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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 15 Aug 2011 13:47:36 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/15/t1313430512k7yddhd1789wl4h.htm/, Retrieved Mon, 13 May 2024 23:45:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123806, Retrieved Mon, 13 May 2024 23:45:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPost Stephan
Estimated Impact136
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B - Sta...] [2011-08-15 17:47:36] [aa66f9be79898bb84b94c54cf72e0d05] [Current]
- R PD    [Exponential Smoothing] [Tijdreeks B stap 27] [2011-08-18 09:17:38] [74be16979710d4c4e7c6647856088456]
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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'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123806&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123806&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123806&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0237763572074504
beta0.134368823669101
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0237763572074504 \tabularnewline
beta & 0.134368823669101 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123806&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]0.0237763572074504[/C][/ROW]
[ROW][C]beta[/C][C]0.134368823669101[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123806&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123806&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
alpha0.0237763572074504
beta0.134368823669101
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310001008.20245726496-8.20245726495762
1410001010.70704334197-10.7070433419674
1510801088.11787261138-8.11787261138102
1610101016.39766127354-6.39766127354233
17960967.197911039356-7.19791103935609
18990998.37280455309-8.37280455308962
19900976.993013933353-76.9930139333527
20920924.569040667687-4.56904066768686
2110801030.9357818177349.0642181822739
22950967.901143575677-17.9011435756769
23950959.467122377879-9.4671223778788
2410601089.53671924066-29.5367192406563
251070971.8606708771398.1393291228693
26970974.346226055047-4.34622605504671
2710701054.3538085626615.6461914373353
28980984.871759029912-4.87175902991157
29970934.92576935621335.0742306437871
301050966.09253557668983.9074644233114
31950880.34673392634269.6532660736584
32960903.00854680945856.991453190542
3311701064.29077792247105.709222077527
34990938.50450199611351.4954980038868
35870941.4503993702-71.4503993702006
3610901051.7522488305938.2477511694101
3710701061.843207274448.15679272556372
38990963.3679691994426.6320308005602
3910801064.9556274952715.0443725047326
40890976.753692915912-86.753692915912
41920964.920004554131-44.9200045541313
4211001042.6643268256857.3356731743233
43930943.093937939835-13.0939379398352
44950951.885680385697-1.88568038569713
4512401159.5974825574380.4025174425728
46950980.473953294753-30.473953294753
47830861.375514933883-31.3755149338832
4812201079.77544959606140.224550403942
4910401063.29665768058-23.2966576805784
501080982.39016573122397.6098342687774
5111601074.8606619940785.139338005925
52900889.67898192602610.3210180739744
53790922.033876438037-132.033876438037
5411001098.294511109741.70548889025667
551000929.2318129193570.7681870806507
56990951.81260538894238.1873946110584
5712501241.79025721928.20974278079939
58970953.46074670600816.5392532939916
59840835.500915308154.49908469184982
6012201223.28940032258-3.28940032258333
6111001044.3221436549355.677856345073
6210301084.13450547222-54.1345054722153
6312101161.1476393318748.8523606681324
64830902.272403132016-72.2724031320158
65810793.63807254655316.3619274534469
6611001104.40540362798-4.40540362798492
6710201003.0173807590516.9826192409456
68950992.740705527736-42.7407055277363
6912801251.4982373639428.5017626360595
70950971.816439122573-21.8164391225735
71720841.101989881472-121.101989881472
7211501217.81080326442-67.8108032644216
7310301094.17852732605-64.1785273260532
7410301022.860634305957.13936569404655
7512001200.98552630257-0.985526302565404
76870821.63792147701148.3620785229886
77880801.74162460689178.2583753931085
7810901093.24767109538-3.24767109537584
799501012.31097016152-62.3109701615157
801060941.136634983986118.863365016014
8112801273.092372015336.90762798467085
82920943.513604024444-23.5136040244438
83630715.566756570622-85.5667565706221
8411101144.99096891121-34.9909689112133
8510201025.63617979956-5.63617979956098
8611301025.470692099104.529307901003
8711601198.42886021959-38.4288602195916
88930866.6950735833463.3049264166606
89930876.71706019227553.282939807725
9011101088.3588857932421.6411142067623
91930950.732208862347-20.7322088623465
9210701057.9232188304712.0767811695291
9312501278.21504475951-28.2150447595077
94840918.159973966413-78.1599739664126
95680628.21820833109551.7817916689054
9611101110.60227783799-0.60227783799337
979901021.15276007441-31.1527600744054
9812101128.2760087448281.7239912551804
9911301161.40922139439-31.4092213943948
100920929.456105867042-9.4561058670422
1011030928.030784760277101.969215239723
10211201110.162622206989.83737779301896
103880931.073672851073-51.073672851073
10410501069.65946738654-19.6594673865397
10512601249.8487791349910.1512208650063
106790842.056961522944-52.0569615229443
107640679.77991204345-39.7799120434502
10811101108.747746990181.25225300982402

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1000 & 1008.20245726496 & -8.20245726495762 \tabularnewline
14 & 1000 & 1010.70704334197 & -10.7070433419674 \tabularnewline
15 & 1080 & 1088.11787261138 & -8.11787261138102 \tabularnewline
16 & 1010 & 1016.39766127354 & -6.39766127354233 \tabularnewline
17 & 960 & 967.197911039356 & -7.19791103935609 \tabularnewline
18 & 990 & 998.37280455309 & -8.37280455308962 \tabularnewline
19 & 900 & 976.993013933353 & -76.9930139333527 \tabularnewline
20 & 920 & 924.569040667687 & -4.56904066768686 \tabularnewline
21 & 1080 & 1030.93578181773 & 49.0642181822739 \tabularnewline
22 & 950 & 967.901143575677 & -17.9011435756769 \tabularnewline
23 & 950 & 959.467122377879 & -9.4671223778788 \tabularnewline
24 & 1060 & 1089.53671924066 & -29.5367192406563 \tabularnewline
25 & 1070 & 971.86067087713 & 98.1393291228693 \tabularnewline
26 & 970 & 974.346226055047 & -4.34622605504671 \tabularnewline
27 & 1070 & 1054.35380856266 & 15.6461914373353 \tabularnewline
28 & 980 & 984.871759029912 & -4.87175902991157 \tabularnewline
29 & 970 & 934.925769356213 & 35.0742306437871 \tabularnewline
30 & 1050 & 966.092535576689 & 83.9074644233114 \tabularnewline
31 & 950 & 880.346733926342 & 69.6532660736584 \tabularnewline
32 & 960 & 903.008546809458 & 56.991453190542 \tabularnewline
33 & 1170 & 1064.29077792247 & 105.709222077527 \tabularnewline
34 & 990 & 938.504501996113 & 51.4954980038868 \tabularnewline
35 & 870 & 941.4503993702 & -71.4503993702006 \tabularnewline
36 & 1090 & 1051.75224883059 & 38.2477511694101 \tabularnewline
37 & 1070 & 1061.84320727444 & 8.15679272556372 \tabularnewline
38 & 990 & 963.36796919944 & 26.6320308005602 \tabularnewline
39 & 1080 & 1064.95562749527 & 15.0443725047326 \tabularnewline
40 & 890 & 976.753692915912 & -86.753692915912 \tabularnewline
41 & 920 & 964.920004554131 & -44.9200045541313 \tabularnewline
42 & 1100 & 1042.66432682568 & 57.3356731743233 \tabularnewline
43 & 930 & 943.093937939835 & -13.0939379398352 \tabularnewline
44 & 950 & 951.885680385697 & -1.88568038569713 \tabularnewline
45 & 1240 & 1159.59748255743 & 80.4025174425728 \tabularnewline
46 & 950 & 980.473953294753 & -30.473953294753 \tabularnewline
47 & 830 & 861.375514933883 & -31.3755149338832 \tabularnewline
48 & 1220 & 1079.77544959606 & 140.224550403942 \tabularnewline
49 & 1040 & 1063.29665768058 & -23.2966576805784 \tabularnewline
50 & 1080 & 982.390165731223 & 97.6098342687774 \tabularnewline
51 & 1160 & 1074.86066199407 & 85.139338005925 \tabularnewline
52 & 900 & 889.678981926026 & 10.3210180739744 \tabularnewline
53 & 790 & 922.033876438037 & -132.033876438037 \tabularnewline
54 & 1100 & 1098.29451110974 & 1.70548889025667 \tabularnewline
55 & 1000 & 929.23181291935 & 70.7681870806507 \tabularnewline
56 & 990 & 951.812605388942 & 38.1873946110584 \tabularnewline
57 & 1250 & 1241.7902572192 & 8.20974278079939 \tabularnewline
58 & 970 & 953.460746706008 & 16.5392532939916 \tabularnewline
59 & 840 & 835.50091530815 & 4.49908469184982 \tabularnewline
60 & 1220 & 1223.28940032258 & -3.28940032258333 \tabularnewline
61 & 1100 & 1044.32214365493 & 55.677856345073 \tabularnewline
62 & 1030 & 1084.13450547222 & -54.1345054722153 \tabularnewline
63 & 1210 & 1161.14763933187 & 48.8523606681324 \tabularnewline
64 & 830 & 902.272403132016 & -72.2724031320158 \tabularnewline
65 & 810 & 793.638072546553 & 16.3619274534469 \tabularnewline
66 & 1100 & 1104.40540362798 & -4.40540362798492 \tabularnewline
67 & 1020 & 1003.01738075905 & 16.9826192409456 \tabularnewline
68 & 950 & 992.740705527736 & -42.7407055277363 \tabularnewline
69 & 1280 & 1251.49823736394 & 28.5017626360595 \tabularnewline
70 & 950 & 971.816439122573 & -21.8164391225735 \tabularnewline
71 & 720 & 841.101989881472 & -121.101989881472 \tabularnewline
72 & 1150 & 1217.81080326442 & -67.8108032644216 \tabularnewline
73 & 1030 & 1094.17852732605 & -64.1785273260532 \tabularnewline
74 & 1030 & 1022.86063430595 & 7.13936569404655 \tabularnewline
75 & 1200 & 1200.98552630257 & -0.985526302565404 \tabularnewline
76 & 870 & 821.637921477011 & 48.3620785229886 \tabularnewline
77 & 880 & 801.741624606891 & 78.2583753931085 \tabularnewline
78 & 1090 & 1093.24767109538 & -3.24767109537584 \tabularnewline
79 & 950 & 1012.31097016152 & -62.3109701615157 \tabularnewline
80 & 1060 & 941.136634983986 & 118.863365016014 \tabularnewline
81 & 1280 & 1273.09237201533 & 6.90762798467085 \tabularnewline
82 & 920 & 943.513604024444 & -23.5136040244438 \tabularnewline
83 & 630 & 715.566756570622 & -85.5667565706221 \tabularnewline
84 & 1110 & 1144.99096891121 & -34.9909689112133 \tabularnewline
85 & 1020 & 1025.63617979956 & -5.63617979956098 \tabularnewline
86 & 1130 & 1025.470692099 & 104.529307901003 \tabularnewline
87 & 1160 & 1198.42886021959 & -38.4288602195916 \tabularnewline
88 & 930 & 866.69507358334 & 63.3049264166606 \tabularnewline
89 & 930 & 876.717060192275 & 53.282939807725 \tabularnewline
90 & 1110 & 1088.35888579324 & 21.6411142067623 \tabularnewline
91 & 930 & 950.732208862347 & -20.7322088623465 \tabularnewline
92 & 1070 & 1057.92321883047 & 12.0767811695291 \tabularnewline
93 & 1250 & 1278.21504475951 & -28.2150447595077 \tabularnewline
94 & 840 & 918.159973966413 & -78.1599739664126 \tabularnewline
95 & 680 & 628.218208331095 & 51.7817916689054 \tabularnewline
96 & 1110 & 1110.60227783799 & -0.60227783799337 \tabularnewline
97 & 990 & 1021.15276007441 & -31.1527600744054 \tabularnewline
98 & 1210 & 1128.27600874482 & 81.7239912551804 \tabularnewline
99 & 1130 & 1161.40922139439 & -31.4092213943948 \tabularnewline
100 & 920 & 929.456105867042 & -9.4561058670422 \tabularnewline
101 & 1030 & 928.030784760277 & 101.969215239723 \tabularnewline
102 & 1120 & 1110.16262220698 & 9.83737779301896 \tabularnewline
103 & 880 & 931.073672851073 & -51.073672851073 \tabularnewline
104 & 1050 & 1069.65946738654 & -19.6594673865397 \tabularnewline
105 & 1260 & 1249.84877913499 & 10.1512208650063 \tabularnewline
106 & 790 & 842.056961522944 & -52.0569615229443 \tabularnewline
107 & 640 & 679.77991204345 & -39.7799120434502 \tabularnewline
108 & 1110 & 1108.74774699018 & 1.25225300982402 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123806&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]-8.20245726495762[/C][/ROW]
[ROW][C]14[/C][C]1000[/C][C]1010.70704334197[/C][C]-10.7070433419674[/C][/ROW]
[ROW][C]15[/C][C]1080[/C][C]1088.11787261138[/C][C]-8.11787261138102[/C][/ROW]
[ROW][C]16[/C][C]1010[/C][C]1016.39766127354[/C][C]-6.39766127354233[/C][/ROW]
[ROW][C]17[/C][C]960[/C][C]967.197911039356[/C][C]-7.19791103935609[/C][/ROW]
[ROW][C]18[/C][C]990[/C][C]998.37280455309[/C][C]-8.37280455308962[/C][/ROW]
[ROW][C]19[/C][C]900[/C][C]976.993013933353[/C][C]-76.9930139333527[/C][/ROW]
[ROW][C]20[/C][C]920[/C][C]924.569040667687[/C][C]-4.56904066768686[/C][/ROW]
[ROW][C]21[/C][C]1080[/C][C]1030.93578181773[/C][C]49.0642181822739[/C][/ROW]
[ROW][C]22[/C][C]950[/C][C]967.901143575677[/C][C]-17.9011435756769[/C][/ROW]
[ROW][C]23[/C][C]950[/C][C]959.467122377879[/C][C]-9.4671223778788[/C][/ROW]
[ROW][C]24[/C][C]1060[/C][C]1089.53671924066[/C][C]-29.5367192406563[/C][/ROW]
[ROW][C]25[/C][C]1070[/C][C]971.86067087713[/C][C]98.1393291228693[/C][/ROW]
[ROW][C]26[/C][C]970[/C][C]974.346226055047[/C][C]-4.34622605504671[/C][/ROW]
[ROW][C]27[/C][C]1070[/C][C]1054.35380856266[/C][C]15.6461914373353[/C][/ROW]
[ROW][C]28[/C][C]980[/C][C]984.871759029912[/C][C]-4.87175902991157[/C][/ROW]
[ROW][C]29[/C][C]970[/C][C]934.925769356213[/C][C]35.0742306437871[/C][/ROW]
[ROW][C]30[/C][C]1050[/C][C]966.092535576689[/C][C]83.9074644233114[/C][/ROW]
[ROW][C]31[/C][C]950[/C][C]880.346733926342[/C][C]69.6532660736584[/C][/ROW]
[ROW][C]32[/C][C]960[/C][C]903.008546809458[/C][C]56.991453190542[/C][/ROW]
[ROW][C]33[/C][C]1170[/C][C]1064.29077792247[/C][C]105.709222077527[/C][/ROW]
[ROW][C]34[/C][C]990[/C][C]938.504501996113[/C][C]51.4954980038868[/C][/ROW]
[ROW][C]35[/C][C]870[/C][C]941.4503993702[/C][C]-71.4503993702006[/C][/ROW]
[ROW][C]36[/C][C]1090[/C][C]1051.75224883059[/C][C]38.2477511694101[/C][/ROW]
[ROW][C]37[/C][C]1070[/C][C]1061.84320727444[/C][C]8.15679272556372[/C][/ROW]
[ROW][C]38[/C][C]990[/C][C]963.36796919944[/C][C]26.6320308005602[/C][/ROW]
[ROW][C]39[/C][C]1080[/C][C]1064.95562749527[/C][C]15.0443725047326[/C][/ROW]
[ROW][C]40[/C][C]890[/C][C]976.753692915912[/C][C]-86.753692915912[/C][/ROW]
[ROW][C]41[/C][C]920[/C][C]964.920004554131[/C][C]-44.9200045541313[/C][/ROW]
[ROW][C]42[/C][C]1100[/C][C]1042.66432682568[/C][C]57.3356731743233[/C][/ROW]
[ROW][C]43[/C][C]930[/C][C]943.093937939835[/C][C]-13.0939379398352[/C][/ROW]
[ROW][C]44[/C][C]950[/C][C]951.885680385697[/C][C]-1.88568038569713[/C][/ROW]
[ROW][C]45[/C][C]1240[/C][C]1159.59748255743[/C][C]80.4025174425728[/C][/ROW]
[ROW][C]46[/C][C]950[/C][C]980.473953294753[/C][C]-30.473953294753[/C][/ROW]
[ROW][C]47[/C][C]830[/C][C]861.375514933883[/C][C]-31.3755149338832[/C][/ROW]
[ROW][C]48[/C][C]1220[/C][C]1079.77544959606[/C][C]140.224550403942[/C][/ROW]
[ROW][C]49[/C][C]1040[/C][C]1063.29665768058[/C][C]-23.2966576805784[/C][/ROW]
[ROW][C]50[/C][C]1080[/C][C]982.390165731223[/C][C]97.6098342687774[/C][/ROW]
[ROW][C]51[/C][C]1160[/C][C]1074.86066199407[/C][C]85.139338005925[/C][/ROW]
[ROW][C]52[/C][C]900[/C][C]889.678981926026[/C][C]10.3210180739744[/C][/ROW]
[ROW][C]53[/C][C]790[/C][C]922.033876438037[/C][C]-132.033876438037[/C][/ROW]
[ROW][C]54[/C][C]1100[/C][C]1098.29451110974[/C][C]1.70548889025667[/C][/ROW]
[ROW][C]55[/C][C]1000[/C][C]929.23181291935[/C][C]70.7681870806507[/C][/ROW]
[ROW][C]56[/C][C]990[/C][C]951.812605388942[/C][C]38.1873946110584[/C][/ROW]
[ROW][C]57[/C][C]1250[/C][C]1241.7902572192[/C][C]8.20974278079939[/C][/ROW]
[ROW][C]58[/C][C]970[/C][C]953.460746706008[/C][C]16.5392532939916[/C][/ROW]
[ROW][C]59[/C][C]840[/C][C]835.50091530815[/C][C]4.49908469184982[/C][/ROW]
[ROW][C]60[/C][C]1220[/C][C]1223.28940032258[/C][C]-3.28940032258333[/C][/ROW]
[ROW][C]61[/C][C]1100[/C][C]1044.32214365493[/C][C]55.677856345073[/C][/ROW]
[ROW][C]62[/C][C]1030[/C][C]1084.13450547222[/C][C]-54.1345054722153[/C][/ROW]
[ROW][C]63[/C][C]1210[/C][C]1161.14763933187[/C][C]48.8523606681324[/C][/ROW]
[ROW][C]64[/C][C]830[/C][C]902.272403132016[/C][C]-72.2724031320158[/C][/ROW]
[ROW][C]65[/C][C]810[/C][C]793.638072546553[/C][C]16.3619274534469[/C][/ROW]
[ROW][C]66[/C][C]1100[/C][C]1104.40540362798[/C][C]-4.40540362798492[/C][/ROW]
[ROW][C]67[/C][C]1020[/C][C]1003.01738075905[/C][C]16.9826192409456[/C][/ROW]
[ROW][C]68[/C][C]950[/C][C]992.740705527736[/C][C]-42.7407055277363[/C][/ROW]
[ROW][C]69[/C][C]1280[/C][C]1251.49823736394[/C][C]28.5017626360595[/C][/ROW]
[ROW][C]70[/C][C]950[/C][C]971.816439122573[/C][C]-21.8164391225735[/C][/ROW]
[ROW][C]71[/C][C]720[/C][C]841.101989881472[/C][C]-121.101989881472[/C][/ROW]
[ROW][C]72[/C][C]1150[/C][C]1217.81080326442[/C][C]-67.8108032644216[/C][/ROW]
[ROW][C]73[/C][C]1030[/C][C]1094.17852732605[/C][C]-64.1785273260532[/C][/ROW]
[ROW][C]74[/C][C]1030[/C][C]1022.86063430595[/C][C]7.13936569404655[/C][/ROW]
[ROW][C]75[/C][C]1200[/C][C]1200.98552630257[/C][C]-0.985526302565404[/C][/ROW]
[ROW][C]76[/C][C]870[/C][C]821.637921477011[/C][C]48.3620785229886[/C][/ROW]
[ROW][C]77[/C][C]880[/C][C]801.741624606891[/C][C]78.2583753931085[/C][/ROW]
[ROW][C]78[/C][C]1090[/C][C]1093.24767109538[/C][C]-3.24767109537584[/C][/ROW]
[ROW][C]79[/C][C]950[/C][C]1012.31097016152[/C][C]-62.3109701615157[/C][/ROW]
[ROW][C]80[/C][C]1060[/C][C]941.136634983986[/C][C]118.863365016014[/C][/ROW]
[ROW][C]81[/C][C]1280[/C][C]1273.09237201533[/C][C]6.90762798467085[/C][/ROW]
[ROW][C]82[/C][C]920[/C][C]943.513604024444[/C][C]-23.5136040244438[/C][/ROW]
[ROW][C]83[/C][C]630[/C][C]715.566756570622[/C][C]-85.5667565706221[/C][/ROW]
[ROW][C]84[/C][C]1110[/C][C]1144.99096891121[/C][C]-34.9909689112133[/C][/ROW]
[ROW][C]85[/C][C]1020[/C][C]1025.63617979956[/C][C]-5.63617979956098[/C][/ROW]
[ROW][C]86[/C][C]1130[/C][C]1025.470692099[/C][C]104.529307901003[/C][/ROW]
[ROW][C]87[/C][C]1160[/C][C]1198.42886021959[/C][C]-38.4288602195916[/C][/ROW]
[ROW][C]88[/C][C]930[/C][C]866.69507358334[/C][C]63.3049264166606[/C][/ROW]
[ROW][C]89[/C][C]930[/C][C]876.717060192275[/C][C]53.282939807725[/C][/ROW]
[ROW][C]90[/C][C]1110[/C][C]1088.35888579324[/C][C]21.6411142067623[/C][/ROW]
[ROW][C]91[/C][C]930[/C][C]950.732208862347[/C][C]-20.7322088623465[/C][/ROW]
[ROW][C]92[/C][C]1070[/C][C]1057.92321883047[/C][C]12.0767811695291[/C][/ROW]
[ROW][C]93[/C][C]1250[/C][C]1278.21504475951[/C][C]-28.2150447595077[/C][/ROW]
[ROW][C]94[/C][C]840[/C][C]918.159973966413[/C][C]-78.1599739664126[/C][/ROW]
[ROW][C]95[/C][C]680[/C][C]628.218208331095[/C][C]51.7817916689054[/C][/ROW]
[ROW][C]96[/C][C]1110[/C][C]1110.60227783799[/C][C]-0.60227783799337[/C][/ROW]
[ROW][C]97[/C][C]990[/C][C]1021.15276007441[/C][C]-31.1527600744054[/C][/ROW]
[ROW][C]98[/C][C]1210[/C][C]1128.27600874482[/C][C]81.7239912551804[/C][/ROW]
[ROW][C]99[/C][C]1130[/C][C]1161.40922139439[/C][C]-31.4092213943948[/C][/ROW]
[ROW][C]100[/C][C]920[/C][C]929.456105867042[/C][C]-9.4561058670422[/C][/ROW]
[ROW][C]101[/C][C]1030[/C][C]928.030784760277[/C][C]101.969215239723[/C][/ROW]
[ROW][C]102[/C][C]1120[/C][C]1110.16262220698[/C][C]9.83737779301896[/C][/ROW]
[ROW][C]103[/C][C]880[/C][C]931.073672851073[/C][C]-51.073672851073[/C][/ROW]
[ROW][C]104[/C][C]1050[/C][C]1069.65946738654[/C][C]-19.6594673865397[/C][/ROW]
[ROW][C]105[/C][C]1260[/C][C]1249.84877913499[/C][C]10.1512208650063[/C][/ROW]
[ROW][C]106[/C][C]790[/C][C]842.056961522944[/C][C]-52.0569615229443[/C][/ROW]
[ROW][C]107[/C][C]640[/C][C]679.77991204345[/C][C]-39.7799120434502[/C][/ROW]
[ROW][C]108[/C][C]1110[/C][C]1108.74774699018[/C][C]1.25225300982402[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123806&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123806&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
1310001008.20245726496-8.20245726495762
1410001010.70704334197-10.7070433419674
1510801088.11787261138-8.11787261138102
1610101016.39766127354-6.39766127354233
17960967.197911039356-7.19791103935609
18990998.37280455309-8.37280455308962
19900976.993013933353-76.9930139333527
20920924.569040667687-4.56904066768686
2110801030.9357818177349.0642181822739
22950967.901143575677-17.9011435756769
23950959.467122377879-9.4671223778788
2410601089.53671924066-29.5367192406563
251070971.8606708771398.1393291228693
26970974.346226055047-4.34622605504671
2710701054.3538085626615.6461914373353
28980984.871759029912-4.87175902991157
29970934.92576935621335.0742306437871
301050966.09253557668983.9074644233114
31950880.34673392634269.6532660736584
32960903.00854680945856.991453190542
3311701064.29077792247105.709222077527
34990938.50450199611351.4954980038868
35870941.4503993702-71.4503993702006
3610901051.7522488305938.2477511694101
3710701061.843207274448.15679272556372
38990963.3679691994426.6320308005602
3910801064.9556274952715.0443725047326
40890976.753692915912-86.753692915912
41920964.920004554131-44.9200045541313
4211001042.6643268256857.3356731743233
43930943.093937939835-13.0939379398352
44950951.885680385697-1.88568038569713
4512401159.5974825574380.4025174425728
46950980.473953294753-30.473953294753
47830861.375514933883-31.3755149338832
4812201079.77544959606140.224550403942
4910401063.29665768058-23.2966576805784
501080982.39016573122397.6098342687774
5111601074.8606619940785.139338005925
52900889.67898192602610.3210180739744
53790922.033876438037-132.033876438037
5411001098.294511109741.70548889025667
551000929.2318129193570.7681870806507
56990951.81260538894238.1873946110584
5712501241.79025721928.20974278079939
58970953.46074670600816.5392532939916
59840835.500915308154.49908469184982
6012201223.28940032258-3.28940032258333
6111001044.3221436549355.677856345073
6210301084.13450547222-54.1345054722153
6312101161.1476393318748.8523606681324
64830902.272403132016-72.2724031320158
65810793.63807254655316.3619274534469
6611001104.40540362798-4.40540362798492
6710201003.0173807590516.9826192409456
68950992.740705527736-42.7407055277363
6912801251.4982373639428.5017626360595
70950971.816439122573-21.8164391225735
71720841.101989881472-121.101989881472
7211501217.81080326442-67.8108032644216
7310301094.17852732605-64.1785273260532
7410301022.860634305957.13936569404655
7512001200.98552630257-0.985526302565404
76870821.63792147701148.3620785229886
77880801.74162460689178.2583753931085
7810901093.24767109538-3.24767109537584
799501012.31097016152-62.3109701615157
801060941.136634983986118.863365016014
8112801273.092372015336.90762798467085
82920943.513604024444-23.5136040244438
83630715.566756570622-85.5667565706221
8411101144.99096891121-34.9909689112133
8510201025.63617979956-5.63617979956098
8611301025.470692099104.529307901003
8711601198.42886021959-38.4288602195916
88930866.6950735833463.3049264166606
89930876.71706019227553.282939807725
9011101088.3588857932421.6411142067623
91930950.732208862347-20.7322088623465
9210701057.9232188304712.0767811695291
9312501278.21504475951-28.2150447595077
94840918.159973966413-78.1599739664126
95680628.21820833109551.7817916689054
9611101110.60227783799-0.60227783799337
979901021.15276007441-31.1527600744054
9812101128.2760087448281.7239912551804
9911301161.40922139439-31.4092213943948
100920929.456105867042-9.4561058670422
1011030928.030784760277101.969215239723
10211201110.162622206989.83737779301896
103880931.073672851073-51.073672851073
10410501069.65946738654-19.6594673865397
10512601249.8487791349910.1512208650063
106790842.056961522944-52.0569615229443
107640679.77991204345-39.7799120434502
10811101108.747746990181.25225300982402







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109989.423481386884.7835445973471094.06341817465
1101207.48517068061102.807180996211312.16316036499
1111127.975663750021023.250091795231232.7012357048
112918.04453791944813.260800727761022.82827511112
1131025.49433423016920.6408005834181130.34786787691
1141114.808918652181009.872915515181219.74492178917
115875.54031750631770.508137645192980.572497367429
1161045.68797121864940.5448820863091150.83106035098
1171255.18964344751149.919897413081360.45938948192
118786.137968509963680.72481450151891.551122518417
119636.960701699036531.386398320255742.535005077818
1201106.934928383521001.180758555961212.68909821107

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 989.423481386 & 884.783544597347 & 1094.06341817465 \tabularnewline
110 & 1207.4851706806 & 1102.80718099621 & 1312.16316036499 \tabularnewline
111 & 1127.97566375002 & 1023.25009179523 & 1232.7012357048 \tabularnewline
112 & 918.04453791944 & 813.26080072776 & 1022.82827511112 \tabularnewline
113 & 1025.49433423016 & 920.640800583418 & 1130.34786787691 \tabularnewline
114 & 1114.80891865218 & 1009.87291551518 & 1219.74492178917 \tabularnewline
115 & 875.54031750631 & 770.508137645192 & 980.572497367429 \tabularnewline
116 & 1045.68797121864 & 940.544882086309 & 1150.83106035098 \tabularnewline
117 & 1255.1896434475 & 1149.91989741308 & 1360.45938948192 \tabularnewline
118 & 786.137968509963 & 680.72481450151 & 891.551122518417 \tabularnewline
119 & 636.960701699036 & 531.386398320255 & 742.535005077818 \tabularnewline
120 & 1106.93492838352 & 1001.18075855596 & 1212.68909821107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123806&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]989.423481386[/C][C]884.783544597347[/C][C]1094.06341817465[/C][/ROW]
[ROW][C]110[/C][C]1207.4851706806[/C][C]1102.80718099621[/C][C]1312.16316036499[/C][/ROW]
[ROW][C]111[/C][C]1127.97566375002[/C][C]1023.25009179523[/C][C]1232.7012357048[/C][/ROW]
[ROW][C]112[/C][C]918.04453791944[/C][C]813.26080072776[/C][C]1022.82827511112[/C][/ROW]
[ROW][C]113[/C][C]1025.49433423016[/C][C]920.640800583418[/C][C]1130.34786787691[/C][/ROW]
[ROW][C]114[/C][C]1114.80891865218[/C][C]1009.87291551518[/C][C]1219.74492178917[/C][/ROW]
[ROW][C]115[/C][C]875.54031750631[/C][C]770.508137645192[/C][C]980.572497367429[/C][/ROW]
[ROW][C]116[/C][C]1045.68797121864[/C][C]940.544882086309[/C][C]1150.83106035098[/C][/ROW]
[ROW][C]117[/C][C]1255.1896434475[/C][C]1149.91989741308[/C][C]1360.45938948192[/C][/ROW]
[ROW][C]118[/C][C]786.137968509963[/C][C]680.72481450151[/C][C]891.551122518417[/C][/ROW]
[ROW][C]119[/C][C]636.960701699036[/C][C]531.386398320255[/C][C]742.535005077818[/C][/ROW]
[ROW][C]120[/C][C]1106.93492838352[/C][C]1001.18075855596[/C][C]1212.68909821107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123806&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123806&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
109989.423481386884.7835445973471094.06341817465
1101207.48517068061102.807180996211312.16316036499
1111127.975663750021023.250091795231232.7012357048
112918.04453791944813.260800727761022.82827511112
1131025.49433423016920.6408005834181130.34786787691
1141114.808918652181009.872915515181219.74492178917
115875.54031750631770.508137645192980.572497367429
1161045.68797121864940.5448820863091150.83106035098
1171255.18964344751149.919897413081360.45938948192
118786.137968509963680.72481450151891.551122518417
119636.960701699036531.386398320255742.535005077818
1201106.934928383521001.180758555961212.68909821107



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')