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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 02 Apr 2015 21:24:11 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/02/t1428006417imwui0lqxt9e1bx.htm/, Retrieved Thu, 09 May 2024 18:57:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278656, Retrieved Thu, 09 May 2024 18:57:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2015-04-02 20:24:11] [ab73e159a571dceeee45078a19254ea4] [Current]
- R PD    [Exponential Smoothing] [additief model do...] [2015-05-25 11:07:59] [69304374246e9fd5f7a19a35f2b701e6]
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Dataseries X:
123,2
136,9
146,8
149,6
146,5
157
147,9
133,6
128,7
100,8
91,8
89,3
96,7
91,6
93,3
93,3
101
100,4
86,9
83,9
80,3
87,7
92,7
95,5
92
87,4
86,8
83,7
85
81,7
90,9
101,5
113,8
120,1
122,1
132,5
140
149,4
144,3
154,4
151,4
145,5
136,8
146,6
145,1
133,6
131,4
127,5
130,1
131,1
132,3
128,6
125,1
128,7
156,1
163,2
159,8
157,4
156,2
152,5
149,4
145,9
144,8
135,9
137,6
136
117,7
111,5
107,8
107,3
102,6
101




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278656&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278656&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278656&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999940449774455
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999940449774455 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278656&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]0.999940449774455[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278656&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278656&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
alpha0.999940449774455
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2136.9123.213.7
3146.8136.899184161919.90081583808998
4149.6146.7994104041842.80058959581623
5146.5149.599833224258-3.09983322425791
6157146.50018459576810.4998154042324
7147.9156.999374733625-9.0993747336245
8133.6147.900541869818-14.3005418698177
9128.7133.600851600494-4.90085160049378
10100.8128.700291846818-27.9002918468182
1191.8100.801661468672-9.00166146867227
1289.391.8005360509707-2.50053605097074
1396.789.30014890748587.39985109251418
1491.696.6995593371984-5.09955933719844
1593.391.60030367990871.69969632009129
1693.393.29989878270080.000101217299217637
1710193.29999999397257.70000000602752
18100.4100.999541463263-0.599541463262938
1986.9100.400035702829-13.5000357028294
2083.986.900803930171-3.00080393017097
2180.383.9001786985509-3.60017869855086
2287.780.30021439145357.39978560854649
2392.787.6995593410985.00044065890198
2495.592.69970222263092.80029777736905
259295.4998332416358-3.49983324163577
2687.492.0002084158589-4.6002084158589
2786.887.4002739434487-0.600273943448727
2883.786.8000357464487-3.10003574644873
298583.70018460782791.29981539217209
3081.784.9999225957002-3.29992259570022
3190.981.70019651113499.19980348886514
32101.590.899452149627310.6005478503727
33113.8101.49936873498512.3006312650154
34120.1113.7992674946346.30073250536618
35122.1120.0996247899582.0003752100418
36132.5122.09988087720510.4001191227949
37140132.4993806705617.50061932943947
38149.4139.9995533364279.40044666357281
39144.3149.399440201281-5.09944020128097
40154.4144.30030367281410.0996963271859
41151.4154.399398560806-2.99939856080579
42145.5151.400178614861-5.90017861486081
43136.8145.500351356967-8.70035135696727
44146.6136.8005181078869.79948189211433
45145.1146.599416438643-1.4994164386431
46133.6145.100089290587-11.5000892905871
47131.4133.600684832911-2.20068483291104
48127.5131.400131051278-3.90013105127815
49130.1127.5002322536842.59976774631623
50131.1130.0998451832441.00015481675564
51132.3131.0999404405551.20005955944492
52128.6132.299928536183-3.6999285361826
53125.1128.600220331579-3.50022033157884
54128.7125.100208438913.59979156108979
55156.1128.69978563160127.4002143683994
56163.2156.0983683110547.10163168894562
57159.8163.199577096231-3.39957709623118
58157.4159.800202445583-2.40020244558286
59156.2157.400142932597-1.200142932597
60152.5156.200071468782-3.70007146878231
61149.4152.500220340091-3.10022034009052
62145.9149.400184618821-3.5001846188205
63144.8145.900208436783-1.10020843678348
64135.9144.800065517661-8.90006551766055
65137.6135.9005300009091.69946999909104
66136137.599898796178-1.59989879617825
67117.7136.000095274334-18.3000952743342
68111.5117.701089774801-6.20108977480109
69107.8111.500369276295-3.70036927629472
70107.3107.800220357825-0.500220357825
71102.6107.300029788235-4.70002978823513
72101102.600279887834-1.60027988783395

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 136.9 & 123.2 & 13.7 \tabularnewline
3 & 146.8 & 136.89918416191 & 9.90081583808998 \tabularnewline
4 & 149.6 & 146.799410404184 & 2.80058959581623 \tabularnewline
5 & 146.5 & 149.599833224258 & -3.09983322425791 \tabularnewline
6 & 157 & 146.500184595768 & 10.4998154042324 \tabularnewline
7 & 147.9 & 156.999374733625 & -9.0993747336245 \tabularnewline
8 & 133.6 & 147.900541869818 & -14.3005418698177 \tabularnewline
9 & 128.7 & 133.600851600494 & -4.90085160049378 \tabularnewline
10 & 100.8 & 128.700291846818 & -27.9002918468182 \tabularnewline
11 & 91.8 & 100.801661468672 & -9.00166146867227 \tabularnewline
12 & 89.3 & 91.8005360509707 & -2.50053605097074 \tabularnewline
13 & 96.7 & 89.3001489074858 & 7.39985109251418 \tabularnewline
14 & 91.6 & 96.6995593371984 & -5.09955933719844 \tabularnewline
15 & 93.3 & 91.6003036799087 & 1.69969632009129 \tabularnewline
16 & 93.3 & 93.2998987827008 & 0.000101217299217637 \tabularnewline
17 & 101 & 93.2999999939725 & 7.70000000602752 \tabularnewline
18 & 100.4 & 100.999541463263 & -0.599541463262938 \tabularnewline
19 & 86.9 & 100.400035702829 & -13.5000357028294 \tabularnewline
20 & 83.9 & 86.900803930171 & -3.00080393017097 \tabularnewline
21 & 80.3 & 83.9001786985509 & -3.60017869855086 \tabularnewline
22 & 87.7 & 80.3002143914535 & 7.39978560854649 \tabularnewline
23 & 92.7 & 87.699559341098 & 5.00044065890198 \tabularnewline
24 & 95.5 & 92.6997022226309 & 2.80029777736905 \tabularnewline
25 & 92 & 95.4998332416358 & -3.49983324163577 \tabularnewline
26 & 87.4 & 92.0002084158589 & -4.6002084158589 \tabularnewline
27 & 86.8 & 87.4002739434487 & -0.600273943448727 \tabularnewline
28 & 83.7 & 86.8000357464487 & -3.10003574644873 \tabularnewline
29 & 85 & 83.7001846078279 & 1.29981539217209 \tabularnewline
30 & 81.7 & 84.9999225957002 & -3.29992259570022 \tabularnewline
31 & 90.9 & 81.7001965111349 & 9.19980348886514 \tabularnewline
32 & 101.5 & 90.8994521496273 & 10.6005478503727 \tabularnewline
33 & 113.8 & 101.499368734985 & 12.3006312650154 \tabularnewline
34 & 120.1 & 113.799267494634 & 6.30073250536618 \tabularnewline
35 & 122.1 & 120.099624789958 & 2.0003752100418 \tabularnewline
36 & 132.5 & 122.099880877205 & 10.4001191227949 \tabularnewline
37 & 140 & 132.499380670561 & 7.50061932943947 \tabularnewline
38 & 149.4 & 139.999553336427 & 9.40044666357281 \tabularnewline
39 & 144.3 & 149.399440201281 & -5.09944020128097 \tabularnewline
40 & 154.4 & 144.300303672814 & 10.0996963271859 \tabularnewline
41 & 151.4 & 154.399398560806 & -2.99939856080579 \tabularnewline
42 & 145.5 & 151.400178614861 & -5.90017861486081 \tabularnewline
43 & 136.8 & 145.500351356967 & -8.70035135696727 \tabularnewline
44 & 146.6 & 136.800518107886 & 9.79948189211433 \tabularnewline
45 & 145.1 & 146.599416438643 & -1.4994164386431 \tabularnewline
46 & 133.6 & 145.100089290587 & -11.5000892905871 \tabularnewline
47 & 131.4 & 133.600684832911 & -2.20068483291104 \tabularnewline
48 & 127.5 & 131.400131051278 & -3.90013105127815 \tabularnewline
49 & 130.1 & 127.500232253684 & 2.59976774631623 \tabularnewline
50 & 131.1 & 130.099845183244 & 1.00015481675564 \tabularnewline
51 & 132.3 & 131.099940440555 & 1.20005955944492 \tabularnewline
52 & 128.6 & 132.299928536183 & -3.6999285361826 \tabularnewline
53 & 125.1 & 128.600220331579 & -3.50022033157884 \tabularnewline
54 & 128.7 & 125.10020843891 & 3.59979156108979 \tabularnewline
55 & 156.1 & 128.699785631601 & 27.4002143683994 \tabularnewline
56 & 163.2 & 156.098368311054 & 7.10163168894562 \tabularnewline
57 & 159.8 & 163.199577096231 & -3.39957709623118 \tabularnewline
58 & 157.4 & 159.800202445583 & -2.40020244558286 \tabularnewline
59 & 156.2 & 157.400142932597 & -1.200142932597 \tabularnewline
60 & 152.5 & 156.200071468782 & -3.70007146878231 \tabularnewline
61 & 149.4 & 152.500220340091 & -3.10022034009052 \tabularnewline
62 & 145.9 & 149.400184618821 & -3.5001846188205 \tabularnewline
63 & 144.8 & 145.900208436783 & -1.10020843678348 \tabularnewline
64 & 135.9 & 144.800065517661 & -8.90006551766055 \tabularnewline
65 & 137.6 & 135.900530000909 & 1.69946999909104 \tabularnewline
66 & 136 & 137.599898796178 & -1.59989879617825 \tabularnewline
67 & 117.7 & 136.000095274334 & -18.3000952743342 \tabularnewline
68 & 111.5 & 117.701089774801 & -6.20108977480109 \tabularnewline
69 & 107.8 & 111.500369276295 & -3.70036927629472 \tabularnewline
70 & 107.3 & 107.800220357825 & -0.500220357825 \tabularnewline
71 & 102.6 & 107.300029788235 & -4.70002978823513 \tabularnewline
72 & 101 & 102.600279887834 & -1.60027988783395 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278656&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]136.9[/C][C]123.2[/C][C]13.7[/C][/ROW]
[ROW][C]3[/C][C]146.8[/C][C]136.89918416191[/C][C]9.90081583808998[/C][/ROW]
[ROW][C]4[/C][C]149.6[/C][C]146.799410404184[/C][C]2.80058959581623[/C][/ROW]
[ROW][C]5[/C][C]146.5[/C][C]149.599833224258[/C][C]-3.09983322425791[/C][/ROW]
[ROW][C]6[/C][C]157[/C][C]146.500184595768[/C][C]10.4998154042324[/C][/ROW]
[ROW][C]7[/C][C]147.9[/C][C]156.999374733625[/C][C]-9.0993747336245[/C][/ROW]
[ROW][C]8[/C][C]133.6[/C][C]147.900541869818[/C][C]-14.3005418698177[/C][/ROW]
[ROW][C]9[/C][C]128.7[/C][C]133.600851600494[/C][C]-4.90085160049378[/C][/ROW]
[ROW][C]10[/C][C]100.8[/C][C]128.700291846818[/C][C]-27.9002918468182[/C][/ROW]
[ROW][C]11[/C][C]91.8[/C][C]100.801661468672[/C][C]-9.00166146867227[/C][/ROW]
[ROW][C]12[/C][C]89.3[/C][C]91.8005360509707[/C][C]-2.50053605097074[/C][/ROW]
[ROW][C]13[/C][C]96.7[/C][C]89.3001489074858[/C][C]7.39985109251418[/C][/ROW]
[ROW][C]14[/C][C]91.6[/C][C]96.6995593371984[/C][C]-5.09955933719844[/C][/ROW]
[ROW][C]15[/C][C]93.3[/C][C]91.6003036799087[/C][C]1.69969632009129[/C][/ROW]
[ROW][C]16[/C][C]93.3[/C][C]93.2998987827008[/C][C]0.000101217299217637[/C][/ROW]
[ROW][C]17[/C][C]101[/C][C]93.2999999939725[/C][C]7.70000000602752[/C][/ROW]
[ROW][C]18[/C][C]100.4[/C][C]100.999541463263[/C][C]-0.599541463262938[/C][/ROW]
[ROW][C]19[/C][C]86.9[/C][C]100.400035702829[/C][C]-13.5000357028294[/C][/ROW]
[ROW][C]20[/C][C]83.9[/C][C]86.900803930171[/C][C]-3.00080393017097[/C][/ROW]
[ROW][C]21[/C][C]80.3[/C][C]83.9001786985509[/C][C]-3.60017869855086[/C][/ROW]
[ROW][C]22[/C][C]87.7[/C][C]80.3002143914535[/C][C]7.39978560854649[/C][/ROW]
[ROW][C]23[/C][C]92.7[/C][C]87.699559341098[/C][C]5.00044065890198[/C][/ROW]
[ROW][C]24[/C][C]95.5[/C][C]92.6997022226309[/C][C]2.80029777736905[/C][/ROW]
[ROW][C]25[/C][C]92[/C][C]95.4998332416358[/C][C]-3.49983324163577[/C][/ROW]
[ROW][C]26[/C][C]87.4[/C][C]92.0002084158589[/C][C]-4.6002084158589[/C][/ROW]
[ROW][C]27[/C][C]86.8[/C][C]87.4002739434487[/C][C]-0.600273943448727[/C][/ROW]
[ROW][C]28[/C][C]83.7[/C][C]86.8000357464487[/C][C]-3.10003574644873[/C][/ROW]
[ROW][C]29[/C][C]85[/C][C]83.7001846078279[/C][C]1.29981539217209[/C][/ROW]
[ROW][C]30[/C][C]81.7[/C][C]84.9999225957002[/C][C]-3.29992259570022[/C][/ROW]
[ROW][C]31[/C][C]90.9[/C][C]81.7001965111349[/C][C]9.19980348886514[/C][/ROW]
[ROW][C]32[/C][C]101.5[/C][C]90.8994521496273[/C][C]10.6005478503727[/C][/ROW]
[ROW][C]33[/C][C]113.8[/C][C]101.499368734985[/C][C]12.3006312650154[/C][/ROW]
[ROW][C]34[/C][C]120.1[/C][C]113.799267494634[/C][C]6.30073250536618[/C][/ROW]
[ROW][C]35[/C][C]122.1[/C][C]120.099624789958[/C][C]2.0003752100418[/C][/ROW]
[ROW][C]36[/C][C]132.5[/C][C]122.099880877205[/C][C]10.4001191227949[/C][/ROW]
[ROW][C]37[/C][C]140[/C][C]132.499380670561[/C][C]7.50061932943947[/C][/ROW]
[ROW][C]38[/C][C]149.4[/C][C]139.999553336427[/C][C]9.40044666357281[/C][/ROW]
[ROW][C]39[/C][C]144.3[/C][C]149.399440201281[/C][C]-5.09944020128097[/C][/ROW]
[ROW][C]40[/C][C]154.4[/C][C]144.300303672814[/C][C]10.0996963271859[/C][/ROW]
[ROW][C]41[/C][C]151.4[/C][C]154.399398560806[/C][C]-2.99939856080579[/C][/ROW]
[ROW][C]42[/C][C]145.5[/C][C]151.400178614861[/C][C]-5.90017861486081[/C][/ROW]
[ROW][C]43[/C][C]136.8[/C][C]145.500351356967[/C][C]-8.70035135696727[/C][/ROW]
[ROW][C]44[/C][C]146.6[/C][C]136.800518107886[/C][C]9.79948189211433[/C][/ROW]
[ROW][C]45[/C][C]145.1[/C][C]146.599416438643[/C][C]-1.4994164386431[/C][/ROW]
[ROW][C]46[/C][C]133.6[/C][C]145.100089290587[/C][C]-11.5000892905871[/C][/ROW]
[ROW][C]47[/C][C]131.4[/C][C]133.600684832911[/C][C]-2.20068483291104[/C][/ROW]
[ROW][C]48[/C][C]127.5[/C][C]131.400131051278[/C][C]-3.90013105127815[/C][/ROW]
[ROW][C]49[/C][C]130.1[/C][C]127.500232253684[/C][C]2.59976774631623[/C][/ROW]
[ROW][C]50[/C][C]131.1[/C][C]130.099845183244[/C][C]1.00015481675564[/C][/ROW]
[ROW][C]51[/C][C]132.3[/C][C]131.099940440555[/C][C]1.20005955944492[/C][/ROW]
[ROW][C]52[/C][C]128.6[/C][C]132.299928536183[/C][C]-3.6999285361826[/C][/ROW]
[ROW][C]53[/C][C]125.1[/C][C]128.600220331579[/C][C]-3.50022033157884[/C][/ROW]
[ROW][C]54[/C][C]128.7[/C][C]125.10020843891[/C][C]3.59979156108979[/C][/ROW]
[ROW][C]55[/C][C]156.1[/C][C]128.699785631601[/C][C]27.4002143683994[/C][/ROW]
[ROW][C]56[/C][C]163.2[/C][C]156.098368311054[/C][C]7.10163168894562[/C][/ROW]
[ROW][C]57[/C][C]159.8[/C][C]163.199577096231[/C][C]-3.39957709623118[/C][/ROW]
[ROW][C]58[/C][C]157.4[/C][C]159.800202445583[/C][C]-2.40020244558286[/C][/ROW]
[ROW][C]59[/C][C]156.2[/C][C]157.400142932597[/C][C]-1.200142932597[/C][/ROW]
[ROW][C]60[/C][C]152.5[/C][C]156.200071468782[/C][C]-3.70007146878231[/C][/ROW]
[ROW][C]61[/C][C]149.4[/C][C]152.500220340091[/C][C]-3.10022034009052[/C][/ROW]
[ROW][C]62[/C][C]145.9[/C][C]149.400184618821[/C][C]-3.5001846188205[/C][/ROW]
[ROW][C]63[/C][C]144.8[/C][C]145.900208436783[/C][C]-1.10020843678348[/C][/ROW]
[ROW][C]64[/C][C]135.9[/C][C]144.800065517661[/C][C]-8.90006551766055[/C][/ROW]
[ROW][C]65[/C][C]137.6[/C][C]135.900530000909[/C][C]1.69946999909104[/C][/ROW]
[ROW][C]66[/C][C]136[/C][C]137.599898796178[/C][C]-1.59989879617825[/C][/ROW]
[ROW][C]67[/C][C]117.7[/C][C]136.000095274334[/C][C]-18.3000952743342[/C][/ROW]
[ROW][C]68[/C][C]111.5[/C][C]117.701089774801[/C][C]-6.20108977480109[/C][/ROW]
[ROW][C]69[/C][C]107.8[/C][C]111.500369276295[/C][C]-3.70036927629472[/C][/ROW]
[ROW][C]70[/C][C]107.3[/C][C]107.800220357825[/C][C]-0.500220357825[/C][/ROW]
[ROW][C]71[/C][C]102.6[/C][C]107.300029788235[/C][C]-4.70002978823513[/C][/ROW]
[ROW][C]72[/C][C]101[/C][C]102.600279887834[/C][C]-1.60027988783395[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278656&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278656&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
2136.9123.213.7
3146.8136.899184161919.90081583808998
4149.6146.7994104041842.80058959581623
5146.5149.599833224258-3.09983322425791
6157146.50018459576810.4998154042324
7147.9156.999374733625-9.0993747336245
8133.6147.900541869818-14.3005418698177
9128.7133.600851600494-4.90085160049378
10100.8128.700291846818-27.9002918468182
1191.8100.801661468672-9.00166146867227
1289.391.8005360509707-2.50053605097074
1396.789.30014890748587.39985109251418
1491.696.6995593371984-5.09955933719844
1593.391.60030367990871.69969632009129
1693.393.29989878270080.000101217299217637
1710193.29999999397257.70000000602752
18100.4100.999541463263-0.599541463262938
1986.9100.400035702829-13.5000357028294
2083.986.900803930171-3.00080393017097
2180.383.9001786985509-3.60017869855086
2287.780.30021439145357.39978560854649
2392.787.6995593410985.00044065890198
2495.592.69970222263092.80029777736905
259295.4998332416358-3.49983324163577
2687.492.0002084158589-4.6002084158589
2786.887.4002739434487-0.600273943448727
2883.786.8000357464487-3.10003574644873
298583.70018460782791.29981539217209
3081.784.9999225957002-3.29992259570022
3190.981.70019651113499.19980348886514
32101.590.899452149627310.6005478503727
33113.8101.49936873498512.3006312650154
34120.1113.7992674946346.30073250536618
35122.1120.0996247899582.0003752100418
36132.5122.09988087720510.4001191227949
37140132.4993806705617.50061932943947
38149.4139.9995533364279.40044666357281
39144.3149.399440201281-5.09944020128097
40154.4144.30030367281410.0996963271859
41151.4154.399398560806-2.99939856080579
42145.5151.400178614861-5.90017861486081
43136.8145.500351356967-8.70035135696727
44146.6136.8005181078869.79948189211433
45145.1146.599416438643-1.4994164386431
46133.6145.100089290587-11.5000892905871
47131.4133.600684832911-2.20068483291104
48127.5131.400131051278-3.90013105127815
49130.1127.5002322536842.59976774631623
50131.1130.0998451832441.00015481675564
51132.3131.0999404405551.20005955944492
52128.6132.299928536183-3.6999285361826
53125.1128.600220331579-3.50022033157884
54128.7125.100208438913.59979156108979
55156.1128.69978563160127.4002143683994
56163.2156.0983683110547.10163168894562
57159.8163.199577096231-3.39957709623118
58157.4159.800202445583-2.40020244558286
59156.2157.400142932597-1.200142932597
60152.5156.200071468782-3.70007146878231
61149.4152.500220340091-3.10022034009052
62145.9149.400184618821-3.5001846188205
63144.8145.900208436783-1.10020843678348
64135.9144.800065517661-8.90006551766055
65137.6135.9005300009091.69946999909104
66136137.599898796178-1.59989879617825
67117.7136.000095274334-18.3000952743342
68111.5117.701089774801-6.20108977480109
69107.8111.500369276295-3.70036927629472
70107.3107.800220357825-0.500220357825
71102.6107.300029788235-4.70002978823513
72101102.600279887834-1.60027988783395







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73101.00009529702885.079145847701116.921044746356
74101.00009529702878.4851430551553123.515047538901
75101.00009529702873.4252967023041128.574893891752
76101.00009529702869.159618531983132.840572062074
77101.00009529702865.4014660578122136.598724536244
78101.00009529702862.0038282090498139.996362385007
79101.00009529702858.8793724888577143.120818105199
80101.00009529702855.9711964323156146.028994161741
81101.00009529702853.2397751970299148.760415397027
82101.00009529702850.6563308456079151.343859748449
83101.00009529702848.1991382770473153.801052317009
84101.00009529702845.8513191971758156.148871396881

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 101.000095297028 & 85.079145847701 & 116.921044746356 \tabularnewline
74 & 101.000095297028 & 78.4851430551553 & 123.515047538901 \tabularnewline
75 & 101.000095297028 & 73.4252967023041 & 128.574893891752 \tabularnewline
76 & 101.000095297028 & 69.159618531983 & 132.840572062074 \tabularnewline
77 & 101.000095297028 & 65.4014660578122 & 136.598724536244 \tabularnewline
78 & 101.000095297028 & 62.0038282090498 & 139.996362385007 \tabularnewline
79 & 101.000095297028 & 58.8793724888577 & 143.120818105199 \tabularnewline
80 & 101.000095297028 & 55.9711964323156 & 146.028994161741 \tabularnewline
81 & 101.000095297028 & 53.2397751970299 & 148.760415397027 \tabularnewline
82 & 101.000095297028 & 50.6563308456079 & 151.343859748449 \tabularnewline
83 & 101.000095297028 & 48.1991382770473 & 153.801052317009 \tabularnewline
84 & 101.000095297028 & 45.8513191971758 & 156.148871396881 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278656&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]101.000095297028[/C][C]85.079145847701[/C][C]116.921044746356[/C][/ROW]
[ROW][C]74[/C][C]101.000095297028[/C][C]78.4851430551553[/C][C]123.515047538901[/C][/ROW]
[ROW][C]75[/C][C]101.000095297028[/C][C]73.4252967023041[/C][C]128.574893891752[/C][/ROW]
[ROW][C]76[/C][C]101.000095297028[/C][C]69.159618531983[/C][C]132.840572062074[/C][/ROW]
[ROW][C]77[/C][C]101.000095297028[/C][C]65.4014660578122[/C][C]136.598724536244[/C][/ROW]
[ROW][C]78[/C][C]101.000095297028[/C][C]62.0038282090498[/C][C]139.996362385007[/C][/ROW]
[ROW][C]79[/C][C]101.000095297028[/C][C]58.8793724888577[/C][C]143.120818105199[/C][/ROW]
[ROW][C]80[/C][C]101.000095297028[/C][C]55.9711964323156[/C][C]146.028994161741[/C][/ROW]
[ROW][C]81[/C][C]101.000095297028[/C][C]53.2397751970299[/C][C]148.760415397027[/C][/ROW]
[ROW][C]82[/C][C]101.000095297028[/C][C]50.6563308456079[/C][C]151.343859748449[/C][/ROW]
[ROW][C]83[/C][C]101.000095297028[/C][C]48.1991382770473[/C][C]153.801052317009[/C][/ROW]
[ROW][C]84[/C][C]101.000095297028[/C][C]45.8513191971758[/C][C]156.148871396881[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278656&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278656&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
73101.00009529702885.079145847701116.921044746356
74101.00009529702878.4851430551553123.515047538901
75101.00009529702873.4252967023041128.574893891752
76101.00009529702869.159618531983132.840572062074
77101.00009529702865.4014660578122136.598724536244
78101.00009529702862.0038282090498139.996362385007
79101.00009529702858.8793724888577143.120818105199
80101.00009529702855.9711964323156146.028994161741
81101.00009529702853.2397751970299148.760415397027
82101.00009529702850.6563308456079151.343859748449
83101.00009529702848.1991382770473153.801052317009
84101.00009529702845.8513191971758156.148871396881



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