Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 20 Dec 2011 11:20:57 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/20/t1324398089hkcu5uqzfyj20ml.htm/, Retrieved Sun, 28 Apr 2024 23:05:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158029, Retrieved Sun, 28 Apr 2024 23:05:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Decomposition by Loess] [HPC Retail Sales] [2008-03-06 11:35:25] [74be16979710d4c4e7c6647856088456]
- RMPD  [Exponential Smoothing] [WS VIII-exponenti...] [2011-11-29 13:32:47] [7c680a04865e75aa8ab422cdbfd97ac3]
- R P     [Exponential Smoothing] [WS VIII-exponenti...] [2011-11-29 13:35:04] [7c680a04865e75aa8ab422cdbfd97ac3]
-   PD      [Exponential Smoothing] [Paper-exponention...] [2011-12-18 17:16:12] [7c680a04865e75aa8ab422cdbfd97ac3]
-   P           [Exponential Smoothing] [Paper exponention...] [2011-12-20 16:20:57] [3e388c05c22237d436c48535c44f60bb] [Current]
Feedback Forum

Post a new message
Dataseries X:
18992
0
21552
1868501
7185612
10348382
6942386
4306121
2833176
1515513
1242981
699343
89497
128
10585
1070323
7167741
13193530
7885720
6785683
3106846
1706331
1286534
499079
24637
16
27309
873433
8435418
11290088
6840395
3803252
4388988
2680940
1174135
328388
22943
5657
28156
770831
8378147
13274946
7297840
2848227
2892179
1762224
1009375
188388
3393
0
13807
2619905
13297704
6240087
5108460
4553381
3148546
2433387
1748108
723454
58525
792
42585
1634386
10360570
6798599
4847748
4971202
343863
2200366
1549422
90144
63288
338
44863
1678135
9293357
9361258
6766402
4331272
3518962
2425786
1701795
552452
16104
0
90198
1731332
7954135
11561342
6834733
4255652
4243070
3415216
1841237
655456




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158029&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158029&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158029&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158029&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158029&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158029&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2018992-18992
3215521.2555034099952321550.74449659
4186850121550.57534576651846950.42465423
571856121868378.903719665317233.09628034
6103483827185260.493877213163121.50612279
7694238610348172.8956488-3405786.89564884
843061216942611.14622268-2636490.14622268
928331764306295.2903522-1473119.2903522
1015155132833273.38343999-1317760.38343999
1112429811515600.11313474-272619.113134739
126993431242999.02202118-543656.022021176
1389497699378.939447636-609881.939447636
1412889537.3174418003-89409.3174418003
1510585133.91057829262510451.0894217074
16107032310584.30911023551059738.69088976
1771677411070252.943895326097488.05610468
18131935307167337.913592736026192.08640727
19788572013193131.6267526-5307411.62675264
2067856837886070.85685529-1100387.85685529
2131068466785755.74329753-3678909.74329753
2217063313107089.20154422-1400758.20154422
2312865341706423.59986829-419889.599868293
244990791286561.75762555-787482.75762555
2524637499131.058092224-474494.058092224
261624668.36736036-24652.36736036
272730917.629693096324127291.3703069037
2887343327307.1958504379846125.804149562
298435418873377.0651941667562040.93480583
30112900888434918.096452182855169.90354782
31684039511289899.2533935-4449504.25339353
3238032526840689.14320571-3037437.14320571
3343889883803452.79573983585535.204260165
3426809404388949.29204688-1708009.29204688
3511741352681052.91130426-1506917.91130426
363283881174234.61776412-845846.617764123
3722943328443.91634967-305500.91634967
38565722963.1957372701-17306.1957372701
39281565658.1440600127522497.8559399872
4077083128154.5127351069742676.487264893
418378147770781.9039141597607365.09608584
42132749468377644.10020964897301.8997904
43729784013274622.2542526-5976782.25425258
4428482277298235.10691349-4450008.10691349
4528921792848521.1765139443657.8234860608
4617622242892176.11391395-1129952.11391395
4710093751762298.69770072-752923.697700724
481883881009424.77349778-821036.773497785
493393188442.276246254-185049.276246254
5003405.23304535301-3405.23304535301
51138070.22510960932335413806.7748903907
52261990513806.08727606592606098.91272393
53132977042619732.718719910677971.2812801
54624008713296998.1117652-7056911.11176519
5551084606240553.51095013-1132093.51095013
5645533815108534.83926198-555153.839261975
5731485464553417.6995334-1404871.6995334
5824333873148638.87179915-715251.871799145
5917481082433434.28312785-685326.283127846
607234541748153.30483811-1024699.30483811
6158525723521.739757342-664996.739757342
6279258568.9609137743-57776.9609137743
6342585795.81945932215741789.1805406778
64163438642582.23744425711591803.76255574
65103605701634280.770690198726289.22930981
66679859910359993.1315352-3561394.13153517
6748477486798834.43294421-1951086.43294421
6849712024847876.98039542123325.019604583
693438634971193.84735769-4627330.84735769
702200366344168.8987814891856197.10121851
7115494222200243.29244997-650821.292449968
72901441549465.02381803-1459321.02381803
736328890240.4712785216-26952.4712785216
7433863289.7817459771-62951.7817459771
7544863342.16155100291444520.8384489971
76167813544860.05686265331633274.94313735
7792933571678027.029156467615329.97084354
7893612589292853.5736759468404.4263240639
7967664029361253.47799123-2594851.47799123
8043312726766573.53774637-2435301.53774637
8135189624331432.99038464-812470.990384636
8224257863519015.70998836-1093229.70998836
8317017952425858.27009419-724063.270094187
845524521701842.86562261-1149390.86562261
8516104552527.982737532-536423.982737532
86016139.4613594951-16139.4613594951
87901981.0669307483325890196.9330692517
88173133290192.03735483151641139.96264517
8979541351731223.509223926222911.49077608
90115613427953723.622230583607618.37776942
91683473311561103.5113113-4726370.51131133
9242556526835045.44599273-2579393.44599273
9342430704255822.51586285-12752.5158628458
9434152164243070.84303007-827854.843030074
9518412373415270.72696811-1574033.72696811
966554561841341.05458676-1185885.05458676

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 0 & 18992 & -18992 \tabularnewline
3 & 21552 & 1.25550340999523 & 21550.74449659 \tabularnewline
4 & 1868501 & 21550.5753457665 & 1846950.42465423 \tabularnewline
5 & 7185612 & 1868378.90371966 & 5317233.09628034 \tabularnewline
6 & 10348382 & 7185260.49387721 & 3163121.50612279 \tabularnewline
7 & 6942386 & 10348172.8956488 & -3405786.89564884 \tabularnewline
8 & 4306121 & 6942611.14622268 & -2636490.14622268 \tabularnewline
9 & 2833176 & 4306295.2903522 & -1473119.2903522 \tabularnewline
10 & 1515513 & 2833273.38343999 & -1317760.38343999 \tabularnewline
11 & 1242981 & 1515600.11313474 & -272619.113134739 \tabularnewline
12 & 699343 & 1242999.02202118 & -543656.022021176 \tabularnewline
13 & 89497 & 699378.939447636 & -609881.939447636 \tabularnewline
14 & 128 & 89537.3174418003 & -89409.3174418003 \tabularnewline
15 & 10585 & 133.910578292625 & 10451.0894217074 \tabularnewline
16 & 1070323 & 10584.3091102355 & 1059738.69088976 \tabularnewline
17 & 7167741 & 1070252.94389532 & 6097488.05610468 \tabularnewline
18 & 13193530 & 7167337.91359273 & 6026192.08640727 \tabularnewline
19 & 7885720 & 13193131.6267526 & -5307411.62675264 \tabularnewline
20 & 6785683 & 7886070.85685529 & -1100387.85685529 \tabularnewline
21 & 3106846 & 6785755.74329753 & -3678909.74329753 \tabularnewline
22 & 1706331 & 3107089.20154422 & -1400758.20154422 \tabularnewline
23 & 1286534 & 1706423.59986829 & -419889.599868293 \tabularnewline
24 & 499079 & 1286561.75762555 & -787482.75762555 \tabularnewline
25 & 24637 & 499131.058092224 & -474494.058092224 \tabularnewline
26 & 16 & 24668.36736036 & -24652.36736036 \tabularnewline
27 & 27309 & 17.6296930963241 & 27291.3703069037 \tabularnewline
28 & 873433 & 27307.1958504379 & 846125.804149562 \tabularnewline
29 & 8435418 & 873377.065194166 & 7562040.93480583 \tabularnewline
30 & 11290088 & 8434918.09645218 & 2855169.90354782 \tabularnewline
31 & 6840395 & 11289899.2533935 & -4449504.25339353 \tabularnewline
32 & 3803252 & 6840689.14320571 & -3037437.14320571 \tabularnewline
33 & 4388988 & 3803452.79573983 & 585535.204260165 \tabularnewline
34 & 2680940 & 4388949.29204688 & -1708009.29204688 \tabularnewline
35 & 1174135 & 2681052.91130426 & -1506917.91130426 \tabularnewline
36 & 328388 & 1174234.61776412 & -845846.617764123 \tabularnewline
37 & 22943 & 328443.91634967 & -305500.91634967 \tabularnewline
38 & 5657 & 22963.1957372701 & -17306.1957372701 \tabularnewline
39 & 28156 & 5658.14406001275 & 22497.8559399872 \tabularnewline
40 & 770831 & 28154.5127351069 & 742676.487264893 \tabularnewline
41 & 8378147 & 770781.903914159 & 7607365.09608584 \tabularnewline
42 & 13274946 & 8377644.1002096 & 4897301.8997904 \tabularnewline
43 & 7297840 & 13274622.2542526 & -5976782.25425258 \tabularnewline
44 & 2848227 & 7298235.10691349 & -4450008.10691349 \tabularnewline
45 & 2892179 & 2848521.17651394 & 43657.8234860608 \tabularnewline
46 & 1762224 & 2892176.11391395 & -1129952.11391395 \tabularnewline
47 & 1009375 & 1762298.69770072 & -752923.697700724 \tabularnewline
48 & 188388 & 1009424.77349778 & -821036.773497785 \tabularnewline
49 & 3393 & 188442.276246254 & -185049.276246254 \tabularnewline
50 & 0 & 3405.23304535301 & -3405.23304535301 \tabularnewline
51 & 13807 & 0.225109609323354 & 13806.7748903907 \tabularnewline
52 & 2619905 & 13806.0872760659 & 2606098.91272393 \tabularnewline
53 & 13297704 & 2619732.7187199 & 10677971.2812801 \tabularnewline
54 & 6240087 & 13296998.1117652 & -7056911.11176519 \tabularnewline
55 & 5108460 & 6240553.51095013 & -1132093.51095013 \tabularnewline
56 & 4553381 & 5108534.83926198 & -555153.839261975 \tabularnewline
57 & 3148546 & 4553417.6995334 & -1404871.6995334 \tabularnewline
58 & 2433387 & 3148638.87179915 & -715251.871799145 \tabularnewline
59 & 1748108 & 2433434.28312785 & -685326.283127846 \tabularnewline
60 & 723454 & 1748153.30483811 & -1024699.30483811 \tabularnewline
61 & 58525 & 723521.739757342 & -664996.739757342 \tabularnewline
62 & 792 & 58568.9609137743 & -57776.9609137743 \tabularnewline
63 & 42585 & 795.819459322157 & 41789.1805406778 \tabularnewline
64 & 1634386 & 42582.2374442571 & 1591803.76255574 \tabularnewline
65 & 10360570 & 1634280.77069019 & 8726289.22930981 \tabularnewline
66 & 6798599 & 10359993.1315352 & -3561394.13153517 \tabularnewline
67 & 4847748 & 6798834.43294421 & -1951086.43294421 \tabularnewline
68 & 4971202 & 4847876.98039542 & 123325.019604583 \tabularnewline
69 & 343863 & 4971193.84735769 & -4627330.84735769 \tabularnewline
70 & 2200366 & 344168.898781489 & 1856197.10121851 \tabularnewline
71 & 1549422 & 2200243.29244997 & -650821.292449968 \tabularnewline
72 & 90144 & 1549465.02381803 & -1459321.02381803 \tabularnewline
73 & 63288 & 90240.4712785216 & -26952.4712785216 \tabularnewline
74 & 338 & 63289.7817459771 & -62951.7817459771 \tabularnewline
75 & 44863 & 342.161551002914 & 44520.8384489971 \tabularnewline
76 & 1678135 & 44860.0568626533 & 1633274.94313735 \tabularnewline
77 & 9293357 & 1678027.02915646 & 7615329.97084354 \tabularnewline
78 & 9361258 & 9292853.57367594 & 68404.4263240639 \tabularnewline
79 & 6766402 & 9361253.47799123 & -2594851.47799123 \tabularnewline
80 & 4331272 & 6766573.53774637 & -2435301.53774637 \tabularnewline
81 & 3518962 & 4331432.99038464 & -812470.990384636 \tabularnewline
82 & 2425786 & 3519015.70998836 & -1093229.70998836 \tabularnewline
83 & 1701795 & 2425858.27009419 & -724063.270094187 \tabularnewline
84 & 552452 & 1701842.86562261 & -1149390.86562261 \tabularnewline
85 & 16104 & 552527.982737532 & -536423.982737532 \tabularnewline
86 & 0 & 16139.4613594951 & -16139.4613594951 \tabularnewline
87 & 90198 & 1.06693074833258 & 90196.9330692517 \tabularnewline
88 & 1731332 & 90192.0373548315 & 1641139.96264517 \tabularnewline
89 & 7954135 & 1731223.50922392 & 6222911.49077608 \tabularnewline
90 & 11561342 & 7953723.62223058 & 3607618.37776942 \tabularnewline
91 & 6834733 & 11561103.5113113 & -4726370.51131133 \tabularnewline
92 & 4255652 & 6835045.44599273 & -2579393.44599273 \tabularnewline
93 & 4243070 & 4255822.51586285 & -12752.5158628458 \tabularnewline
94 & 3415216 & 4243070.84303007 & -827854.843030074 \tabularnewline
95 & 1841237 & 3415270.72696811 & -1574033.72696811 \tabularnewline
96 & 655456 & 1841341.05458676 & -1185885.05458676 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158029&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]2[/C][C]0[/C][C]18992[/C][C]-18992[/C][/ROW]
[ROW][C]3[/C][C]21552[/C][C]1.25550340999523[/C][C]21550.74449659[/C][/ROW]
[ROW][C]4[/C][C]1868501[/C][C]21550.5753457665[/C][C]1846950.42465423[/C][/ROW]
[ROW][C]5[/C][C]7185612[/C][C]1868378.90371966[/C][C]5317233.09628034[/C][/ROW]
[ROW][C]6[/C][C]10348382[/C][C]7185260.49387721[/C][C]3163121.50612279[/C][/ROW]
[ROW][C]7[/C][C]6942386[/C][C]10348172.8956488[/C][C]-3405786.89564884[/C][/ROW]
[ROW][C]8[/C][C]4306121[/C][C]6942611.14622268[/C][C]-2636490.14622268[/C][/ROW]
[ROW][C]9[/C][C]2833176[/C][C]4306295.2903522[/C][C]-1473119.2903522[/C][/ROW]
[ROW][C]10[/C][C]1515513[/C][C]2833273.38343999[/C][C]-1317760.38343999[/C][/ROW]
[ROW][C]11[/C][C]1242981[/C][C]1515600.11313474[/C][C]-272619.113134739[/C][/ROW]
[ROW][C]12[/C][C]699343[/C][C]1242999.02202118[/C][C]-543656.022021176[/C][/ROW]
[ROW][C]13[/C][C]89497[/C][C]699378.939447636[/C][C]-609881.939447636[/C][/ROW]
[ROW][C]14[/C][C]128[/C][C]89537.3174418003[/C][C]-89409.3174418003[/C][/ROW]
[ROW][C]15[/C][C]10585[/C][C]133.910578292625[/C][C]10451.0894217074[/C][/ROW]
[ROW][C]16[/C][C]1070323[/C][C]10584.3091102355[/C][C]1059738.69088976[/C][/ROW]
[ROW][C]17[/C][C]7167741[/C][C]1070252.94389532[/C][C]6097488.05610468[/C][/ROW]
[ROW][C]18[/C][C]13193530[/C][C]7167337.91359273[/C][C]6026192.08640727[/C][/ROW]
[ROW][C]19[/C][C]7885720[/C][C]13193131.6267526[/C][C]-5307411.62675264[/C][/ROW]
[ROW][C]20[/C][C]6785683[/C][C]7886070.85685529[/C][C]-1100387.85685529[/C][/ROW]
[ROW][C]21[/C][C]3106846[/C][C]6785755.74329753[/C][C]-3678909.74329753[/C][/ROW]
[ROW][C]22[/C][C]1706331[/C][C]3107089.20154422[/C][C]-1400758.20154422[/C][/ROW]
[ROW][C]23[/C][C]1286534[/C][C]1706423.59986829[/C][C]-419889.599868293[/C][/ROW]
[ROW][C]24[/C][C]499079[/C][C]1286561.75762555[/C][C]-787482.75762555[/C][/ROW]
[ROW][C]25[/C][C]24637[/C][C]499131.058092224[/C][C]-474494.058092224[/C][/ROW]
[ROW][C]26[/C][C]16[/C][C]24668.36736036[/C][C]-24652.36736036[/C][/ROW]
[ROW][C]27[/C][C]27309[/C][C]17.6296930963241[/C][C]27291.3703069037[/C][/ROW]
[ROW][C]28[/C][C]873433[/C][C]27307.1958504379[/C][C]846125.804149562[/C][/ROW]
[ROW][C]29[/C][C]8435418[/C][C]873377.065194166[/C][C]7562040.93480583[/C][/ROW]
[ROW][C]30[/C][C]11290088[/C][C]8434918.09645218[/C][C]2855169.90354782[/C][/ROW]
[ROW][C]31[/C][C]6840395[/C][C]11289899.2533935[/C][C]-4449504.25339353[/C][/ROW]
[ROW][C]32[/C][C]3803252[/C][C]6840689.14320571[/C][C]-3037437.14320571[/C][/ROW]
[ROW][C]33[/C][C]4388988[/C][C]3803452.79573983[/C][C]585535.204260165[/C][/ROW]
[ROW][C]34[/C][C]2680940[/C][C]4388949.29204688[/C][C]-1708009.29204688[/C][/ROW]
[ROW][C]35[/C][C]1174135[/C][C]2681052.91130426[/C][C]-1506917.91130426[/C][/ROW]
[ROW][C]36[/C][C]328388[/C][C]1174234.61776412[/C][C]-845846.617764123[/C][/ROW]
[ROW][C]37[/C][C]22943[/C][C]328443.91634967[/C][C]-305500.91634967[/C][/ROW]
[ROW][C]38[/C][C]5657[/C][C]22963.1957372701[/C][C]-17306.1957372701[/C][/ROW]
[ROW][C]39[/C][C]28156[/C][C]5658.14406001275[/C][C]22497.8559399872[/C][/ROW]
[ROW][C]40[/C][C]770831[/C][C]28154.5127351069[/C][C]742676.487264893[/C][/ROW]
[ROW][C]41[/C][C]8378147[/C][C]770781.903914159[/C][C]7607365.09608584[/C][/ROW]
[ROW][C]42[/C][C]13274946[/C][C]8377644.1002096[/C][C]4897301.8997904[/C][/ROW]
[ROW][C]43[/C][C]7297840[/C][C]13274622.2542526[/C][C]-5976782.25425258[/C][/ROW]
[ROW][C]44[/C][C]2848227[/C][C]7298235.10691349[/C][C]-4450008.10691349[/C][/ROW]
[ROW][C]45[/C][C]2892179[/C][C]2848521.17651394[/C][C]43657.8234860608[/C][/ROW]
[ROW][C]46[/C][C]1762224[/C][C]2892176.11391395[/C][C]-1129952.11391395[/C][/ROW]
[ROW][C]47[/C][C]1009375[/C][C]1762298.69770072[/C][C]-752923.697700724[/C][/ROW]
[ROW][C]48[/C][C]188388[/C][C]1009424.77349778[/C][C]-821036.773497785[/C][/ROW]
[ROW][C]49[/C][C]3393[/C][C]188442.276246254[/C][C]-185049.276246254[/C][/ROW]
[ROW][C]50[/C][C]0[/C][C]3405.23304535301[/C][C]-3405.23304535301[/C][/ROW]
[ROW][C]51[/C][C]13807[/C][C]0.225109609323354[/C][C]13806.7748903907[/C][/ROW]
[ROW][C]52[/C][C]2619905[/C][C]13806.0872760659[/C][C]2606098.91272393[/C][/ROW]
[ROW][C]53[/C][C]13297704[/C][C]2619732.7187199[/C][C]10677971.2812801[/C][/ROW]
[ROW][C]54[/C][C]6240087[/C][C]13296998.1117652[/C][C]-7056911.11176519[/C][/ROW]
[ROW][C]55[/C][C]5108460[/C][C]6240553.51095013[/C][C]-1132093.51095013[/C][/ROW]
[ROW][C]56[/C][C]4553381[/C][C]5108534.83926198[/C][C]-555153.839261975[/C][/ROW]
[ROW][C]57[/C][C]3148546[/C][C]4553417.6995334[/C][C]-1404871.6995334[/C][/ROW]
[ROW][C]58[/C][C]2433387[/C][C]3148638.87179915[/C][C]-715251.871799145[/C][/ROW]
[ROW][C]59[/C][C]1748108[/C][C]2433434.28312785[/C][C]-685326.283127846[/C][/ROW]
[ROW][C]60[/C][C]723454[/C][C]1748153.30483811[/C][C]-1024699.30483811[/C][/ROW]
[ROW][C]61[/C][C]58525[/C][C]723521.739757342[/C][C]-664996.739757342[/C][/ROW]
[ROW][C]62[/C][C]792[/C][C]58568.9609137743[/C][C]-57776.9609137743[/C][/ROW]
[ROW][C]63[/C][C]42585[/C][C]795.819459322157[/C][C]41789.1805406778[/C][/ROW]
[ROW][C]64[/C][C]1634386[/C][C]42582.2374442571[/C][C]1591803.76255574[/C][/ROW]
[ROW][C]65[/C][C]10360570[/C][C]1634280.77069019[/C][C]8726289.22930981[/C][/ROW]
[ROW][C]66[/C][C]6798599[/C][C]10359993.1315352[/C][C]-3561394.13153517[/C][/ROW]
[ROW][C]67[/C][C]4847748[/C][C]6798834.43294421[/C][C]-1951086.43294421[/C][/ROW]
[ROW][C]68[/C][C]4971202[/C][C]4847876.98039542[/C][C]123325.019604583[/C][/ROW]
[ROW][C]69[/C][C]343863[/C][C]4971193.84735769[/C][C]-4627330.84735769[/C][/ROW]
[ROW][C]70[/C][C]2200366[/C][C]344168.898781489[/C][C]1856197.10121851[/C][/ROW]
[ROW][C]71[/C][C]1549422[/C][C]2200243.29244997[/C][C]-650821.292449968[/C][/ROW]
[ROW][C]72[/C][C]90144[/C][C]1549465.02381803[/C][C]-1459321.02381803[/C][/ROW]
[ROW][C]73[/C][C]63288[/C][C]90240.4712785216[/C][C]-26952.4712785216[/C][/ROW]
[ROW][C]74[/C][C]338[/C][C]63289.7817459771[/C][C]-62951.7817459771[/C][/ROW]
[ROW][C]75[/C][C]44863[/C][C]342.161551002914[/C][C]44520.8384489971[/C][/ROW]
[ROW][C]76[/C][C]1678135[/C][C]44860.0568626533[/C][C]1633274.94313735[/C][/ROW]
[ROW][C]77[/C][C]9293357[/C][C]1678027.02915646[/C][C]7615329.97084354[/C][/ROW]
[ROW][C]78[/C][C]9361258[/C][C]9292853.57367594[/C][C]68404.4263240639[/C][/ROW]
[ROW][C]79[/C][C]6766402[/C][C]9361253.47799123[/C][C]-2594851.47799123[/C][/ROW]
[ROW][C]80[/C][C]4331272[/C][C]6766573.53774637[/C][C]-2435301.53774637[/C][/ROW]
[ROW][C]81[/C][C]3518962[/C][C]4331432.99038464[/C][C]-812470.990384636[/C][/ROW]
[ROW][C]82[/C][C]2425786[/C][C]3519015.70998836[/C][C]-1093229.70998836[/C][/ROW]
[ROW][C]83[/C][C]1701795[/C][C]2425858.27009419[/C][C]-724063.270094187[/C][/ROW]
[ROW][C]84[/C][C]552452[/C][C]1701842.86562261[/C][C]-1149390.86562261[/C][/ROW]
[ROW][C]85[/C][C]16104[/C][C]552527.982737532[/C][C]-536423.982737532[/C][/ROW]
[ROW][C]86[/C][C]0[/C][C]16139.4613594951[/C][C]-16139.4613594951[/C][/ROW]
[ROW][C]87[/C][C]90198[/C][C]1.06693074833258[/C][C]90196.9330692517[/C][/ROW]
[ROW][C]88[/C][C]1731332[/C][C]90192.0373548315[/C][C]1641139.96264517[/C][/ROW]
[ROW][C]89[/C][C]7954135[/C][C]1731223.50922392[/C][C]6222911.49077608[/C][/ROW]
[ROW][C]90[/C][C]11561342[/C][C]7953723.62223058[/C][C]3607618.37776942[/C][/ROW]
[ROW][C]91[/C][C]6834733[/C][C]11561103.5113113[/C][C]-4726370.51131133[/C][/ROW]
[ROW][C]92[/C][C]4255652[/C][C]6835045.44599273[/C][C]-2579393.44599273[/C][/ROW]
[ROW][C]93[/C][C]4243070[/C][C]4255822.51586285[/C][C]-12752.5158628458[/C][/ROW]
[ROW][C]94[/C][C]3415216[/C][C]4243070.84303007[/C][C]-827854.843030074[/C][/ROW]
[ROW][C]95[/C][C]1841237[/C][C]3415270.72696811[/C][C]-1574033.72696811[/C][/ROW]
[ROW][C]96[/C][C]655456[/C][C]1841341.05458676[/C][C]-1185885.05458676[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158029&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158029&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
2018992-18992
3215521.2555034099952321550.74449659
4186850121550.57534576651846950.42465423
571856121868378.903719665317233.09628034
6103483827185260.493877213163121.50612279
7694238610348172.8956488-3405786.89564884
843061216942611.14622268-2636490.14622268
928331764306295.2903522-1473119.2903522
1015155132833273.38343999-1317760.38343999
1112429811515600.11313474-272619.113134739
126993431242999.02202118-543656.022021176
1389497699378.939447636-609881.939447636
1412889537.3174418003-89409.3174418003
1510585133.91057829262510451.0894217074
16107032310584.30911023551059738.69088976
1771677411070252.943895326097488.05610468
18131935307167337.913592736026192.08640727
19788572013193131.6267526-5307411.62675264
2067856837886070.85685529-1100387.85685529
2131068466785755.74329753-3678909.74329753
2217063313107089.20154422-1400758.20154422
2312865341706423.59986829-419889.599868293
244990791286561.75762555-787482.75762555
2524637499131.058092224-474494.058092224
261624668.36736036-24652.36736036
272730917.629693096324127291.3703069037
2887343327307.1958504379846125.804149562
298435418873377.0651941667562040.93480583
30112900888434918.096452182855169.90354782
31684039511289899.2533935-4449504.25339353
3238032526840689.14320571-3037437.14320571
3343889883803452.79573983585535.204260165
3426809404388949.29204688-1708009.29204688
3511741352681052.91130426-1506917.91130426
363283881174234.61776412-845846.617764123
3722943328443.91634967-305500.91634967
38565722963.1957372701-17306.1957372701
39281565658.1440600127522497.8559399872
4077083128154.5127351069742676.487264893
418378147770781.9039141597607365.09608584
42132749468377644.10020964897301.8997904
43729784013274622.2542526-5976782.25425258
4428482277298235.10691349-4450008.10691349
4528921792848521.1765139443657.8234860608
4617622242892176.11391395-1129952.11391395
4710093751762298.69770072-752923.697700724
481883881009424.77349778-821036.773497785
493393188442.276246254-185049.276246254
5003405.23304535301-3405.23304535301
51138070.22510960932335413806.7748903907
52261990513806.08727606592606098.91272393
53132977042619732.718719910677971.2812801
54624008713296998.1117652-7056911.11176519
5551084606240553.51095013-1132093.51095013
5645533815108534.83926198-555153.839261975
5731485464553417.6995334-1404871.6995334
5824333873148638.87179915-715251.871799145
5917481082433434.28312785-685326.283127846
607234541748153.30483811-1024699.30483811
6158525723521.739757342-664996.739757342
6279258568.9609137743-57776.9609137743
6342585795.81945932215741789.1805406778
64163438642582.23744425711591803.76255574
65103605701634280.770690198726289.22930981
66679859910359993.1315352-3561394.13153517
6748477486798834.43294421-1951086.43294421
6849712024847876.98039542123325.019604583
693438634971193.84735769-4627330.84735769
702200366344168.8987814891856197.10121851
7115494222200243.29244997-650821.292449968
72901441549465.02381803-1459321.02381803
736328890240.4712785216-26952.4712785216
7433863289.7817459771-62951.7817459771
7544863342.16155100291444520.8384489971
76167813544860.05686265331633274.94313735
7792933571678027.029156467615329.97084354
7893612589292853.5736759468404.4263240639
7967664029361253.47799123-2594851.47799123
8043312726766573.53774637-2435301.53774637
8135189624331432.99038464-812470.990384636
8224257863519015.70998836-1093229.70998836
8317017952425858.27009419-724063.270094187
845524521701842.86562261-1149390.86562261
8516104552527.982737532-536423.982737532
86016139.4613594951-16139.4613594951
87901981.0669307483325890196.9330692517
88173133290192.03735483151641139.96264517
8979541351731223.509223926222911.49077608
90115613427953723.622230583607618.37776942
91683473311561103.5113113-4726370.51131133
9242556526835045.44599273-2579393.44599273
9342430704255822.51586285-12752.5158628458
9434152164243070.84303007-827854.843030074
9518412373415270.72696811-1574033.72696811
966554561841341.05458676-1185885.05458676







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97655534.395257471-5381726.033019046692794.82353399
98655534.395257471-7882158.976842989193227.76735793
99655534.395257471-9800846.5634290811111915.353944
100655534.395257471-11418387.8088312729456.599345
101655534.395257471-12843476.384334214154545.1748491
102655534.395257471-14131858.433253815442927.2237687
103655534.395257471-15316650.217433516627719.0079484
104655534.395257471-16419429.028980217730497.8194952
105655534.395257471-17455182.613636218766251.4041511
106655534.395257471-18434823.516877219745892.3073922
107655534.395257471-19366589.863935920677658.6544508
108655534.395257471-20256881.880432821567950.6709477

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 655534.395257471 & -5381726.03301904 & 6692794.82353399 \tabularnewline
98 & 655534.395257471 & -7882158.97684298 & 9193227.76735793 \tabularnewline
99 & 655534.395257471 & -9800846.56342908 & 11111915.353944 \tabularnewline
100 & 655534.395257471 & -11418387.80883 & 12729456.599345 \tabularnewline
101 & 655534.395257471 & -12843476.3843342 & 14154545.1748491 \tabularnewline
102 & 655534.395257471 & -14131858.4332538 & 15442927.2237687 \tabularnewline
103 & 655534.395257471 & -15316650.2174335 & 16627719.0079484 \tabularnewline
104 & 655534.395257471 & -16419429.0289802 & 17730497.8194952 \tabularnewline
105 & 655534.395257471 & -17455182.6136362 & 18766251.4041511 \tabularnewline
106 & 655534.395257471 & -18434823.5168772 & 19745892.3073922 \tabularnewline
107 & 655534.395257471 & -19366589.8639359 & 20677658.6544508 \tabularnewline
108 & 655534.395257471 & -20256881.8804328 & 21567950.6709477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158029&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]97[/C][C]655534.395257471[/C][C]-5381726.03301904[/C][C]6692794.82353399[/C][/ROW]
[ROW][C]98[/C][C]655534.395257471[/C][C]-7882158.97684298[/C][C]9193227.76735793[/C][/ROW]
[ROW][C]99[/C][C]655534.395257471[/C][C]-9800846.56342908[/C][C]11111915.353944[/C][/ROW]
[ROW][C]100[/C][C]655534.395257471[/C][C]-11418387.80883[/C][C]12729456.599345[/C][/ROW]
[ROW][C]101[/C][C]655534.395257471[/C][C]-12843476.3843342[/C][C]14154545.1748491[/C][/ROW]
[ROW][C]102[/C][C]655534.395257471[/C][C]-14131858.4332538[/C][C]15442927.2237687[/C][/ROW]
[ROW][C]103[/C][C]655534.395257471[/C][C]-15316650.2174335[/C][C]16627719.0079484[/C][/ROW]
[ROW][C]104[/C][C]655534.395257471[/C][C]-16419429.0289802[/C][C]17730497.8194952[/C][/ROW]
[ROW][C]105[/C][C]655534.395257471[/C][C]-17455182.6136362[/C][C]18766251.4041511[/C][/ROW]
[ROW][C]106[/C][C]655534.395257471[/C][C]-18434823.5168772[/C][C]19745892.3073922[/C][/ROW]
[ROW][C]107[/C][C]655534.395257471[/C][C]-19366589.8639359[/C][C]20677658.6544508[/C][/ROW]
[ROW][C]108[/C][C]655534.395257471[/C][C]-20256881.8804328[/C][C]21567950.6709477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158029&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158029&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
97655534.395257471-5381726.033019046692794.82353399
98655534.395257471-7882158.976842989193227.76735793
99655534.395257471-9800846.5634290811111915.353944
100655534.395257471-11418387.8088312729456.599345
101655534.395257471-12843476.384334214154545.1748491
102655534.395257471-14131858.433253815442927.2237687
103655534.395257471-15316650.217433516627719.0079484
104655534.395257471-16419429.028980217730497.8194952
105655534.395257471-17455182.613636218766251.4041511
106655534.395257471-18434823.516877219745892.3073922
107655534.395257471-19366589.863935920677658.6544508
108655534.395257471-20256881.880432821567950.6709477



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')