Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 05 May 2008 09:50:24 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/05/t12100027084chkn74qwmmicmu.htm/, Retrieved Thu, 31 Oct 2024 23:12:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=11531, Retrieved Thu, 31 Oct 2024 23:12:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVraag 3, exponential smoothing
Estimated Impact187
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2008-05-05 15:50:24] [6a51056b3b816eefd2f21a61f6d63f28] [Current]
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Dataseries X:
56421
53152
53536
52408
41454
38271
35306
26414
31917
38030
27534
18387
50556
43901
48572
43899
37532
40357
35489
29027
34485
42598
30306
26451
47460
50104
61465
53726
39477
43895
31481
29896
33842
39120
33702
25094
51442
45594
52518
48564
41745
49585
32747
33379
35645
37034
35681
20972
58552
54955
65540
51570
51145
46641
35704
33253
35193
41668
34865
21210
56126
49231
59723
48103
47472
50497
40059
34149
36860
46356
36577




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11531&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11531&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11531&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.580952155663673
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.580952155663673 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11531&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]0.580952155663673[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11531&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11531&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
alpha0.580952155663673
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
35353653152384
45240853375.0856277749-967.085627774853
54145452813.2551476077-11359.2551476077
63827146214.0713828713-7943.07138287133
73530641599.5269404018-6293.5269404018
82641437943.288897648-11529.2888976480
93191731245.3236592901671.676340709866
103803031635.53547733386394.46452266618
112753435350.4134260916-7816.41342609162
121838730809.4511966452-12422.4511966452
135055623592.601395327426963.3986046726
144390139257.04593873084643.95406126919
154857241954.96106142826617.03893857179
164389945799.1440969020-1900.14409690195
173753244695.2512877352-7163.25128773516
184035740533.7450105648-176.745010564839
193548940431.0646156744-4942.0646156744
202902737559.9615237692-8532.9615237692
213448532602.71913234031882.28086765969
224259833696.23425997178901.7657400283
233030638867.7342558542-8561.73425585416
242645133893.7762836962-7442.77628369618
254746029569.879357560417890.1206424396
265010439963.183509868910140.8164901311
276146545854.512710000315610.4872899997
285372654923.458952086-1197.45895208598
293947754227.7925925529-14750.7925925529
304389545658.2878381615-1763.28783816154
313148144633.9019675261-13152.9019675261
322989636992.6952162588-7096.69521625883
333384232869.8548322852972.145167714807
343912033434.62466308715685.37533691287
353370236737.5557208237-3035.55572082374
362509434974.043081174-9880.043081174
375144229234.21075511622207.789244884
384559442135.87378945593458.12621054411
395251844144.87966602858373.12033397146
404856449009.2619736806-445.261973680586
414174548750.5860702358-7005.58607023579
424958544680.67574104494904.32425895509
433274747529.8534913585-14782.8534913585
443337938941.7228886935-5562.72288869353
453564535710.0470351474-65.0470351473705
463703435672.2578198591361.74218014102
473568136463.3648748701-782.36487487005
482097236008.8483142988-15036.8483142988
495855227273.158871719231278.8411282808
505495545444.66905185559510.33094814451
516554050969.71631725514570.2836827450
525157059434.354031377-7864.35403137694
535114554865.5406039462-3720.54060394621
544664152704.0845198494-6063.08451984944
553570449181.7224980719-13477.7224980719
563325341351.8105593802-8098.81055938023
573519336646.7891065966-1453.78910659657
584166835802.20719123895865.79280876107
593486539209.9521681651-4344.95216816515
602121036685.7428398141-15475.7428398141
615612627695.076676527428430.9233234726
624923144212.08286880745018.91713119259
635972347127.833595271112595.1664047289
644810354445.022669041-6342.02266904102
654747250760.6109281938-3288.61092819376
665049748850.08532032051646.91467967952
674005949806.8639536744-9747.86395367444
683414944143.8213766711-9994.82137667106
693686038337.3083524207-1477.30835242065
704635637479.06288050198876.93711949808
713657742636.1386357652-6059.1386357652

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 53536 & 53152 & 384 \tabularnewline
4 & 52408 & 53375.0856277749 & -967.085627774853 \tabularnewline
5 & 41454 & 52813.2551476077 & -11359.2551476077 \tabularnewline
6 & 38271 & 46214.0713828713 & -7943.07138287133 \tabularnewline
7 & 35306 & 41599.5269404018 & -6293.5269404018 \tabularnewline
8 & 26414 & 37943.288897648 & -11529.2888976480 \tabularnewline
9 & 31917 & 31245.3236592901 & 671.676340709866 \tabularnewline
10 & 38030 & 31635.5354773338 & 6394.46452266618 \tabularnewline
11 & 27534 & 35350.4134260916 & -7816.41342609162 \tabularnewline
12 & 18387 & 30809.4511966452 & -12422.4511966452 \tabularnewline
13 & 50556 & 23592.6013953274 & 26963.3986046726 \tabularnewline
14 & 43901 & 39257.0459387308 & 4643.95406126919 \tabularnewline
15 & 48572 & 41954.9610614282 & 6617.03893857179 \tabularnewline
16 & 43899 & 45799.1440969020 & -1900.14409690195 \tabularnewline
17 & 37532 & 44695.2512877352 & -7163.25128773516 \tabularnewline
18 & 40357 & 40533.7450105648 & -176.745010564839 \tabularnewline
19 & 35489 & 40431.0646156744 & -4942.0646156744 \tabularnewline
20 & 29027 & 37559.9615237692 & -8532.9615237692 \tabularnewline
21 & 34485 & 32602.7191323403 & 1882.28086765969 \tabularnewline
22 & 42598 & 33696.2342599717 & 8901.7657400283 \tabularnewline
23 & 30306 & 38867.7342558542 & -8561.73425585416 \tabularnewline
24 & 26451 & 33893.7762836962 & -7442.77628369618 \tabularnewline
25 & 47460 & 29569.8793575604 & 17890.1206424396 \tabularnewline
26 & 50104 & 39963.1835098689 & 10140.8164901311 \tabularnewline
27 & 61465 & 45854.5127100003 & 15610.4872899997 \tabularnewline
28 & 53726 & 54923.458952086 & -1197.45895208598 \tabularnewline
29 & 39477 & 54227.7925925529 & -14750.7925925529 \tabularnewline
30 & 43895 & 45658.2878381615 & -1763.28783816154 \tabularnewline
31 & 31481 & 44633.9019675261 & -13152.9019675261 \tabularnewline
32 & 29896 & 36992.6952162588 & -7096.69521625883 \tabularnewline
33 & 33842 & 32869.8548322852 & 972.145167714807 \tabularnewline
34 & 39120 & 33434.6246630871 & 5685.37533691287 \tabularnewline
35 & 33702 & 36737.5557208237 & -3035.55572082374 \tabularnewline
36 & 25094 & 34974.043081174 & -9880.043081174 \tabularnewline
37 & 51442 & 29234.210755116 & 22207.789244884 \tabularnewline
38 & 45594 & 42135.8737894559 & 3458.12621054411 \tabularnewline
39 & 52518 & 44144.8796660285 & 8373.12033397146 \tabularnewline
40 & 48564 & 49009.2619736806 & -445.261973680586 \tabularnewline
41 & 41745 & 48750.5860702358 & -7005.58607023579 \tabularnewline
42 & 49585 & 44680.6757410449 & 4904.32425895509 \tabularnewline
43 & 32747 & 47529.8534913585 & -14782.8534913585 \tabularnewline
44 & 33379 & 38941.7228886935 & -5562.72288869353 \tabularnewline
45 & 35645 & 35710.0470351474 & -65.0470351473705 \tabularnewline
46 & 37034 & 35672.257819859 & 1361.74218014102 \tabularnewline
47 & 35681 & 36463.3648748701 & -782.36487487005 \tabularnewline
48 & 20972 & 36008.8483142988 & -15036.8483142988 \tabularnewline
49 & 58552 & 27273.1588717192 & 31278.8411282808 \tabularnewline
50 & 54955 & 45444.6690518555 & 9510.33094814451 \tabularnewline
51 & 65540 & 50969.716317255 & 14570.2836827450 \tabularnewline
52 & 51570 & 59434.354031377 & -7864.35403137694 \tabularnewline
53 & 51145 & 54865.5406039462 & -3720.54060394621 \tabularnewline
54 & 46641 & 52704.0845198494 & -6063.08451984944 \tabularnewline
55 & 35704 & 49181.7224980719 & -13477.7224980719 \tabularnewline
56 & 33253 & 41351.8105593802 & -8098.81055938023 \tabularnewline
57 & 35193 & 36646.7891065966 & -1453.78910659657 \tabularnewline
58 & 41668 & 35802.2071912389 & 5865.79280876107 \tabularnewline
59 & 34865 & 39209.9521681651 & -4344.95216816515 \tabularnewline
60 & 21210 & 36685.7428398141 & -15475.7428398141 \tabularnewline
61 & 56126 & 27695.0766765274 & 28430.9233234726 \tabularnewline
62 & 49231 & 44212.0828688074 & 5018.91713119259 \tabularnewline
63 & 59723 & 47127.8335952711 & 12595.1664047289 \tabularnewline
64 & 48103 & 54445.022669041 & -6342.02266904102 \tabularnewline
65 & 47472 & 50760.6109281938 & -3288.61092819376 \tabularnewline
66 & 50497 & 48850.0853203205 & 1646.91467967952 \tabularnewline
67 & 40059 & 49806.8639536744 & -9747.86395367444 \tabularnewline
68 & 34149 & 44143.8213766711 & -9994.82137667106 \tabularnewline
69 & 36860 & 38337.3083524207 & -1477.30835242065 \tabularnewline
70 & 46356 & 37479.0628805019 & 8876.93711949808 \tabularnewline
71 & 36577 & 42636.1386357652 & -6059.1386357652 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11531&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]53536[/C][C]53152[/C][C]384[/C][/ROW]
[ROW][C]4[/C][C]52408[/C][C]53375.0856277749[/C][C]-967.085627774853[/C][/ROW]
[ROW][C]5[/C][C]41454[/C][C]52813.2551476077[/C][C]-11359.2551476077[/C][/ROW]
[ROW][C]6[/C][C]38271[/C][C]46214.0713828713[/C][C]-7943.07138287133[/C][/ROW]
[ROW][C]7[/C][C]35306[/C][C]41599.5269404018[/C][C]-6293.5269404018[/C][/ROW]
[ROW][C]8[/C][C]26414[/C][C]37943.288897648[/C][C]-11529.2888976480[/C][/ROW]
[ROW][C]9[/C][C]31917[/C][C]31245.3236592901[/C][C]671.676340709866[/C][/ROW]
[ROW][C]10[/C][C]38030[/C][C]31635.5354773338[/C][C]6394.46452266618[/C][/ROW]
[ROW][C]11[/C][C]27534[/C][C]35350.4134260916[/C][C]-7816.41342609162[/C][/ROW]
[ROW][C]12[/C][C]18387[/C][C]30809.4511966452[/C][C]-12422.4511966452[/C][/ROW]
[ROW][C]13[/C][C]50556[/C][C]23592.6013953274[/C][C]26963.3986046726[/C][/ROW]
[ROW][C]14[/C][C]43901[/C][C]39257.0459387308[/C][C]4643.95406126919[/C][/ROW]
[ROW][C]15[/C][C]48572[/C][C]41954.9610614282[/C][C]6617.03893857179[/C][/ROW]
[ROW][C]16[/C][C]43899[/C][C]45799.1440969020[/C][C]-1900.14409690195[/C][/ROW]
[ROW][C]17[/C][C]37532[/C][C]44695.2512877352[/C][C]-7163.25128773516[/C][/ROW]
[ROW][C]18[/C][C]40357[/C][C]40533.7450105648[/C][C]-176.745010564839[/C][/ROW]
[ROW][C]19[/C][C]35489[/C][C]40431.0646156744[/C][C]-4942.0646156744[/C][/ROW]
[ROW][C]20[/C][C]29027[/C][C]37559.9615237692[/C][C]-8532.9615237692[/C][/ROW]
[ROW][C]21[/C][C]34485[/C][C]32602.7191323403[/C][C]1882.28086765969[/C][/ROW]
[ROW][C]22[/C][C]42598[/C][C]33696.2342599717[/C][C]8901.7657400283[/C][/ROW]
[ROW][C]23[/C][C]30306[/C][C]38867.7342558542[/C][C]-8561.73425585416[/C][/ROW]
[ROW][C]24[/C][C]26451[/C][C]33893.7762836962[/C][C]-7442.77628369618[/C][/ROW]
[ROW][C]25[/C][C]47460[/C][C]29569.8793575604[/C][C]17890.1206424396[/C][/ROW]
[ROW][C]26[/C][C]50104[/C][C]39963.1835098689[/C][C]10140.8164901311[/C][/ROW]
[ROW][C]27[/C][C]61465[/C][C]45854.5127100003[/C][C]15610.4872899997[/C][/ROW]
[ROW][C]28[/C][C]53726[/C][C]54923.458952086[/C][C]-1197.45895208598[/C][/ROW]
[ROW][C]29[/C][C]39477[/C][C]54227.7925925529[/C][C]-14750.7925925529[/C][/ROW]
[ROW][C]30[/C][C]43895[/C][C]45658.2878381615[/C][C]-1763.28783816154[/C][/ROW]
[ROW][C]31[/C][C]31481[/C][C]44633.9019675261[/C][C]-13152.9019675261[/C][/ROW]
[ROW][C]32[/C][C]29896[/C][C]36992.6952162588[/C][C]-7096.69521625883[/C][/ROW]
[ROW][C]33[/C][C]33842[/C][C]32869.8548322852[/C][C]972.145167714807[/C][/ROW]
[ROW][C]34[/C][C]39120[/C][C]33434.6246630871[/C][C]5685.37533691287[/C][/ROW]
[ROW][C]35[/C][C]33702[/C][C]36737.5557208237[/C][C]-3035.55572082374[/C][/ROW]
[ROW][C]36[/C][C]25094[/C][C]34974.043081174[/C][C]-9880.043081174[/C][/ROW]
[ROW][C]37[/C][C]51442[/C][C]29234.210755116[/C][C]22207.789244884[/C][/ROW]
[ROW][C]38[/C][C]45594[/C][C]42135.8737894559[/C][C]3458.12621054411[/C][/ROW]
[ROW][C]39[/C][C]52518[/C][C]44144.8796660285[/C][C]8373.12033397146[/C][/ROW]
[ROW][C]40[/C][C]48564[/C][C]49009.2619736806[/C][C]-445.261973680586[/C][/ROW]
[ROW][C]41[/C][C]41745[/C][C]48750.5860702358[/C][C]-7005.58607023579[/C][/ROW]
[ROW][C]42[/C][C]49585[/C][C]44680.6757410449[/C][C]4904.32425895509[/C][/ROW]
[ROW][C]43[/C][C]32747[/C][C]47529.8534913585[/C][C]-14782.8534913585[/C][/ROW]
[ROW][C]44[/C][C]33379[/C][C]38941.7228886935[/C][C]-5562.72288869353[/C][/ROW]
[ROW][C]45[/C][C]35645[/C][C]35710.0470351474[/C][C]-65.0470351473705[/C][/ROW]
[ROW][C]46[/C][C]37034[/C][C]35672.257819859[/C][C]1361.74218014102[/C][/ROW]
[ROW][C]47[/C][C]35681[/C][C]36463.3648748701[/C][C]-782.36487487005[/C][/ROW]
[ROW][C]48[/C][C]20972[/C][C]36008.8483142988[/C][C]-15036.8483142988[/C][/ROW]
[ROW][C]49[/C][C]58552[/C][C]27273.1588717192[/C][C]31278.8411282808[/C][/ROW]
[ROW][C]50[/C][C]54955[/C][C]45444.6690518555[/C][C]9510.33094814451[/C][/ROW]
[ROW][C]51[/C][C]65540[/C][C]50969.716317255[/C][C]14570.2836827450[/C][/ROW]
[ROW][C]52[/C][C]51570[/C][C]59434.354031377[/C][C]-7864.35403137694[/C][/ROW]
[ROW][C]53[/C][C]51145[/C][C]54865.5406039462[/C][C]-3720.54060394621[/C][/ROW]
[ROW][C]54[/C][C]46641[/C][C]52704.0845198494[/C][C]-6063.08451984944[/C][/ROW]
[ROW][C]55[/C][C]35704[/C][C]49181.7224980719[/C][C]-13477.7224980719[/C][/ROW]
[ROW][C]56[/C][C]33253[/C][C]41351.8105593802[/C][C]-8098.81055938023[/C][/ROW]
[ROW][C]57[/C][C]35193[/C][C]36646.7891065966[/C][C]-1453.78910659657[/C][/ROW]
[ROW][C]58[/C][C]41668[/C][C]35802.2071912389[/C][C]5865.79280876107[/C][/ROW]
[ROW][C]59[/C][C]34865[/C][C]39209.9521681651[/C][C]-4344.95216816515[/C][/ROW]
[ROW][C]60[/C][C]21210[/C][C]36685.7428398141[/C][C]-15475.7428398141[/C][/ROW]
[ROW][C]61[/C][C]56126[/C][C]27695.0766765274[/C][C]28430.9233234726[/C][/ROW]
[ROW][C]62[/C][C]49231[/C][C]44212.0828688074[/C][C]5018.91713119259[/C][/ROW]
[ROW][C]63[/C][C]59723[/C][C]47127.8335952711[/C][C]12595.1664047289[/C][/ROW]
[ROW][C]64[/C][C]48103[/C][C]54445.022669041[/C][C]-6342.02266904102[/C][/ROW]
[ROW][C]65[/C][C]47472[/C][C]50760.6109281938[/C][C]-3288.61092819376[/C][/ROW]
[ROW][C]66[/C][C]50497[/C][C]48850.0853203205[/C][C]1646.91467967952[/C][/ROW]
[ROW][C]67[/C][C]40059[/C][C]49806.8639536744[/C][C]-9747.86395367444[/C][/ROW]
[ROW][C]68[/C][C]34149[/C][C]44143.8213766711[/C][C]-9994.82137667106[/C][/ROW]
[ROW][C]69[/C][C]36860[/C][C]38337.3083524207[/C][C]-1477.30835242065[/C][/ROW]
[ROW][C]70[/C][C]46356[/C][C]37479.0628805019[/C][C]8876.93711949808[/C][/ROW]
[ROW][C]71[/C][C]36577[/C][C]42636.1386357652[/C][C]-6059.1386357652[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11531&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11531&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
35353653152384
45240853375.0856277749-967.085627774853
54145452813.2551476077-11359.2551476077
63827146214.0713828713-7943.07138287133
73530641599.5269404018-6293.5269404018
82641437943.288897648-11529.2888976480
93191731245.3236592901671.676340709866
103803031635.53547733386394.46452266618
112753435350.4134260916-7816.41342609162
121838730809.4511966452-12422.4511966452
135055623592.601395327426963.3986046726
144390139257.04593873084643.95406126919
154857241954.96106142826617.03893857179
164389945799.1440969020-1900.14409690195
173753244695.2512877352-7163.25128773516
184035740533.7450105648-176.745010564839
193548940431.0646156744-4942.0646156744
202902737559.9615237692-8532.9615237692
213448532602.71913234031882.28086765969
224259833696.23425997178901.7657400283
233030638867.7342558542-8561.73425585416
242645133893.7762836962-7442.77628369618
254746029569.879357560417890.1206424396
265010439963.183509868910140.8164901311
276146545854.512710000315610.4872899997
285372654923.458952086-1197.45895208598
293947754227.7925925529-14750.7925925529
304389545658.2878381615-1763.28783816154
313148144633.9019675261-13152.9019675261
322989636992.6952162588-7096.69521625883
333384232869.8548322852972.145167714807
343912033434.62466308715685.37533691287
353370236737.5557208237-3035.55572082374
362509434974.043081174-9880.043081174
375144229234.21075511622207.789244884
384559442135.87378945593458.12621054411
395251844144.87966602858373.12033397146
404856449009.2619736806-445.261973680586
414174548750.5860702358-7005.58607023579
424958544680.67574104494904.32425895509
433274747529.8534913585-14782.8534913585
443337938941.7228886935-5562.72288869353
453564535710.0470351474-65.0470351473705
463703435672.2578198591361.74218014102
473568136463.3648748701-782.36487487005
482097236008.8483142988-15036.8483142988
495855227273.158871719231278.8411282808
505495545444.66905185559510.33094814451
516554050969.71631725514570.2836827450
525157059434.354031377-7864.35403137694
535114554865.5406039462-3720.54060394621
544664152704.0845198494-6063.08451984944
553570449181.7224980719-13477.7224980719
563325341351.8105593802-8098.81055938023
573519336646.7891065966-1453.78910659657
584166835802.20719123895865.79280876107
593486539209.9521681651-4344.95216816515
602121036685.7428398141-15475.7428398141
615612627695.076676527428430.9233234726
624923144212.08286880745018.91713119259
635972347127.833595271112595.1664047289
644810354445.022669041-6342.02266904102
654747250760.6109281938-3288.61092819376
665049748850.08532032051646.91467967952
674005949806.8639536744-9747.86395367444
683414944143.8213766711-9994.82137667106
693686038337.3083524207-1477.30835242065
704635637479.06288050198876.93711949808
713657742636.1386357652-6059.1386357652







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7239116.068983852418610.572225801459621.5657419033
7339116.068983852415401.345340862662830.7926268422
7439116.068983852412577.402144082265654.7358236226
7539116.068983852410026.318936778168205.8190309267
7639116.06898385247681.5930383208670550.5449293839
7739116.06898385245500.0162985780472732.1216691267
7839116.06898385243451.6368657311274780.5011019736
7939116.06898385241514.6801999654276717.4577677393
8039116.0689838524-327.27213535251978559.4101030572
8139116.0689838524-2086.9634144420480319.1013821468
8239116.0689838524-3774.5197155795882006.6576832843
8339116.0689838524-5398.1458149372383630.283782642

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
72 & 39116.0689838524 & 18610.5722258014 & 59621.5657419033 \tabularnewline
73 & 39116.0689838524 & 15401.3453408626 & 62830.7926268422 \tabularnewline
74 & 39116.0689838524 & 12577.4021440822 & 65654.7358236226 \tabularnewline
75 & 39116.0689838524 & 10026.3189367781 & 68205.8190309267 \tabularnewline
76 & 39116.0689838524 & 7681.59303832086 & 70550.5449293839 \tabularnewline
77 & 39116.0689838524 & 5500.01629857804 & 72732.1216691267 \tabularnewline
78 & 39116.0689838524 & 3451.63686573112 & 74780.5011019736 \tabularnewline
79 & 39116.0689838524 & 1514.68019996542 & 76717.4577677393 \tabularnewline
80 & 39116.0689838524 & -327.272135352519 & 78559.4101030572 \tabularnewline
81 & 39116.0689838524 & -2086.96341444204 & 80319.1013821468 \tabularnewline
82 & 39116.0689838524 & -3774.51971557958 & 82006.6576832843 \tabularnewline
83 & 39116.0689838524 & -5398.14581493723 & 83630.283782642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11531&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]72[/C][C]39116.0689838524[/C][C]18610.5722258014[/C][C]59621.5657419033[/C][/ROW]
[ROW][C]73[/C][C]39116.0689838524[/C][C]15401.3453408626[/C][C]62830.7926268422[/C][/ROW]
[ROW][C]74[/C][C]39116.0689838524[/C][C]12577.4021440822[/C][C]65654.7358236226[/C][/ROW]
[ROW][C]75[/C][C]39116.0689838524[/C][C]10026.3189367781[/C][C]68205.8190309267[/C][/ROW]
[ROW][C]76[/C][C]39116.0689838524[/C][C]7681.59303832086[/C][C]70550.5449293839[/C][/ROW]
[ROW][C]77[/C][C]39116.0689838524[/C][C]5500.01629857804[/C][C]72732.1216691267[/C][/ROW]
[ROW][C]78[/C][C]39116.0689838524[/C][C]3451.63686573112[/C][C]74780.5011019736[/C][/ROW]
[ROW][C]79[/C][C]39116.0689838524[/C][C]1514.68019996542[/C][C]76717.4577677393[/C][/ROW]
[ROW][C]80[/C][C]39116.0689838524[/C][C]-327.272135352519[/C][C]78559.4101030572[/C][/ROW]
[ROW][C]81[/C][C]39116.0689838524[/C][C]-2086.96341444204[/C][C]80319.1013821468[/C][/ROW]
[ROW][C]82[/C][C]39116.0689838524[/C][C]-3774.51971557958[/C][C]82006.6576832843[/C][/ROW]
[ROW][C]83[/C][C]39116.0689838524[/C][C]-5398.14581493723[/C][C]83630.283782642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11531&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11531&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
7239116.068983852418610.572225801459621.5657419033
7339116.068983852415401.345340862662830.7926268422
7439116.068983852412577.402144082265654.7358236226
7539116.068983852410026.318936778168205.8190309267
7639116.06898385247681.5930383208670550.5449293839
7739116.06898385245500.0162985780472732.1216691267
7839116.06898385243451.6368657311274780.5011019736
7939116.06898385241514.6801999654276717.4577677393
8039116.0689838524-327.27213535251978559.4101030572
8139116.0689838524-2086.9634144420480319.1013821468
8239116.0689838524-3774.5197155795882006.6576832843
8339116.0689838524-5398.1458149372383630.283782642



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')