Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 29 Apr 2008 06:09:24 -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/Apr/29/t12094710117s6ilyidti6b0ya.htm/, Retrieved Sun, 12 May 2024 20:41:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=11032, Retrieved Sun, 12 May 2024 20:41:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsexponential,smoothing,double
Estimated Impact226
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2008-04-29 12:09:24] [be9d907f730a9e9810527c97ce58429f] [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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11032&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11032&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11032&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.580952155659036
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.580952155659036 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11032&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]0.580952155659036[/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=11032&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11032&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
alpha0.580952155659036
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
35353653152384
45240853375.0856277731-967.085627773064
54145452813.2551476114-11359.2551476114
63827146214.0713829256-7943.07138292557
73530641599.5269404614-6293.52694046136
82641437943.2888977021-11529.2888977021
93191731245.3236593663671.676340633712
103803031635.53547736266394.46452263738
112753435350.413426074-7816.41342607403
121838730809.4511966741-12422.4511966741
135055623592.601395397126963.3986046029
144390139257.0459386354643.954061365
154857241954.96106136656617.03893863347
164389945799.1440968454-1900.14409684543
173753244695.2512877203-7163.25128772028
184035740533.7450105918-176.745010591818
193548940431.0646156865-4942.06461568653
202902737559.9615237972-8532.9615237972
213448532602.71913239161882.28086760840
224259833696.23425998458901.76574001554
233030638867.7342558182-8561.73425581824
242645133893.7762837208-7442.77628372082
254746029569.879357605317890.1206423947
265010439963.183509804710140.8164901953
276146545854.512709926415610.4872900736
285372654923.4589519826-1197.45895198263
293947754227.7925925151-14750.7925925151
304389545658.2878382141-1763.28783821412
313148144633.9019675563-13152.9019675563
322989636992.6952163325-7096.69521633247
333384232869.854832349972.14516765104
343912033434.62466310935685.37533689065
353370236737.5557208067-3035.55572080669
362509434974.0430811809-9880.04308118093
375144229234.210755164722207.7892448353
384559442135.87378937333458.12621062667
395251844144.87966597798373.1203340221
404856449009.2619736206-445.261973620552
414174548750.5860702127-7005.5860702127
424958544680.67574106774904.32425893228
433274747529.8534913453-14782.8534913453
443337938941.7228887566-5562.72288875656
453564535710.0470351996-65.0470351995755
463703435672.25781988121361.74218011885
473568136463.3648748730-782.364874873034
482097236008.8483143036-15036.8483143036
495855227273.15887179131278.841128209
505495545444.66905174059510.33094825948
516554050969.716317162714570.2836828373
525157059434.3540312707-7864.3540312707
535114554865.5406039382-3720.54060393816
544664152704.0845198633-6063.08451986332
553570449181.7224981058-13477.7224981058
563325341351.8105594569-8098.81055945695
573519336646.7891066663-1453.78910666627
584166835802.20719127495865.79280872512
593486539209.952168153-4344.95216815301
602121036685.7428398291-15475.7428398291
615612627695.076676605528430.9233233945
624923144212.08286870835018.9171312917
635972347127.833595206312595.1664047937
644810354445.0226689555-6342.02266895545
654747250760.6109281873-3288.61092818731
665049748850.0853203331646.91467966697
674005949806.8639536721-9747.86395367207
683414944143.8213767153-9994.82137671526
693686038337.3083524855-1477.30835248552
704635637479.06288053608876.93711946404
713657742636.1386357383-6059.1386357383

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 53536 & 53152 & 384 \tabularnewline
4 & 52408 & 53375.0856277731 & -967.085627773064 \tabularnewline
5 & 41454 & 52813.2551476114 & -11359.2551476114 \tabularnewline
6 & 38271 & 46214.0713829256 & -7943.07138292557 \tabularnewline
7 & 35306 & 41599.5269404614 & -6293.52694046136 \tabularnewline
8 & 26414 & 37943.2888977021 & -11529.2888977021 \tabularnewline
9 & 31917 & 31245.3236593663 & 671.676340633712 \tabularnewline
10 & 38030 & 31635.5354773626 & 6394.46452263738 \tabularnewline
11 & 27534 & 35350.413426074 & -7816.41342607403 \tabularnewline
12 & 18387 & 30809.4511966741 & -12422.4511966741 \tabularnewline
13 & 50556 & 23592.6013953971 & 26963.3986046029 \tabularnewline
14 & 43901 & 39257.045938635 & 4643.954061365 \tabularnewline
15 & 48572 & 41954.9610613665 & 6617.03893863347 \tabularnewline
16 & 43899 & 45799.1440968454 & -1900.14409684543 \tabularnewline
17 & 37532 & 44695.2512877203 & -7163.25128772028 \tabularnewline
18 & 40357 & 40533.7450105918 & -176.745010591818 \tabularnewline
19 & 35489 & 40431.0646156865 & -4942.06461568653 \tabularnewline
20 & 29027 & 37559.9615237972 & -8532.9615237972 \tabularnewline
21 & 34485 & 32602.7191323916 & 1882.28086760840 \tabularnewline
22 & 42598 & 33696.2342599845 & 8901.76574001554 \tabularnewline
23 & 30306 & 38867.7342558182 & -8561.73425581824 \tabularnewline
24 & 26451 & 33893.7762837208 & -7442.77628372082 \tabularnewline
25 & 47460 & 29569.8793576053 & 17890.1206423947 \tabularnewline
26 & 50104 & 39963.1835098047 & 10140.8164901953 \tabularnewline
27 & 61465 & 45854.5127099264 & 15610.4872900736 \tabularnewline
28 & 53726 & 54923.4589519826 & -1197.45895198263 \tabularnewline
29 & 39477 & 54227.7925925151 & -14750.7925925151 \tabularnewline
30 & 43895 & 45658.2878382141 & -1763.28783821412 \tabularnewline
31 & 31481 & 44633.9019675563 & -13152.9019675563 \tabularnewline
32 & 29896 & 36992.6952163325 & -7096.69521633247 \tabularnewline
33 & 33842 & 32869.854832349 & 972.14516765104 \tabularnewline
34 & 39120 & 33434.6246631093 & 5685.37533689065 \tabularnewline
35 & 33702 & 36737.5557208067 & -3035.55572080669 \tabularnewline
36 & 25094 & 34974.0430811809 & -9880.04308118093 \tabularnewline
37 & 51442 & 29234.2107551647 & 22207.7892448353 \tabularnewline
38 & 45594 & 42135.8737893733 & 3458.12621062667 \tabularnewline
39 & 52518 & 44144.8796659779 & 8373.1203340221 \tabularnewline
40 & 48564 & 49009.2619736206 & -445.261973620552 \tabularnewline
41 & 41745 & 48750.5860702127 & -7005.5860702127 \tabularnewline
42 & 49585 & 44680.6757410677 & 4904.32425893228 \tabularnewline
43 & 32747 & 47529.8534913453 & -14782.8534913453 \tabularnewline
44 & 33379 & 38941.7228887566 & -5562.72288875656 \tabularnewline
45 & 35645 & 35710.0470351996 & -65.0470351995755 \tabularnewline
46 & 37034 & 35672.2578198812 & 1361.74218011885 \tabularnewline
47 & 35681 & 36463.3648748730 & -782.364874873034 \tabularnewline
48 & 20972 & 36008.8483143036 & -15036.8483143036 \tabularnewline
49 & 58552 & 27273.158871791 & 31278.841128209 \tabularnewline
50 & 54955 & 45444.6690517405 & 9510.33094825948 \tabularnewline
51 & 65540 & 50969.7163171627 & 14570.2836828373 \tabularnewline
52 & 51570 & 59434.3540312707 & -7864.3540312707 \tabularnewline
53 & 51145 & 54865.5406039382 & -3720.54060393816 \tabularnewline
54 & 46641 & 52704.0845198633 & -6063.08451986332 \tabularnewline
55 & 35704 & 49181.7224981058 & -13477.7224981058 \tabularnewline
56 & 33253 & 41351.8105594569 & -8098.81055945695 \tabularnewline
57 & 35193 & 36646.7891066663 & -1453.78910666627 \tabularnewline
58 & 41668 & 35802.2071912749 & 5865.79280872512 \tabularnewline
59 & 34865 & 39209.952168153 & -4344.95216815301 \tabularnewline
60 & 21210 & 36685.7428398291 & -15475.7428398291 \tabularnewline
61 & 56126 & 27695.0766766055 & 28430.9233233945 \tabularnewline
62 & 49231 & 44212.0828687083 & 5018.9171312917 \tabularnewline
63 & 59723 & 47127.8335952063 & 12595.1664047937 \tabularnewline
64 & 48103 & 54445.0226689555 & -6342.02266895545 \tabularnewline
65 & 47472 & 50760.6109281873 & -3288.61092818731 \tabularnewline
66 & 50497 & 48850.085320333 & 1646.91467966697 \tabularnewline
67 & 40059 & 49806.8639536721 & -9747.86395367207 \tabularnewline
68 & 34149 & 44143.8213767153 & -9994.82137671526 \tabularnewline
69 & 36860 & 38337.3083524855 & -1477.30835248552 \tabularnewline
70 & 46356 & 37479.0628805360 & 8876.93711946404 \tabularnewline
71 & 36577 & 42636.1386357383 & -6059.1386357383 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11032&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]53375.0856277731[/C][C]-967.085627773064[/C][/ROW]
[ROW][C]5[/C][C]41454[/C][C]52813.2551476114[/C][C]-11359.2551476114[/C][/ROW]
[ROW][C]6[/C][C]38271[/C][C]46214.0713829256[/C][C]-7943.07138292557[/C][/ROW]
[ROW][C]7[/C][C]35306[/C][C]41599.5269404614[/C][C]-6293.52694046136[/C][/ROW]
[ROW][C]8[/C][C]26414[/C][C]37943.2888977021[/C][C]-11529.2888977021[/C][/ROW]
[ROW][C]9[/C][C]31917[/C][C]31245.3236593663[/C][C]671.676340633712[/C][/ROW]
[ROW][C]10[/C][C]38030[/C][C]31635.5354773626[/C][C]6394.46452263738[/C][/ROW]
[ROW][C]11[/C][C]27534[/C][C]35350.413426074[/C][C]-7816.41342607403[/C][/ROW]
[ROW][C]12[/C][C]18387[/C][C]30809.4511966741[/C][C]-12422.4511966741[/C][/ROW]
[ROW][C]13[/C][C]50556[/C][C]23592.6013953971[/C][C]26963.3986046029[/C][/ROW]
[ROW][C]14[/C][C]43901[/C][C]39257.045938635[/C][C]4643.954061365[/C][/ROW]
[ROW][C]15[/C][C]48572[/C][C]41954.9610613665[/C][C]6617.03893863347[/C][/ROW]
[ROW][C]16[/C][C]43899[/C][C]45799.1440968454[/C][C]-1900.14409684543[/C][/ROW]
[ROW][C]17[/C][C]37532[/C][C]44695.2512877203[/C][C]-7163.25128772028[/C][/ROW]
[ROW][C]18[/C][C]40357[/C][C]40533.7450105918[/C][C]-176.745010591818[/C][/ROW]
[ROW][C]19[/C][C]35489[/C][C]40431.0646156865[/C][C]-4942.06461568653[/C][/ROW]
[ROW][C]20[/C][C]29027[/C][C]37559.9615237972[/C][C]-8532.9615237972[/C][/ROW]
[ROW][C]21[/C][C]34485[/C][C]32602.7191323916[/C][C]1882.28086760840[/C][/ROW]
[ROW][C]22[/C][C]42598[/C][C]33696.2342599845[/C][C]8901.76574001554[/C][/ROW]
[ROW][C]23[/C][C]30306[/C][C]38867.7342558182[/C][C]-8561.73425581824[/C][/ROW]
[ROW][C]24[/C][C]26451[/C][C]33893.7762837208[/C][C]-7442.77628372082[/C][/ROW]
[ROW][C]25[/C][C]47460[/C][C]29569.8793576053[/C][C]17890.1206423947[/C][/ROW]
[ROW][C]26[/C][C]50104[/C][C]39963.1835098047[/C][C]10140.8164901953[/C][/ROW]
[ROW][C]27[/C][C]61465[/C][C]45854.5127099264[/C][C]15610.4872900736[/C][/ROW]
[ROW][C]28[/C][C]53726[/C][C]54923.4589519826[/C][C]-1197.45895198263[/C][/ROW]
[ROW][C]29[/C][C]39477[/C][C]54227.7925925151[/C][C]-14750.7925925151[/C][/ROW]
[ROW][C]30[/C][C]43895[/C][C]45658.2878382141[/C][C]-1763.28783821412[/C][/ROW]
[ROW][C]31[/C][C]31481[/C][C]44633.9019675563[/C][C]-13152.9019675563[/C][/ROW]
[ROW][C]32[/C][C]29896[/C][C]36992.6952163325[/C][C]-7096.69521633247[/C][/ROW]
[ROW][C]33[/C][C]33842[/C][C]32869.854832349[/C][C]972.14516765104[/C][/ROW]
[ROW][C]34[/C][C]39120[/C][C]33434.6246631093[/C][C]5685.37533689065[/C][/ROW]
[ROW][C]35[/C][C]33702[/C][C]36737.5557208067[/C][C]-3035.55572080669[/C][/ROW]
[ROW][C]36[/C][C]25094[/C][C]34974.0430811809[/C][C]-9880.04308118093[/C][/ROW]
[ROW][C]37[/C][C]51442[/C][C]29234.2107551647[/C][C]22207.7892448353[/C][/ROW]
[ROW][C]38[/C][C]45594[/C][C]42135.8737893733[/C][C]3458.12621062667[/C][/ROW]
[ROW][C]39[/C][C]52518[/C][C]44144.8796659779[/C][C]8373.1203340221[/C][/ROW]
[ROW][C]40[/C][C]48564[/C][C]49009.2619736206[/C][C]-445.261973620552[/C][/ROW]
[ROW][C]41[/C][C]41745[/C][C]48750.5860702127[/C][C]-7005.5860702127[/C][/ROW]
[ROW][C]42[/C][C]49585[/C][C]44680.6757410677[/C][C]4904.32425893228[/C][/ROW]
[ROW][C]43[/C][C]32747[/C][C]47529.8534913453[/C][C]-14782.8534913453[/C][/ROW]
[ROW][C]44[/C][C]33379[/C][C]38941.7228887566[/C][C]-5562.72288875656[/C][/ROW]
[ROW][C]45[/C][C]35645[/C][C]35710.0470351996[/C][C]-65.0470351995755[/C][/ROW]
[ROW][C]46[/C][C]37034[/C][C]35672.2578198812[/C][C]1361.74218011885[/C][/ROW]
[ROW][C]47[/C][C]35681[/C][C]36463.3648748730[/C][C]-782.364874873034[/C][/ROW]
[ROW][C]48[/C][C]20972[/C][C]36008.8483143036[/C][C]-15036.8483143036[/C][/ROW]
[ROW][C]49[/C][C]58552[/C][C]27273.158871791[/C][C]31278.841128209[/C][/ROW]
[ROW][C]50[/C][C]54955[/C][C]45444.6690517405[/C][C]9510.33094825948[/C][/ROW]
[ROW][C]51[/C][C]65540[/C][C]50969.7163171627[/C][C]14570.2836828373[/C][/ROW]
[ROW][C]52[/C][C]51570[/C][C]59434.3540312707[/C][C]-7864.3540312707[/C][/ROW]
[ROW][C]53[/C][C]51145[/C][C]54865.5406039382[/C][C]-3720.54060393816[/C][/ROW]
[ROW][C]54[/C][C]46641[/C][C]52704.0845198633[/C][C]-6063.08451986332[/C][/ROW]
[ROW][C]55[/C][C]35704[/C][C]49181.7224981058[/C][C]-13477.7224981058[/C][/ROW]
[ROW][C]56[/C][C]33253[/C][C]41351.8105594569[/C][C]-8098.81055945695[/C][/ROW]
[ROW][C]57[/C][C]35193[/C][C]36646.7891066663[/C][C]-1453.78910666627[/C][/ROW]
[ROW][C]58[/C][C]41668[/C][C]35802.2071912749[/C][C]5865.79280872512[/C][/ROW]
[ROW][C]59[/C][C]34865[/C][C]39209.952168153[/C][C]-4344.95216815301[/C][/ROW]
[ROW][C]60[/C][C]21210[/C][C]36685.7428398291[/C][C]-15475.7428398291[/C][/ROW]
[ROW][C]61[/C][C]56126[/C][C]27695.0766766055[/C][C]28430.9233233945[/C][/ROW]
[ROW][C]62[/C][C]49231[/C][C]44212.0828687083[/C][C]5018.9171312917[/C][/ROW]
[ROW][C]63[/C][C]59723[/C][C]47127.8335952063[/C][C]12595.1664047937[/C][/ROW]
[ROW][C]64[/C][C]48103[/C][C]54445.0226689555[/C][C]-6342.02266895545[/C][/ROW]
[ROW][C]65[/C][C]47472[/C][C]50760.6109281873[/C][C]-3288.61092818731[/C][/ROW]
[ROW][C]66[/C][C]50497[/C][C]48850.085320333[/C][C]1646.91467966697[/C][/ROW]
[ROW][C]67[/C][C]40059[/C][C]49806.8639536721[/C][C]-9747.86395367207[/C][/ROW]
[ROW][C]68[/C][C]34149[/C][C]44143.8213767153[/C][C]-9994.82137671526[/C][/ROW]
[ROW][C]69[/C][C]36860[/C][C]38337.3083524855[/C][C]-1477.30835248552[/C][/ROW]
[ROW][C]70[/C][C]46356[/C][C]37479.0628805360[/C][C]8876.93711946404[/C][/ROW]
[ROW][C]71[/C][C]36577[/C][C]42636.1386357383[/C][C]-6059.1386357383[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11032&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11032&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
45240853375.0856277731-967.085627773064
54145452813.2551476114-11359.2551476114
63827146214.0713829256-7943.07138292557
73530641599.5269404614-6293.52694046136
82641437943.2888977021-11529.2888977021
93191731245.3236593663671.676340633712
103803031635.53547736266394.46452263738
112753435350.413426074-7816.41342607403
121838730809.4511966741-12422.4511966741
135055623592.601395397126963.3986046029
144390139257.0459386354643.954061365
154857241954.96106136656617.03893863347
164389945799.1440968454-1900.14409684543
173753244695.2512877203-7163.25128772028
184035740533.7450105918-176.745010591818
193548940431.0646156865-4942.06461568653
202902737559.9615237972-8532.9615237972
213448532602.71913239161882.28086760840
224259833696.23425998458901.76574001554
233030638867.7342558182-8561.73425581824
242645133893.7762837208-7442.77628372082
254746029569.879357605317890.1206423947
265010439963.183509804710140.8164901953
276146545854.512709926415610.4872900736
285372654923.4589519826-1197.45895198263
293947754227.7925925151-14750.7925925151
304389545658.2878382141-1763.28783821412
313148144633.9019675563-13152.9019675563
322989636992.6952163325-7096.69521633247
333384232869.854832349972.14516765104
343912033434.62466310935685.37533689065
353370236737.5557208067-3035.55572080669
362509434974.0430811809-9880.04308118093
375144229234.210755164722207.7892448353
384559442135.87378937333458.12621062667
395251844144.87966597798373.1203340221
404856449009.2619736206-445.261973620552
414174548750.5860702127-7005.5860702127
424958544680.67574106774904.32425893228
433274747529.8534913453-14782.8534913453
443337938941.7228887566-5562.72288875656
453564535710.0470351996-65.0470351995755
463703435672.25781988121361.74218011885
473568136463.3648748730-782.364874873034
482097236008.8483143036-15036.8483143036
495855227273.15887179131278.841128209
505495545444.66905174059510.33094825948
516554050969.716317162714570.2836828373
525157059434.3540312707-7864.3540312707
535114554865.5406039382-3720.54060393816
544664152704.0845198633-6063.08451986332
553570449181.7224981058-13477.7224981058
563325341351.8105594569-8098.81055945695
573519336646.7891066663-1453.78910666627
584166835802.20719127495865.79280872512
593486539209.952168153-4344.95216815301
602121036685.7428398291-15475.7428398291
615612627695.076676605528430.9233233945
624923144212.08286870835018.9171312917
635972347127.833595206312595.1664047937
644810354445.0226689555-6342.02266895545
654747250760.6109281873-3288.61092818731
665049748850.0853203331646.91467966697
674005949806.8639536721-9747.86395367207
683414944143.8213767153-9994.82137671526
693686038337.3083524855-1477.30835248552
704635637479.06288053608876.93711946404
713657742636.1386357383-6059.1386357383







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7239116.068983869218610.572225818459621.56574192
7339116.068983869215401.345340927362830.792626811
7439116.068983869212577.402144184665654.7358235538
7539116.068983869210026.318936911968205.8190308264
7639116.06898386927681.5930384820770550.5449292563
7739116.06898386925500.0162987636172732.1216689748
7839116.06898386923451.6368659387874780.5011017996
7939116.06898386921514.6802001934176717.457767545
8039116.0689838692-327.27213510564678559.410102844
8139116.0689838692-2086.9634141774880319.1013819159
8239116.0689838692-3774.5197152983282006.6576830367
8339116.0689838692-5398.1458146401683630.2837823785

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
72 & 39116.0689838692 & 18610.5722258184 & 59621.56574192 \tabularnewline
73 & 39116.0689838692 & 15401.3453409273 & 62830.792626811 \tabularnewline
74 & 39116.0689838692 & 12577.4021441846 & 65654.7358235538 \tabularnewline
75 & 39116.0689838692 & 10026.3189369119 & 68205.8190308264 \tabularnewline
76 & 39116.0689838692 & 7681.59303848207 & 70550.5449292563 \tabularnewline
77 & 39116.0689838692 & 5500.01629876361 & 72732.1216689748 \tabularnewline
78 & 39116.0689838692 & 3451.63686593878 & 74780.5011017996 \tabularnewline
79 & 39116.0689838692 & 1514.68020019341 & 76717.457767545 \tabularnewline
80 & 39116.0689838692 & -327.272135105646 & 78559.410102844 \tabularnewline
81 & 39116.0689838692 & -2086.96341417748 & 80319.1013819159 \tabularnewline
82 & 39116.0689838692 & -3774.51971529832 & 82006.6576830367 \tabularnewline
83 & 39116.0689838692 & -5398.14581464016 & 83630.2837823785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11032&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]39116.0689838692[/C][C]18610.5722258184[/C][C]59621.56574192[/C][/ROW]
[ROW][C]73[/C][C]39116.0689838692[/C][C]15401.3453409273[/C][C]62830.792626811[/C][/ROW]
[ROW][C]74[/C][C]39116.0689838692[/C][C]12577.4021441846[/C][C]65654.7358235538[/C][/ROW]
[ROW][C]75[/C][C]39116.0689838692[/C][C]10026.3189369119[/C][C]68205.8190308264[/C][/ROW]
[ROW][C]76[/C][C]39116.0689838692[/C][C]7681.59303848207[/C][C]70550.5449292563[/C][/ROW]
[ROW][C]77[/C][C]39116.0689838692[/C][C]5500.01629876361[/C][C]72732.1216689748[/C][/ROW]
[ROW][C]78[/C][C]39116.0689838692[/C][C]3451.63686593878[/C][C]74780.5011017996[/C][/ROW]
[ROW][C]79[/C][C]39116.0689838692[/C][C]1514.68020019341[/C][C]76717.457767545[/C][/ROW]
[ROW][C]80[/C][C]39116.0689838692[/C][C]-327.272135105646[/C][C]78559.410102844[/C][/ROW]
[ROW][C]81[/C][C]39116.0689838692[/C][C]-2086.96341417748[/C][C]80319.1013819159[/C][/ROW]
[ROW][C]82[/C][C]39116.0689838692[/C][C]-3774.51971529832[/C][C]82006.6576830367[/C][/ROW]
[ROW][C]83[/C][C]39116.0689838692[/C][C]-5398.14581464016[/C][C]83630.2837823785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11032&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11032&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
7239116.068983869218610.572225818459621.56574192
7339116.068983869215401.345340927362830.792626811
7439116.068983869212577.402144184665654.7358235538
7539116.068983869210026.318936911968205.8190308264
7639116.06898386927681.5930384820770550.5449292563
7739116.06898386925500.0162987636172732.1216689748
7839116.06898386923451.6368659387874780.5011017996
7939116.06898386921514.6802001934176717.457767545
8039116.0689838692-327.27213510564678559.410102844
8139116.0689838692-2086.9634141774880319.1013819159
8239116.0689838692-3774.5197152983282006.6576830367
8339116.0689838692-5398.1458146401683630.2837823785



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')