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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 21:40:08 +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/2011/May/19/t1305840995ftvzuulj9kxs3st.htm/, Retrieved Sat, 11 May 2024 19:16:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122238, Retrieved Sat, 11 May 2024 19:16:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact86
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Opdracht 10: oefe...] [2011-05-19 12:50:35] [808f4e1f780d0664aa07fd0f8d2182ae]
- R       [Exponential Smoothing] [Opdracht 10 - Fre...] [2011-05-19 21:40:08] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
101397
97994
94044
91159
87239
89235
118647
125620
125154
117529
109459
108483
107137
104699
100804
96066
91971
93228
120144
127233
127166
118194
109940
106683
102834
99882
96666
92540
88744
89321
115870
122401
122030
113802
105791
103076
98658
96945
92497
90687
88796
90015
113228
118711
117460
106556
97347
92657
93118
89037
83570
81693
75956
73993
97088
102394
96549
89727
82336
82653
82303
79596
74472
73562
66618
69029
89899
93774
90305
83799
80320
82497
84420
84646
84186
83269
77793
81145
101691
107357
104253
95963
91432
94324
93855
92183
87600
83641
78195
79604
100846
105293
102518
93132
87479
85476




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' @ www.yougetit.org

\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' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122238&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' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122238&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122238&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' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.900408097789281
beta0.0913871909632014
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.900408097789281 \tabularnewline
beta & 0.0913871909632014 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122238&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]0.900408097789281[/C][/ROW]
[ROW][C]beta[/C][C]0.0913871909632014[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122238&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122238&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
alpha0.900408097789281
beta0.0913871909632014
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13107137104619.1203626992517.87963730095
14104699104788.600903621-89.6009036205942
15100804101107.044012316-303.044012315717
169606696386.2418227676-320.241822767552
179197192309.220569077-338.220569077064
189322893634.1045092177-406.10450921765
19120144122385.200894548-2241.20089454768
20127233127026.648110507206.351889492697
21127166126297.101235628868.898764372294
22118194119071.112083861-877.112083861415
23109940109936.7395746413.260425358676
24106683108778.639780748-2095.63978074784
25102834105602.799011237-2768.79901123731
2699882100189.850993115-307.850993115338
279666695816.083271503849.916728497075
289254091796.5158977738743.484102226226
298874488399.5644798924344.435520107581
308932189906.1450994609-585.14509946086
31115870116615.235722145-745.235722144673
32122401122198.509350494202.490649505969
33122030121160.191647546869.808352453896
34113802113723.64418616678.355813833914
35105791105567.788681764223.211318235582
36103076104192.210454025-1116.21045402451
3798658101690.265688471-3032.26568847099
389694596181.177528213763.822471787091
399249792895.7512132914-398.751213291398
409068787741.8926883042945.10731169602
418879686365.17943182542430.82056817465
429001589813.0884135216201.911586478367
43113228117711.978961515-4483.9789615154
44118711119881.489988966-1170.48998896581
45117460117571.564277521-111.564277521087
46106556109282.327540962-2726.32754096226
479734798716.4097847291-1369.40978472913
489265795381.3184261404-2724.31842614038
499311890740.79213266352377.20786733653
508903790403.0112230851-1366.01122308514
518357085030.5374366513-1460.53743665128
528169379214.13694026682478.86305973321
537595677325.3747977432-1369.37479774318
547399376233.3805450807-2240.38054508073
559708895444.61494446531643.3850555347
56102394101691.388380141702.611619859439
5796549100651.459162345-4102.45916234482
588972789026.4971809714700.50281902864
598233682293.222696575142.7773034248821
608265379892.38464016122760.61535983883
618230380791.18518347541511.81481652455
627959679495.9221631644100.07783683564
637447275849.6665180149-1377.66651801491
647356270905.860706022656.13929398003
656661869263.4236282681-2645.42362826811
666902966804.21721410972224.78278589029
678989989254.2266601605644.773339839463
689377494445.8340541212-671.83405412118
699030592023.1095263779-1718.10952637788
708379983829.4686167014-30.4686167014152
718032077121.04413437033198.9558656297
728249778436.38977145384060.61022854624
738442081063.61421711693356.3857828831
748464682051.20824988392594.79175011608
758418681278.48977967682907.51022032321
768326981537.27809406971731.7219059303
777779379128.9254372178-1335.92543721777
788114579776.99758410161368.0024158984
79101691106489.155519651-4798.15551965068
80107357108517.851037485-1160.85103748459
81104253106482.644097461-2229.64409746086
829596398107.6606378548-2144.66063785483
839143289747.98854465111684.01145534891
849432490266.99269408464057.00730591537
859385593303.7147578206551.285242179409
869218391819.453980905363.546019094982
878760088951.4032495159-1351.40324951588
888364184976.6796240965-1335.67962409648
897819579089.8023914219-894.802391421894
907960480062.2492385634-458.249238563352
91100846103405.854953713-2559.85495371318
92105293107280.903532959-1987.90353295897
93102518103862.126563669-1344.12656366943
949313295938.0798448168-2806.07984481685
958747987048.8786534814430.121346518601
968547686129.19066623-653.190666229959

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 107137 & 104619.120362699 & 2517.87963730095 \tabularnewline
14 & 104699 & 104788.600903621 & -89.6009036205942 \tabularnewline
15 & 100804 & 101107.044012316 & -303.044012315717 \tabularnewline
16 & 96066 & 96386.2418227676 & -320.241822767552 \tabularnewline
17 & 91971 & 92309.220569077 & -338.220569077064 \tabularnewline
18 & 93228 & 93634.1045092177 & -406.10450921765 \tabularnewline
19 & 120144 & 122385.200894548 & -2241.20089454768 \tabularnewline
20 & 127233 & 127026.648110507 & 206.351889492697 \tabularnewline
21 & 127166 & 126297.101235628 & 868.898764372294 \tabularnewline
22 & 118194 & 119071.112083861 & -877.112083861415 \tabularnewline
23 & 109940 & 109936.739574641 & 3.260425358676 \tabularnewline
24 & 106683 & 108778.639780748 & -2095.63978074784 \tabularnewline
25 & 102834 & 105602.799011237 & -2768.79901123731 \tabularnewline
26 & 99882 & 100189.850993115 & -307.850993115338 \tabularnewline
27 & 96666 & 95816.083271503 & 849.916728497075 \tabularnewline
28 & 92540 & 91796.5158977738 & 743.484102226226 \tabularnewline
29 & 88744 & 88399.5644798924 & 344.435520107581 \tabularnewline
30 & 89321 & 89906.1450994609 & -585.14509946086 \tabularnewline
31 & 115870 & 116615.235722145 & -745.235722144673 \tabularnewline
32 & 122401 & 122198.509350494 & 202.490649505969 \tabularnewline
33 & 122030 & 121160.191647546 & 869.808352453896 \tabularnewline
34 & 113802 & 113723.644186166 & 78.355813833914 \tabularnewline
35 & 105791 & 105567.788681764 & 223.211318235582 \tabularnewline
36 & 103076 & 104192.210454025 & -1116.21045402451 \tabularnewline
37 & 98658 & 101690.265688471 & -3032.26568847099 \tabularnewline
38 & 96945 & 96181.177528213 & 763.822471787091 \tabularnewline
39 & 92497 & 92895.7512132914 & -398.751213291398 \tabularnewline
40 & 90687 & 87741.892688304 & 2945.10731169602 \tabularnewline
41 & 88796 & 86365.1794318254 & 2430.82056817465 \tabularnewline
42 & 90015 & 89813.0884135216 & 201.911586478367 \tabularnewline
43 & 113228 & 117711.978961515 & -4483.9789615154 \tabularnewline
44 & 118711 & 119881.489988966 & -1170.48998896581 \tabularnewline
45 & 117460 & 117571.564277521 & -111.564277521087 \tabularnewline
46 & 106556 & 109282.327540962 & -2726.32754096226 \tabularnewline
47 & 97347 & 98716.4097847291 & -1369.40978472913 \tabularnewline
48 & 92657 & 95381.3184261404 & -2724.31842614038 \tabularnewline
49 & 93118 & 90740.7921326635 & 2377.20786733653 \tabularnewline
50 & 89037 & 90403.0112230851 & -1366.01122308514 \tabularnewline
51 & 83570 & 85030.5374366513 & -1460.53743665128 \tabularnewline
52 & 81693 & 79214.1369402668 & 2478.86305973321 \tabularnewline
53 & 75956 & 77325.3747977432 & -1369.37479774318 \tabularnewline
54 & 73993 & 76233.3805450807 & -2240.38054508073 \tabularnewline
55 & 97088 & 95444.6149444653 & 1643.3850555347 \tabularnewline
56 & 102394 & 101691.388380141 & 702.611619859439 \tabularnewline
57 & 96549 & 100651.459162345 & -4102.45916234482 \tabularnewline
58 & 89727 & 89026.4971809714 & 700.50281902864 \tabularnewline
59 & 82336 & 82293.2226965751 & 42.7773034248821 \tabularnewline
60 & 82653 & 79892.3846401612 & 2760.61535983883 \tabularnewline
61 & 82303 & 80791.1851834754 & 1511.81481652455 \tabularnewline
62 & 79596 & 79495.9221631644 & 100.07783683564 \tabularnewline
63 & 74472 & 75849.6665180149 & -1377.66651801491 \tabularnewline
64 & 73562 & 70905.86070602 & 2656.13929398003 \tabularnewline
65 & 66618 & 69263.4236282681 & -2645.42362826811 \tabularnewline
66 & 69029 & 66804.2172141097 & 2224.78278589029 \tabularnewline
67 & 89899 & 89254.2266601605 & 644.773339839463 \tabularnewline
68 & 93774 & 94445.8340541212 & -671.83405412118 \tabularnewline
69 & 90305 & 92023.1095263779 & -1718.10952637788 \tabularnewline
70 & 83799 & 83829.4686167014 & -30.4686167014152 \tabularnewline
71 & 80320 & 77121.0441343703 & 3198.9558656297 \tabularnewline
72 & 82497 & 78436.3897714538 & 4060.61022854624 \tabularnewline
73 & 84420 & 81063.6142171169 & 3356.3857828831 \tabularnewline
74 & 84646 & 82051.2082498839 & 2594.79175011608 \tabularnewline
75 & 84186 & 81278.4897796768 & 2907.51022032321 \tabularnewline
76 & 83269 & 81537.2780940697 & 1731.7219059303 \tabularnewline
77 & 77793 & 79128.9254372178 & -1335.92543721777 \tabularnewline
78 & 81145 & 79776.9975841016 & 1368.0024158984 \tabularnewline
79 & 101691 & 106489.155519651 & -4798.15551965068 \tabularnewline
80 & 107357 & 108517.851037485 & -1160.85103748459 \tabularnewline
81 & 104253 & 106482.644097461 & -2229.64409746086 \tabularnewline
82 & 95963 & 98107.6606378548 & -2144.66063785483 \tabularnewline
83 & 91432 & 89747.9885446511 & 1684.01145534891 \tabularnewline
84 & 94324 & 90266.9926940846 & 4057.00730591537 \tabularnewline
85 & 93855 & 93303.7147578206 & 551.285242179409 \tabularnewline
86 & 92183 & 91819.453980905 & 363.546019094982 \tabularnewline
87 & 87600 & 88951.4032495159 & -1351.40324951588 \tabularnewline
88 & 83641 & 84976.6796240965 & -1335.67962409648 \tabularnewline
89 & 78195 & 79089.8023914219 & -894.802391421894 \tabularnewline
90 & 79604 & 80062.2492385634 & -458.249238563352 \tabularnewline
91 & 100846 & 103405.854953713 & -2559.85495371318 \tabularnewline
92 & 105293 & 107280.903532959 & -1987.90353295897 \tabularnewline
93 & 102518 & 103862.126563669 & -1344.12656366943 \tabularnewline
94 & 93132 & 95938.0798448168 & -2806.07984481685 \tabularnewline
95 & 87479 & 87048.8786534814 & 430.121346518601 \tabularnewline
96 & 85476 & 86129.19066623 & -653.190666229959 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122238&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]13[/C][C]107137[/C][C]104619.120362699[/C][C]2517.87963730095[/C][/ROW]
[ROW][C]14[/C][C]104699[/C][C]104788.600903621[/C][C]-89.6009036205942[/C][/ROW]
[ROW][C]15[/C][C]100804[/C][C]101107.044012316[/C][C]-303.044012315717[/C][/ROW]
[ROW][C]16[/C][C]96066[/C][C]96386.2418227676[/C][C]-320.241822767552[/C][/ROW]
[ROW][C]17[/C][C]91971[/C][C]92309.220569077[/C][C]-338.220569077064[/C][/ROW]
[ROW][C]18[/C][C]93228[/C][C]93634.1045092177[/C][C]-406.10450921765[/C][/ROW]
[ROW][C]19[/C][C]120144[/C][C]122385.200894548[/C][C]-2241.20089454768[/C][/ROW]
[ROW][C]20[/C][C]127233[/C][C]127026.648110507[/C][C]206.351889492697[/C][/ROW]
[ROW][C]21[/C][C]127166[/C][C]126297.101235628[/C][C]868.898764372294[/C][/ROW]
[ROW][C]22[/C][C]118194[/C][C]119071.112083861[/C][C]-877.112083861415[/C][/ROW]
[ROW][C]23[/C][C]109940[/C][C]109936.739574641[/C][C]3.260425358676[/C][/ROW]
[ROW][C]24[/C][C]106683[/C][C]108778.639780748[/C][C]-2095.63978074784[/C][/ROW]
[ROW][C]25[/C][C]102834[/C][C]105602.799011237[/C][C]-2768.79901123731[/C][/ROW]
[ROW][C]26[/C][C]99882[/C][C]100189.850993115[/C][C]-307.850993115338[/C][/ROW]
[ROW][C]27[/C][C]96666[/C][C]95816.083271503[/C][C]849.916728497075[/C][/ROW]
[ROW][C]28[/C][C]92540[/C][C]91796.5158977738[/C][C]743.484102226226[/C][/ROW]
[ROW][C]29[/C][C]88744[/C][C]88399.5644798924[/C][C]344.435520107581[/C][/ROW]
[ROW][C]30[/C][C]89321[/C][C]89906.1450994609[/C][C]-585.14509946086[/C][/ROW]
[ROW][C]31[/C][C]115870[/C][C]116615.235722145[/C][C]-745.235722144673[/C][/ROW]
[ROW][C]32[/C][C]122401[/C][C]122198.509350494[/C][C]202.490649505969[/C][/ROW]
[ROW][C]33[/C][C]122030[/C][C]121160.191647546[/C][C]869.808352453896[/C][/ROW]
[ROW][C]34[/C][C]113802[/C][C]113723.644186166[/C][C]78.355813833914[/C][/ROW]
[ROW][C]35[/C][C]105791[/C][C]105567.788681764[/C][C]223.211318235582[/C][/ROW]
[ROW][C]36[/C][C]103076[/C][C]104192.210454025[/C][C]-1116.21045402451[/C][/ROW]
[ROW][C]37[/C][C]98658[/C][C]101690.265688471[/C][C]-3032.26568847099[/C][/ROW]
[ROW][C]38[/C][C]96945[/C][C]96181.177528213[/C][C]763.822471787091[/C][/ROW]
[ROW][C]39[/C][C]92497[/C][C]92895.7512132914[/C][C]-398.751213291398[/C][/ROW]
[ROW][C]40[/C][C]90687[/C][C]87741.892688304[/C][C]2945.10731169602[/C][/ROW]
[ROW][C]41[/C][C]88796[/C][C]86365.1794318254[/C][C]2430.82056817465[/C][/ROW]
[ROW][C]42[/C][C]90015[/C][C]89813.0884135216[/C][C]201.911586478367[/C][/ROW]
[ROW][C]43[/C][C]113228[/C][C]117711.978961515[/C][C]-4483.9789615154[/C][/ROW]
[ROW][C]44[/C][C]118711[/C][C]119881.489988966[/C][C]-1170.48998896581[/C][/ROW]
[ROW][C]45[/C][C]117460[/C][C]117571.564277521[/C][C]-111.564277521087[/C][/ROW]
[ROW][C]46[/C][C]106556[/C][C]109282.327540962[/C][C]-2726.32754096226[/C][/ROW]
[ROW][C]47[/C][C]97347[/C][C]98716.4097847291[/C][C]-1369.40978472913[/C][/ROW]
[ROW][C]48[/C][C]92657[/C][C]95381.3184261404[/C][C]-2724.31842614038[/C][/ROW]
[ROW][C]49[/C][C]93118[/C][C]90740.7921326635[/C][C]2377.20786733653[/C][/ROW]
[ROW][C]50[/C][C]89037[/C][C]90403.0112230851[/C][C]-1366.01122308514[/C][/ROW]
[ROW][C]51[/C][C]83570[/C][C]85030.5374366513[/C][C]-1460.53743665128[/C][/ROW]
[ROW][C]52[/C][C]81693[/C][C]79214.1369402668[/C][C]2478.86305973321[/C][/ROW]
[ROW][C]53[/C][C]75956[/C][C]77325.3747977432[/C][C]-1369.37479774318[/C][/ROW]
[ROW][C]54[/C][C]73993[/C][C]76233.3805450807[/C][C]-2240.38054508073[/C][/ROW]
[ROW][C]55[/C][C]97088[/C][C]95444.6149444653[/C][C]1643.3850555347[/C][/ROW]
[ROW][C]56[/C][C]102394[/C][C]101691.388380141[/C][C]702.611619859439[/C][/ROW]
[ROW][C]57[/C][C]96549[/C][C]100651.459162345[/C][C]-4102.45916234482[/C][/ROW]
[ROW][C]58[/C][C]89727[/C][C]89026.4971809714[/C][C]700.50281902864[/C][/ROW]
[ROW][C]59[/C][C]82336[/C][C]82293.2226965751[/C][C]42.7773034248821[/C][/ROW]
[ROW][C]60[/C][C]82653[/C][C]79892.3846401612[/C][C]2760.61535983883[/C][/ROW]
[ROW][C]61[/C][C]82303[/C][C]80791.1851834754[/C][C]1511.81481652455[/C][/ROW]
[ROW][C]62[/C][C]79596[/C][C]79495.9221631644[/C][C]100.07783683564[/C][/ROW]
[ROW][C]63[/C][C]74472[/C][C]75849.6665180149[/C][C]-1377.66651801491[/C][/ROW]
[ROW][C]64[/C][C]73562[/C][C]70905.86070602[/C][C]2656.13929398003[/C][/ROW]
[ROW][C]65[/C][C]66618[/C][C]69263.4236282681[/C][C]-2645.42362826811[/C][/ROW]
[ROW][C]66[/C][C]69029[/C][C]66804.2172141097[/C][C]2224.78278589029[/C][/ROW]
[ROW][C]67[/C][C]89899[/C][C]89254.2266601605[/C][C]644.773339839463[/C][/ROW]
[ROW][C]68[/C][C]93774[/C][C]94445.8340541212[/C][C]-671.83405412118[/C][/ROW]
[ROW][C]69[/C][C]90305[/C][C]92023.1095263779[/C][C]-1718.10952637788[/C][/ROW]
[ROW][C]70[/C][C]83799[/C][C]83829.4686167014[/C][C]-30.4686167014152[/C][/ROW]
[ROW][C]71[/C][C]80320[/C][C]77121.0441343703[/C][C]3198.9558656297[/C][/ROW]
[ROW][C]72[/C][C]82497[/C][C]78436.3897714538[/C][C]4060.61022854624[/C][/ROW]
[ROW][C]73[/C][C]84420[/C][C]81063.6142171169[/C][C]3356.3857828831[/C][/ROW]
[ROW][C]74[/C][C]84646[/C][C]82051.2082498839[/C][C]2594.79175011608[/C][/ROW]
[ROW][C]75[/C][C]84186[/C][C]81278.4897796768[/C][C]2907.51022032321[/C][/ROW]
[ROW][C]76[/C][C]83269[/C][C]81537.2780940697[/C][C]1731.7219059303[/C][/ROW]
[ROW][C]77[/C][C]77793[/C][C]79128.9254372178[/C][C]-1335.92543721777[/C][/ROW]
[ROW][C]78[/C][C]81145[/C][C]79776.9975841016[/C][C]1368.0024158984[/C][/ROW]
[ROW][C]79[/C][C]101691[/C][C]106489.155519651[/C][C]-4798.15551965068[/C][/ROW]
[ROW][C]80[/C][C]107357[/C][C]108517.851037485[/C][C]-1160.85103748459[/C][/ROW]
[ROW][C]81[/C][C]104253[/C][C]106482.644097461[/C][C]-2229.64409746086[/C][/ROW]
[ROW][C]82[/C][C]95963[/C][C]98107.6606378548[/C][C]-2144.66063785483[/C][/ROW]
[ROW][C]83[/C][C]91432[/C][C]89747.9885446511[/C][C]1684.01145534891[/C][/ROW]
[ROW][C]84[/C][C]94324[/C][C]90266.9926940846[/C][C]4057.00730591537[/C][/ROW]
[ROW][C]85[/C][C]93855[/C][C]93303.7147578206[/C][C]551.285242179409[/C][/ROW]
[ROW][C]86[/C][C]92183[/C][C]91819.453980905[/C][C]363.546019094982[/C][/ROW]
[ROW][C]87[/C][C]87600[/C][C]88951.4032495159[/C][C]-1351.40324951588[/C][/ROW]
[ROW][C]88[/C][C]83641[/C][C]84976.6796240965[/C][C]-1335.67962409648[/C][/ROW]
[ROW][C]89[/C][C]78195[/C][C]79089.8023914219[/C][C]-894.802391421894[/C][/ROW]
[ROW][C]90[/C][C]79604[/C][C]80062.2492385634[/C][C]-458.249238563352[/C][/ROW]
[ROW][C]91[/C][C]100846[/C][C]103405.854953713[/C][C]-2559.85495371318[/C][/ROW]
[ROW][C]92[/C][C]105293[/C][C]107280.903532959[/C][C]-1987.90353295897[/C][/ROW]
[ROW][C]93[/C][C]102518[/C][C]103862.126563669[/C][C]-1344.12656366943[/C][/ROW]
[ROW][C]94[/C][C]93132[/C][C]95938.0798448168[/C][C]-2806.07984481685[/C][/ROW]
[ROW][C]95[/C][C]87479[/C][C]87048.8786534814[/C][C]430.121346518601[/C][/ROW]
[ROW][C]96[/C][C]85476[/C][C]86129.19066623[/C][C]-653.190666229959[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122238&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122238&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
13107137104619.1203626992517.87963730095
14104699104788.600903621-89.6009036205942
15100804101107.044012316-303.044012315717
169606696386.2418227676-320.241822767552
179197192309.220569077-338.220569077064
189322893634.1045092177-406.10450921765
19120144122385.200894548-2241.20089454768
20127233127026.648110507206.351889492697
21127166126297.101235628868.898764372294
22118194119071.112083861-877.112083861415
23109940109936.7395746413.260425358676
24106683108778.639780748-2095.63978074784
25102834105602.799011237-2768.79901123731
2699882100189.850993115-307.850993115338
279666695816.083271503849.916728497075
289254091796.5158977738743.484102226226
298874488399.5644798924344.435520107581
308932189906.1450994609-585.14509946086
31115870116615.235722145-745.235722144673
32122401122198.509350494202.490649505969
33122030121160.191647546869.808352453896
34113802113723.64418616678.355813833914
35105791105567.788681764223.211318235582
36103076104192.210454025-1116.21045402451
3798658101690.265688471-3032.26568847099
389694596181.177528213763.822471787091
399249792895.7512132914-398.751213291398
409068787741.8926883042945.10731169602
418879686365.17943182542430.82056817465
429001589813.0884135216201.911586478367
43113228117711.978961515-4483.9789615154
44118711119881.489988966-1170.48998896581
45117460117571.564277521-111.564277521087
46106556109282.327540962-2726.32754096226
479734798716.4097847291-1369.40978472913
489265795381.3184261404-2724.31842614038
499311890740.79213266352377.20786733653
508903790403.0112230851-1366.01122308514
518357085030.5374366513-1460.53743665128
528169379214.13694026682478.86305973321
537595677325.3747977432-1369.37479774318
547399376233.3805450807-2240.38054508073
559708895444.61494446531643.3850555347
56102394101691.388380141702.611619859439
5796549100651.459162345-4102.45916234482
588972789026.4971809714700.50281902864
598233682293.222696575142.7773034248821
608265379892.38464016122760.61535983883
618230380791.18518347541511.81481652455
627959679495.9221631644100.07783683564
637447275849.6665180149-1377.66651801491
647356270905.860706022656.13929398003
656661869263.4236282681-2645.42362826811
666902966804.21721410972224.78278589029
678989989254.2266601605644.773339839463
689377494445.8340541212-671.83405412118
699030592023.1095263779-1718.10952637788
708379983829.4686167014-30.4686167014152
718032077121.04413437033198.9558656297
728249778436.38977145384060.61022854624
738442081063.61421711693356.3857828831
748464682051.20824988392594.79175011608
758418681278.48977967682907.51022032321
768326981537.27809406971731.7219059303
777779379128.9254372178-1335.92543721777
788114579776.99758410161368.0024158984
79101691106489.155519651-4798.15551965068
80107357108517.851037485-1160.85103748459
81104253106482.644097461-2229.64409746086
829596398107.6606378548-2144.66063785483
839143289747.98854465111684.01145534891
849432490266.99269408464057.00730591537
859385593303.7147578206551.285242179409
869218391819.453980905363.546019094982
878760088951.4032495159-1351.40324951588
888364184976.6796240965-1335.67962409648
897819579089.8023914219-894.802391421894
907960480062.2492385634-458.249238563352
91100846103405.854953713-2559.85495371318
92105293107280.903532959-1987.90353295897
93102518103862.126563669-1344.12656366943
949313295938.0798448168-2806.07984481685
958747987048.8786534814430.121346518601
968547686129.19066623-653.190666229959







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9783765.890628166479993.191901931787538.5893544011
9881073.738760562875853.82668393586293.6508371907
9977223.784688400370831.865694045283615.7036827553
10074029.825155724866555.300606539181504.3497049105
10169294.415435209660975.53051159677613.3003588231
10270334.260542469460605.847024124280062.6740608145
10390435.423194178276592.3904681818104278.455920175
10495480.65778442279408.2751073703111553.040461474
10593668.729135795976418.8715391528110918.586732439
10687123.602123175669620.3753603256104626.828886026
10781425.480846168463634.28493779899216.6767545387
10880026.695623104461478.153026563198575.2382196458

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 83765.8906281664 & 79993.1919019317 & 87538.5893544011 \tabularnewline
98 & 81073.7387605628 & 75853.826683935 & 86293.6508371907 \tabularnewline
99 & 77223.7846884003 & 70831.8656940452 & 83615.7036827553 \tabularnewline
100 & 74029.8251557248 & 66555.3006065391 & 81504.3497049105 \tabularnewline
101 & 69294.4154352096 & 60975.530511596 & 77613.3003588231 \tabularnewline
102 & 70334.2605424694 & 60605.8470241242 & 80062.6740608145 \tabularnewline
103 & 90435.4231941782 & 76592.3904681818 & 104278.455920175 \tabularnewline
104 & 95480.657784422 & 79408.2751073703 & 111553.040461474 \tabularnewline
105 & 93668.7291357959 & 76418.8715391528 & 110918.586732439 \tabularnewline
106 & 87123.6021231756 & 69620.3753603256 & 104626.828886026 \tabularnewline
107 & 81425.4808461684 & 63634.284937798 & 99216.6767545387 \tabularnewline
108 & 80026.6956231044 & 61478.1530265631 & 98575.2382196458 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122238&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]97[/C][C]83765.8906281664[/C][C]79993.1919019317[/C][C]87538.5893544011[/C][/ROW]
[ROW][C]98[/C][C]81073.7387605628[/C][C]75853.826683935[/C][C]86293.6508371907[/C][/ROW]
[ROW][C]99[/C][C]77223.7846884003[/C][C]70831.8656940452[/C][C]83615.7036827553[/C][/ROW]
[ROW][C]100[/C][C]74029.8251557248[/C][C]66555.3006065391[/C][C]81504.3497049105[/C][/ROW]
[ROW][C]101[/C][C]69294.4154352096[/C][C]60975.530511596[/C][C]77613.3003588231[/C][/ROW]
[ROW][C]102[/C][C]70334.2605424694[/C][C]60605.8470241242[/C][C]80062.6740608145[/C][/ROW]
[ROW][C]103[/C][C]90435.4231941782[/C][C]76592.3904681818[/C][C]104278.455920175[/C][/ROW]
[ROW][C]104[/C][C]95480.657784422[/C][C]79408.2751073703[/C][C]111553.040461474[/C][/ROW]
[ROW][C]105[/C][C]93668.7291357959[/C][C]76418.8715391528[/C][C]110918.586732439[/C][/ROW]
[ROW][C]106[/C][C]87123.6021231756[/C][C]69620.3753603256[/C][C]104626.828886026[/C][/ROW]
[ROW][C]107[/C][C]81425.4808461684[/C][C]63634.284937798[/C][C]99216.6767545387[/C][/ROW]
[ROW][C]108[/C][C]80026.6956231044[/C][C]61478.1530265631[/C][C]98575.2382196458[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122238&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122238&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
9783765.890628166479993.191901931787538.5893544011
9881073.738760562875853.82668393586293.6508371907
9977223.784688400370831.865694045283615.7036827553
10074029.825155724866555.300606539181504.3497049105
10169294.415435209660975.53051159677613.3003588231
10270334.260542469460605.847024124280062.6740608145
10390435.423194178276592.3904681818104278.455920175
10495480.65778442279408.2751073703111553.040461474
10593668.729135795976418.8715391528110918.586732439
10687123.602123175669620.3753603256104626.828886026
10781425.480846168463634.28493779899216.6767545387
10880026.695623104461478.153026563198575.2382196458



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