.1851879667702.81481203441
45134704136661.307942291-1957.30794229129
46123725133880.685925718-10155.6859257181
47118277122711.668969138-4434.66896913821
48121225117180.6945342144044.30546578608
49120528120204.365111436323.634888563713
50118240119513.420449994-1273.42044999418
51112514117201.594242673-4687.59424267305
52107304111387.887474446-4083.88747444596
53100001106101.476301967-6100.47630196731
5410208298684.33394377843397.66605622161
55130455100828.90563831529626.0943616851
56135574129756.2217452855817.77825471495
57132540134984.074709635-2444.07470963462
58119920131904.345091628-11984.345091628
59112454119060.113188675-6606.1131886752
60109415111470.510161552-2055.51016155169
61109843108393.0507420721449.94925792758
62106365108848.179874186-2483.17987418637
63102304105323.718582868-3019.71858286794
6497968101206.218437133-3238.2184371327
659246296809.6300714954-4347.63007149541
669228691222.28416925271063.71583074726
6712009291066.186719046329025.8132809537
68126656119415.2713262557240.72867374505
69124144126114.748263615-1970.74826361489
70114045123565.87477324-9520.87477323953
71108120113288.735387912-5168.73538791177
72105698107267.026275897-1569.02627589693
73111203104815.6691650216387.33083497874
74110030110440.178686565-410.17868656505
75104009109259.504078838-5250.50407883839
7699772103140.265041823-3368.26504182321
779630198840.2434520573-2539.24345205733
789768095321.73318871282358.26681128721
7912156396744.857306528324818.1426934717
80134210121092.21470957113117.7852904294
81133111133984.653733206-873.653733205952
82124527132869.307321481-8342.30732148126
83117589124129.219405837-6540.2194058371
84115699117068.849277817-1369.84927781702







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85115153.21884845595306.3228946517135000.114802258
86114607.4376969186275.8920123762142938.983381443
87114061.65654536479038.7012526267149084.611838102
88113515.87539381972699.6063273803154332.144460258
89112970.09424227466915.4143292481159024.7741553
90112424.31309072961511.8357063484163336.790475109
91111878.53193918456386.3338669209167370.730011446
92111332.75078763851472.7439873065171192.75758797
93110786.96963609346725.551864047174848.38740814
94110241.18848454842111.9411880031178370.435781093
95109695.40733300337607.381443545181783.433222461
96109149.62618145833193.0039743275185106.248388588

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 115153.218848455 & 95306.3228946517 & 135000.114802258 \tabularnewline
86 & 114607.43769691 & 86275.8920123762 & 142938.983381443 \tabularnewline
87 & 114061.656545364 & 79038.7012526267 & 149084.611838102 \tabularnewline
88 & 113515.875393819 & 72699.6063273803 & 154332.144460258 \tabularnewline
89 & 112970.094242274 & 66915.4143292481 & 159024.7741553 \tabularnewline
90 & 112424.313090729 & 61511.8357063484 & 163336.790475109 \tabularnewline
91 & 111878.531939184 & 56386.3338669209 & 167370.730011446 \tabularnewline
92 & 111332.750787638 & 51472.7439873065 & 171192.75758797 \tabularnewline
93 & 110786.969636093 & 46725.551864047 & 174848.38740814 \tabularnewline
94 & 110241.188484548 & 42111.9411880031 & 178370.435781093 \tabularnewline
95 & 109695.407333003 & 37607.381443545 & 181783.433222461 \tabularnewline
96 & 109149.626181458 & 33193.0039743275 & 185106.248388588 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232379&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]85[/C][C]115153.218848455[/C][C]95306.3228946517[/C][C]135000.114802258[/C][/ROW]
[ROW][C]86[/C][C]114607.43769691[/C][C]86275.8920123762[/C][C]142938.983381443[/C][/ROW]
[ROW][C]87[/C][C]114061.656545364[/C][C]79038.7012526267[/C][C]149084.611838102[/C][/ROW]
[ROW][C]88[/C][C]113515.875393819[/C][C]72699.6063273803[/C][C]154332.144460258[/C][/ROW]
[ROW][C]89[/C][C]112970.094242274[/C][C]66915.4143292481[/C][C]159024.7741553[/C][/ROW]
[ROW][C]90[/C][C]112424.313090729[/C][C]61511.8357063484[/C][C]163336.790475109[/C][/ROW]
[ROW][C]91[/C][C]111878.531939184[/C][C]56386.3338669209[/C][C]167370.730011446[/C][/ROW]
[ROW][C]92[/C][C]111332.750787638[/C][C]51472.7439873065[/C][C]171192.75758797[/C][/ROW]
[ROW][C]93[/C][C]110786.969636093[/C][C]46725.551864047[/C][C]174848.38740814[/C][/ROW]
[ROW][C]94[/C][C]110241.188484548[/C][C]42111.9411880031[/C][C]178370.435781093[/C][/ROW]
[ROW][C]95[/C][C]109695.407333003[/C][C]37607.381443545[/C][C]181783.433222461[/C][/ROW]
[ROW][C]96[/C][C]109149.626181458[/C][C]33193.0039743275[/C][C]185106.248388588[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232379&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232379&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
85115153.21884845595306.3228946517135000.114802258
86114607.4376969186275.8920123762142938.983381443
87114061.65654536479038.7012526267149084.611838102
88113515.87539381972699.6063273803154332.144460258
89112970.09424227466915.4143292481159024.7741553
90112424.31309072961511.8357063484163336.790475109
91111878.53193918456386.3338669209167370.730011446
92111332.75078763851472.7439873065171192.75758797
93110786.96963609346725.551864047174848.38740814
94110241.18848454842111.9411880031178370.435781093
95109695.40733300337607.381443545181783.433222461
96109149.62618145833193.0039743275185106.248388588



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')