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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 computationThu, 11 Aug 2016 21:39:38 +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/2016/Aug/11/t1470948003upnsr1qerdk3jny.htm/, Retrieved Sun, 05 May 2024 18:50:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296375, Retrieved Sun, 05 May 2024 18:50:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Reeks B stap 27] [2016-08-11 20:39:38] [efea2b8bc7c91838390b884e612c3e3f] [Current]
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Dataseries X:
910
910
970
950
980
860
920
950
900
950
950
940
860
810
870
960
970
860
850
910
970
980
970
1000
910
740
810
1050
920
830
880
910
880
960
900
1110
870
720
780
970
1020
830
820
920
840
920
920
1150
820
760
760
960
1010
790
820
880
820
870
870
1230
760
810
850
990
940
850
860
860
780
880
850
1220
850
800
840
1090
810
870
810
860
800
870
860
1220
820
860
750
1020
780
830
860
850
820
790
1020
1230
760
880
760
1090
840
900
930
820
780
870
990
1270




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=296375&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=296375&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296375&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
alpha0.00416862035087096
beta0.773393375868385
gamma0.90002897868697

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00416862035087096 \tabularnewline
beta & 0.773393375868385 \tabularnewline
gamma & 0.90002897868697 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296375&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]0.00416862035087096[/C][/ROW]
[ROW][C]beta[/C][C]0.773393375868385[/C][/ROW]
[ROW][C]gamma[/C][C]0.90002897868697[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296375&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296375&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
alpha0.00416862035087096
beta0.773393375868385
gamma0.90002897868697







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13860873.165087160519-13.1650871605192
14810825.265411933244-15.2654119332443
15870883.709418345952-13.7094183459525
16960969.017393008472-9.01739300847191
17970975.213296642609-5.21329664260941
18860860.004826304234-0.00482630423402952
19850903.237336376164-53.237336376164
20910937.005251975083-27.0052519750825
21970893.89073395047976.1092660495212
22980946.15307903198933.846920968011
23970944.7893913451925.21060865481
241000933.96637073860866.0336292613918
25910844.80360429768765.1963957023127
26740796.667842995945-56.6678429959446
27810855.486668907799-45.4866689077991
281050943.396339913395106.603660086605
29920953.872823172228-33.8728231722281
30830845.540475121422-15.5404751214217
31880841.42614614412238.5738538558782
32910898.85870813673411.1412918632659
33880948.414684058947-68.4146840589469
34960962.370837469054-2.37083746905398
35900953.516307871699-53.5163078716986
361110978.573918478193131.426081521807
37870890.409007034406-20.4090070344058
38720734.901882244974-14.9018822449739
39780802.955507257054-22.9555072570539
409701024.15888219667-54.1588821966702
411020909.418111573115110.581888426885
42830819.5499560293710.45004397063
43820863.583231733511-43.5832317335112
44920895.52145871137124.4785412886289
45840874.084702359568-34.0847023595678
46920946.365493512386-26.3654935123864
47920892.33290026766827.6670997323324
4811501080.9828542010769.0171457989311
49820859.701235255685-39.7012352556852
50760711.17230750520348.8276924947974
51760771.604028671224-11.6040286712242
52960962.500649191931-2.50064919193073
531010995.58777721303714.4122227869628
54790818.038763069272-28.038763069272
55820813.4949051469086.50509485309249
56880905.547473553326-25.5474735533257
57820832.354614591609-12.3546145916088
58870910.634815268206-40.6348152682056
59870905.027252243126-35.0272522431263
6012301127.14944526436102.850554735639
61760812.776736503637-52.7767365036366
62810744.32355309365.6764469070001
63850750.46409525534299.5359047446578
64990947.60460827770442.3953917222964
65940995.888187358045-55.8881873580449
66850782.95315115819767.0468488418035
67860809.96500039545950.034999604541
68860873.470776219267-13.4707762192672
69780813.482885272121-33.4828852721211
70880866.48279040709113.5172095929092
71850866.965706613691-16.9657066136912
7212201211.346251707028.65374829298048
73850760.78403311956489.2159668804364
74800799.946430821490.0535691785104291
75840836.8481138714183.15188612858162
761090982.449737557907107.550262442093
77810943.835476867429-133.835476867429
78870841.48029825957128.5197017404291
79810853.408511473828-43.4085114738281
80860859.6417048651450.358295134854529
81800782.00875144142517.9912485585745
82870877.472989779332-7.47298977933212
83860850.7860779265039.21392207349732
8412201218.274904720451.72509527954662
85820840.384218899776-20.3842188997763
86860799.10544600239860.8945539976019
87750839.096460326253-89.096460326253
8810201077.29961542375-57.2996154237549
89780821.473114774172-41.4731147741717
90830864.494385921518-34.4943859215176
91860811.27379811998348.7262018800175
92850856.651721025276-6.65172102527617
93820794.72607911982925.2739208801709
94790866.780933539319-76.7809335393187
951020854.292208918927165.707791081073
9612301213.9688974672616.0311025327367
97760818.218812248948-58.218812248948
98880849.33944148787830.6605585121224
99760755.029064811774.97093518823021
10010901020.8649834134669.1350165865363
101840781.19313092980858.8068690701923
102900831.45334473614868.5466552638522
103930854.29430758933375.7056924106674
104820851.325338760914-31.3253387609137
105780818.937948565751-38.9379485657508
106870800.02135716368769.9786428363134
1079901007.65401995948-17.6540199594762
10812701234.4540249147435.5459750852592

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 860 & 873.165087160519 & -13.1650871605192 \tabularnewline
14 & 810 & 825.265411933244 & -15.2654119332443 \tabularnewline
15 & 870 & 883.709418345952 & -13.7094183459525 \tabularnewline
16 & 960 & 969.017393008472 & -9.01739300847191 \tabularnewline
17 & 970 & 975.213296642609 & -5.21329664260941 \tabularnewline
18 & 860 & 860.004826304234 & -0.00482630423402952 \tabularnewline
19 & 850 & 903.237336376164 & -53.237336376164 \tabularnewline
20 & 910 & 937.005251975083 & -27.0052519750825 \tabularnewline
21 & 970 & 893.890733950479 & 76.1092660495212 \tabularnewline
22 & 980 & 946.153079031989 & 33.846920968011 \tabularnewline
23 & 970 & 944.78939134519 & 25.21060865481 \tabularnewline
24 & 1000 & 933.966370738608 & 66.0336292613918 \tabularnewline
25 & 910 & 844.803604297687 & 65.1963957023127 \tabularnewline
26 & 740 & 796.667842995945 & -56.6678429959446 \tabularnewline
27 & 810 & 855.486668907799 & -45.4866689077991 \tabularnewline
28 & 1050 & 943.396339913395 & 106.603660086605 \tabularnewline
29 & 920 & 953.872823172228 & -33.8728231722281 \tabularnewline
30 & 830 & 845.540475121422 & -15.5404751214217 \tabularnewline
31 & 880 & 841.426146144122 & 38.5738538558782 \tabularnewline
32 & 910 & 898.858708136734 & 11.1412918632659 \tabularnewline
33 & 880 & 948.414684058947 & -68.4146840589469 \tabularnewline
34 & 960 & 962.370837469054 & -2.37083746905398 \tabularnewline
35 & 900 & 953.516307871699 & -53.5163078716986 \tabularnewline
36 & 1110 & 978.573918478193 & 131.426081521807 \tabularnewline
37 & 870 & 890.409007034406 & -20.4090070344058 \tabularnewline
38 & 720 & 734.901882244974 & -14.9018822449739 \tabularnewline
39 & 780 & 802.955507257054 & -22.9555072570539 \tabularnewline
40 & 970 & 1024.15888219667 & -54.1588821966702 \tabularnewline
41 & 1020 & 909.418111573115 & 110.581888426885 \tabularnewline
42 & 830 & 819.54995602937 & 10.45004397063 \tabularnewline
43 & 820 & 863.583231733511 & -43.5832317335112 \tabularnewline
44 & 920 & 895.521458711371 & 24.4785412886289 \tabularnewline
45 & 840 & 874.084702359568 & -34.0847023595678 \tabularnewline
46 & 920 & 946.365493512386 & -26.3654935123864 \tabularnewline
47 & 920 & 892.332900267668 & 27.6670997323324 \tabularnewline
48 & 1150 & 1080.98285420107 & 69.0171457989311 \tabularnewline
49 & 820 & 859.701235255685 & -39.7012352556852 \tabularnewline
50 & 760 & 711.172307505203 & 48.8276924947974 \tabularnewline
51 & 760 & 771.604028671224 & -11.6040286712242 \tabularnewline
52 & 960 & 962.500649191931 & -2.50064919193073 \tabularnewline
53 & 1010 & 995.587777213037 & 14.4122227869628 \tabularnewline
54 & 790 & 818.038763069272 & -28.038763069272 \tabularnewline
55 & 820 & 813.494905146908 & 6.50509485309249 \tabularnewline
56 & 880 & 905.547473553326 & -25.5474735533257 \tabularnewline
57 & 820 & 832.354614591609 & -12.3546145916088 \tabularnewline
58 & 870 & 910.634815268206 & -40.6348152682056 \tabularnewline
59 & 870 & 905.027252243126 & -35.0272522431263 \tabularnewline
60 & 1230 & 1127.14944526436 & 102.850554735639 \tabularnewline
61 & 760 & 812.776736503637 & -52.7767365036366 \tabularnewline
62 & 810 & 744.323553093 & 65.6764469070001 \tabularnewline
63 & 850 & 750.464095255342 & 99.5359047446578 \tabularnewline
64 & 990 & 947.604608277704 & 42.3953917222964 \tabularnewline
65 & 940 & 995.888187358045 & -55.8881873580449 \tabularnewline
66 & 850 & 782.953151158197 & 67.0468488418035 \tabularnewline
67 & 860 & 809.965000395459 & 50.034999604541 \tabularnewline
68 & 860 & 873.470776219267 & -13.4707762192672 \tabularnewline
69 & 780 & 813.482885272121 & -33.4828852721211 \tabularnewline
70 & 880 & 866.482790407091 & 13.5172095929092 \tabularnewline
71 & 850 & 866.965706613691 & -16.9657066136912 \tabularnewline
72 & 1220 & 1211.34625170702 & 8.65374829298048 \tabularnewline
73 & 850 & 760.784033119564 & 89.2159668804364 \tabularnewline
74 & 800 & 799.94643082149 & 0.0535691785104291 \tabularnewline
75 & 840 & 836.848113871418 & 3.15188612858162 \tabularnewline
76 & 1090 & 982.449737557907 & 107.550262442093 \tabularnewline
77 & 810 & 943.835476867429 & -133.835476867429 \tabularnewline
78 & 870 & 841.480298259571 & 28.5197017404291 \tabularnewline
79 & 810 & 853.408511473828 & -43.4085114738281 \tabularnewline
80 & 860 & 859.641704865145 & 0.358295134854529 \tabularnewline
81 & 800 & 782.008751441425 & 17.9912485585745 \tabularnewline
82 & 870 & 877.472989779332 & -7.47298977933212 \tabularnewline
83 & 860 & 850.786077926503 & 9.21392207349732 \tabularnewline
84 & 1220 & 1218.27490472045 & 1.72509527954662 \tabularnewline
85 & 820 & 840.384218899776 & -20.3842188997763 \tabularnewline
86 & 860 & 799.105446002398 & 60.8945539976019 \tabularnewline
87 & 750 & 839.096460326253 & -89.096460326253 \tabularnewline
88 & 1020 & 1077.29961542375 & -57.2996154237549 \tabularnewline
89 & 780 & 821.473114774172 & -41.4731147741717 \tabularnewline
90 & 830 & 864.494385921518 & -34.4943859215176 \tabularnewline
91 & 860 & 811.273798119983 & 48.7262018800175 \tabularnewline
92 & 850 & 856.651721025276 & -6.65172102527617 \tabularnewline
93 & 820 & 794.726079119829 & 25.2739208801709 \tabularnewline
94 & 790 & 866.780933539319 & -76.7809335393187 \tabularnewline
95 & 1020 & 854.292208918927 & 165.707791081073 \tabularnewline
96 & 1230 & 1213.96889746726 & 16.0311025327367 \tabularnewline
97 & 760 & 818.218812248948 & -58.218812248948 \tabularnewline
98 & 880 & 849.339441487878 & 30.6605585121224 \tabularnewline
99 & 760 & 755.02906481177 & 4.97093518823021 \tabularnewline
100 & 1090 & 1020.86498341346 & 69.1350165865363 \tabularnewline
101 & 840 & 781.193130929808 & 58.8068690701923 \tabularnewline
102 & 900 & 831.453344736148 & 68.5466552638522 \tabularnewline
103 & 930 & 854.294307589333 & 75.7056924106674 \tabularnewline
104 & 820 & 851.325338760914 & -31.3253387609137 \tabularnewline
105 & 780 & 818.937948565751 & -38.9379485657508 \tabularnewline
106 & 870 & 800.021357163687 & 69.9786428363134 \tabularnewline
107 & 990 & 1007.65401995948 & -17.6540199594762 \tabularnewline
108 & 1270 & 1234.45402491474 & 35.5459750852592 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296375&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]860[/C][C]873.165087160519[/C][C]-13.1650871605192[/C][/ROW]
[ROW][C]14[/C][C]810[/C][C]825.265411933244[/C][C]-15.2654119332443[/C][/ROW]
[ROW][C]15[/C][C]870[/C][C]883.709418345952[/C][C]-13.7094183459525[/C][/ROW]
[ROW][C]16[/C][C]960[/C][C]969.017393008472[/C][C]-9.01739300847191[/C][/ROW]
[ROW][C]17[/C][C]970[/C][C]975.213296642609[/C][C]-5.21329664260941[/C][/ROW]
[ROW][C]18[/C][C]860[/C][C]860.004826304234[/C][C]-0.00482630423402952[/C][/ROW]
[ROW][C]19[/C][C]850[/C][C]903.237336376164[/C][C]-53.237336376164[/C][/ROW]
[ROW][C]20[/C][C]910[/C][C]937.005251975083[/C][C]-27.0052519750825[/C][/ROW]
[ROW][C]21[/C][C]970[/C][C]893.890733950479[/C][C]76.1092660495212[/C][/ROW]
[ROW][C]22[/C][C]980[/C][C]946.153079031989[/C][C]33.846920968011[/C][/ROW]
[ROW][C]23[/C][C]970[/C][C]944.78939134519[/C][C]25.21060865481[/C][/ROW]
[ROW][C]24[/C][C]1000[/C][C]933.966370738608[/C][C]66.0336292613918[/C][/ROW]
[ROW][C]25[/C][C]910[/C][C]844.803604297687[/C][C]65.1963957023127[/C][/ROW]
[ROW][C]26[/C][C]740[/C][C]796.667842995945[/C][C]-56.6678429959446[/C][/ROW]
[ROW][C]27[/C][C]810[/C][C]855.486668907799[/C][C]-45.4866689077991[/C][/ROW]
[ROW][C]28[/C][C]1050[/C][C]943.396339913395[/C][C]106.603660086605[/C][/ROW]
[ROW][C]29[/C][C]920[/C][C]953.872823172228[/C][C]-33.8728231722281[/C][/ROW]
[ROW][C]30[/C][C]830[/C][C]845.540475121422[/C][C]-15.5404751214217[/C][/ROW]
[ROW][C]31[/C][C]880[/C][C]841.426146144122[/C][C]38.5738538558782[/C][/ROW]
[ROW][C]32[/C][C]910[/C][C]898.858708136734[/C][C]11.1412918632659[/C][/ROW]
[ROW][C]33[/C][C]880[/C][C]948.414684058947[/C][C]-68.4146840589469[/C][/ROW]
[ROW][C]34[/C][C]960[/C][C]962.370837469054[/C][C]-2.37083746905398[/C][/ROW]
[ROW][C]35[/C][C]900[/C][C]953.516307871699[/C][C]-53.5163078716986[/C][/ROW]
[ROW][C]36[/C][C]1110[/C][C]978.573918478193[/C][C]131.426081521807[/C][/ROW]
[ROW][C]37[/C][C]870[/C][C]890.409007034406[/C][C]-20.4090070344058[/C][/ROW]
[ROW][C]38[/C][C]720[/C][C]734.901882244974[/C][C]-14.9018822449739[/C][/ROW]
[ROW][C]39[/C][C]780[/C][C]802.955507257054[/C][C]-22.9555072570539[/C][/ROW]
[ROW][C]40[/C][C]970[/C][C]1024.15888219667[/C][C]-54.1588821966702[/C][/ROW]
[ROW][C]41[/C][C]1020[/C][C]909.418111573115[/C][C]110.581888426885[/C][/ROW]
[ROW][C]42[/C][C]830[/C][C]819.54995602937[/C][C]10.45004397063[/C][/ROW]
[ROW][C]43[/C][C]820[/C][C]863.583231733511[/C][C]-43.5832317335112[/C][/ROW]
[ROW][C]44[/C][C]920[/C][C]895.521458711371[/C][C]24.4785412886289[/C][/ROW]
[ROW][C]45[/C][C]840[/C][C]874.084702359568[/C][C]-34.0847023595678[/C][/ROW]
[ROW][C]46[/C][C]920[/C][C]946.365493512386[/C][C]-26.3654935123864[/C][/ROW]
[ROW][C]47[/C][C]920[/C][C]892.332900267668[/C][C]27.6670997323324[/C][/ROW]
[ROW][C]48[/C][C]1150[/C][C]1080.98285420107[/C][C]69.0171457989311[/C][/ROW]
[ROW][C]49[/C][C]820[/C][C]859.701235255685[/C][C]-39.7012352556852[/C][/ROW]
[ROW][C]50[/C][C]760[/C][C]711.172307505203[/C][C]48.8276924947974[/C][/ROW]
[ROW][C]51[/C][C]760[/C][C]771.604028671224[/C][C]-11.6040286712242[/C][/ROW]
[ROW][C]52[/C][C]960[/C][C]962.500649191931[/C][C]-2.50064919193073[/C][/ROW]
[ROW][C]53[/C][C]1010[/C][C]995.587777213037[/C][C]14.4122227869628[/C][/ROW]
[ROW][C]54[/C][C]790[/C][C]818.038763069272[/C][C]-28.038763069272[/C][/ROW]
[ROW][C]55[/C][C]820[/C][C]813.494905146908[/C][C]6.50509485309249[/C][/ROW]
[ROW][C]56[/C][C]880[/C][C]905.547473553326[/C][C]-25.5474735533257[/C][/ROW]
[ROW][C]57[/C][C]820[/C][C]832.354614591609[/C][C]-12.3546145916088[/C][/ROW]
[ROW][C]58[/C][C]870[/C][C]910.634815268206[/C][C]-40.6348152682056[/C][/ROW]
[ROW][C]59[/C][C]870[/C][C]905.027252243126[/C][C]-35.0272522431263[/C][/ROW]
[ROW][C]60[/C][C]1230[/C][C]1127.14944526436[/C][C]102.850554735639[/C][/ROW]
[ROW][C]61[/C][C]760[/C][C]812.776736503637[/C][C]-52.7767365036366[/C][/ROW]
[ROW][C]62[/C][C]810[/C][C]744.323553093[/C][C]65.6764469070001[/C][/ROW]
[ROW][C]63[/C][C]850[/C][C]750.464095255342[/C][C]99.5359047446578[/C][/ROW]
[ROW][C]64[/C][C]990[/C][C]947.604608277704[/C][C]42.3953917222964[/C][/ROW]
[ROW][C]65[/C][C]940[/C][C]995.888187358045[/C][C]-55.8881873580449[/C][/ROW]
[ROW][C]66[/C][C]850[/C][C]782.953151158197[/C][C]67.0468488418035[/C][/ROW]
[ROW][C]67[/C][C]860[/C][C]809.965000395459[/C][C]50.034999604541[/C][/ROW]
[ROW][C]68[/C][C]860[/C][C]873.470776219267[/C][C]-13.4707762192672[/C][/ROW]
[ROW][C]69[/C][C]780[/C][C]813.482885272121[/C][C]-33.4828852721211[/C][/ROW]
[ROW][C]70[/C][C]880[/C][C]866.482790407091[/C][C]13.5172095929092[/C][/ROW]
[ROW][C]71[/C][C]850[/C][C]866.965706613691[/C][C]-16.9657066136912[/C][/ROW]
[ROW][C]72[/C][C]1220[/C][C]1211.34625170702[/C][C]8.65374829298048[/C][/ROW]
[ROW][C]73[/C][C]850[/C][C]760.784033119564[/C][C]89.2159668804364[/C][/ROW]
[ROW][C]74[/C][C]800[/C][C]799.94643082149[/C][C]0.0535691785104291[/C][/ROW]
[ROW][C]75[/C][C]840[/C][C]836.848113871418[/C][C]3.15188612858162[/C][/ROW]
[ROW][C]76[/C][C]1090[/C][C]982.449737557907[/C][C]107.550262442093[/C][/ROW]
[ROW][C]77[/C][C]810[/C][C]943.835476867429[/C][C]-133.835476867429[/C][/ROW]
[ROW][C]78[/C][C]870[/C][C]841.480298259571[/C][C]28.5197017404291[/C][/ROW]
[ROW][C]79[/C][C]810[/C][C]853.408511473828[/C][C]-43.4085114738281[/C][/ROW]
[ROW][C]80[/C][C]860[/C][C]859.641704865145[/C][C]0.358295134854529[/C][/ROW]
[ROW][C]81[/C][C]800[/C][C]782.008751441425[/C][C]17.9912485585745[/C][/ROW]
[ROW][C]82[/C][C]870[/C][C]877.472989779332[/C][C]-7.47298977933212[/C][/ROW]
[ROW][C]83[/C][C]860[/C][C]850.786077926503[/C][C]9.21392207349732[/C][/ROW]
[ROW][C]84[/C][C]1220[/C][C]1218.27490472045[/C][C]1.72509527954662[/C][/ROW]
[ROW][C]85[/C][C]820[/C][C]840.384218899776[/C][C]-20.3842188997763[/C][/ROW]
[ROW][C]86[/C][C]860[/C][C]799.105446002398[/C][C]60.8945539976019[/C][/ROW]
[ROW][C]87[/C][C]750[/C][C]839.096460326253[/C][C]-89.096460326253[/C][/ROW]
[ROW][C]88[/C][C]1020[/C][C]1077.29961542375[/C][C]-57.2996154237549[/C][/ROW]
[ROW][C]89[/C][C]780[/C][C]821.473114774172[/C][C]-41.4731147741717[/C][/ROW]
[ROW][C]90[/C][C]830[/C][C]864.494385921518[/C][C]-34.4943859215176[/C][/ROW]
[ROW][C]91[/C][C]860[/C][C]811.273798119983[/C][C]48.7262018800175[/C][/ROW]
[ROW][C]92[/C][C]850[/C][C]856.651721025276[/C][C]-6.65172102527617[/C][/ROW]
[ROW][C]93[/C][C]820[/C][C]794.726079119829[/C][C]25.2739208801709[/C][/ROW]
[ROW][C]94[/C][C]790[/C][C]866.780933539319[/C][C]-76.7809335393187[/C][/ROW]
[ROW][C]95[/C][C]1020[/C][C]854.292208918927[/C][C]165.707791081073[/C][/ROW]
[ROW][C]96[/C][C]1230[/C][C]1213.96889746726[/C][C]16.0311025327367[/C][/ROW]
[ROW][C]97[/C][C]760[/C][C]818.218812248948[/C][C]-58.218812248948[/C][/ROW]
[ROW][C]98[/C][C]880[/C][C]849.339441487878[/C][C]30.6605585121224[/C][/ROW]
[ROW][C]99[/C][C]760[/C][C]755.02906481177[/C][C]4.97093518823021[/C][/ROW]
[ROW][C]100[/C][C]1090[/C][C]1020.86498341346[/C][C]69.1350165865363[/C][/ROW]
[ROW][C]101[/C][C]840[/C][C]781.193130929808[/C][C]58.8068690701923[/C][/ROW]
[ROW][C]102[/C][C]900[/C][C]831.453344736148[/C][C]68.5466552638522[/C][/ROW]
[ROW][C]103[/C][C]930[/C][C]854.294307589333[/C][C]75.7056924106674[/C][/ROW]
[ROW][C]104[/C][C]820[/C][C]851.325338760914[/C][C]-31.3253387609137[/C][/ROW]
[ROW][C]105[/C][C]780[/C][C]818.937948565751[/C][C]-38.9379485657508[/C][/ROW]
[ROW][C]106[/C][C]870[/C][C]800.021357163687[/C][C]69.9786428363134[/C][/ROW]
[ROW][C]107[/C][C]990[/C][C]1007.65401995948[/C][C]-17.6540199594762[/C][/ROW]
[ROW][C]108[/C][C]1270[/C][C]1234.45402491474[/C][C]35.5459750852592[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296375&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296375&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
13860873.165087160519-13.1650871605192
14810825.265411933244-15.2654119332443
15870883.709418345952-13.7094183459525
16960969.017393008472-9.01739300847191
17970975.213296642609-5.21329664260941
18860860.004826304234-0.00482630423402952
19850903.237336376164-53.237336376164
20910937.005251975083-27.0052519750825
21970893.89073395047976.1092660495212
22980946.15307903198933.846920968011
23970944.7893913451925.21060865481
241000933.96637073860866.0336292613918
25910844.80360429768765.1963957023127
26740796.667842995945-56.6678429959446
27810855.486668907799-45.4866689077991
281050943.396339913395106.603660086605
29920953.872823172228-33.8728231722281
30830845.540475121422-15.5404751214217
31880841.42614614412238.5738538558782
32910898.85870813673411.1412918632659
33880948.414684058947-68.4146840589469
34960962.370837469054-2.37083746905398
35900953.516307871699-53.5163078716986
361110978.573918478193131.426081521807
37870890.409007034406-20.4090070344058
38720734.901882244974-14.9018822449739
39780802.955507257054-22.9555072570539
409701024.15888219667-54.1588821966702
411020909.418111573115110.581888426885
42830819.5499560293710.45004397063
43820863.583231733511-43.5832317335112
44920895.52145871137124.4785412886289
45840874.084702359568-34.0847023595678
46920946.365493512386-26.3654935123864
47920892.33290026766827.6670997323324
4811501080.9828542010769.0171457989311
49820859.701235255685-39.7012352556852
50760711.17230750520348.8276924947974
51760771.604028671224-11.6040286712242
52960962.500649191931-2.50064919193073
531010995.58777721303714.4122227869628
54790818.038763069272-28.038763069272
55820813.4949051469086.50509485309249
56880905.547473553326-25.5474735533257
57820832.354614591609-12.3546145916088
58870910.634815268206-40.6348152682056
59870905.027252243126-35.0272522431263
6012301127.14944526436102.850554735639
61760812.776736503637-52.7767365036366
62810744.32355309365.6764469070001
63850750.46409525534299.5359047446578
64990947.60460827770442.3953917222964
65940995.888187358045-55.8881873580449
66850782.95315115819767.0468488418035
67860809.96500039545950.034999604541
68860873.470776219267-13.4707762192672
69780813.482885272121-33.4828852721211
70880866.48279040709113.5172095929092
71850866.965706613691-16.9657066136912
7212201211.346251707028.65374829298048
73850760.78403311956489.2159668804364
74800799.946430821490.0535691785104291
75840836.8481138714183.15188612858162
761090982.449737557907107.550262442093
77810943.835476867429-133.835476867429
78870841.48029825957128.5197017404291
79810853.408511473828-43.4085114738281
80860859.6417048651450.358295134854529
81800782.00875144142517.9912485585745
82870877.472989779332-7.47298977933212
83860850.7860779265039.21392207349732
8412201218.274904720451.72509527954662
85820840.384218899776-20.3842188997763
86860799.10544600239860.8945539976019
87750839.096460326253-89.096460326253
8810201077.29961542375-57.2996154237549
89780821.473114774172-41.4731147741717
90830864.494385921518-34.4943859215176
91860811.27379811998348.7262018800175
92850856.651721025276-6.65172102527617
93820794.72607911982925.2739208801709
94790866.780933539319-76.7809335393187
951020854.292208918927165.707791081073
9612301213.9688974672616.0311025327367
97760818.218812248948-58.218812248948
98880849.33944148787830.6605585121224
99760755.029064811774.97093518823021
10010901020.8649834134669.1350165865363
101840781.19313092980858.8068690701923
102900831.45334473614868.5466552638522
103930854.29430758933375.7056924106674
104820851.325338760914-31.3253387609137
105780818.937948565751-38.9379485657508
106870800.02135716368769.9786428363134
1079901007.65401995948-17.6540199594762
10812701234.4540249147435.5459750852592







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109770.629749721483677.498561660104863.760937782862
110883.402130489534790.266825217701976.537435761367
111765.896617602969672.756703156544859.036532049395
1121093.07356517823999.904108108941186.24302224751
113842.250645036743749.080017315163935.421272758323
114902.076799611527808.873040596892995.280558626162
115931.61351975743838.3666647661031024.86037474876
116831.442716463308738.180707087046924.70472583957
117792.084662519446698.790753564833885.378571474058
118872.022273708862778.628493378813965.41605403891
1191002.18786758709908.6069489639461095.76878621024
1201279.734205520571096.77556828131462.69284275984

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 770.629749721483 & 677.498561660104 & 863.760937782862 \tabularnewline
110 & 883.402130489534 & 790.266825217701 & 976.537435761367 \tabularnewline
111 & 765.896617602969 & 672.756703156544 & 859.036532049395 \tabularnewline
112 & 1093.07356517823 & 999.90410810894 & 1186.24302224751 \tabularnewline
113 & 842.250645036743 & 749.080017315163 & 935.421272758323 \tabularnewline
114 & 902.076799611527 & 808.873040596892 & 995.280558626162 \tabularnewline
115 & 931.61351975743 & 838.366664766103 & 1024.86037474876 \tabularnewline
116 & 831.442716463308 & 738.180707087046 & 924.70472583957 \tabularnewline
117 & 792.084662519446 & 698.790753564833 & 885.378571474058 \tabularnewline
118 & 872.022273708862 & 778.628493378813 & 965.41605403891 \tabularnewline
119 & 1002.18786758709 & 908.606948963946 & 1095.76878621024 \tabularnewline
120 & 1279.73420552057 & 1096.7755682813 & 1462.69284275984 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296375&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]109[/C][C]770.629749721483[/C][C]677.498561660104[/C][C]863.760937782862[/C][/ROW]
[ROW][C]110[/C][C]883.402130489534[/C][C]790.266825217701[/C][C]976.537435761367[/C][/ROW]
[ROW][C]111[/C][C]765.896617602969[/C][C]672.756703156544[/C][C]859.036532049395[/C][/ROW]
[ROW][C]112[/C][C]1093.07356517823[/C][C]999.90410810894[/C][C]1186.24302224751[/C][/ROW]
[ROW][C]113[/C][C]842.250645036743[/C][C]749.080017315163[/C][C]935.421272758323[/C][/ROW]
[ROW][C]114[/C][C]902.076799611527[/C][C]808.873040596892[/C][C]995.280558626162[/C][/ROW]
[ROW][C]115[/C][C]931.61351975743[/C][C]838.366664766103[/C][C]1024.86037474876[/C][/ROW]
[ROW][C]116[/C][C]831.442716463308[/C][C]738.180707087046[/C][C]924.70472583957[/C][/ROW]
[ROW][C]117[/C][C]792.084662519446[/C][C]698.790753564833[/C][C]885.378571474058[/C][/ROW]
[ROW][C]118[/C][C]872.022273708862[/C][C]778.628493378813[/C][C]965.41605403891[/C][/ROW]
[ROW][C]119[/C][C]1002.18786758709[/C][C]908.606948963946[/C][C]1095.76878621024[/C][/ROW]
[ROW][C]120[/C][C]1279.73420552057[/C][C]1096.7755682813[/C][C]1462.69284275984[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296375&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296375&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
109770.629749721483677.498561660104863.760937782862
110883.402130489534790.266825217701976.537435761367
111765.896617602969672.756703156544859.036532049395
1121093.07356517823999.904108108941186.24302224751
113842.250645036743749.080017315163935.421272758323
114902.076799611527808.873040596892995.280558626162
115931.61351975743838.3666647661031024.86037474876
116831.442716463308738.180707087046924.70472583957
117792.084662519446698.790753564833885.378571474058
118872.022273708862778.628493378813965.41605403891
1191002.18786758709908.6069489639461095.76878621024
1201279.734205520571096.77556828131462.69284275984



Parameters (Session):
par1 = 0.1 ; par2 = 0.9 ; par3 = 0.1 ;
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')