Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 19 May 2017 06:45:20 +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/2017/May/19/t1495172878ubxn2ak4mjoedfp.htm/, Retrieved Sun, 19 May 2024 06:37:00 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 19 May 2024 06:37:00 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
45570
45118
41921
40167
37315
39206
57075
58664
51705
45527
41057
40867
41484
39738
37254
35177
32846
34079
51287
52800
48443
42223
38796
38952
42343
42023
39340
37149
35431
36537
49626
58677
56009
50069
46470
45603
46729
46989
44666
42920
40125
40941
57748
61246
59809
52682
48394
47436
49750
48172
44960
41831
38672
39704
56207
59254
57374
51309
47083
45092
46353
45348
42867
39980
36790
37504
53331
55997
54764
48590
45565
44959




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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.451144434695918
beta0.0799548849214091
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.451144434695918 \tabularnewline
beta & 0.0799548849214091 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.451144434695918[/C][/ROW]
[ROW][C]beta[/C][C]0.0799548849214091[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.451144434695918
beta0.0799548849214091
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134148443907.5723824786-2423.57238247864
143973841082.8692359108-1344.86923591078
153725437853.0559615959-599.055961595863
163517735238.4368604277-61.4368604277188
173284632568.4371900411277.562809958887
183407933567.512358321511.487641678992
195128752270.1963862843-983.196386284268
205280053259.8886252445-459.888625244545
214844345945.28784636052497.71215363954
224222340819.83767695311403.16232304688
233879636950.95119367061845.04880632941
243895237633.6807984321318.31920156796
254234337658.09977408374684.9002259163
264202338960.27477089793062.72522910214
273934038615.1322652234724.867734776562
283714937427.4900146295-278.490014629526
293543135372.421316692558.5786833074744
303653736919.9863794454-382.986379445421
314962654885.3954498993-5259.39544989928
325867754565.50468541594111.49531458409
335600951433.82931660984575.1706833902
345006947217.07499945712851.92500054291
354647044868.79196543521601.20803456478
364560345768.0904330324-165.090433032383
374672947533.2105162459-804.210516245905
384698945832.83153386821156.1684661318
394466643639.80622406261026.19377593738
404292042343.6720130835576.327986916491
414012541196.3510001022-1071.35100010216
424094142288.1404814472-1347.14048144723
435774857403.6956898173344.304310182699
446124665218.8437683881-3972.84376838811
455980958866.5381324944942.461867505626
465268252106.1418073173575.858192682652
474839448003.5078089527390.492191047306
484743647302.4307192567133.569280743301
494975048777.5527717488972.447228251214
504817248944.8020531015-772.802053101514
514496045730.7489081325-770.748908132518
524183143232.758593779-1401.75859377903
533867240073.0810173079-1401.08101730787
543970440637.2362575025-933.236257502511
555620756655.301175651-448.30117565101
565925461502.2089544932-2248.20895449323
575737458446.7952231248-1072.79522312477
585130950324.3613184574984.638681542565
594708346067.49931298041015.50068701959
604509245293.0146779568-201.014677956751
614635346851.1819435488-498.181943548836
624534845117.5959905541230.404009445905
634286742113.9681184109753.031881589064
643998039768.7620138139211.237986186134
653679037207.0056481269-417.005648126877
663750438377.2518842928-873.251884292797
675333154596.0531151998-1265.05311519984
685599757964.6525549949-1967.65255499486
695476455569.1168107127-805.116810712716
704859048594.5082236668-4.50822366676584
714556543770.48680583041794.51319416965
724495942570.00794218742388.99205781263

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 41484 & 43907.5723824786 & -2423.57238247864 \tabularnewline
14 & 39738 & 41082.8692359108 & -1344.86923591078 \tabularnewline
15 & 37254 & 37853.0559615959 & -599.055961595863 \tabularnewline
16 & 35177 & 35238.4368604277 & -61.4368604277188 \tabularnewline
17 & 32846 & 32568.4371900411 & 277.562809958887 \tabularnewline
18 & 34079 & 33567.512358321 & 511.487641678992 \tabularnewline
19 & 51287 & 52270.1963862843 & -983.196386284268 \tabularnewline
20 & 52800 & 53259.8886252445 & -459.888625244545 \tabularnewline
21 & 48443 & 45945.2878463605 & 2497.71215363954 \tabularnewline
22 & 42223 & 40819.8376769531 & 1403.16232304688 \tabularnewline
23 & 38796 & 36950.9511936706 & 1845.04880632941 \tabularnewline
24 & 38952 & 37633.680798432 & 1318.31920156796 \tabularnewline
25 & 42343 & 37658.0997740837 & 4684.9002259163 \tabularnewline
26 & 42023 & 38960.2747708979 & 3062.72522910214 \tabularnewline
27 & 39340 & 38615.1322652234 & 724.867734776562 \tabularnewline
28 & 37149 & 37427.4900146295 & -278.490014629526 \tabularnewline
29 & 35431 & 35372.4213166925 & 58.5786833074744 \tabularnewline
30 & 36537 & 36919.9863794454 & -382.986379445421 \tabularnewline
31 & 49626 & 54885.3954498993 & -5259.39544989928 \tabularnewline
32 & 58677 & 54565.5046854159 & 4111.49531458409 \tabularnewline
33 & 56009 & 51433.8293166098 & 4575.1706833902 \tabularnewline
34 & 50069 & 47217.0749994571 & 2851.92500054291 \tabularnewline
35 & 46470 & 44868.7919654352 & 1601.20803456478 \tabularnewline
36 & 45603 & 45768.0904330324 & -165.090433032383 \tabularnewline
37 & 46729 & 47533.2105162459 & -804.210516245905 \tabularnewline
38 & 46989 & 45832.8315338682 & 1156.1684661318 \tabularnewline
39 & 44666 & 43639.8062240626 & 1026.19377593738 \tabularnewline
40 & 42920 & 42343.6720130835 & 576.327986916491 \tabularnewline
41 & 40125 & 41196.3510001022 & -1071.35100010216 \tabularnewline
42 & 40941 & 42288.1404814472 & -1347.14048144723 \tabularnewline
43 & 57748 & 57403.6956898173 & 344.304310182699 \tabularnewline
44 & 61246 & 65218.8437683881 & -3972.84376838811 \tabularnewline
45 & 59809 & 58866.5381324944 & 942.461867505626 \tabularnewline
46 & 52682 & 52106.1418073173 & 575.858192682652 \tabularnewline
47 & 48394 & 48003.5078089527 & 390.492191047306 \tabularnewline
48 & 47436 & 47302.4307192567 & 133.569280743301 \tabularnewline
49 & 49750 & 48777.5527717488 & 972.447228251214 \tabularnewline
50 & 48172 & 48944.8020531015 & -772.802053101514 \tabularnewline
51 & 44960 & 45730.7489081325 & -770.748908132518 \tabularnewline
52 & 41831 & 43232.758593779 & -1401.75859377903 \tabularnewline
53 & 38672 & 40073.0810173079 & -1401.08101730787 \tabularnewline
54 & 39704 & 40637.2362575025 & -933.236257502511 \tabularnewline
55 & 56207 & 56655.301175651 & -448.30117565101 \tabularnewline
56 & 59254 & 61502.2089544932 & -2248.20895449323 \tabularnewline
57 & 57374 & 58446.7952231248 & -1072.79522312477 \tabularnewline
58 & 51309 & 50324.3613184574 & 984.638681542565 \tabularnewline
59 & 47083 & 46067.4993129804 & 1015.50068701959 \tabularnewline
60 & 45092 & 45293.0146779568 & -201.014677956751 \tabularnewline
61 & 46353 & 46851.1819435488 & -498.181943548836 \tabularnewline
62 & 45348 & 45117.5959905541 & 230.404009445905 \tabularnewline
63 & 42867 & 42113.9681184109 & 753.031881589064 \tabularnewline
64 & 39980 & 39768.7620138139 & 211.237986186134 \tabularnewline
65 & 36790 & 37207.0056481269 & -417.005648126877 \tabularnewline
66 & 37504 & 38377.2518842928 & -873.251884292797 \tabularnewline
67 & 53331 & 54596.0531151998 & -1265.05311519984 \tabularnewline
68 & 55997 & 57964.6525549949 & -1967.65255499486 \tabularnewline
69 & 54764 & 55569.1168107127 & -805.116810712716 \tabularnewline
70 & 48590 & 48594.5082236668 & -4.50822366676584 \tabularnewline
71 & 45565 & 43770.4868058304 & 1794.51319416965 \tabularnewline
72 & 44959 & 42570.0079421874 & 2388.99205781263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]41484[/C][C]43907.5723824786[/C][C]-2423.57238247864[/C][/ROW]
[ROW][C]14[/C][C]39738[/C][C]41082.8692359108[/C][C]-1344.86923591078[/C][/ROW]
[ROW][C]15[/C][C]37254[/C][C]37853.0559615959[/C][C]-599.055961595863[/C][/ROW]
[ROW][C]16[/C][C]35177[/C][C]35238.4368604277[/C][C]-61.4368604277188[/C][/ROW]
[ROW][C]17[/C][C]32846[/C][C]32568.4371900411[/C][C]277.562809958887[/C][/ROW]
[ROW][C]18[/C][C]34079[/C][C]33567.512358321[/C][C]511.487641678992[/C][/ROW]
[ROW][C]19[/C][C]51287[/C][C]52270.1963862843[/C][C]-983.196386284268[/C][/ROW]
[ROW][C]20[/C][C]52800[/C][C]53259.8886252445[/C][C]-459.888625244545[/C][/ROW]
[ROW][C]21[/C][C]48443[/C][C]45945.2878463605[/C][C]2497.71215363954[/C][/ROW]
[ROW][C]22[/C][C]42223[/C][C]40819.8376769531[/C][C]1403.16232304688[/C][/ROW]
[ROW][C]23[/C][C]38796[/C][C]36950.9511936706[/C][C]1845.04880632941[/C][/ROW]
[ROW][C]24[/C][C]38952[/C][C]37633.680798432[/C][C]1318.31920156796[/C][/ROW]
[ROW][C]25[/C][C]42343[/C][C]37658.0997740837[/C][C]4684.9002259163[/C][/ROW]
[ROW][C]26[/C][C]42023[/C][C]38960.2747708979[/C][C]3062.72522910214[/C][/ROW]
[ROW][C]27[/C][C]39340[/C][C]38615.1322652234[/C][C]724.867734776562[/C][/ROW]
[ROW][C]28[/C][C]37149[/C][C]37427.4900146295[/C][C]-278.490014629526[/C][/ROW]
[ROW][C]29[/C][C]35431[/C][C]35372.4213166925[/C][C]58.5786833074744[/C][/ROW]
[ROW][C]30[/C][C]36537[/C][C]36919.9863794454[/C][C]-382.986379445421[/C][/ROW]
[ROW][C]31[/C][C]49626[/C][C]54885.3954498993[/C][C]-5259.39544989928[/C][/ROW]
[ROW][C]32[/C][C]58677[/C][C]54565.5046854159[/C][C]4111.49531458409[/C][/ROW]
[ROW][C]33[/C][C]56009[/C][C]51433.8293166098[/C][C]4575.1706833902[/C][/ROW]
[ROW][C]34[/C][C]50069[/C][C]47217.0749994571[/C][C]2851.92500054291[/C][/ROW]
[ROW][C]35[/C][C]46470[/C][C]44868.7919654352[/C][C]1601.20803456478[/C][/ROW]
[ROW][C]36[/C][C]45603[/C][C]45768.0904330324[/C][C]-165.090433032383[/C][/ROW]
[ROW][C]37[/C][C]46729[/C][C]47533.2105162459[/C][C]-804.210516245905[/C][/ROW]
[ROW][C]38[/C][C]46989[/C][C]45832.8315338682[/C][C]1156.1684661318[/C][/ROW]
[ROW][C]39[/C][C]44666[/C][C]43639.8062240626[/C][C]1026.19377593738[/C][/ROW]
[ROW][C]40[/C][C]42920[/C][C]42343.6720130835[/C][C]576.327986916491[/C][/ROW]
[ROW][C]41[/C][C]40125[/C][C]41196.3510001022[/C][C]-1071.35100010216[/C][/ROW]
[ROW][C]42[/C][C]40941[/C][C]42288.1404814472[/C][C]-1347.14048144723[/C][/ROW]
[ROW][C]43[/C][C]57748[/C][C]57403.6956898173[/C][C]344.304310182699[/C][/ROW]
[ROW][C]44[/C][C]61246[/C][C]65218.8437683881[/C][C]-3972.84376838811[/C][/ROW]
[ROW][C]45[/C][C]59809[/C][C]58866.5381324944[/C][C]942.461867505626[/C][/ROW]
[ROW][C]46[/C][C]52682[/C][C]52106.1418073173[/C][C]575.858192682652[/C][/ROW]
[ROW][C]47[/C][C]48394[/C][C]48003.5078089527[/C][C]390.492191047306[/C][/ROW]
[ROW][C]48[/C][C]47436[/C][C]47302.4307192567[/C][C]133.569280743301[/C][/ROW]
[ROW][C]49[/C][C]49750[/C][C]48777.5527717488[/C][C]972.447228251214[/C][/ROW]
[ROW][C]50[/C][C]48172[/C][C]48944.8020531015[/C][C]-772.802053101514[/C][/ROW]
[ROW][C]51[/C][C]44960[/C][C]45730.7489081325[/C][C]-770.748908132518[/C][/ROW]
[ROW][C]52[/C][C]41831[/C][C]43232.758593779[/C][C]-1401.75859377903[/C][/ROW]
[ROW][C]53[/C][C]38672[/C][C]40073.0810173079[/C][C]-1401.08101730787[/C][/ROW]
[ROW][C]54[/C][C]39704[/C][C]40637.2362575025[/C][C]-933.236257502511[/C][/ROW]
[ROW][C]55[/C][C]56207[/C][C]56655.301175651[/C][C]-448.30117565101[/C][/ROW]
[ROW][C]56[/C][C]59254[/C][C]61502.2089544932[/C][C]-2248.20895449323[/C][/ROW]
[ROW][C]57[/C][C]57374[/C][C]58446.7952231248[/C][C]-1072.79522312477[/C][/ROW]
[ROW][C]58[/C][C]51309[/C][C]50324.3613184574[/C][C]984.638681542565[/C][/ROW]
[ROW][C]59[/C][C]47083[/C][C]46067.4993129804[/C][C]1015.50068701959[/C][/ROW]
[ROW][C]60[/C][C]45092[/C][C]45293.0146779568[/C][C]-201.014677956751[/C][/ROW]
[ROW][C]61[/C][C]46353[/C][C]46851.1819435488[/C][C]-498.181943548836[/C][/ROW]
[ROW][C]62[/C][C]45348[/C][C]45117.5959905541[/C][C]230.404009445905[/C][/ROW]
[ROW][C]63[/C][C]42867[/C][C]42113.9681184109[/C][C]753.031881589064[/C][/ROW]
[ROW][C]64[/C][C]39980[/C][C]39768.7620138139[/C][C]211.237986186134[/C][/ROW]
[ROW][C]65[/C][C]36790[/C][C]37207.0056481269[/C][C]-417.005648126877[/C][/ROW]
[ROW][C]66[/C][C]37504[/C][C]38377.2518842928[/C][C]-873.251884292797[/C][/ROW]
[ROW][C]67[/C][C]53331[/C][C]54596.0531151998[/C][C]-1265.05311519984[/C][/ROW]
[ROW][C]68[/C][C]55997[/C][C]57964.6525549949[/C][C]-1967.65255499486[/C][/ROW]
[ROW][C]69[/C][C]54764[/C][C]55569.1168107127[/C][C]-805.116810712716[/C][/ROW]
[ROW][C]70[/C][C]48590[/C][C]48594.5082236668[/C][C]-4.50822366676584[/C][/ROW]
[ROW][C]71[/C][C]45565[/C][C]43770.4868058304[/C][C]1794.51319416965[/C][/ROW]
[ROW][C]72[/C][C]44959[/C][C]42570.0079421874[/C][C]2388.99205781263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
134148443907.5723824786-2423.57238247864
143973841082.8692359108-1344.86923591078
153725437853.0559615959-599.055961595863
163517735238.4368604277-61.4368604277188
173284632568.4371900411277.562809958887
183407933567.512358321511.487641678992
195128752270.1963862843-983.196386284268
205280053259.8886252445-459.888625244545
214844345945.28784636052497.71215363954
224222340819.83767695311403.16232304688
233879636950.95119367061845.04880632941
243895237633.6807984321318.31920156796
254234337658.09977408374684.9002259163
264202338960.27477089793062.72522910214
273934038615.1322652234724.867734776562
283714937427.4900146295-278.490014629526
293543135372.421316692558.5786833074744
303653736919.9863794454-382.986379445421
314962654885.3954498993-5259.39544989928
325867754565.50468541594111.49531458409
335600951433.82931660984575.1706833902
345006947217.07499945712851.92500054291
354647044868.79196543521601.20803456478
364560345768.0904330324-165.090433032383
374672947533.2105162459-804.210516245905
384698945832.83153386821156.1684661318
394466643639.80622406261026.19377593738
404292042343.6720130835576.327986916491
414012541196.3510001022-1071.35100010216
424094142288.1404814472-1347.14048144723
435774857403.6956898173344.304310182699
446124665218.8437683881-3972.84376838811
455980958866.5381324944942.461867505626
465268252106.1418073173575.858192682652
474839448003.5078089527390.492191047306
484743647302.4307192567133.569280743301
494975048777.5527717488972.447228251214
504817248944.8020531015-772.802053101514
514496045730.7489081325-770.748908132518
524183143232.758593779-1401.75859377903
533867240073.0810173079-1401.08101730787
543970440637.2362575025-933.236257502511
555620756655.301175651-448.30117565101
565925461502.2089544932-2248.20895449323
575737458446.7952231248-1072.79522312477
585130950324.3613184574984.638681542565
594708346067.49931298041015.50068701959
604509245293.0146779568-201.014677956751
614635346851.1819435488-498.181943548836
624534845117.5959905541230.404009445905
634286742113.9681184109753.031881589064
643998039768.7620138139211.237986186134
653679037207.0056481269-417.005648126877
663750438377.2518842928-873.251884292797
675333154596.0531151998-1265.05311519984
685599757964.6525549949-1967.65255499486
695476455569.1168107127-805.116810712716
704859048594.5082236668-4.50822366676584
714556543770.48680583041794.51319416965
724495942570.00794218742388.99205781263







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7345117.214921954241638.783335779548595.6465081289
7444009.913953614140140.592155444147879.2357517841
7541182.521379920936906.443411309445458.5993485325
7638166.393342260533468.463245462342864.3234390586
7735123.074315919129988.850866631640257.2977652066
7836204.630134576330620.237729020441789.0225401322
7952607.444142619846559.502544224458655.3857410152
8056211.863963395549687.431912291262736.2960144999
8155463.787844519248450.317047402562477.2586416358
8249442.56314782441927.860178155756957.2661174923
8345758.882567616937731.076893733853786.6882414999
8444161.275909764535608.792743161952713.759076367

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 45117.2149219542 & 41638.7833357795 & 48595.6465081289 \tabularnewline
74 & 44009.9139536141 & 40140.5921554441 & 47879.2357517841 \tabularnewline
75 & 41182.5213799209 & 36906.4434113094 & 45458.5993485325 \tabularnewline
76 & 38166.3933422605 & 33468.4632454623 & 42864.3234390586 \tabularnewline
77 & 35123.0743159191 & 29988.8508666316 & 40257.2977652066 \tabularnewline
78 & 36204.6301345763 & 30620.2377290204 & 41789.0225401322 \tabularnewline
79 & 52607.4441426198 & 46559.5025442244 & 58655.3857410152 \tabularnewline
80 & 56211.8639633955 & 49687.4319122912 & 62736.2960144999 \tabularnewline
81 & 55463.7878445192 & 48450.3170474025 & 62477.2586416358 \tabularnewline
82 & 49442.563147824 & 41927.8601781557 & 56957.2661174923 \tabularnewline
83 & 45758.8825676169 & 37731.0768937338 & 53786.6882414999 \tabularnewline
84 & 44161.2759097645 & 35608.7927431619 & 52713.759076367 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]73[/C][C]45117.2149219542[/C][C]41638.7833357795[/C][C]48595.6465081289[/C][/ROW]
[ROW][C]74[/C][C]44009.9139536141[/C][C]40140.5921554441[/C][C]47879.2357517841[/C][/ROW]
[ROW][C]75[/C][C]41182.5213799209[/C][C]36906.4434113094[/C][C]45458.5993485325[/C][/ROW]
[ROW][C]76[/C][C]38166.3933422605[/C][C]33468.4632454623[/C][C]42864.3234390586[/C][/ROW]
[ROW][C]77[/C][C]35123.0743159191[/C][C]29988.8508666316[/C][C]40257.2977652066[/C][/ROW]
[ROW][C]78[/C][C]36204.6301345763[/C][C]30620.2377290204[/C][C]41789.0225401322[/C][/ROW]
[ROW][C]79[/C][C]52607.4441426198[/C][C]46559.5025442244[/C][C]58655.3857410152[/C][/ROW]
[ROW][C]80[/C][C]56211.8639633955[/C][C]49687.4319122912[/C][C]62736.2960144999[/C][/ROW]
[ROW][C]81[/C][C]55463.7878445192[/C][C]48450.3170474025[/C][C]62477.2586416358[/C][/ROW]
[ROW][C]82[/C][C]49442.563147824[/C][C]41927.8601781557[/C][C]56957.2661174923[/C][/ROW]
[ROW][C]83[/C][C]45758.8825676169[/C][C]37731.0768937338[/C][C]53786.6882414999[/C][/ROW]
[ROW][C]84[/C][C]44161.2759097645[/C][C]35608.7927431619[/C][C]52713.759076367[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
7345117.214921954241638.783335779548595.6465081289
7444009.913953614140140.592155444147879.2357517841
7541182.521379920936906.443411309445458.5993485325
7638166.393342260533468.463245462342864.3234390586
7735123.074315919129988.850866631640257.2977652066
7836204.630134576330620.237729020441789.0225401322
7952607.444142619846559.502544224458655.3857410152
8056211.863963395549687.431912291262736.2960144999
8155463.787844519248450.317047402562477.2586416358
8249442.56314782441927.860178155756957.2661174923
8345758.882567616937731.076893733853786.6882414999
8444161.275909764535608.792743161952713.759076367



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')