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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 04 Aug 2013 13:46:41 -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/2013/Aug/04/t1375638548w0tbcs7d3gceenn.htm/, Retrieved Sat, 04 May 2024 12:18:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210938, Retrieved Sat, 04 May 2024 12:18:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsOngenae Olivier
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS B - STA...] [2013-08-04 17:46:41] [a14baeeafb42bd31c8e1f231a0a4996d] [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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210938&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210938&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210938&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0237763572067335
beta0.13436882367833
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0237763572067335 \tabularnewline
beta & 0.13436882367833 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210938&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]0.0237763572067335[/C][/ROW]
[ROW][C]beta[/C][C]0.13436882367833[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210938&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210938&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
alpha0.0237763572067335
beta0.13436882367833
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310001008.20245726496-8.20245726495727
1410001010.70704334197-10.7070433419719
1510801088.11787261139-8.11787261139102
1610101016.39766127355-6.39766127355438
17960967.197911039368-7.19791103936836
18990998.372804553102-8.3728045531019
19900976.993013933364-76.9930139333644
20920924.569040667738-4.5690406677378
2110801030.9357818177649.064218182237
22950967.901143575667-17.901143575667
23950959.467122377869-9.46712237786937
2410601089.53671924064-29.5367192406402
251070971.86067087711398.1393291228869
26970974.346226054947-4.34622605494735
2710701054.3538085625615.6461914374379
28980984.871759029796-4.87175902979595
29970934.92576935609935.0742306439007
301050966.09253557655383.9074644234466
31950880.34673392611369.6532660738873
32960903.0085468092256.9914531907805
3311701064.29077792228105.709222077719
34990938.5045019958951.4954980041101
35870941.450399370001-71.4503993700012
3610901051.7522488304838.2477511695197
3710701061.843207274448.15679272556417
38990963.36796919948126.632030800519
3910801064.9556274953515.0443725046466
40890976.753692916035-86.7536929160347
41920964.920004554381-44.9200045543805
4211001042.6643268260457.3356731739573
43930943.093937940225-13.0939379402249
44950951.885680386139-1.88568038613892
4512401159.5974825579480.4025174420617
46950980.473953295228-30.4739532952279
47830861.375514934302-31.3755149343025
4812201079.77544959651140.224550403493
4910401063.29665768093-23.2966576809251
501080982.39016573159697.6098342684037
5111601074.8606619943985.1393380056113
52900889.67898192622610.3210180737744
53790922.033876438224-132.033876438224
5411001098.294511110091.70548888991425
551000929.2318129196970.7681870803096
56990951.81260538925238.1873946107482
5712501241.790257219578.20974278043013
58970953.46074670636816.5392532936319
59840835.5009153084994.49908469150103
6012201223.28940032306-3.28940032305854
6111001044.3221436553955.6778563446064
6210301084.13450547273-54.1345054727276
6312101161.1476393324748.8523606675258
64830902.272403132579-72.2724031325787
65810793.63807254704616.3619274529535
6611001104.40540362846-4.40540362846355
6710201003.0173807595816.9826192404179
68950992.740705528265-42.7407055282653
6912801251.4982373644828.5017626355175
70950971.816439123085-21.816439123085
71720841.101989881976-121.101989881976
7211501217.81080326497-67.8108032649707
7310301094.17852732664-64.1785273266419
7410301022.860634306497.13936569351472
7512001200.98552630307-0.985526303074266
76870821.6379214774148.3620785225897
77880801.74162460722578.2583753927754
7810901093.24767109562-3.2476710956164
799501012.31097016174-62.3109701617417
801060941.136634984189118.863365015811
8112801273.092372015456.90762798454853
82920943.513604024529-23.5136040245293
83630715.566756570624-85.5667565706236
8411101144.99096891122-34.9909689112226
8510201025.63617979955-5.63617979955097
8611301025.47069209901104.529307900994
8711601198.42886021955-38.428860219547
88930866.69507358337563.3049264166248
89930876.71706019233953.2829398076608
9011101088.3588857932721.6411142067259
91930950.732208862339-20.7322088623392
9210701057.9232188305912.0767811694134
9312501278.21504475963-28.2150447596252
94840918.159973966533-78.1599739665335
95680628.21820833120151.7817916687986
9611101110.60227783805-0.602277838046575
979901021.15276007447-31.1527600744679
9812101128.2760087449981.7239912550106
9911301161.40922139448-31.4092213944816
100920929.456105867204-9.4561058672042
1011030928.030784760481101.969215239519
10211201110.162622207139.83737779287208
103880931.073672851197-51.0736728511971
10410501069.65946738671-19.6594673867075
10512601249.8487791351510.1512208648512
106790842.056961523035-52.0569615230346
107640679.779912043618-39.7799120436177
10811101108.747746990361.25225300963984

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1000 & 1008.20245726496 & -8.20245726495727 \tabularnewline
14 & 1000 & 1010.70704334197 & -10.7070433419719 \tabularnewline
15 & 1080 & 1088.11787261139 & -8.11787261139102 \tabularnewline
16 & 1010 & 1016.39766127355 & -6.39766127355438 \tabularnewline
17 & 960 & 967.197911039368 & -7.19791103936836 \tabularnewline
18 & 990 & 998.372804553102 & -8.3728045531019 \tabularnewline
19 & 900 & 976.993013933364 & -76.9930139333644 \tabularnewline
20 & 920 & 924.569040667738 & -4.5690406677378 \tabularnewline
21 & 1080 & 1030.93578181776 & 49.064218182237 \tabularnewline
22 & 950 & 967.901143575667 & -17.901143575667 \tabularnewline
23 & 950 & 959.467122377869 & -9.46712237786937 \tabularnewline
24 & 1060 & 1089.53671924064 & -29.5367192406402 \tabularnewline
25 & 1070 & 971.860670877113 & 98.1393291228869 \tabularnewline
26 & 970 & 974.346226054947 & -4.34622605494735 \tabularnewline
27 & 1070 & 1054.35380856256 & 15.6461914374379 \tabularnewline
28 & 980 & 984.871759029796 & -4.87175902979595 \tabularnewline
29 & 970 & 934.925769356099 & 35.0742306439007 \tabularnewline
30 & 1050 & 966.092535576553 & 83.9074644234466 \tabularnewline
31 & 950 & 880.346733926113 & 69.6532660738873 \tabularnewline
32 & 960 & 903.00854680922 & 56.9914531907805 \tabularnewline
33 & 1170 & 1064.29077792228 & 105.709222077719 \tabularnewline
34 & 990 & 938.50450199589 & 51.4954980041101 \tabularnewline
35 & 870 & 941.450399370001 & -71.4503993700012 \tabularnewline
36 & 1090 & 1051.75224883048 & 38.2477511695197 \tabularnewline
37 & 1070 & 1061.84320727444 & 8.15679272556417 \tabularnewline
38 & 990 & 963.367969199481 & 26.632030800519 \tabularnewline
39 & 1080 & 1064.95562749535 & 15.0443725046466 \tabularnewline
40 & 890 & 976.753692916035 & -86.7536929160347 \tabularnewline
41 & 920 & 964.920004554381 & -44.9200045543805 \tabularnewline
42 & 1100 & 1042.66432682604 & 57.3356731739573 \tabularnewline
43 & 930 & 943.093937940225 & -13.0939379402249 \tabularnewline
44 & 950 & 951.885680386139 & -1.88568038613892 \tabularnewline
45 & 1240 & 1159.59748255794 & 80.4025174420617 \tabularnewline
46 & 950 & 980.473953295228 & -30.4739532952279 \tabularnewline
47 & 830 & 861.375514934302 & -31.3755149343025 \tabularnewline
48 & 1220 & 1079.77544959651 & 140.224550403493 \tabularnewline
49 & 1040 & 1063.29665768093 & -23.2966576809251 \tabularnewline
50 & 1080 & 982.390165731596 & 97.6098342684037 \tabularnewline
51 & 1160 & 1074.86066199439 & 85.1393380056113 \tabularnewline
52 & 900 & 889.678981926226 & 10.3210180737744 \tabularnewline
53 & 790 & 922.033876438224 & -132.033876438224 \tabularnewline
54 & 1100 & 1098.29451111009 & 1.70548888991425 \tabularnewline
55 & 1000 & 929.23181291969 & 70.7681870803096 \tabularnewline
56 & 990 & 951.812605389252 & 38.1873946107482 \tabularnewline
57 & 1250 & 1241.79025721957 & 8.20974278043013 \tabularnewline
58 & 970 & 953.460746706368 & 16.5392532936319 \tabularnewline
59 & 840 & 835.500915308499 & 4.49908469150103 \tabularnewline
60 & 1220 & 1223.28940032306 & -3.28940032305854 \tabularnewline
61 & 1100 & 1044.32214365539 & 55.6778563446064 \tabularnewline
62 & 1030 & 1084.13450547273 & -54.1345054727276 \tabularnewline
63 & 1210 & 1161.14763933247 & 48.8523606675258 \tabularnewline
64 & 830 & 902.272403132579 & -72.2724031325787 \tabularnewline
65 & 810 & 793.638072547046 & 16.3619274529535 \tabularnewline
66 & 1100 & 1104.40540362846 & -4.40540362846355 \tabularnewline
67 & 1020 & 1003.01738075958 & 16.9826192404179 \tabularnewline
68 & 950 & 992.740705528265 & -42.7407055282653 \tabularnewline
69 & 1280 & 1251.49823736448 & 28.5017626355175 \tabularnewline
70 & 950 & 971.816439123085 & -21.816439123085 \tabularnewline
71 & 720 & 841.101989881976 & -121.101989881976 \tabularnewline
72 & 1150 & 1217.81080326497 & -67.8108032649707 \tabularnewline
73 & 1030 & 1094.17852732664 & -64.1785273266419 \tabularnewline
74 & 1030 & 1022.86063430649 & 7.13936569351472 \tabularnewline
75 & 1200 & 1200.98552630307 & -0.985526303074266 \tabularnewline
76 & 870 & 821.63792147741 & 48.3620785225897 \tabularnewline
77 & 880 & 801.741624607225 & 78.2583753927754 \tabularnewline
78 & 1090 & 1093.24767109562 & -3.2476710956164 \tabularnewline
79 & 950 & 1012.31097016174 & -62.3109701617417 \tabularnewline
80 & 1060 & 941.136634984189 & 118.863365015811 \tabularnewline
81 & 1280 & 1273.09237201545 & 6.90762798454853 \tabularnewline
82 & 920 & 943.513604024529 & -23.5136040245293 \tabularnewline
83 & 630 & 715.566756570624 & -85.5667565706236 \tabularnewline
84 & 1110 & 1144.99096891122 & -34.9909689112226 \tabularnewline
85 & 1020 & 1025.63617979955 & -5.63617979955097 \tabularnewline
86 & 1130 & 1025.47069209901 & 104.529307900994 \tabularnewline
87 & 1160 & 1198.42886021955 & -38.428860219547 \tabularnewline
88 & 930 & 866.695073583375 & 63.3049264166248 \tabularnewline
89 & 930 & 876.717060192339 & 53.2829398076608 \tabularnewline
90 & 1110 & 1088.35888579327 & 21.6411142067259 \tabularnewline
91 & 930 & 950.732208862339 & -20.7322088623392 \tabularnewline
92 & 1070 & 1057.92321883059 & 12.0767811694134 \tabularnewline
93 & 1250 & 1278.21504475963 & -28.2150447596252 \tabularnewline
94 & 840 & 918.159973966533 & -78.1599739665335 \tabularnewline
95 & 680 & 628.218208331201 & 51.7817916687986 \tabularnewline
96 & 1110 & 1110.60227783805 & -0.602277838046575 \tabularnewline
97 & 990 & 1021.15276007447 & -31.1527600744679 \tabularnewline
98 & 1210 & 1128.27600874499 & 81.7239912550106 \tabularnewline
99 & 1130 & 1161.40922139448 & -31.4092213944816 \tabularnewline
100 & 920 & 929.456105867204 & -9.4561058672042 \tabularnewline
101 & 1030 & 928.030784760481 & 101.969215239519 \tabularnewline
102 & 1120 & 1110.16262220713 & 9.83737779287208 \tabularnewline
103 & 880 & 931.073672851197 & -51.0736728511971 \tabularnewline
104 & 1050 & 1069.65946738671 & -19.6594673867075 \tabularnewline
105 & 1260 & 1249.84877913515 & 10.1512208648512 \tabularnewline
106 & 790 & 842.056961523035 & -52.0569615230346 \tabularnewline
107 & 640 & 679.779912043618 & -39.7799120436177 \tabularnewline
108 & 1110 & 1108.74774699036 & 1.25225300963984 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210938&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]-8.20245726495727[/C][/ROW]
[ROW][C]14[/C][C]1000[/C][C]1010.70704334197[/C][C]-10.7070433419719[/C][/ROW]
[ROW][C]15[/C][C]1080[/C][C]1088.11787261139[/C][C]-8.11787261139102[/C][/ROW]
[ROW][C]16[/C][C]1010[/C][C]1016.39766127355[/C][C]-6.39766127355438[/C][/ROW]
[ROW][C]17[/C][C]960[/C][C]967.197911039368[/C][C]-7.19791103936836[/C][/ROW]
[ROW][C]18[/C][C]990[/C][C]998.372804553102[/C][C]-8.3728045531019[/C][/ROW]
[ROW][C]19[/C][C]900[/C][C]976.993013933364[/C][C]-76.9930139333644[/C][/ROW]
[ROW][C]20[/C][C]920[/C][C]924.569040667738[/C][C]-4.5690406677378[/C][/ROW]
[ROW][C]21[/C][C]1080[/C][C]1030.93578181776[/C][C]49.064218182237[/C][/ROW]
[ROW][C]22[/C][C]950[/C][C]967.901143575667[/C][C]-17.901143575667[/C][/ROW]
[ROW][C]23[/C][C]950[/C][C]959.467122377869[/C][C]-9.46712237786937[/C][/ROW]
[ROW][C]24[/C][C]1060[/C][C]1089.53671924064[/C][C]-29.5367192406402[/C][/ROW]
[ROW][C]25[/C][C]1070[/C][C]971.860670877113[/C][C]98.1393291228869[/C][/ROW]
[ROW][C]26[/C][C]970[/C][C]974.346226054947[/C][C]-4.34622605494735[/C][/ROW]
[ROW][C]27[/C][C]1070[/C][C]1054.35380856256[/C][C]15.6461914374379[/C][/ROW]
[ROW][C]28[/C][C]980[/C][C]984.871759029796[/C][C]-4.87175902979595[/C][/ROW]
[ROW][C]29[/C][C]970[/C][C]934.925769356099[/C][C]35.0742306439007[/C][/ROW]
[ROW][C]30[/C][C]1050[/C][C]966.092535576553[/C][C]83.9074644234466[/C][/ROW]
[ROW][C]31[/C][C]950[/C][C]880.346733926113[/C][C]69.6532660738873[/C][/ROW]
[ROW][C]32[/C][C]960[/C][C]903.00854680922[/C][C]56.9914531907805[/C][/ROW]
[ROW][C]33[/C][C]1170[/C][C]1064.29077792228[/C][C]105.709222077719[/C][/ROW]
[ROW][C]34[/C][C]990[/C][C]938.50450199589[/C][C]51.4954980041101[/C][/ROW]
[ROW][C]35[/C][C]870[/C][C]941.450399370001[/C][C]-71.4503993700012[/C][/ROW]
[ROW][C]36[/C][C]1090[/C][C]1051.75224883048[/C][C]38.2477511695197[/C][/ROW]
[ROW][C]37[/C][C]1070[/C][C]1061.84320727444[/C][C]8.15679272556417[/C][/ROW]
[ROW][C]38[/C][C]990[/C][C]963.367969199481[/C][C]26.632030800519[/C][/ROW]
[ROW][C]39[/C][C]1080[/C][C]1064.95562749535[/C][C]15.0443725046466[/C][/ROW]
[ROW][C]40[/C][C]890[/C][C]976.753692916035[/C][C]-86.7536929160347[/C][/ROW]
[ROW][C]41[/C][C]920[/C][C]964.920004554381[/C][C]-44.9200045543805[/C][/ROW]
[ROW][C]42[/C][C]1100[/C][C]1042.66432682604[/C][C]57.3356731739573[/C][/ROW]
[ROW][C]43[/C][C]930[/C][C]943.093937940225[/C][C]-13.0939379402249[/C][/ROW]
[ROW][C]44[/C][C]950[/C][C]951.885680386139[/C][C]-1.88568038613892[/C][/ROW]
[ROW][C]45[/C][C]1240[/C][C]1159.59748255794[/C][C]80.4025174420617[/C][/ROW]
[ROW][C]46[/C][C]950[/C][C]980.473953295228[/C][C]-30.4739532952279[/C][/ROW]
[ROW][C]47[/C][C]830[/C][C]861.375514934302[/C][C]-31.3755149343025[/C][/ROW]
[ROW][C]48[/C][C]1220[/C][C]1079.77544959651[/C][C]140.224550403493[/C][/ROW]
[ROW][C]49[/C][C]1040[/C][C]1063.29665768093[/C][C]-23.2966576809251[/C][/ROW]
[ROW][C]50[/C][C]1080[/C][C]982.390165731596[/C][C]97.6098342684037[/C][/ROW]
[ROW][C]51[/C][C]1160[/C][C]1074.86066199439[/C][C]85.1393380056113[/C][/ROW]
[ROW][C]52[/C][C]900[/C][C]889.678981926226[/C][C]10.3210180737744[/C][/ROW]
[ROW][C]53[/C][C]790[/C][C]922.033876438224[/C][C]-132.033876438224[/C][/ROW]
[ROW][C]54[/C][C]1100[/C][C]1098.29451111009[/C][C]1.70548888991425[/C][/ROW]
[ROW][C]55[/C][C]1000[/C][C]929.23181291969[/C][C]70.7681870803096[/C][/ROW]
[ROW][C]56[/C][C]990[/C][C]951.812605389252[/C][C]38.1873946107482[/C][/ROW]
[ROW][C]57[/C][C]1250[/C][C]1241.79025721957[/C][C]8.20974278043013[/C][/ROW]
[ROW][C]58[/C][C]970[/C][C]953.460746706368[/C][C]16.5392532936319[/C][/ROW]
[ROW][C]59[/C][C]840[/C][C]835.500915308499[/C][C]4.49908469150103[/C][/ROW]
[ROW][C]60[/C][C]1220[/C][C]1223.28940032306[/C][C]-3.28940032305854[/C][/ROW]
[ROW][C]61[/C][C]1100[/C][C]1044.32214365539[/C][C]55.6778563446064[/C][/ROW]
[ROW][C]62[/C][C]1030[/C][C]1084.13450547273[/C][C]-54.1345054727276[/C][/ROW]
[ROW][C]63[/C][C]1210[/C][C]1161.14763933247[/C][C]48.8523606675258[/C][/ROW]
[ROW][C]64[/C][C]830[/C][C]902.272403132579[/C][C]-72.2724031325787[/C][/ROW]
[ROW][C]65[/C][C]810[/C][C]793.638072547046[/C][C]16.3619274529535[/C][/ROW]
[ROW][C]66[/C][C]1100[/C][C]1104.40540362846[/C][C]-4.40540362846355[/C][/ROW]
[ROW][C]67[/C][C]1020[/C][C]1003.01738075958[/C][C]16.9826192404179[/C][/ROW]
[ROW][C]68[/C][C]950[/C][C]992.740705528265[/C][C]-42.7407055282653[/C][/ROW]
[ROW][C]69[/C][C]1280[/C][C]1251.49823736448[/C][C]28.5017626355175[/C][/ROW]
[ROW][C]70[/C][C]950[/C][C]971.816439123085[/C][C]-21.816439123085[/C][/ROW]
[ROW][C]71[/C][C]720[/C][C]841.101989881976[/C][C]-121.101989881976[/C][/ROW]
[ROW][C]72[/C][C]1150[/C][C]1217.81080326497[/C][C]-67.8108032649707[/C][/ROW]
[ROW][C]73[/C][C]1030[/C][C]1094.17852732664[/C][C]-64.1785273266419[/C][/ROW]
[ROW][C]74[/C][C]1030[/C][C]1022.86063430649[/C][C]7.13936569351472[/C][/ROW]
[ROW][C]75[/C][C]1200[/C][C]1200.98552630307[/C][C]-0.985526303074266[/C][/ROW]
[ROW][C]76[/C][C]870[/C][C]821.63792147741[/C][C]48.3620785225897[/C][/ROW]
[ROW][C]77[/C][C]880[/C][C]801.741624607225[/C][C]78.2583753927754[/C][/ROW]
[ROW][C]78[/C][C]1090[/C][C]1093.24767109562[/C][C]-3.2476710956164[/C][/ROW]
[ROW][C]79[/C][C]950[/C][C]1012.31097016174[/C][C]-62.3109701617417[/C][/ROW]
[ROW][C]80[/C][C]1060[/C][C]941.136634984189[/C][C]118.863365015811[/C][/ROW]
[ROW][C]81[/C][C]1280[/C][C]1273.09237201545[/C][C]6.90762798454853[/C][/ROW]
[ROW][C]82[/C][C]920[/C][C]943.513604024529[/C][C]-23.5136040245293[/C][/ROW]
[ROW][C]83[/C][C]630[/C][C]715.566756570624[/C][C]-85.5667565706236[/C][/ROW]
[ROW][C]84[/C][C]1110[/C][C]1144.99096891122[/C][C]-34.9909689112226[/C][/ROW]
[ROW][C]85[/C][C]1020[/C][C]1025.63617979955[/C][C]-5.63617979955097[/C][/ROW]
[ROW][C]86[/C][C]1130[/C][C]1025.47069209901[/C][C]104.529307900994[/C][/ROW]
[ROW][C]87[/C][C]1160[/C][C]1198.42886021955[/C][C]-38.428860219547[/C][/ROW]
[ROW][C]88[/C][C]930[/C][C]866.695073583375[/C][C]63.3049264166248[/C][/ROW]
[ROW][C]89[/C][C]930[/C][C]876.717060192339[/C][C]53.2829398076608[/C][/ROW]
[ROW][C]90[/C][C]1110[/C][C]1088.35888579327[/C][C]21.6411142067259[/C][/ROW]
[ROW][C]91[/C][C]930[/C][C]950.732208862339[/C][C]-20.7322088623392[/C][/ROW]
[ROW][C]92[/C][C]1070[/C][C]1057.92321883059[/C][C]12.0767811694134[/C][/ROW]
[ROW][C]93[/C][C]1250[/C][C]1278.21504475963[/C][C]-28.2150447596252[/C][/ROW]
[ROW][C]94[/C][C]840[/C][C]918.159973966533[/C][C]-78.1599739665335[/C][/ROW]
[ROW][C]95[/C][C]680[/C][C]628.218208331201[/C][C]51.7817916687986[/C][/ROW]
[ROW][C]96[/C][C]1110[/C][C]1110.60227783805[/C][C]-0.602277838046575[/C][/ROW]
[ROW][C]97[/C][C]990[/C][C]1021.15276007447[/C][C]-31.1527600744679[/C][/ROW]
[ROW][C]98[/C][C]1210[/C][C]1128.27600874499[/C][C]81.7239912550106[/C][/ROW]
[ROW][C]99[/C][C]1130[/C][C]1161.40922139448[/C][C]-31.4092213944816[/C][/ROW]
[ROW][C]100[/C][C]920[/C][C]929.456105867204[/C][C]-9.4561058672042[/C][/ROW]
[ROW][C]101[/C][C]1030[/C][C]928.030784760481[/C][C]101.969215239519[/C][/ROW]
[ROW][C]102[/C][C]1120[/C][C]1110.16262220713[/C][C]9.83737779287208[/C][/ROW]
[ROW][C]103[/C][C]880[/C][C]931.073672851197[/C][C]-51.0736728511971[/C][/ROW]
[ROW][C]104[/C][C]1050[/C][C]1069.65946738671[/C][C]-19.6594673867075[/C][/ROW]
[ROW][C]105[/C][C]1260[/C][C]1249.84877913515[/C][C]10.1512208648512[/C][/ROW]
[ROW][C]106[/C][C]790[/C][C]842.056961523035[/C][C]-52.0569615230346[/C][/ROW]
[ROW][C]107[/C][C]640[/C][C]679.779912043618[/C][C]-39.7799120436177[/C][/ROW]
[ROW][C]108[/C][C]1110[/C][C]1108.74774699036[/C][C]1.25225300963984[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210938&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210938&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
1310001008.20245726496-8.20245726495727
1410001010.70704334197-10.7070433419719
1510801088.11787261139-8.11787261139102
1610101016.39766127355-6.39766127355438
17960967.197911039368-7.19791103936836
18990998.372804553102-8.3728045531019
19900976.993013933364-76.9930139333644
20920924.569040667738-4.5690406677378
2110801030.9357818177649.064218182237
22950967.901143575667-17.901143575667
23950959.467122377869-9.46712237786937
2410601089.53671924064-29.5367192406402
251070971.86067087711398.1393291228869
26970974.346226054947-4.34622605494735
2710701054.3538085625615.6461914374379
28980984.871759029796-4.87175902979595
29970934.92576935609935.0742306439007
301050966.09253557655383.9074644234466
31950880.34673392611369.6532660738873
32960903.0085468092256.9914531907805
3311701064.29077792228105.709222077719
34990938.5045019958951.4954980041101
35870941.450399370001-71.4503993700012
3610901051.7522488304838.2477511695197
3710701061.843207274448.15679272556417
38990963.36796919948126.632030800519
3910801064.9556274953515.0443725046466
40890976.753692916035-86.7536929160347
41920964.920004554381-44.9200045543805
4211001042.6643268260457.3356731739573
43930943.093937940225-13.0939379402249
44950951.885680386139-1.88568038613892
4512401159.5974825579480.4025174420617
46950980.473953295228-30.4739532952279
47830861.375514934302-31.3755149343025
4812201079.77544959651140.224550403493
4910401063.29665768093-23.2966576809251
501080982.39016573159697.6098342684037
5111601074.8606619943985.1393380056113
52900889.67898192622610.3210180737744
53790922.033876438224-132.033876438224
5411001098.294511110091.70548888991425
551000929.2318129196970.7681870803096
56990951.81260538925238.1873946107482
5712501241.790257219578.20974278043013
58970953.46074670636816.5392532936319
59840835.5009153084994.49908469150103
6012201223.28940032306-3.28940032305854
6111001044.3221436553955.6778563446064
6210301084.13450547273-54.1345054727276
6312101161.1476393324748.8523606675258
64830902.272403132579-72.2724031325787
65810793.63807254704616.3619274529535
6611001104.40540362846-4.40540362846355
6710201003.0173807595816.9826192404179
68950992.740705528265-42.7407055282653
6912801251.4982373644828.5017626355175
70950971.816439123085-21.816439123085
71720841.101989881976-121.101989881976
7211501217.81080326497-67.8108032649707
7310301094.17852732664-64.1785273266419
7410301022.860634306497.13936569351472
7512001200.98552630307-0.985526303074266
76870821.6379214774148.3620785225897
77880801.74162460722578.2583753927754
7810901093.24767109562-3.2476710956164
799501012.31097016174-62.3109701617417
801060941.136634984189118.863365015811
8112801273.092372015456.90762798454853
82920943.513604024529-23.5136040245293
83630715.566756570624-85.5667565706236
8411101144.99096891122-34.9909689112226
8510201025.63617979955-5.63617979955097
8611301025.47069209901104.529307900994
8711601198.42886021955-38.428860219547
88930866.69507358337563.3049264166248
89930876.71706019233953.2829398076608
9011101088.3588857932721.6411142067259
91930950.732208862339-20.7322088623392
9210701057.9232188305912.0767811694134
9312501278.21504475963-28.2150447596252
94840918.159973966533-78.1599739665335
95680628.21820833120151.7817916687986
9611101110.60227783805-0.602277838046575
979901021.15276007447-31.1527600744679
9812101128.2760087449981.7239912550106
9911301161.40922139448-31.4092213944816
100920929.456105867204-9.4561058672042
1011030928.030784760481101.969215239519
10211201110.162622207139.83737779287208
103880931.073672851197-51.0736728511971
10410501069.65946738671-19.6594673867075
10512601249.8487791351510.1512208648512
106790842.056961523035-52.0569615230346
107640679.779912043618-39.7799120436177
10811101108.747746990361.25225300963984







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109989.423481386149884.783544597461094.06341817484
1101207.485170680811102.807180996381312.16316036523
1111127.975663750191023.250091795371232.701235705
112918.044537919598813.2608007278871022.82827511131
1131025.49433423039920.6408005836151130.34786787717
1141114.808918652391009.872915515371219.74492178942
115875.540317506472770.508137645324980.572497367621
1161045.68797121878940.5448820864141150.83106035115
1171255.189643447641149.919897413191360.45938948209
118786.137968510051680.724814501563891.55112251854
119636.960701699094531.386398320275742.535005077913
1201106.934928383581001.180758555991212.68909821117

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 989.423481386149 & 884.78354459746 & 1094.06341817484 \tabularnewline
110 & 1207.48517068081 & 1102.80718099638 & 1312.16316036523 \tabularnewline
111 & 1127.97566375019 & 1023.25009179537 & 1232.701235705 \tabularnewline
112 & 918.044537919598 & 813.260800727887 & 1022.82827511131 \tabularnewline
113 & 1025.49433423039 & 920.640800583615 & 1130.34786787717 \tabularnewline
114 & 1114.80891865239 & 1009.87291551537 & 1219.74492178942 \tabularnewline
115 & 875.540317506472 & 770.508137645324 & 980.572497367621 \tabularnewline
116 & 1045.68797121878 & 940.544882086414 & 1150.83106035115 \tabularnewline
117 & 1255.18964344764 & 1149.91989741319 & 1360.45938948209 \tabularnewline
118 & 786.137968510051 & 680.724814501563 & 891.55112251854 \tabularnewline
119 & 636.960701699094 & 531.386398320275 & 742.535005077913 \tabularnewline
120 & 1106.93492838358 & 1001.18075855599 & 1212.68909821117 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210938&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]989.423481386149[/C][C]884.78354459746[/C][C]1094.06341817484[/C][/ROW]
[ROW][C]110[/C][C]1207.48517068081[/C][C]1102.80718099638[/C][C]1312.16316036523[/C][/ROW]
[ROW][C]111[/C][C]1127.97566375019[/C][C]1023.25009179537[/C][C]1232.701235705[/C][/ROW]
[ROW][C]112[/C][C]918.044537919598[/C][C]813.260800727887[/C][C]1022.82827511131[/C][/ROW]
[ROW][C]113[/C][C]1025.49433423039[/C][C]920.640800583615[/C][C]1130.34786787717[/C][/ROW]
[ROW][C]114[/C][C]1114.80891865239[/C][C]1009.87291551537[/C][C]1219.74492178942[/C][/ROW]
[ROW][C]115[/C][C]875.540317506472[/C][C]770.508137645324[/C][C]980.572497367621[/C][/ROW]
[ROW][C]116[/C][C]1045.68797121878[/C][C]940.544882086414[/C][C]1150.83106035115[/C][/ROW]
[ROW][C]117[/C][C]1255.18964344764[/C][C]1149.91989741319[/C][C]1360.45938948209[/C][/ROW]
[ROW][C]118[/C][C]786.137968510051[/C][C]680.724814501563[/C][C]891.55112251854[/C][/ROW]
[ROW][C]119[/C][C]636.960701699094[/C][C]531.386398320275[/C][C]742.535005077913[/C][/ROW]
[ROW][C]120[/C][C]1106.93492838358[/C][C]1001.18075855599[/C][C]1212.68909821117[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210938&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210938&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
109989.423481386149884.783544597461094.06341817484
1101207.485170680811102.807180996381312.16316036523
1111127.975663750191023.250091795371232.701235705
112918.044537919598813.2608007278871022.82827511131
1131025.49433423039920.6408005836151130.34786787717
1141114.808918652391009.872915515371219.74492178942
115875.540317506472770.508137645324980.572497367621
1161045.68797121878940.5448820864141150.83106035115
1171255.189643447641149.919897413191360.45938948209
118786.137968510051680.724814501563891.55112251854
119636.960701699094531.386398320275742.535005077913
1201106.934928383581001.180758555991212.68909821117



Parameters (Session):
par1 = additive ; par2 = 12 ;
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')