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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 12 Aug 2016 14:34:00 +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/12/t14710088520vp5ajvmon92ltu.htm/, Retrieved Sun, 05 May 2024 16:21:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296433, Retrieved Sun, 05 May 2024 16:21:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-08-12 13:34:00] [b787349f7d799cee4daf21043f8c3664] [Current]
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Dataseries X:
990
1050
1000
1040
1030
980
990
940
1050
990
980
1110
1000
1000
1080
1010
960
990
900
920
1080
950
950
1060
1070
970
1070
980
970
1050
950
960
1170
990
870
1090
1070
990
1080
890
920
1100
930
950
1240
950
830
1220
1040
1080
1160
900
790
1100
1000
990
1250
970
840
1220
1100
1030
1210
830
810
1100
1020
950
1280
950
720
1150
1030
1030
1200
870
880
1090
950
1060
1280
920
630
1110
1020
1130
1160
930
930
1110
930
1070
1250
840
680
1110
990
1210
1130
920
1030
1120
880
1050
1260
790
640
1110




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296433&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296433&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296433&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0237763572041562
beta0.134368823717335
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0237763572041562 \tabularnewline
beta & 0.134368823717335 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296433&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]0.0237763572041562[/C][/ROW]
[ROW][C]beta[/C][C]0.134368823717335[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296433&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296433&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
alpha0.0237763572041562
beta0.134368823717335
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310001008.20245726496-8.20245726495773
1410001010.70704334199-10.7070433419888
1510801088.11787261142-8.11787261142376
1610101016.39766127359-6.39766127359167
17960967.197911039401-7.19791103940145
18990998.372804553129-8.37280455312862
19900976.993013933383-76.9930139333833
20920924.569040667881-4.56904066788081
2110801030.9357818178449.0642181821627
22950967.901143575565-17.9011435755649
23950959.467122377757-9.46712237775716
2410601089.53671924049-29.5367192404913
251070971.86067087694298.1393291230582
26970974.346226054482-4.3462260544818
2710701054.3538085620915.6461914379142
28980984.871759029278-4.87175902927765
29970934.92576935559435.0742306444065
301050966.0925355759883.9074644240202
31950880.34673392522669.6532660747743
32960903.00854680834156.991453191659
3311701064.29077792162105.709222078382
34990938.50450199517251.4954980048281
35870941.450399369432-71.4503993694323
3610901051.7522488302938.2477511697132
3710701061.843207274698.1567927253061
38990963.36796919993326.6320308000671
3910801064.9556274960115.0443725039868
40890976.753692916869-86.7536929168692
41920964.920004555699-44.9200045556994
4211001042.664326827857.335673172201
43930943.093937942077-13.0939379420768
44950951.885680388177-1.88568038817675
4512401159.5974825602280.4025174397839
46950980.473953297362-30.4739532973624
47830861.375514936213-31.375514936213
4812201079.77544959851140.224550401492
4910401063.29665768256-23.2966576825579
501080982.3901657333297.6098342666795
5111601074.860661995985.1393380040972
52900889.67898192734610.3210180726536
53790922.033876439329-132.033876439329
5411001098.294511111771.70548888823487
551000929.23181292137570.7681870786247
56990951.81260539084738.1873946091533
5712501241.79025722148.20974277859659
58970953.46074670818216.539253291818
59840835.5009153102934.49908468970716
6012201223.28940032533-3.28940032532955
6111001044.3221436576455.6778563423641
6210301084.13450547515-54.1345054751482
6312101161.1476393352248.8523606647764
64830902.272403135157-72.2724031351571
65810793.6380725493516.3619274506502
6611001104.40540363071-4.40540363071068
6710201003.01738076216.9826192379991
68950992.740705530676-42.7407055306763
6912801251.4982373669228.5017626330809
70950971.816439125394-21.8164391253937
71720841.101989884234-121.101989884234
7211501217.81080326735-67.8108032673517
7310301094.17852732912-64.1785273291193
7410301022.86063430877.13936569130135
7512001200.98552630516-0.985526305155418
76870821.6379214790448.3620785209598
77880801.74162460858278.2583753914182
7810901093.24767109661-3.24767109661434
799501012.31097016266-62.310970162663
801060941.136634984992118.863365015008
8112801273.092372015966.90762798404421
82920943.513604024891-23.5136040248913
83630715.566756570673-85.5667565706733
8411101144.9909689113-34.9909689112951
8510201025.63617979955-5.6361797995537
8611301025.47069209908104.529307900916
8711601198.42886021945-38.4288602194547
88930866.69507358358663.3049264164137
89930876.71706019266853.2829398073319
9011101088.3588857935121.6411142064858
91930950.732208862437-20.7322088624368
9210701057.9232188311512.0767811688547
9312501278.21504476019-28.2150447601923
94840918.15997396711-78.1599739671102
95680628.21820833171751.7817916682834
9611101110.60227783838-0.602277838375812
979901021.15276007484-31.152760074844
9812101128.2760087457681.7239912542404
9911301161.40922139496-31.4092213949575
100920929.456105867956-9.45610586795624
1011030928.030784761379101.969215238621
10211201110.162622207829.83737779217608
103880931.073672851813-51.0736728518126
10410501069.65946738748-19.6594673874779
10512601249.8487791358710.1512208641338
106790842.056961523517-52.056961523517
107640679.77991204438-39.77991204438
10811101108.747746991171.25225300882971

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1000 & 1008.20245726496 & -8.20245726495773 \tabularnewline
14 & 1000 & 1010.70704334199 & -10.7070433419888 \tabularnewline
15 & 1080 & 1088.11787261142 & -8.11787261142376 \tabularnewline
16 & 1010 & 1016.39766127359 & -6.39766127359167 \tabularnewline
17 & 960 & 967.197911039401 & -7.19791103940145 \tabularnewline
18 & 990 & 998.372804553129 & -8.37280455312862 \tabularnewline
19 & 900 & 976.993013933383 & -76.9930139333833 \tabularnewline
20 & 920 & 924.569040667881 & -4.56904066788081 \tabularnewline
21 & 1080 & 1030.93578181784 & 49.0642181821627 \tabularnewline
22 & 950 & 967.901143575565 & -17.9011435755649 \tabularnewline
23 & 950 & 959.467122377757 & -9.46712237775716 \tabularnewline
24 & 1060 & 1089.53671924049 & -29.5367192404913 \tabularnewline
25 & 1070 & 971.860670876942 & 98.1393291230582 \tabularnewline
26 & 970 & 974.346226054482 & -4.3462260544818 \tabularnewline
27 & 1070 & 1054.35380856209 & 15.6461914379142 \tabularnewline
28 & 980 & 984.871759029278 & -4.87175902927765 \tabularnewline
29 & 970 & 934.925769355594 & 35.0742306444065 \tabularnewline
30 & 1050 & 966.09253557598 & 83.9074644240202 \tabularnewline
31 & 950 & 880.346733925226 & 69.6532660747743 \tabularnewline
32 & 960 & 903.008546808341 & 56.991453191659 \tabularnewline
33 & 1170 & 1064.29077792162 & 105.709222078382 \tabularnewline
34 & 990 & 938.504501995172 & 51.4954980048281 \tabularnewline
35 & 870 & 941.450399369432 & -71.4503993694323 \tabularnewline
36 & 1090 & 1051.75224883029 & 38.2477511697132 \tabularnewline
37 & 1070 & 1061.84320727469 & 8.1567927253061 \tabularnewline
38 & 990 & 963.367969199933 & 26.6320308000671 \tabularnewline
39 & 1080 & 1064.95562749601 & 15.0443725039868 \tabularnewline
40 & 890 & 976.753692916869 & -86.7536929168692 \tabularnewline
41 & 920 & 964.920004555699 & -44.9200045556994 \tabularnewline
42 & 1100 & 1042.6643268278 & 57.335673172201 \tabularnewline
43 & 930 & 943.093937942077 & -13.0939379420768 \tabularnewline
44 & 950 & 951.885680388177 & -1.88568038817675 \tabularnewline
45 & 1240 & 1159.59748256022 & 80.4025174397839 \tabularnewline
46 & 950 & 980.473953297362 & -30.4739532973624 \tabularnewline
47 & 830 & 861.375514936213 & -31.375514936213 \tabularnewline
48 & 1220 & 1079.77544959851 & 140.224550401492 \tabularnewline
49 & 1040 & 1063.29665768256 & -23.2966576825579 \tabularnewline
50 & 1080 & 982.39016573332 & 97.6098342666795 \tabularnewline
51 & 1160 & 1074.8606619959 & 85.1393380040972 \tabularnewline
52 & 900 & 889.678981927346 & 10.3210180726536 \tabularnewline
53 & 790 & 922.033876439329 & -132.033876439329 \tabularnewline
54 & 1100 & 1098.29451111177 & 1.70548888823487 \tabularnewline
55 & 1000 & 929.231812921375 & 70.7681870786247 \tabularnewline
56 & 990 & 951.812605390847 & 38.1873946091533 \tabularnewline
57 & 1250 & 1241.7902572214 & 8.20974277859659 \tabularnewline
58 & 970 & 953.460746708182 & 16.539253291818 \tabularnewline
59 & 840 & 835.500915310293 & 4.49908468970716 \tabularnewline
60 & 1220 & 1223.28940032533 & -3.28940032532955 \tabularnewline
61 & 1100 & 1044.32214365764 & 55.6778563423641 \tabularnewline
62 & 1030 & 1084.13450547515 & -54.1345054751482 \tabularnewline
63 & 1210 & 1161.14763933522 & 48.8523606647764 \tabularnewline
64 & 830 & 902.272403135157 & -72.2724031351571 \tabularnewline
65 & 810 & 793.63807254935 & 16.3619274506502 \tabularnewline
66 & 1100 & 1104.40540363071 & -4.40540363071068 \tabularnewline
67 & 1020 & 1003.017380762 & 16.9826192379991 \tabularnewline
68 & 950 & 992.740705530676 & -42.7407055306763 \tabularnewline
69 & 1280 & 1251.49823736692 & 28.5017626330809 \tabularnewline
70 & 950 & 971.816439125394 & -21.8164391253937 \tabularnewline
71 & 720 & 841.101989884234 & -121.101989884234 \tabularnewline
72 & 1150 & 1217.81080326735 & -67.8108032673517 \tabularnewline
73 & 1030 & 1094.17852732912 & -64.1785273291193 \tabularnewline
74 & 1030 & 1022.8606343087 & 7.13936569130135 \tabularnewline
75 & 1200 & 1200.98552630516 & -0.985526305155418 \tabularnewline
76 & 870 & 821.63792147904 & 48.3620785209598 \tabularnewline
77 & 880 & 801.741624608582 & 78.2583753914182 \tabularnewline
78 & 1090 & 1093.24767109661 & -3.24767109661434 \tabularnewline
79 & 950 & 1012.31097016266 & -62.310970162663 \tabularnewline
80 & 1060 & 941.136634984992 & 118.863365015008 \tabularnewline
81 & 1280 & 1273.09237201596 & 6.90762798404421 \tabularnewline
82 & 920 & 943.513604024891 & -23.5136040248913 \tabularnewline
83 & 630 & 715.566756570673 & -85.5667565706733 \tabularnewline
84 & 1110 & 1144.9909689113 & -34.9909689112951 \tabularnewline
85 & 1020 & 1025.63617979955 & -5.6361797995537 \tabularnewline
86 & 1130 & 1025.47069209908 & 104.529307900916 \tabularnewline
87 & 1160 & 1198.42886021945 & -38.4288602194547 \tabularnewline
88 & 930 & 866.695073583586 & 63.3049264164137 \tabularnewline
89 & 930 & 876.717060192668 & 53.2829398073319 \tabularnewline
90 & 1110 & 1088.35888579351 & 21.6411142064858 \tabularnewline
91 & 930 & 950.732208862437 & -20.7322088624368 \tabularnewline
92 & 1070 & 1057.92321883115 & 12.0767811688547 \tabularnewline
93 & 1250 & 1278.21504476019 & -28.2150447601923 \tabularnewline
94 & 840 & 918.15997396711 & -78.1599739671102 \tabularnewline
95 & 680 & 628.218208331717 & 51.7817916682834 \tabularnewline
96 & 1110 & 1110.60227783838 & -0.602277838375812 \tabularnewline
97 & 990 & 1021.15276007484 & -31.152760074844 \tabularnewline
98 & 1210 & 1128.27600874576 & 81.7239912542404 \tabularnewline
99 & 1130 & 1161.40922139496 & -31.4092213949575 \tabularnewline
100 & 920 & 929.456105867956 & -9.45610586795624 \tabularnewline
101 & 1030 & 928.030784761379 & 101.969215238621 \tabularnewline
102 & 1120 & 1110.16262220782 & 9.83737779217608 \tabularnewline
103 & 880 & 931.073672851813 & -51.0736728518126 \tabularnewline
104 & 1050 & 1069.65946738748 & -19.6594673874779 \tabularnewline
105 & 1260 & 1249.84877913587 & 10.1512208641338 \tabularnewline
106 & 790 & 842.056961523517 & -52.056961523517 \tabularnewline
107 & 640 & 679.77991204438 & -39.77991204438 \tabularnewline
108 & 1110 & 1108.74774699117 & 1.25225300882971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296433&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]1000[/C][C]1008.20245726496[/C][C]-8.20245726495773[/C][/ROW]
[ROW][C]14[/C][C]1000[/C][C]1010.70704334199[/C][C]-10.7070433419888[/C][/ROW]
[ROW][C]15[/C][C]1080[/C][C]1088.11787261142[/C][C]-8.11787261142376[/C][/ROW]
[ROW][C]16[/C][C]1010[/C][C]1016.39766127359[/C][C]-6.39766127359167[/C][/ROW]
[ROW][C]17[/C][C]960[/C][C]967.197911039401[/C][C]-7.19791103940145[/C][/ROW]
[ROW][C]18[/C][C]990[/C][C]998.372804553129[/C][C]-8.37280455312862[/C][/ROW]
[ROW][C]19[/C][C]900[/C][C]976.993013933383[/C][C]-76.9930139333833[/C][/ROW]
[ROW][C]20[/C][C]920[/C][C]924.569040667881[/C][C]-4.56904066788081[/C][/ROW]
[ROW][C]21[/C][C]1080[/C][C]1030.93578181784[/C][C]49.0642181821627[/C][/ROW]
[ROW][C]22[/C][C]950[/C][C]967.901143575565[/C][C]-17.9011435755649[/C][/ROW]
[ROW][C]23[/C][C]950[/C][C]959.467122377757[/C][C]-9.46712237775716[/C][/ROW]
[ROW][C]24[/C][C]1060[/C][C]1089.53671924049[/C][C]-29.5367192404913[/C][/ROW]
[ROW][C]25[/C][C]1070[/C][C]971.860670876942[/C][C]98.1393291230582[/C][/ROW]
[ROW][C]26[/C][C]970[/C][C]974.346226054482[/C][C]-4.3462260544818[/C][/ROW]
[ROW][C]27[/C][C]1070[/C][C]1054.35380856209[/C][C]15.6461914379142[/C][/ROW]
[ROW][C]28[/C][C]980[/C][C]984.871759029278[/C][C]-4.87175902927765[/C][/ROW]
[ROW][C]29[/C][C]970[/C][C]934.925769355594[/C][C]35.0742306444065[/C][/ROW]
[ROW][C]30[/C][C]1050[/C][C]966.09253557598[/C][C]83.9074644240202[/C][/ROW]
[ROW][C]31[/C][C]950[/C][C]880.346733925226[/C][C]69.6532660747743[/C][/ROW]
[ROW][C]32[/C][C]960[/C][C]903.008546808341[/C][C]56.991453191659[/C][/ROW]
[ROW][C]33[/C][C]1170[/C][C]1064.29077792162[/C][C]105.709222078382[/C][/ROW]
[ROW][C]34[/C][C]990[/C][C]938.504501995172[/C][C]51.4954980048281[/C][/ROW]
[ROW][C]35[/C][C]870[/C][C]941.450399369432[/C][C]-71.4503993694323[/C][/ROW]
[ROW][C]36[/C][C]1090[/C][C]1051.75224883029[/C][C]38.2477511697132[/C][/ROW]
[ROW][C]37[/C][C]1070[/C][C]1061.84320727469[/C][C]8.1567927253061[/C][/ROW]
[ROW][C]38[/C][C]990[/C][C]963.367969199933[/C][C]26.6320308000671[/C][/ROW]
[ROW][C]39[/C][C]1080[/C][C]1064.95562749601[/C][C]15.0443725039868[/C][/ROW]
[ROW][C]40[/C][C]890[/C][C]976.753692916869[/C][C]-86.7536929168692[/C][/ROW]
[ROW][C]41[/C][C]920[/C][C]964.920004555699[/C][C]-44.9200045556994[/C][/ROW]
[ROW][C]42[/C][C]1100[/C][C]1042.6643268278[/C][C]57.335673172201[/C][/ROW]
[ROW][C]43[/C][C]930[/C][C]943.093937942077[/C][C]-13.0939379420768[/C][/ROW]
[ROW][C]44[/C][C]950[/C][C]951.885680388177[/C][C]-1.88568038817675[/C][/ROW]
[ROW][C]45[/C][C]1240[/C][C]1159.59748256022[/C][C]80.4025174397839[/C][/ROW]
[ROW][C]46[/C][C]950[/C][C]980.473953297362[/C][C]-30.4739532973624[/C][/ROW]
[ROW][C]47[/C][C]830[/C][C]861.375514936213[/C][C]-31.375514936213[/C][/ROW]
[ROW][C]48[/C][C]1220[/C][C]1079.77544959851[/C][C]140.224550401492[/C][/ROW]
[ROW][C]49[/C][C]1040[/C][C]1063.29665768256[/C][C]-23.2966576825579[/C][/ROW]
[ROW][C]50[/C][C]1080[/C][C]982.39016573332[/C][C]97.6098342666795[/C][/ROW]
[ROW][C]51[/C][C]1160[/C][C]1074.8606619959[/C][C]85.1393380040972[/C][/ROW]
[ROW][C]52[/C][C]900[/C][C]889.678981927346[/C][C]10.3210180726536[/C][/ROW]
[ROW][C]53[/C][C]790[/C][C]922.033876439329[/C][C]-132.033876439329[/C][/ROW]
[ROW][C]54[/C][C]1100[/C][C]1098.29451111177[/C][C]1.70548888823487[/C][/ROW]
[ROW][C]55[/C][C]1000[/C][C]929.231812921375[/C][C]70.7681870786247[/C][/ROW]
[ROW][C]56[/C][C]990[/C][C]951.812605390847[/C][C]38.1873946091533[/C][/ROW]
[ROW][C]57[/C][C]1250[/C][C]1241.7902572214[/C][C]8.20974277859659[/C][/ROW]
[ROW][C]58[/C][C]970[/C][C]953.460746708182[/C][C]16.539253291818[/C][/ROW]
[ROW][C]59[/C][C]840[/C][C]835.500915310293[/C][C]4.49908468970716[/C][/ROW]
[ROW][C]60[/C][C]1220[/C][C]1223.28940032533[/C][C]-3.28940032532955[/C][/ROW]
[ROW][C]61[/C][C]1100[/C][C]1044.32214365764[/C][C]55.6778563423641[/C][/ROW]
[ROW][C]62[/C][C]1030[/C][C]1084.13450547515[/C][C]-54.1345054751482[/C][/ROW]
[ROW][C]63[/C][C]1210[/C][C]1161.14763933522[/C][C]48.8523606647764[/C][/ROW]
[ROW][C]64[/C][C]830[/C][C]902.272403135157[/C][C]-72.2724031351571[/C][/ROW]
[ROW][C]65[/C][C]810[/C][C]793.63807254935[/C][C]16.3619274506502[/C][/ROW]
[ROW][C]66[/C][C]1100[/C][C]1104.40540363071[/C][C]-4.40540363071068[/C][/ROW]
[ROW][C]67[/C][C]1020[/C][C]1003.017380762[/C][C]16.9826192379991[/C][/ROW]
[ROW][C]68[/C][C]950[/C][C]992.740705530676[/C][C]-42.7407055306763[/C][/ROW]
[ROW][C]69[/C][C]1280[/C][C]1251.49823736692[/C][C]28.5017626330809[/C][/ROW]
[ROW][C]70[/C][C]950[/C][C]971.816439125394[/C][C]-21.8164391253937[/C][/ROW]
[ROW][C]71[/C][C]720[/C][C]841.101989884234[/C][C]-121.101989884234[/C][/ROW]
[ROW][C]72[/C][C]1150[/C][C]1217.81080326735[/C][C]-67.8108032673517[/C][/ROW]
[ROW][C]73[/C][C]1030[/C][C]1094.17852732912[/C][C]-64.1785273291193[/C][/ROW]
[ROW][C]74[/C][C]1030[/C][C]1022.8606343087[/C][C]7.13936569130135[/C][/ROW]
[ROW][C]75[/C][C]1200[/C][C]1200.98552630516[/C][C]-0.985526305155418[/C][/ROW]
[ROW][C]76[/C][C]870[/C][C]821.63792147904[/C][C]48.3620785209598[/C][/ROW]
[ROW][C]77[/C][C]880[/C][C]801.741624608582[/C][C]78.2583753914182[/C][/ROW]
[ROW][C]78[/C][C]1090[/C][C]1093.24767109661[/C][C]-3.24767109661434[/C][/ROW]
[ROW][C]79[/C][C]950[/C][C]1012.31097016266[/C][C]-62.310970162663[/C][/ROW]
[ROW][C]80[/C][C]1060[/C][C]941.136634984992[/C][C]118.863365015008[/C][/ROW]
[ROW][C]81[/C][C]1280[/C][C]1273.09237201596[/C][C]6.90762798404421[/C][/ROW]
[ROW][C]82[/C][C]920[/C][C]943.513604024891[/C][C]-23.5136040248913[/C][/ROW]
[ROW][C]83[/C][C]630[/C][C]715.566756570673[/C][C]-85.5667565706733[/C][/ROW]
[ROW][C]84[/C][C]1110[/C][C]1144.9909689113[/C][C]-34.9909689112951[/C][/ROW]
[ROW][C]85[/C][C]1020[/C][C]1025.63617979955[/C][C]-5.6361797995537[/C][/ROW]
[ROW][C]86[/C][C]1130[/C][C]1025.47069209908[/C][C]104.529307900916[/C][/ROW]
[ROW][C]87[/C][C]1160[/C][C]1198.42886021945[/C][C]-38.4288602194547[/C][/ROW]
[ROW][C]88[/C][C]930[/C][C]866.695073583586[/C][C]63.3049264164137[/C][/ROW]
[ROW][C]89[/C][C]930[/C][C]876.717060192668[/C][C]53.2829398073319[/C][/ROW]
[ROW][C]90[/C][C]1110[/C][C]1088.35888579351[/C][C]21.6411142064858[/C][/ROW]
[ROW][C]91[/C][C]930[/C][C]950.732208862437[/C][C]-20.7322088624368[/C][/ROW]
[ROW][C]92[/C][C]1070[/C][C]1057.92321883115[/C][C]12.0767811688547[/C][/ROW]
[ROW][C]93[/C][C]1250[/C][C]1278.21504476019[/C][C]-28.2150447601923[/C][/ROW]
[ROW][C]94[/C][C]840[/C][C]918.15997396711[/C][C]-78.1599739671102[/C][/ROW]
[ROW][C]95[/C][C]680[/C][C]628.218208331717[/C][C]51.7817916682834[/C][/ROW]
[ROW][C]96[/C][C]1110[/C][C]1110.60227783838[/C][C]-0.602277838375812[/C][/ROW]
[ROW][C]97[/C][C]990[/C][C]1021.15276007484[/C][C]-31.152760074844[/C][/ROW]
[ROW][C]98[/C][C]1210[/C][C]1128.27600874576[/C][C]81.7239912542404[/C][/ROW]
[ROW][C]99[/C][C]1130[/C][C]1161.40922139496[/C][C]-31.4092213949575[/C][/ROW]
[ROW][C]100[/C][C]920[/C][C]929.456105867956[/C][C]-9.45610586795624[/C][/ROW]
[ROW][C]101[/C][C]1030[/C][C]928.030784761379[/C][C]101.969215238621[/C][/ROW]
[ROW][C]102[/C][C]1120[/C][C]1110.16262220782[/C][C]9.83737779217608[/C][/ROW]
[ROW][C]103[/C][C]880[/C][C]931.073672851813[/C][C]-51.0736728518126[/C][/ROW]
[ROW][C]104[/C][C]1050[/C][C]1069.65946738748[/C][C]-19.6594673874779[/C][/ROW]
[ROW][C]105[/C][C]1260[/C][C]1249.84877913587[/C][C]10.1512208641338[/C][/ROW]
[ROW][C]106[/C][C]790[/C][C]842.056961523517[/C][C]-52.056961523517[/C][/ROW]
[ROW][C]107[/C][C]640[/C][C]679.77991204438[/C][C]-39.77991204438[/C][/ROW]
[ROW][C]108[/C][C]1110[/C][C]1108.74774699117[/C][C]1.25225300882971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296433&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296433&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
1310001008.20245726496-8.20245726495773
1410001010.70704334199-10.7070433419888
1510801088.11787261142-8.11787261142376
1610101016.39766127359-6.39766127359167
17960967.197911039401-7.19791103940145
18990998.372804553129-8.37280455312862
19900976.993013933383-76.9930139333833
20920924.569040667881-4.56904066788081
2110801030.9357818178449.0642181821627
22950967.901143575565-17.9011435755649
23950959.467122377757-9.46712237775716
2410601089.53671924049-29.5367192404913
251070971.86067087694298.1393291230582
26970974.346226054482-4.3462260544818
2710701054.3538085620915.6461914379142
28980984.871759029278-4.87175902927765
29970934.92576935559435.0742306444065
301050966.0925355759883.9074644240202
31950880.34673392522669.6532660747743
32960903.00854680834156.991453191659
3311701064.29077792162105.709222078382
34990938.50450199517251.4954980048281
35870941.450399369432-71.4503993694323
3610901051.7522488302938.2477511697132
3710701061.843207274698.1567927253061
38990963.36796919993326.6320308000671
3910801064.9556274960115.0443725039868
40890976.753692916869-86.7536929168692
41920964.920004555699-44.9200045556994
4211001042.664326827857.335673172201
43930943.093937942077-13.0939379420768
44950951.885680388177-1.88568038817675
4512401159.5974825602280.4025174397839
46950980.473953297362-30.4739532973624
47830861.375514936213-31.375514936213
4812201079.77544959851140.224550401492
4910401063.29665768256-23.2966576825579
501080982.3901657333297.6098342666795
5111601074.860661995985.1393380040972
52900889.67898192734610.3210180726536
53790922.033876439329-132.033876439329
5411001098.294511111771.70548888823487
551000929.23181292137570.7681870786247
56990951.81260539084738.1873946091533
5712501241.79025722148.20974277859659
58970953.46074670818216.539253291818
59840835.5009153102934.49908468970716
6012201223.28940032533-3.28940032532955
6111001044.3221436576455.6778563423641
6210301084.13450547515-54.1345054751482
6312101161.1476393352248.8523606647764
64830902.272403135157-72.2724031351571
65810793.6380725493516.3619274506502
6611001104.40540363071-4.40540363071068
6710201003.01738076216.9826192379991
68950992.740705530676-42.7407055306763
6912801251.4982373669228.5017626330809
70950971.816439125394-21.8164391253937
71720841.101989884234-121.101989884234
7211501217.81080326735-67.8108032673517
7310301094.17852732912-64.1785273291193
7410301022.86063430877.13936569130135
7512001200.98552630516-0.985526305155418
76870821.6379214790448.3620785209598
77880801.74162460858278.2583753914182
7810901093.24767109661-3.24767109661434
799501012.31097016266-62.310970162663
801060941.136634984992118.863365015008
8112801273.092372015966.90762798404421
82920943.513604024891-23.5136040248913
83630715.566756570673-85.5667565706733
8411101144.9909689113-34.9909689112951
8510201025.63617979955-5.6361797995537
8611301025.47069209908104.529307900916
8711601198.42886021945-38.4288602194547
88930866.69507358358663.3049264164137
89930876.71706019266853.2829398073319
9011101088.3588857935121.6411142064858
91930950.732208862437-20.7322088624368
9210701057.9232188311512.0767811688547
9312501278.21504476019-28.2150447601923
94840918.15997396711-78.1599739671102
95680628.21820833171751.7817916682834
9611101110.60227783838-0.602277838375812
979901021.15276007484-31.152760074844
9812101128.2760087457681.7239912542404
9911301161.40922139496-31.4092213949575
100920929.456105867956-9.45610586795624
1011030928.030784761379101.969215238621
10211201110.162622207829.83737779217608
103880931.073672851813-51.0736728518126
10410501069.65946738748-19.6594673874779
10512601249.8487791358710.1512208641338
106790842.056961523517-52.056961523517
107640679.77991204438-39.77991204438
10811101108.747746991171.25225300882971







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109989.423481386822884.7835445979641094.06341817568
1101207.485170681691102.80718099711312.16316036628
1111127.975663750931023.250091795951232.7012357059
112918.044537920282813.2608007284131022.82827511215
1131025.49433423132920.6408005843851130.34786787825
1141114.808918653271009.872915516081219.74492179045
115875.540317507125770.508137645814980.572497368436
1161045.68797121933940.5448820867961150.83106035187
1171255.189643448181149.919897413551360.45938948281
118786.137968510408680.724814501725891.551122519092
119636.960701699339531.386398320306742.535005078373
1201106.934928383841001.180758556011212.68909821167

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 989.423481386822 & 884.783544597964 & 1094.06341817568 \tabularnewline
110 & 1207.48517068169 & 1102.8071809971 & 1312.16316036628 \tabularnewline
111 & 1127.97566375093 & 1023.25009179595 & 1232.7012357059 \tabularnewline
112 & 918.044537920282 & 813.260800728413 & 1022.82827511215 \tabularnewline
113 & 1025.49433423132 & 920.640800584385 & 1130.34786787825 \tabularnewline
114 & 1114.80891865327 & 1009.87291551608 & 1219.74492179045 \tabularnewline
115 & 875.540317507125 & 770.508137645814 & 980.572497368436 \tabularnewline
116 & 1045.68797121933 & 940.544882086796 & 1150.83106035187 \tabularnewline
117 & 1255.18964344818 & 1149.91989741355 & 1360.45938948281 \tabularnewline
118 & 786.137968510408 & 680.724814501725 & 891.551122519092 \tabularnewline
119 & 636.960701699339 & 531.386398320306 & 742.535005078373 \tabularnewline
120 & 1106.93492838384 & 1001.18075855601 & 1212.68909821167 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296433&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]989.423481386822[/C][C]884.783544597964[/C][C]1094.06341817568[/C][/ROW]
[ROW][C]110[/C][C]1207.48517068169[/C][C]1102.8071809971[/C][C]1312.16316036628[/C][/ROW]
[ROW][C]111[/C][C]1127.97566375093[/C][C]1023.25009179595[/C][C]1232.7012357059[/C][/ROW]
[ROW][C]112[/C][C]918.044537920282[/C][C]813.260800728413[/C][C]1022.82827511215[/C][/ROW]
[ROW][C]113[/C][C]1025.49433423132[/C][C]920.640800584385[/C][C]1130.34786787825[/C][/ROW]
[ROW][C]114[/C][C]1114.80891865327[/C][C]1009.87291551608[/C][C]1219.74492179045[/C][/ROW]
[ROW][C]115[/C][C]875.540317507125[/C][C]770.508137645814[/C][C]980.572497368436[/C][/ROW]
[ROW][C]116[/C][C]1045.68797121933[/C][C]940.544882086796[/C][C]1150.83106035187[/C][/ROW]
[ROW][C]117[/C][C]1255.18964344818[/C][C]1149.91989741355[/C][C]1360.45938948281[/C][/ROW]
[ROW][C]118[/C][C]786.137968510408[/C][C]680.724814501725[/C][C]891.551122519092[/C][/ROW]
[ROW][C]119[/C][C]636.960701699339[/C][C]531.386398320306[/C][C]742.535005078373[/C][/ROW]
[ROW][C]120[/C][C]1106.93492838384[/C][C]1001.18075855601[/C][C]1212.68909821167[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296433&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296433&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
109989.423481386822884.7835445979641094.06341817568
1101207.485170681691102.80718099711312.16316036628
1111127.975663750931023.250091795951232.7012357059
112918.044537920282813.2608007284131022.82827511215
1131025.49433423132920.6408005843851130.34786787825
1141114.808918653271009.872915516081219.74492179045
115875.540317507125770.508137645814980.572497368436
1161045.68797121933940.5448820867961150.83106035187
1171255.189643448181149.919897413551360.45938948281
118786.137968510408680.724814501725891.551122519092
119636.960701699339531.386398320306742.535005078373
1201106.934928383841001.180758556011212.68909821167



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