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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 May 2014 10:17:01 -0400
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/May/21/t14006818590wlqp8lef9x4g5v.htm/, Retrieved Mon, 13 May 2024 21:38:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235046, Retrieved Mon, 13 May 2024 21:38:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Niet werkende wer...] [2014-05-21 14:17:01] [778963f9ed1fb67b9d5ff0854a52552f] [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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235046&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235046&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235046&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0187104010474274
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0187104010474274 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235046&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]0.0187104010474274[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235046&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235046&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
beta0.0187104010474274
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3116615120106-3491
4113719113939.681989943-220.681989943434
5110737111039.552941408-302.552941407645
6112093108051.8920545364041.10794546417
7143565109483.50280487134081.4971951286
8149946141593.1812856898352.81871431097
9149147148130.465873711016.53412628974
10134339147350.485634892-13011.4856348915
11122683132299.03552044-9616.03552043988
12115614120463.115639366-4849.11563936614
13116566113303.3867410283262.61325897176
14111272114316.431543566-3044.43154356626
15104609108965.469008425-4356.4690084247
16101802102220.957726126-418.957726126377
179454299406.1188590486-4864.11885904863
189305192055.1092444535995.890755546527
1912412990582.742759889233546.2572401108
20130374122288.4066864928085.59331350819
21123946128684.691380094-4738.69138009395
22114971122168.028563932-7197.02856393241
23105531113058.369273151-7527.36927315145
24104919103477.5291752191441.47082478131
25104782102892.4996724491889.50032755148
26101281102790.852981356-1509.85298135625
279454599261.6030265524-4716.60302655243
289324892437.3534923441810.646507655882
298403191155.5210136101-7124.52101361005
308748681805.21836817465680.7816318254
3111586785366.508070768930500.4919292311
32120327114318.1845069096008.81549309136
33117008118890.611854604-1882.61185460437
34108811115536.387431788-6725.38743178808
35104519107213.55273574-2694.55273574
36106758102871.1365734113886.86342658913
37109337105182.8613469394154.13865306108
38109078107839.5869471441238.41305285569
39108293107603.758152026689.241847974379
40106534106831.65414342-297.654143419888
4199197105067.084915023-5870.08491502306
4210349397620.25327208055872.74672791947
43130676102026.1347186128649.8652813901
44137448129745.1851879797702.81481202054
45134704136661.307942306-1957.30794230642
46123725133880.685925733-10155.6859257325
47118277122711.66896915-4434.66896915039
48121225117180.6945342254044.305465775
49120528120204.365111448323.634888552057
50118240119513.420450006-1273.42045000569
51112514117201.594242684-4687.59424268409
52107304111387.887474456-4083.88747445587
53100001106101.476301976-6100.47630197623
5410208298684.33394378593397.66605621408
55130455100828.90563832329626.0943616771
56135574129756.2217452995817.77825470117
57132540134984.074709649-2444.07470964929
58119920131904.345091642-11984.3450916419
59112454119060.113188686-6606.11318868649
60109415111470.510161561-2055.51016156147
61109843108393.0507420821449.94925791842
62106365108848.179874196-2483.17987419566
63102304105323.718582877-3019.71858287657
6497968101206.218437141-3238.21843714057
659246296809.6300715025-4347.6300715025
669228691222.28416925881063.71583074117
6712009291066.186719052529025.8132809475
68126656119415.2713262677240.72867373323
69124144126114.748263628-1970.74826362793
70114045123565.874773252-9520.87477325193
71108120113288.735387922-5168.73538792205
72105698107267.026275906-1569.026275906
73111203104815.669165036387.33083497015
74110030110440.178686575-410.178686574727
75104009109259.504078848-5250.50407884781
7699772103140.265041831-3368.26504183142
779630198840.2434520647-2539.24345206472
789768095321.73318871952358.26681128047
7912156396744.857306535424818.1426934646
80134210121092.21470958213117.7852904176
81133111133984.65373322-873.653733220184
82124527132869.307321495-8342.30732149506
83117589124129.219405849-6540.219405849
84115699117068.849277827-1369.84927782739

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 116615 & 120106 & -3491 \tabularnewline
4 & 113719 & 113939.681989943 & -220.681989943434 \tabularnewline
5 & 110737 & 111039.552941408 & -302.552941407645 \tabularnewline
6 & 112093 & 108051.892054536 & 4041.10794546417 \tabularnewline
7 & 143565 & 109483.502804871 & 34081.4971951286 \tabularnewline
8 & 149946 & 141593.181285689 & 8352.81871431097 \tabularnewline
9 & 149147 & 148130.46587371 & 1016.53412628974 \tabularnewline
10 & 134339 & 147350.485634892 & -13011.4856348915 \tabularnewline
11 & 122683 & 132299.03552044 & -9616.03552043988 \tabularnewline
12 & 115614 & 120463.115639366 & -4849.11563936614 \tabularnewline
13 & 116566 & 113303.386741028 & 3262.61325897176 \tabularnewline
14 & 111272 & 114316.431543566 & -3044.43154356626 \tabularnewline
15 & 104609 & 108965.469008425 & -4356.4690084247 \tabularnewline
16 & 101802 & 102220.957726126 & -418.957726126377 \tabularnewline
17 & 94542 & 99406.1188590486 & -4864.11885904863 \tabularnewline
18 & 93051 & 92055.1092444535 & 995.890755546527 \tabularnewline
19 & 124129 & 90582.7427598892 & 33546.2572401108 \tabularnewline
20 & 130374 & 122288.406686492 & 8085.59331350819 \tabularnewline
21 & 123946 & 128684.691380094 & -4738.69138009395 \tabularnewline
22 & 114971 & 122168.028563932 & -7197.02856393241 \tabularnewline
23 & 105531 & 113058.369273151 & -7527.36927315145 \tabularnewline
24 & 104919 & 103477.529175219 & 1441.47082478131 \tabularnewline
25 & 104782 & 102892.499672449 & 1889.50032755148 \tabularnewline
26 & 101281 & 102790.852981356 & -1509.85298135625 \tabularnewline
27 & 94545 & 99261.6030265524 & -4716.60302655243 \tabularnewline
28 & 93248 & 92437.3534923441 & 810.646507655882 \tabularnewline
29 & 84031 & 91155.5210136101 & -7124.52101361005 \tabularnewline
30 & 87486 & 81805.2183681746 & 5680.7816318254 \tabularnewline
31 & 115867 & 85366.5080707689 & 30500.4919292311 \tabularnewline
32 & 120327 & 114318.184506909 & 6008.81549309136 \tabularnewline
33 & 117008 & 118890.611854604 & -1882.61185460437 \tabularnewline
34 & 108811 & 115536.387431788 & -6725.38743178808 \tabularnewline
35 & 104519 & 107213.55273574 & -2694.55273574 \tabularnewline
36 & 106758 & 102871.136573411 & 3886.86342658913 \tabularnewline
37 & 109337 & 105182.861346939 & 4154.13865306108 \tabularnewline
38 & 109078 & 107839.586947144 & 1238.41305285569 \tabularnewline
39 & 108293 & 107603.758152026 & 689.241847974379 \tabularnewline
40 & 106534 & 106831.65414342 & -297.654143419888 \tabularnewline
41 & 99197 & 105067.084915023 & -5870.08491502306 \tabularnewline
42 & 103493 & 97620.2532720805 & 5872.74672791947 \tabularnewline
43 & 130676 & 102026.13471861 & 28649.8652813901 \tabularnewline
44 & 137448 & 129745.185187979 & 7702.81481202054 \tabularnewline
45 & 134704 & 136661.307942306 & -1957.30794230642 \tabularnewline
46 & 123725 & 133880.685925733 & -10155.6859257325 \tabularnewline
47 & 118277 & 122711.66896915 & -4434.66896915039 \tabularnewline
48 & 121225 & 117180.694534225 & 4044.305465775 \tabularnewline
49 & 120528 & 120204.365111448 & 323.634888552057 \tabularnewline
50 & 118240 & 119513.420450006 & -1273.42045000569 \tabularnewline
51 & 112514 & 117201.594242684 & -4687.59424268409 \tabularnewline
52 & 107304 & 111387.887474456 & -4083.88747445587 \tabularnewline
53 & 100001 & 106101.476301976 & -6100.47630197623 \tabularnewline
54 & 102082 & 98684.3339437859 & 3397.66605621408 \tabularnewline
55 & 130455 & 100828.905638323 & 29626.0943616771 \tabularnewline
56 & 135574 & 129756.221745299 & 5817.77825470117 \tabularnewline
57 & 132540 & 134984.074709649 & -2444.07470964929 \tabularnewline
58 & 119920 & 131904.345091642 & -11984.3450916419 \tabularnewline
59 & 112454 & 119060.113188686 & -6606.11318868649 \tabularnewline
60 & 109415 & 111470.510161561 & -2055.51016156147 \tabularnewline
61 & 109843 & 108393.050742082 & 1449.94925791842 \tabularnewline
62 & 106365 & 108848.179874196 & -2483.17987419566 \tabularnewline
63 & 102304 & 105323.718582877 & -3019.71858287657 \tabularnewline
64 & 97968 & 101206.218437141 & -3238.21843714057 \tabularnewline
65 & 92462 & 96809.6300715025 & -4347.6300715025 \tabularnewline
66 & 92286 & 91222.2841692588 & 1063.71583074117 \tabularnewline
67 & 120092 & 91066.1867190525 & 29025.8132809475 \tabularnewline
68 & 126656 & 119415.271326267 & 7240.72867373323 \tabularnewline
69 & 124144 & 126114.748263628 & -1970.74826362793 \tabularnewline
70 & 114045 & 123565.874773252 & -9520.87477325193 \tabularnewline
71 & 108120 & 113288.735387922 & -5168.73538792205 \tabularnewline
72 & 105698 & 107267.026275906 & -1569.026275906 \tabularnewline
73 & 111203 & 104815.66916503 & 6387.33083497015 \tabularnewline
74 & 110030 & 110440.178686575 & -410.178686574727 \tabularnewline
75 & 104009 & 109259.504078848 & -5250.50407884781 \tabularnewline
76 & 99772 & 103140.265041831 & -3368.26504183142 \tabularnewline
77 & 96301 & 98840.2434520647 & -2539.24345206472 \tabularnewline
78 & 97680 & 95321.7331887195 & 2358.26681128047 \tabularnewline
79 & 121563 & 96744.8573065354 & 24818.1426934646 \tabularnewline
80 & 134210 & 121092.214709582 & 13117.7852904176 \tabularnewline
81 & 133111 & 133984.65373322 & -873.653733220184 \tabularnewline
82 & 124527 & 132869.307321495 & -8342.30732149506 \tabularnewline
83 & 117589 & 124129.219405849 & -6540.219405849 \tabularnewline
84 & 115699 & 117068.849277827 & -1369.84927782739 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235046&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]113939.681989943[/C][C]-220.681989943434[/C][/ROW]
[ROW][C]5[/C][C]110737[/C][C]111039.552941408[/C][C]-302.552941407645[/C][/ROW]
[ROW][C]6[/C][C]112093[/C][C]108051.892054536[/C][C]4041.10794546417[/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]141593.181285689[/C][C]8352.81871431097[/C][/ROW]
[ROW][C]9[/C][C]149147[/C][C]148130.46587371[/C][C]1016.53412628974[/C][/ROW]
[ROW][C]10[/C][C]134339[/C][C]147350.485634892[/C][C]-13011.4856348915[/C][/ROW]
[ROW][C]11[/C][C]122683[/C][C]132299.03552044[/C][C]-9616.03552043988[/C][/ROW]
[ROW][C]12[/C][C]115614[/C][C]120463.115639366[/C][C]-4849.11563936614[/C][/ROW]
[ROW][C]13[/C][C]116566[/C][C]113303.386741028[/C][C]3262.61325897176[/C][/ROW]
[ROW][C]14[/C][C]111272[/C][C]114316.431543566[/C][C]-3044.43154356626[/C][/ROW]
[ROW][C]15[/C][C]104609[/C][C]108965.469008425[/C][C]-4356.4690084247[/C][/ROW]
[ROW][C]16[/C][C]101802[/C][C]102220.957726126[/C][C]-418.957726126377[/C][/ROW]
[ROW][C]17[/C][C]94542[/C][C]99406.1188590486[/C][C]-4864.11885904863[/C][/ROW]
[ROW][C]18[/C][C]93051[/C][C]92055.1092444535[/C][C]995.890755546527[/C][/ROW]
[ROW][C]19[/C][C]124129[/C][C]90582.7427598892[/C][C]33546.2572401108[/C][/ROW]
[ROW][C]20[/C][C]130374[/C][C]122288.406686492[/C][C]8085.59331350819[/C][/ROW]
[ROW][C]21[/C][C]123946[/C][C]128684.691380094[/C][C]-4738.69138009395[/C][/ROW]
[ROW][C]22[/C][C]114971[/C][C]122168.028563932[/C][C]-7197.02856393241[/C][/ROW]
[ROW][C]23[/C][C]105531[/C][C]113058.369273151[/C][C]-7527.36927315145[/C][/ROW]
[ROW][C]24[/C][C]104919[/C][C]103477.529175219[/C][C]1441.47082478131[/C][/ROW]
[ROW][C]25[/C][C]104782[/C][C]102892.499672449[/C][C]1889.50032755148[/C][/ROW]
[ROW][C]26[/C][C]101281[/C][C]102790.852981356[/C][C]-1509.85298135625[/C][/ROW]
[ROW][C]27[/C][C]94545[/C][C]99261.6030265524[/C][C]-4716.60302655243[/C][/ROW]
[ROW][C]28[/C][C]93248[/C][C]92437.3534923441[/C][C]810.646507655882[/C][/ROW]
[ROW][C]29[/C][C]84031[/C][C]91155.5210136101[/C][C]-7124.52101361005[/C][/ROW]
[ROW][C]30[/C][C]87486[/C][C]81805.2183681746[/C][C]5680.7816318254[/C][/ROW]
[ROW][C]31[/C][C]115867[/C][C]85366.5080707689[/C][C]30500.4919292311[/C][/ROW]
[ROW][C]32[/C][C]120327[/C][C]114318.184506909[/C][C]6008.81549309136[/C][/ROW]
[ROW][C]33[/C][C]117008[/C][C]118890.611854604[/C][C]-1882.61185460437[/C][/ROW]
[ROW][C]34[/C][C]108811[/C][C]115536.387431788[/C][C]-6725.38743178808[/C][/ROW]
[ROW][C]35[/C][C]104519[/C][C]107213.55273574[/C][C]-2694.55273574[/C][/ROW]
[ROW][C]36[/C][C]106758[/C][C]102871.136573411[/C][C]3886.86342658913[/C][/ROW]
[ROW][C]37[/C][C]109337[/C][C]105182.861346939[/C][C]4154.13865306108[/C][/ROW]
[ROW][C]38[/C][C]109078[/C][C]107839.586947144[/C][C]1238.41305285569[/C][/ROW]
[ROW][C]39[/C][C]108293[/C][C]107603.758152026[/C][C]689.241847974379[/C][/ROW]
[ROW][C]40[/C][C]106534[/C][C]106831.65414342[/C][C]-297.654143419888[/C][/ROW]
[ROW][C]41[/C][C]99197[/C][C]105067.084915023[/C][C]-5870.08491502306[/C][/ROW]
[ROW][C]42[/C][C]103493[/C][C]97620.2532720805[/C][C]5872.74672791947[/C][/ROW]
[ROW][C]43[/C][C]130676[/C][C]102026.13471861[/C][C]28649.8652813901[/C][/ROW]
[ROW][C]44[/C][C]137448[/C][C]129745.185187979[/C][C]7702.81481202054[/C][/ROW]
[ROW][C]45[/C][C]134704[/C][C]136661.307942306[/C][C]-1957.30794230642[/C][/ROW]
[ROW][C]46[/C][C]123725[/C][C]133880.685925733[/C][C]-10155.6859257325[/C][/ROW]
[ROW][C]47[/C][C]118277[/C][C]122711.66896915[/C][C]-4434.66896915039[/C][/ROW]
[ROW][C]48[/C][C]121225[/C][C]117180.694534225[/C][C]4044.305465775[/C][/ROW]
[ROW][C]49[/C][C]120528[/C][C]120204.365111448[/C][C]323.634888552057[/C][/ROW]
[ROW][C]50[/C][C]118240[/C][C]119513.420450006[/C][C]-1273.42045000569[/C][/ROW]
[ROW][C]51[/C][C]112514[/C][C]117201.594242684[/C][C]-4687.59424268409[/C][/ROW]
[ROW][C]52[/C][C]107304[/C][C]111387.887474456[/C][C]-4083.88747445587[/C][/ROW]
[ROW][C]53[/C][C]100001[/C][C]106101.476301976[/C][C]-6100.47630197623[/C][/ROW]
[ROW][C]54[/C][C]102082[/C][C]98684.3339437859[/C][C]3397.66605621408[/C][/ROW]
[ROW][C]55[/C][C]130455[/C][C]100828.905638323[/C][C]29626.0943616771[/C][/ROW]
[ROW][C]56[/C][C]135574[/C][C]129756.221745299[/C][C]5817.77825470117[/C][/ROW]
[ROW][C]57[/C][C]132540[/C][C]134984.074709649[/C][C]-2444.07470964929[/C][/ROW]
[ROW][C]58[/C][C]119920[/C][C]131904.345091642[/C][C]-11984.3450916419[/C][/ROW]
[ROW][C]59[/C][C]112454[/C][C]119060.113188686[/C][C]-6606.11318868649[/C][/ROW]
[ROW][C]60[/C][C]109415[/C][C]111470.510161561[/C][C]-2055.51016156147[/C][/ROW]
[ROW][C]61[/C][C]109843[/C][C]108393.050742082[/C][C]1449.94925791842[/C][/ROW]
[ROW][C]62[/C][C]106365[/C][C]108848.179874196[/C][C]-2483.17987419566[/C][/ROW]
[ROW][C]63[/C][C]102304[/C][C]105323.718582877[/C][C]-3019.71858287657[/C][/ROW]
[ROW][C]64[/C][C]97968[/C][C]101206.218437141[/C][C]-3238.21843714057[/C][/ROW]
[ROW][C]65[/C][C]92462[/C][C]96809.6300715025[/C][C]-4347.6300715025[/C][/ROW]
[ROW][C]66[/C][C]92286[/C][C]91222.2841692588[/C][C]1063.71583074117[/C][/ROW]
[ROW][C]67[/C][C]120092[/C][C]91066.1867190525[/C][C]29025.8132809475[/C][/ROW]
[ROW][C]68[/C][C]126656[/C][C]119415.271326267[/C][C]7240.72867373323[/C][/ROW]
[ROW][C]69[/C][C]124144[/C][C]126114.748263628[/C][C]-1970.74826362793[/C][/ROW]
[ROW][C]70[/C][C]114045[/C][C]123565.874773252[/C][C]-9520.87477325193[/C][/ROW]
[ROW][C]71[/C][C]108120[/C][C]113288.735387922[/C][C]-5168.73538792205[/C][/ROW]
[ROW][C]72[/C][C]105698[/C][C]107267.026275906[/C][C]-1569.026275906[/C][/ROW]
[ROW][C]73[/C][C]111203[/C][C]104815.66916503[/C][C]6387.33083497015[/C][/ROW]
[ROW][C]74[/C][C]110030[/C][C]110440.178686575[/C][C]-410.178686574727[/C][/ROW]
[ROW][C]75[/C][C]104009[/C][C]109259.504078848[/C][C]-5250.50407884781[/C][/ROW]
[ROW][C]76[/C][C]99772[/C][C]103140.265041831[/C][C]-3368.26504183142[/C][/ROW]
[ROW][C]77[/C][C]96301[/C][C]98840.2434520647[/C][C]-2539.24345206472[/C][/ROW]
[ROW][C]78[/C][C]97680[/C][C]95321.7331887195[/C][C]2358.26681128047[/C][/ROW]
[ROW][C]79[/C][C]121563[/C][C]96744.8573065354[/C][C]24818.1426934646[/C][/ROW]
[ROW][C]80[/C][C]134210[/C][C]121092.214709582[/C][C]13117.7852904176[/C][/ROW]
[ROW][C]81[/C][C]133111[/C][C]133984.65373322[/C][C]-873.653733220184[/C][/ROW]
[ROW][C]82[/C][C]124527[/C][C]132869.307321495[/C][C]-8342.30732149506[/C][/ROW]
[ROW][C]83[/C][C]117589[/C][C]124129.219405849[/C][C]-6540.219405849[/C][/ROW]
[ROW][C]84[/C][C]115699[/C][C]117068.849277827[/C][C]-1369.84927782739[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235046&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235046&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
4113719113939.681989943-220.681989943434
5110737111039.552941408-302.552941407645
6112093108051.8920545364041.10794546417
7143565109483.50280487134081.4971951286
8149946141593.1812856898352.81871431097
9149147148130.465873711016.53412628974
10134339147350.485634892-13011.4856348915
11122683132299.03552044-9616.03552043988
12115614120463.115639366-4849.11563936614
13116566113303.3867410283262.61325897176
14111272114316.431543566-3044.43154356626
15104609108965.469008425-4356.4690084247
16101802102220.957726126-418.957726126377
179454299406.1188590486-4864.11885904863
189305192055.1092444535995.890755546527
1912412990582.742759889233546.2572401108
20130374122288.4066864928085.59331350819
21123946128684.691380094-4738.69138009395
22114971122168.028563932-7197.02856393241
23105531113058.369273151-7527.36927315145
24104919103477.5291752191441.47082478131
25104782102892.4996724491889.50032755148
26101281102790.852981356-1509.85298135625
279454599261.6030265524-4716.60302655243
289324892437.3534923441810.646507655882
298403191155.5210136101-7124.52101361005
308748681805.21836817465680.7816318254
3111586785366.508070768930500.4919292311
32120327114318.1845069096008.81549309136
33117008118890.611854604-1882.61185460437
34108811115536.387431788-6725.38743178808
35104519107213.55273574-2694.55273574
36106758102871.1365734113886.86342658913
37109337105182.8613469394154.13865306108
38109078107839.5869471441238.41305285569
39108293107603.758152026689.241847974379
40106534106831.65414342-297.654143419888
4199197105067.084915023-5870.08491502306
4210349397620.25327208055872.74672791947
43130676102026.1347186128649.8652813901
44137448129745.1851879797702.81481202054
45134704136661.307942306-1957.30794230642
46123725133880.685925733-10155.6859257325
47118277122711.66896915-4434.66896915039
48121225117180.6945342254044.305465775
49120528120204.365111448323.634888552057
50118240119513.420450006-1273.42045000569
51112514117201.594242684-4687.59424268409
52107304111387.887474456-4083.88747445587
53100001106101.476301976-6100.47630197623
5410208298684.33394378593397.66605621408
55130455100828.90563832329626.0943616771
56135574129756.2217452995817.77825470117
57132540134984.074709649-2444.07470964929
58119920131904.345091642-11984.3450916419
59112454119060.113188686-6606.11318868649
60109415111470.510161561-2055.51016156147
61109843108393.0507420821449.94925791842
62106365108848.179874196-2483.17987419566
63102304105323.718582877-3019.71858287657
6497968101206.218437141-3238.21843714057
659246296809.6300715025-4347.6300715025
669228691222.28416925881063.71583074117
6712009291066.186719052529025.8132809475
68126656119415.2713262677240.72867373323
69124144126114.748263628-1970.74826362793
70114045123565.874773252-9520.87477325193
71108120113288.735387922-5168.73538792205
72105698107267.026275906-1569.026275906
73111203104815.669165036387.33083497015
74110030110440.178686575-410.178686574727
75104009109259.504078848-5250.50407884781
7699772103140.265041831-3368.26504183142
779630198840.2434520647-2539.24345206472
789768095321.73318871952358.26681128047
7912156396744.857306535424818.1426934646
80134210121092.21470958213117.7852904176
81133111133984.65373322-873.653733220184
82124527132869.307321495-8342.30732149506
83117589124129.219405849-6540.219405849
84115699117068.849277827-1369.84927782739







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85115153.21884846595306.3228946595135000.11480227
86114607.43769692986275.8920123903142938.983381469
87114061.65654539479038.701252646149084.611838142
88113515.87539385972699.6063274037154332.144460314
89112970.09424232466915.414329275159024.774155372
90112424.31309078861511.835706378163336.790475199
91111878.53193925356386.3338669527167370.730011553
92111332.75078771851472.7439873397171192.757588096
93110786.96963618246725.551864081174848.387408284
94110241.18848464742111.9411880375178370.435781257
95109695.40733311237607.3814435792181783.433222644
96109149.62618157733193.0039743611185106.248388792

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 115153.218848465 & 95306.3228946595 & 135000.11480227 \tabularnewline
86 & 114607.437696929 & 86275.8920123903 & 142938.983381469 \tabularnewline
87 & 114061.656545394 & 79038.701252646 & 149084.611838142 \tabularnewline
88 & 113515.875393859 & 72699.6063274037 & 154332.144460314 \tabularnewline
89 & 112970.094242324 & 66915.414329275 & 159024.774155372 \tabularnewline
90 & 112424.313090788 & 61511.835706378 & 163336.790475199 \tabularnewline
91 & 111878.531939253 & 56386.3338669527 & 167370.730011553 \tabularnewline
92 & 111332.750787718 & 51472.7439873397 & 171192.757588096 \tabularnewline
93 & 110786.969636182 & 46725.551864081 & 174848.387408284 \tabularnewline
94 & 110241.188484647 & 42111.9411880375 & 178370.435781257 \tabularnewline
95 & 109695.407333112 & 37607.3814435792 & 181783.433222644 \tabularnewline
96 & 109149.626181577 & 33193.0039743611 & 185106.248388792 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235046&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]115153.218848465[/C][C]95306.3228946595[/C][C]135000.11480227[/C][/ROW]
[ROW][C]86[/C][C]114607.437696929[/C][C]86275.8920123903[/C][C]142938.983381469[/C][/ROW]
[ROW][C]87[/C][C]114061.656545394[/C][C]79038.701252646[/C][C]149084.611838142[/C][/ROW]
[ROW][C]88[/C][C]113515.875393859[/C][C]72699.6063274037[/C][C]154332.144460314[/C][/ROW]
[ROW][C]89[/C][C]112970.094242324[/C][C]66915.414329275[/C][C]159024.774155372[/C][/ROW]
[ROW][C]90[/C][C]112424.313090788[/C][C]61511.835706378[/C][C]163336.790475199[/C][/ROW]
[ROW][C]91[/C][C]111878.531939253[/C][C]56386.3338669527[/C][C]167370.730011553[/C][/ROW]
[ROW][C]92[/C][C]111332.750787718[/C][C]51472.7439873397[/C][C]171192.757588096[/C][/ROW]
[ROW][C]93[/C][C]110786.969636182[/C][C]46725.551864081[/C][C]174848.387408284[/C][/ROW]
[ROW][C]94[/C][C]110241.188484647[/C][C]42111.9411880375[/C][C]178370.435781257[/C][/ROW]
[ROW][C]95[/C][C]109695.407333112[/C][C]37607.3814435792[/C][C]181783.433222644[/C][/ROW]
[ROW][C]96[/C][C]109149.626181577[/C][C]33193.0039743611[/C][C]185106.248388792[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235046&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235046&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
85115153.21884846595306.3228946595135000.11480227
86114607.43769692986275.8920123903142938.983381469
87114061.65654539479038.701252646149084.611838142
88113515.87539385972699.6063274037154332.144460314
89112970.09424232466915.414329275159024.774155372
90112424.31309078861511.835706378163336.790475199
91111878.53193925356386.3338669527167370.730011553
92111332.75078771851472.7439873397171192.757588096
93110786.96963618246725.551864081174848.387408284
94110241.18848464742111.9411880375178370.435781257
95109695.40733311237607.3814435792181783.433222644
96109149.62618157733193.0039743611185106.248388792



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')