Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 10 Aug 2015 13:54:46 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Aug/10/t1439211304i5e8kivg621aktd.htm/, Retrieved Sun, 19 May 2024 11:11:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279992, Retrieved Sun, 19 May 2024 11:11:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [omzetontwikkeling...] [2014-09-24 09:10:11] [3d50c3f1d1505d45371c80c331b9aa00]
- R  D  [Histogram] [] [2015-07-23 12:50:11] [74be16979710d4c4e7c6647856088456]
- RMPD    [Harrell-Davis Quantiles] [] [2015-08-10 08:16:05] [74be16979710d4c4e7c6647856088456]
- RMP       [Mean versus Median] [] [2015-08-10 09:14:26] [74be16979710d4c4e7c6647856088456]
- RMP         [Mean Plot] [] [2015-08-10 09:32:31] [74be16979710d4c4e7c6647856088456]
- RMP           [(Partial) Autocorrelation Function] [] [2015-08-10 11:22:46] [74be16979710d4c4e7c6647856088456]
- RM                [Exponential Smoothing] [] [2015-08-10 12:54:46] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
1053000
1014000
1072500
858000
1111500
1092000
1170000
1209000
1345500
1170000
1111500
1384500
1170000
877500
1033500
780000
1092000
897000
1189500
1072500
1131000
1267500
1248000
1482000
1072500
897000
994500
721500
1033500
799500
1131000
1072500
955500
1365000
1228500
1404000
1053000
975000
877500
721500
955500
858000
1170000
1131000
975000
1306500
1209000
1560000
1248000
760500
760500
760500
897000
897000
1209000
1111500
994500
1248000
1150500
1657500
1306500
760500
799500
663000
916500
1053000
1326000
1306500
1053000
1228500
1092000
1560000
1189500
955500
858000
643500
955500
1150500
1345500
1267500
936000
1345500
1053000
1618500
1345500
975000
897000
604500
955500
916500
1384500
1384500
1053000
1365000
1014000
1579500
1345500
994500
760500
526500
1033500
994500
1306500
1501500
1111500
1248000
936000
1618500




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279992&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279992&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279992&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.616435516556409
beta0.0182153483451265
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.616435516556409 \tabularnewline
beta & 0.0182153483451265 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279992&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]0.616435516556409[/C][/ROW]
[ROW][C]beta[/C][C]0.0182153483451265[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279992&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279992&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
alpha0.616435516556409
beta0.0182153483451265
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3107250097500097500
4858000997197.250161722-139197.250161722
51111500871922.920126161239577.079873839
61092000982828.652128599109171.347871401
711700001014573.49941243155426.500587572
812090001076576.88574177132423.114258228
913455001125887.09228414219612.907715855
1011700001231410.12698197-61410.1269819732
1111115001163011.03312718-51511.0331271752
1213845001100135.69615495284364.303845055
1311700001247498.85554266-77498.8555426644
148775001170926.50865698-293426.508656975
151033500957953.92210885775546.0778911427
16780000973277.418303135-193277.418303135
171092000820718.331323044271281.668676956
18897000957576.075095522-60576.0750955215
191189500889184.735392672300315.264607328
2010725001046631.7513764825868.248623521
2111310001035190.3431923995809.656807612
2212675001067939.11022169199560.88977831
2312480001166884.6090863181115.3909136939
2414820001193726.9069525288273.093047502
2510725001351505.46963933-279005.469639326
268970001156460.54112968-259460.541129676
27994500970550.42528988923949.5747101113
28721500959613.290504318-238113.290504318
291033500784457.622073079249042.377926921
30799500912398.40392783-112898.40392783
311131000815958.343331219315041.656668781
321072500986853.20790412985646.7920958709
339555001017302.62315204-61802.6231520425
341365000956165.025773593408834.974226407
3512285001189735.7981951838764.2018048202
3614040001195617.07009492208382.929905081
3710530001308397.1962654-255397.196265401
389750001132419.03098337-157419.03098337
398775001015070.49323846-137570.493238464
40721500908412.576767593-186912.576767593
41955500769239.683294289186260.316705711
42858000862195.255468949-4195.25546894944
431170000837700.141835261332299.858164739
4411310001024363.82548199106636.174518008
459750001073117.77336591-98117.7733659116
461306500994552.391599173311947.608400827
4712090001172268.6063319636731.3936680371
4815600001180744.21324516379255.786754844
4912480001404622.52819354-156622.528193545
507605001296407.76746699-535907.767466994
51760500948370.626998594-187870.626998594
52760500812766.419190456-52266.419190456
53897000760166.583199862136833.416800138
54897000825671.04830509371328.9516949066
551209000851597.158013688357402.841986312
5611115001057882.5032008253617.4967991761
579945001077505.82096852-83005.8209685222
5812480001011977.63513687236022.364863126
5911505001145759.95164954740.04835049552
6016575001137024.85796076520475.142039245
6113065001452051.39391686-145551.393916859
627605001354881.18155403-594381.181554026
63799500974362.285998845-174862.285998845
64663000850486.281022514-187486.281022514
65916500716723.191010057199776.808989943
661053000823926.035346114229073.964653886
671326000951760.864061709374239.135938291
6813065001173282.83707008133217.16292992
6910530001247726.14623822-194726.146238217
7012285001117827.0526141110672.947385898
7110920001177429.50791605-85429.5079160475
7215600001115188.19216703444811.807832973
7311895001384801.0641706-195301.064170599
749555001257632.67214586-302132.672145864
758580001061216.95947828-203216.959478277
76643500923494.565799681-279994.565799681
77955500735299.785180194220200.214819806
781150500857915.36994696292584.63005304
7913455001028436.59127705317063.408722954
8012675001217607.5754618449892.4245381621
819360001242645.09746461-306645.097464608
8213455001044457.03656051301042.963439489
8310530001224249.76669132-171249.766691322
8416185001110981.59073997507518.409260032
8513455001421828.94090392-76328.9409039186
869750001371914.98197504-396914.981975041
878970001119923.6065465-222923.606546505
88604500972683.577247605-368183.577247605
89955500731765.961300156223734.038699844
90916500858239.60396560658260.3960343937
911384500883363.598202459501136.401797541
9213845001187119.14584276197380.854157243
9310530001305845.2937911-252845.293791102
9413650001144196.95811434220803.041885658
9510140001277001.58521939-263001.585219385
9615795001108618.72074652470881.279253483
9713455001397914.65065143-52414.6506514349
989945001364043.84119371-369543.841193706
997605001130533.87993152-370033.87993152
100526500892566.883526515-366066.883526515
1011033500652934.870506169380565.129493831
102994500877826.557028862116673.442971138
1031306500941356.113437737365143.886562263
10415015001162151.72623182339348.273768185
10511115001370856.40896973-259356.408969728
10612480001207586.055164440413.9448356
1079360001229558.58577789-293558.585777888
10816185001042362.33865137576137.661348627

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1072500 & 975000 & 97500 \tabularnewline
4 & 858000 & 997197.250161722 & -139197.250161722 \tabularnewline
5 & 1111500 & 871922.920126161 & 239577.079873839 \tabularnewline
6 & 1092000 & 982828.652128599 & 109171.347871401 \tabularnewline
7 & 1170000 & 1014573.49941243 & 155426.500587572 \tabularnewline
8 & 1209000 & 1076576.88574177 & 132423.114258228 \tabularnewline
9 & 1345500 & 1125887.09228414 & 219612.907715855 \tabularnewline
10 & 1170000 & 1231410.12698197 & -61410.1269819732 \tabularnewline
11 & 1111500 & 1163011.03312718 & -51511.0331271752 \tabularnewline
12 & 1384500 & 1100135.69615495 & 284364.303845055 \tabularnewline
13 & 1170000 & 1247498.85554266 & -77498.8555426644 \tabularnewline
14 & 877500 & 1170926.50865698 & -293426.508656975 \tabularnewline
15 & 1033500 & 957953.922108857 & 75546.0778911427 \tabularnewline
16 & 780000 & 973277.418303135 & -193277.418303135 \tabularnewline
17 & 1092000 & 820718.331323044 & 271281.668676956 \tabularnewline
18 & 897000 & 957576.075095522 & -60576.0750955215 \tabularnewline
19 & 1189500 & 889184.735392672 & 300315.264607328 \tabularnewline
20 & 1072500 & 1046631.75137648 & 25868.248623521 \tabularnewline
21 & 1131000 & 1035190.34319239 & 95809.656807612 \tabularnewline
22 & 1267500 & 1067939.11022169 & 199560.88977831 \tabularnewline
23 & 1248000 & 1166884.60908631 & 81115.3909136939 \tabularnewline
24 & 1482000 & 1193726.9069525 & 288273.093047502 \tabularnewline
25 & 1072500 & 1351505.46963933 & -279005.469639326 \tabularnewline
26 & 897000 & 1156460.54112968 & -259460.541129676 \tabularnewline
27 & 994500 & 970550.425289889 & 23949.5747101113 \tabularnewline
28 & 721500 & 959613.290504318 & -238113.290504318 \tabularnewline
29 & 1033500 & 784457.622073079 & 249042.377926921 \tabularnewline
30 & 799500 & 912398.40392783 & -112898.40392783 \tabularnewline
31 & 1131000 & 815958.343331219 & 315041.656668781 \tabularnewline
32 & 1072500 & 986853.207904129 & 85646.7920958709 \tabularnewline
33 & 955500 & 1017302.62315204 & -61802.6231520425 \tabularnewline
34 & 1365000 & 956165.025773593 & 408834.974226407 \tabularnewline
35 & 1228500 & 1189735.79819518 & 38764.2018048202 \tabularnewline
36 & 1404000 & 1195617.07009492 & 208382.929905081 \tabularnewline
37 & 1053000 & 1308397.1962654 & -255397.196265401 \tabularnewline
38 & 975000 & 1132419.03098337 & -157419.03098337 \tabularnewline
39 & 877500 & 1015070.49323846 & -137570.493238464 \tabularnewline
40 & 721500 & 908412.576767593 & -186912.576767593 \tabularnewline
41 & 955500 & 769239.683294289 & 186260.316705711 \tabularnewline
42 & 858000 & 862195.255468949 & -4195.25546894944 \tabularnewline
43 & 1170000 & 837700.141835261 & 332299.858164739 \tabularnewline
44 & 1131000 & 1024363.82548199 & 106636.174518008 \tabularnewline
45 & 975000 & 1073117.77336591 & -98117.7733659116 \tabularnewline
46 & 1306500 & 994552.391599173 & 311947.608400827 \tabularnewline
47 & 1209000 & 1172268.60633196 & 36731.3936680371 \tabularnewline
48 & 1560000 & 1180744.21324516 & 379255.786754844 \tabularnewline
49 & 1248000 & 1404622.52819354 & -156622.528193545 \tabularnewline
50 & 760500 & 1296407.76746699 & -535907.767466994 \tabularnewline
51 & 760500 & 948370.626998594 & -187870.626998594 \tabularnewline
52 & 760500 & 812766.419190456 & -52266.419190456 \tabularnewline
53 & 897000 & 760166.583199862 & 136833.416800138 \tabularnewline
54 & 897000 & 825671.048305093 & 71328.9516949066 \tabularnewline
55 & 1209000 & 851597.158013688 & 357402.841986312 \tabularnewline
56 & 1111500 & 1057882.50320082 & 53617.4967991761 \tabularnewline
57 & 994500 & 1077505.82096852 & -83005.8209685222 \tabularnewline
58 & 1248000 & 1011977.63513687 & 236022.364863126 \tabularnewline
59 & 1150500 & 1145759.9516495 & 4740.04835049552 \tabularnewline
60 & 1657500 & 1137024.85796076 & 520475.142039245 \tabularnewline
61 & 1306500 & 1452051.39391686 & -145551.393916859 \tabularnewline
62 & 760500 & 1354881.18155403 & -594381.181554026 \tabularnewline
63 & 799500 & 974362.285998845 & -174862.285998845 \tabularnewline
64 & 663000 & 850486.281022514 & -187486.281022514 \tabularnewline
65 & 916500 & 716723.191010057 & 199776.808989943 \tabularnewline
66 & 1053000 & 823926.035346114 & 229073.964653886 \tabularnewline
67 & 1326000 & 951760.864061709 & 374239.135938291 \tabularnewline
68 & 1306500 & 1173282.83707008 & 133217.16292992 \tabularnewline
69 & 1053000 & 1247726.14623822 & -194726.146238217 \tabularnewline
70 & 1228500 & 1117827.0526141 & 110672.947385898 \tabularnewline
71 & 1092000 & 1177429.50791605 & -85429.5079160475 \tabularnewline
72 & 1560000 & 1115188.19216703 & 444811.807832973 \tabularnewline
73 & 1189500 & 1384801.0641706 & -195301.064170599 \tabularnewline
74 & 955500 & 1257632.67214586 & -302132.672145864 \tabularnewline
75 & 858000 & 1061216.95947828 & -203216.959478277 \tabularnewline
76 & 643500 & 923494.565799681 & -279994.565799681 \tabularnewline
77 & 955500 & 735299.785180194 & 220200.214819806 \tabularnewline
78 & 1150500 & 857915.36994696 & 292584.63005304 \tabularnewline
79 & 1345500 & 1028436.59127705 & 317063.408722954 \tabularnewline
80 & 1267500 & 1217607.57546184 & 49892.4245381621 \tabularnewline
81 & 936000 & 1242645.09746461 & -306645.097464608 \tabularnewline
82 & 1345500 & 1044457.03656051 & 301042.963439489 \tabularnewline
83 & 1053000 & 1224249.76669132 & -171249.766691322 \tabularnewline
84 & 1618500 & 1110981.59073997 & 507518.409260032 \tabularnewline
85 & 1345500 & 1421828.94090392 & -76328.9409039186 \tabularnewline
86 & 975000 & 1371914.98197504 & -396914.981975041 \tabularnewline
87 & 897000 & 1119923.6065465 & -222923.606546505 \tabularnewline
88 & 604500 & 972683.577247605 & -368183.577247605 \tabularnewline
89 & 955500 & 731765.961300156 & 223734.038699844 \tabularnewline
90 & 916500 & 858239.603965606 & 58260.3960343937 \tabularnewline
91 & 1384500 & 883363.598202459 & 501136.401797541 \tabularnewline
92 & 1384500 & 1187119.14584276 & 197380.854157243 \tabularnewline
93 & 1053000 & 1305845.2937911 & -252845.293791102 \tabularnewline
94 & 1365000 & 1144196.95811434 & 220803.041885658 \tabularnewline
95 & 1014000 & 1277001.58521939 & -263001.585219385 \tabularnewline
96 & 1579500 & 1108618.72074652 & 470881.279253483 \tabularnewline
97 & 1345500 & 1397914.65065143 & -52414.6506514349 \tabularnewline
98 & 994500 & 1364043.84119371 & -369543.841193706 \tabularnewline
99 & 760500 & 1130533.87993152 & -370033.87993152 \tabularnewline
100 & 526500 & 892566.883526515 & -366066.883526515 \tabularnewline
101 & 1033500 & 652934.870506169 & 380565.129493831 \tabularnewline
102 & 994500 & 877826.557028862 & 116673.442971138 \tabularnewline
103 & 1306500 & 941356.113437737 & 365143.886562263 \tabularnewline
104 & 1501500 & 1162151.72623182 & 339348.273768185 \tabularnewline
105 & 1111500 & 1370856.40896973 & -259356.408969728 \tabularnewline
106 & 1248000 & 1207586.0551644 & 40413.9448356 \tabularnewline
107 & 936000 & 1229558.58577789 & -293558.585777888 \tabularnewline
108 & 1618500 & 1042362.33865137 & 576137.661348627 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279992&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]3[/C][C]1072500[/C][C]975000[/C][C]97500[/C][/ROW]
[ROW][C]4[/C][C]858000[/C][C]997197.250161722[/C][C]-139197.250161722[/C][/ROW]
[ROW][C]5[/C][C]1111500[/C][C]871922.920126161[/C][C]239577.079873839[/C][/ROW]
[ROW][C]6[/C][C]1092000[/C][C]982828.652128599[/C][C]109171.347871401[/C][/ROW]
[ROW][C]7[/C][C]1170000[/C][C]1014573.49941243[/C][C]155426.500587572[/C][/ROW]
[ROW][C]8[/C][C]1209000[/C][C]1076576.88574177[/C][C]132423.114258228[/C][/ROW]
[ROW][C]9[/C][C]1345500[/C][C]1125887.09228414[/C][C]219612.907715855[/C][/ROW]
[ROW][C]10[/C][C]1170000[/C][C]1231410.12698197[/C][C]-61410.1269819732[/C][/ROW]
[ROW][C]11[/C][C]1111500[/C][C]1163011.03312718[/C][C]-51511.0331271752[/C][/ROW]
[ROW][C]12[/C][C]1384500[/C][C]1100135.69615495[/C][C]284364.303845055[/C][/ROW]
[ROW][C]13[/C][C]1170000[/C][C]1247498.85554266[/C][C]-77498.8555426644[/C][/ROW]
[ROW][C]14[/C][C]877500[/C][C]1170926.50865698[/C][C]-293426.508656975[/C][/ROW]
[ROW][C]15[/C][C]1033500[/C][C]957953.922108857[/C][C]75546.0778911427[/C][/ROW]
[ROW][C]16[/C][C]780000[/C][C]973277.418303135[/C][C]-193277.418303135[/C][/ROW]
[ROW][C]17[/C][C]1092000[/C][C]820718.331323044[/C][C]271281.668676956[/C][/ROW]
[ROW][C]18[/C][C]897000[/C][C]957576.075095522[/C][C]-60576.0750955215[/C][/ROW]
[ROW][C]19[/C][C]1189500[/C][C]889184.735392672[/C][C]300315.264607328[/C][/ROW]
[ROW][C]20[/C][C]1072500[/C][C]1046631.75137648[/C][C]25868.248623521[/C][/ROW]
[ROW][C]21[/C][C]1131000[/C][C]1035190.34319239[/C][C]95809.656807612[/C][/ROW]
[ROW][C]22[/C][C]1267500[/C][C]1067939.11022169[/C][C]199560.88977831[/C][/ROW]
[ROW][C]23[/C][C]1248000[/C][C]1166884.60908631[/C][C]81115.3909136939[/C][/ROW]
[ROW][C]24[/C][C]1482000[/C][C]1193726.9069525[/C][C]288273.093047502[/C][/ROW]
[ROW][C]25[/C][C]1072500[/C][C]1351505.46963933[/C][C]-279005.469639326[/C][/ROW]
[ROW][C]26[/C][C]897000[/C][C]1156460.54112968[/C][C]-259460.541129676[/C][/ROW]
[ROW][C]27[/C][C]994500[/C][C]970550.425289889[/C][C]23949.5747101113[/C][/ROW]
[ROW][C]28[/C][C]721500[/C][C]959613.290504318[/C][C]-238113.290504318[/C][/ROW]
[ROW][C]29[/C][C]1033500[/C][C]784457.622073079[/C][C]249042.377926921[/C][/ROW]
[ROW][C]30[/C][C]799500[/C][C]912398.40392783[/C][C]-112898.40392783[/C][/ROW]
[ROW][C]31[/C][C]1131000[/C][C]815958.343331219[/C][C]315041.656668781[/C][/ROW]
[ROW][C]32[/C][C]1072500[/C][C]986853.207904129[/C][C]85646.7920958709[/C][/ROW]
[ROW][C]33[/C][C]955500[/C][C]1017302.62315204[/C][C]-61802.6231520425[/C][/ROW]
[ROW][C]34[/C][C]1365000[/C][C]956165.025773593[/C][C]408834.974226407[/C][/ROW]
[ROW][C]35[/C][C]1228500[/C][C]1189735.79819518[/C][C]38764.2018048202[/C][/ROW]
[ROW][C]36[/C][C]1404000[/C][C]1195617.07009492[/C][C]208382.929905081[/C][/ROW]
[ROW][C]37[/C][C]1053000[/C][C]1308397.1962654[/C][C]-255397.196265401[/C][/ROW]
[ROW][C]38[/C][C]975000[/C][C]1132419.03098337[/C][C]-157419.03098337[/C][/ROW]
[ROW][C]39[/C][C]877500[/C][C]1015070.49323846[/C][C]-137570.493238464[/C][/ROW]
[ROW][C]40[/C][C]721500[/C][C]908412.576767593[/C][C]-186912.576767593[/C][/ROW]
[ROW][C]41[/C][C]955500[/C][C]769239.683294289[/C][C]186260.316705711[/C][/ROW]
[ROW][C]42[/C][C]858000[/C][C]862195.255468949[/C][C]-4195.25546894944[/C][/ROW]
[ROW][C]43[/C][C]1170000[/C][C]837700.141835261[/C][C]332299.858164739[/C][/ROW]
[ROW][C]44[/C][C]1131000[/C][C]1024363.82548199[/C][C]106636.174518008[/C][/ROW]
[ROW][C]45[/C][C]975000[/C][C]1073117.77336591[/C][C]-98117.7733659116[/C][/ROW]
[ROW][C]46[/C][C]1306500[/C][C]994552.391599173[/C][C]311947.608400827[/C][/ROW]
[ROW][C]47[/C][C]1209000[/C][C]1172268.60633196[/C][C]36731.3936680371[/C][/ROW]
[ROW][C]48[/C][C]1560000[/C][C]1180744.21324516[/C][C]379255.786754844[/C][/ROW]
[ROW][C]49[/C][C]1248000[/C][C]1404622.52819354[/C][C]-156622.528193545[/C][/ROW]
[ROW][C]50[/C][C]760500[/C][C]1296407.76746699[/C][C]-535907.767466994[/C][/ROW]
[ROW][C]51[/C][C]760500[/C][C]948370.626998594[/C][C]-187870.626998594[/C][/ROW]
[ROW][C]52[/C][C]760500[/C][C]812766.419190456[/C][C]-52266.419190456[/C][/ROW]
[ROW][C]53[/C][C]897000[/C][C]760166.583199862[/C][C]136833.416800138[/C][/ROW]
[ROW][C]54[/C][C]897000[/C][C]825671.048305093[/C][C]71328.9516949066[/C][/ROW]
[ROW][C]55[/C][C]1209000[/C][C]851597.158013688[/C][C]357402.841986312[/C][/ROW]
[ROW][C]56[/C][C]1111500[/C][C]1057882.50320082[/C][C]53617.4967991761[/C][/ROW]
[ROW][C]57[/C][C]994500[/C][C]1077505.82096852[/C][C]-83005.8209685222[/C][/ROW]
[ROW][C]58[/C][C]1248000[/C][C]1011977.63513687[/C][C]236022.364863126[/C][/ROW]
[ROW][C]59[/C][C]1150500[/C][C]1145759.9516495[/C][C]4740.04835049552[/C][/ROW]
[ROW][C]60[/C][C]1657500[/C][C]1137024.85796076[/C][C]520475.142039245[/C][/ROW]
[ROW][C]61[/C][C]1306500[/C][C]1452051.39391686[/C][C]-145551.393916859[/C][/ROW]
[ROW][C]62[/C][C]760500[/C][C]1354881.18155403[/C][C]-594381.181554026[/C][/ROW]
[ROW][C]63[/C][C]799500[/C][C]974362.285998845[/C][C]-174862.285998845[/C][/ROW]
[ROW][C]64[/C][C]663000[/C][C]850486.281022514[/C][C]-187486.281022514[/C][/ROW]
[ROW][C]65[/C][C]916500[/C][C]716723.191010057[/C][C]199776.808989943[/C][/ROW]
[ROW][C]66[/C][C]1053000[/C][C]823926.035346114[/C][C]229073.964653886[/C][/ROW]
[ROW][C]67[/C][C]1326000[/C][C]951760.864061709[/C][C]374239.135938291[/C][/ROW]
[ROW][C]68[/C][C]1306500[/C][C]1173282.83707008[/C][C]133217.16292992[/C][/ROW]
[ROW][C]69[/C][C]1053000[/C][C]1247726.14623822[/C][C]-194726.146238217[/C][/ROW]
[ROW][C]70[/C][C]1228500[/C][C]1117827.0526141[/C][C]110672.947385898[/C][/ROW]
[ROW][C]71[/C][C]1092000[/C][C]1177429.50791605[/C][C]-85429.5079160475[/C][/ROW]
[ROW][C]72[/C][C]1560000[/C][C]1115188.19216703[/C][C]444811.807832973[/C][/ROW]
[ROW][C]73[/C][C]1189500[/C][C]1384801.0641706[/C][C]-195301.064170599[/C][/ROW]
[ROW][C]74[/C][C]955500[/C][C]1257632.67214586[/C][C]-302132.672145864[/C][/ROW]
[ROW][C]75[/C][C]858000[/C][C]1061216.95947828[/C][C]-203216.959478277[/C][/ROW]
[ROW][C]76[/C][C]643500[/C][C]923494.565799681[/C][C]-279994.565799681[/C][/ROW]
[ROW][C]77[/C][C]955500[/C][C]735299.785180194[/C][C]220200.214819806[/C][/ROW]
[ROW][C]78[/C][C]1150500[/C][C]857915.36994696[/C][C]292584.63005304[/C][/ROW]
[ROW][C]79[/C][C]1345500[/C][C]1028436.59127705[/C][C]317063.408722954[/C][/ROW]
[ROW][C]80[/C][C]1267500[/C][C]1217607.57546184[/C][C]49892.4245381621[/C][/ROW]
[ROW][C]81[/C][C]936000[/C][C]1242645.09746461[/C][C]-306645.097464608[/C][/ROW]
[ROW][C]82[/C][C]1345500[/C][C]1044457.03656051[/C][C]301042.963439489[/C][/ROW]
[ROW][C]83[/C][C]1053000[/C][C]1224249.76669132[/C][C]-171249.766691322[/C][/ROW]
[ROW][C]84[/C][C]1618500[/C][C]1110981.59073997[/C][C]507518.409260032[/C][/ROW]
[ROW][C]85[/C][C]1345500[/C][C]1421828.94090392[/C][C]-76328.9409039186[/C][/ROW]
[ROW][C]86[/C][C]975000[/C][C]1371914.98197504[/C][C]-396914.981975041[/C][/ROW]
[ROW][C]87[/C][C]897000[/C][C]1119923.6065465[/C][C]-222923.606546505[/C][/ROW]
[ROW][C]88[/C][C]604500[/C][C]972683.577247605[/C][C]-368183.577247605[/C][/ROW]
[ROW][C]89[/C][C]955500[/C][C]731765.961300156[/C][C]223734.038699844[/C][/ROW]
[ROW][C]90[/C][C]916500[/C][C]858239.603965606[/C][C]58260.3960343937[/C][/ROW]
[ROW][C]91[/C][C]1384500[/C][C]883363.598202459[/C][C]501136.401797541[/C][/ROW]
[ROW][C]92[/C][C]1384500[/C][C]1187119.14584276[/C][C]197380.854157243[/C][/ROW]
[ROW][C]93[/C][C]1053000[/C][C]1305845.2937911[/C][C]-252845.293791102[/C][/ROW]
[ROW][C]94[/C][C]1365000[/C][C]1144196.95811434[/C][C]220803.041885658[/C][/ROW]
[ROW][C]95[/C][C]1014000[/C][C]1277001.58521939[/C][C]-263001.585219385[/C][/ROW]
[ROW][C]96[/C][C]1579500[/C][C]1108618.72074652[/C][C]470881.279253483[/C][/ROW]
[ROW][C]97[/C][C]1345500[/C][C]1397914.65065143[/C][C]-52414.6506514349[/C][/ROW]
[ROW][C]98[/C][C]994500[/C][C]1364043.84119371[/C][C]-369543.841193706[/C][/ROW]
[ROW][C]99[/C][C]760500[/C][C]1130533.87993152[/C][C]-370033.87993152[/C][/ROW]
[ROW][C]100[/C][C]526500[/C][C]892566.883526515[/C][C]-366066.883526515[/C][/ROW]
[ROW][C]101[/C][C]1033500[/C][C]652934.870506169[/C][C]380565.129493831[/C][/ROW]
[ROW][C]102[/C][C]994500[/C][C]877826.557028862[/C][C]116673.442971138[/C][/ROW]
[ROW][C]103[/C][C]1306500[/C][C]941356.113437737[/C][C]365143.886562263[/C][/ROW]
[ROW][C]104[/C][C]1501500[/C][C]1162151.72623182[/C][C]339348.273768185[/C][/ROW]
[ROW][C]105[/C][C]1111500[/C][C]1370856.40896973[/C][C]-259356.408969728[/C][/ROW]
[ROW][C]106[/C][C]1248000[/C][C]1207586.0551644[/C][C]40413.9448356[/C][/ROW]
[ROW][C]107[/C][C]936000[/C][C]1229558.58577789[/C][C]-293558.585777888[/C][/ROW]
[ROW][C]108[/C][C]1618500[/C][C]1042362.33865137[/C][C]576137.661348627[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279992&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279992&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
3107250097500097500
4858000997197.250161722-139197.250161722
51111500871922.920126161239577.079873839
61092000982828.652128599109171.347871401
711700001014573.49941243155426.500587572
812090001076576.88574177132423.114258228
913455001125887.09228414219612.907715855
1011700001231410.12698197-61410.1269819732
1111115001163011.03312718-51511.0331271752
1213845001100135.69615495284364.303845055
1311700001247498.85554266-77498.8555426644
148775001170926.50865698-293426.508656975
151033500957953.92210885775546.0778911427
16780000973277.418303135-193277.418303135
171092000820718.331323044271281.668676956
18897000957576.075095522-60576.0750955215
191189500889184.735392672300315.264607328
2010725001046631.7513764825868.248623521
2111310001035190.3431923995809.656807612
2212675001067939.11022169199560.88977831
2312480001166884.6090863181115.3909136939
2414820001193726.9069525288273.093047502
2510725001351505.46963933-279005.469639326
268970001156460.54112968-259460.541129676
27994500970550.42528988923949.5747101113
28721500959613.290504318-238113.290504318
291033500784457.622073079249042.377926921
30799500912398.40392783-112898.40392783
311131000815958.343331219315041.656668781
321072500986853.20790412985646.7920958709
339555001017302.62315204-61802.6231520425
341365000956165.025773593408834.974226407
3512285001189735.7981951838764.2018048202
3614040001195617.07009492208382.929905081
3710530001308397.1962654-255397.196265401
389750001132419.03098337-157419.03098337
398775001015070.49323846-137570.493238464
40721500908412.576767593-186912.576767593
41955500769239.683294289186260.316705711
42858000862195.255468949-4195.25546894944
431170000837700.141835261332299.858164739
4411310001024363.82548199106636.174518008
459750001073117.77336591-98117.7733659116
461306500994552.391599173311947.608400827
4712090001172268.6063319636731.3936680371
4815600001180744.21324516379255.786754844
4912480001404622.52819354-156622.528193545
507605001296407.76746699-535907.767466994
51760500948370.626998594-187870.626998594
52760500812766.419190456-52266.419190456
53897000760166.583199862136833.416800138
54897000825671.04830509371328.9516949066
551209000851597.158013688357402.841986312
5611115001057882.5032008253617.4967991761
579945001077505.82096852-83005.8209685222
5812480001011977.63513687236022.364863126
5911505001145759.95164954740.04835049552
6016575001137024.85796076520475.142039245
6113065001452051.39391686-145551.393916859
627605001354881.18155403-594381.181554026
63799500974362.285998845-174862.285998845
64663000850486.281022514-187486.281022514
65916500716723.191010057199776.808989943
661053000823926.035346114229073.964653886
671326000951760.864061709374239.135938291
6813065001173282.83707008133217.16292992
6910530001247726.14623822-194726.146238217
7012285001117827.0526141110672.947385898
7110920001177429.50791605-85429.5079160475
7215600001115188.19216703444811.807832973
7311895001384801.0641706-195301.064170599
749555001257632.67214586-302132.672145864
758580001061216.95947828-203216.959478277
76643500923494.565799681-279994.565799681
77955500735299.785180194220200.214819806
781150500857915.36994696292584.63005304
7913455001028436.59127705317063.408722954
8012675001217607.5754618449892.4245381621
819360001242645.09746461-306645.097464608
8213455001044457.03656051301042.963439489
8310530001224249.76669132-171249.766691322
8416185001110981.59073997507518.409260032
8513455001421828.94090392-76328.9409039186
869750001371914.98197504-396914.981975041
878970001119923.6065465-222923.606546505
88604500972683.577247605-368183.577247605
89955500731765.961300156223734.038699844
90916500858239.60396560658260.3960343937
911384500883363.598202459501136.401797541
9213845001187119.14584276197380.854157243
9310530001305845.2937911-252845.293791102
9413650001144196.95811434220803.041885658
9510140001277001.58521939-263001.585219385
9615795001108618.72074652470881.279253483
9713455001397914.65065143-52414.6506514349
989945001364043.84119371-369543.841193706
997605001130533.87993152-370033.87993152
100526500892566.883526515-366066.883526515
1011033500652934.870506169380565.129493831
102994500877826.557028862116673.442971138
1031306500941356.113437737365143.886562263
10415015001162151.72623182339348.273768185
10511115001370856.40896973-259356.408969728
10612480001207586.055164440413.9448356
1079360001229558.58577789-293558.585777888
10816185001042362.33865137576137.661348627







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091397746.95910782895477.2373920331900016.68082361
1101397979.86268322804969.2013468191990990.52401963
1111398212.76625863723945.6240896412072479.90842761
1121398445.66983403649271.3968970452147619.94277102
1131398678.57340944579164.6959477082218192.45087116
1141398911.47698484512501.5799271962285321.37404248
1151399144.38056024448521.3026756642349767.45844482
1161399377.28413565386681.9689518022412072.59931949
1171399610.18771105326582.3151022612472638.06031984
1181399843.09128646267916.0210055162531770.16156739
1191400075.99486186210443.4269058672589708.56281785
1201400308.89843726153973.1922394452646644.60463508

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1397746.95910782 & 895477.237392033 & 1900016.68082361 \tabularnewline
110 & 1397979.86268322 & 804969.201346819 & 1990990.52401963 \tabularnewline
111 & 1398212.76625863 & 723945.624089641 & 2072479.90842761 \tabularnewline
112 & 1398445.66983403 & 649271.396897045 & 2147619.94277102 \tabularnewline
113 & 1398678.57340944 & 579164.695947708 & 2218192.45087116 \tabularnewline
114 & 1398911.47698484 & 512501.579927196 & 2285321.37404248 \tabularnewline
115 & 1399144.38056024 & 448521.302675664 & 2349767.45844482 \tabularnewline
116 & 1399377.28413565 & 386681.968951802 & 2412072.59931949 \tabularnewline
117 & 1399610.18771105 & 326582.315102261 & 2472638.06031984 \tabularnewline
118 & 1399843.09128646 & 267916.021005516 & 2531770.16156739 \tabularnewline
119 & 1400075.99486186 & 210443.426905867 & 2589708.56281785 \tabularnewline
120 & 1400308.89843726 & 153973.192239445 & 2646644.60463508 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279992&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]1397746.95910782[/C][C]895477.237392033[/C][C]1900016.68082361[/C][/ROW]
[ROW][C]110[/C][C]1397979.86268322[/C][C]804969.201346819[/C][C]1990990.52401963[/C][/ROW]
[ROW][C]111[/C][C]1398212.76625863[/C][C]723945.624089641[/C][C]2072479.90842761[/C][/ROW]
[ROW][C]112[/C][C]1398445.66983403[/C][C]649271.396897045[/C][C]2147619.94277102[/C][/ROW]
[ROW][C]113[/C][C]1398678.57340944[/C][C]579164.695947708[/C][C]2218192.45087116[/C][/ROW]
[ROW][C]114[/C][C]1398911.47698484[/C][C]512501.579927196[/C][C]2285321.37404248[/C][/ROW]
[ROW][C]115[/C][C]1399144.38056024[/C][C]448521.302675664[/C][C]2349767.45844482[/C][/ROW]
[ROW][C]116[/C][C]1399377.28413565[/C][C]386681.968951802[/C][C]2412072.59931949[/C][/ROW]
[ROW][C]117[/C][C]1399610.18771105[/C][C]326582.315102261[/C][C]2472638.06031984[/C][/ROW]
[ROW][C]118[/C][C]1399843.09128646[/C][C]267916.021005516[/C][C]2531770.16156739[/C][/ROW]
[ROW][C]119[/C][C]1400075.99486186[/C][C]210443.426905867[/C][C]2589708.56281785[/C][/ROW]
[ROW][C]120[/C][C]1400308.89843726[/C][C]153973.192239445[/C][C]2646644.60463508[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279992&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279992&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
1091397746.95910782895477.2373920331900016.68082361
1101397979.86268322804969.2013468191990990.52401963
1111398212.76625863723945.6240896412072479.90842761
1121398445.66983403649271.3968970452147619.94277102
1131398678.57340944579164.6959477082218192.45087116
1141398911.47698484512501.5799271962285321.37404248
1151399144.38056024448521.3026756642349767.45844482
1161399377.28413565386681.9689518022412072.59931949
1171399610.18771105326582.3151022612472638.06031984
1181399843.09128646267916.0210055162531770.16156739
1191400075.99486186210443.4269058672589708.56281785
1201400308.89843726153973.1922394452646644.60463508



Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')