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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 13 Dec 2013 04:46:41 -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/2013/Dec/13/t1386928027f33aoramviztauz.htm/, Retrieved Tue, 19 Nov 2019 08:22:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232287, Retrieved Tue, 19 Nov 2019 08:22:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact48
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-13 09:46:41] [bce350b408d16201af89ab48c2896e6e] [Current]
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Dataseries X:
13953,3
14657,7
16686,2
15232,4
15014,1
16688,6
13969,6
14546,8
16292
15039
17433,8
17798,4
16870,9
16659,3
19620,4
15953,5
17420,9
17647,5
15200,8
15637,3
17124,5
17659,4
17815
16165,6
17416,6
16823,9
19171,2
16806,8
18112,8
18485,5
17668
16324,3
17877,5
20136,7
19307
17776,3
19861,3
18757
19879,3
21068,4
19358
20639,2
20008,1
18150,1
21180,4
20428,9
17241,2
15969,3
14972,4
14488,3
15885,1
14305,3
13891,5
15431,6
14199,3
13542,6
16226,3
16786,1
16034,3
16744,5
15896,5
15781,8
18590,3
17416,8
16983
18829,4
16748,6
16502,8
18616,6
19136,4
19523,9
18970,2
20118,2
20125,4
23117,8
20014,6
22228,5
20819,1
19208,9
19953,3
21041,3
20006,8
21045,1
20496,3
20873,5
21304,2
23137,8
20514,2
21343,5
20967,2
20024,4
19602,7
19804,1
22173,9
21802,6
19452,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 7 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232287&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232287&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232287&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 time7 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.513796008648427
beta0.100960013583531
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.513796008648427 \tabularnewline
beta & 0.100960013583531 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232287&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]0.513796008648427[/C][/ROW]
[ROW][C]beta[/C][C]0.100960013583531[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232287&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232287&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
alpha0.513796008648427
beta0.100960013583531
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
316686.215362.11324.1
415232.416815.5021384009-1583.10213840088
515014.116693.0753988116-1678.97539881158
616688.616434.2961182923254.30388170771
713969.617182.0194833285-3212.41948332849
814546.815981.9168598607-1435.11685986069
91629215620.5416259991671.4583740009
101503916376.3468000802-1337.3468000802
1117433.816030.66390091641403.13609908358
1217798.417165.8148483332632.585151666844
1316870.917937.8737904645-1066.97379046451
1416659.317781.3591581323-1122.05915813225
1519620.417538.33747509852082.06252490148
1615953.519049.583245266-3096.083245266
1717420.917739.7157185222-318.815718522208
1817647.517840.2592813822-192.759281382172
1915200.817995.571164832-2794.77116483199
2015637.316669.0069770679-1031.70697706792
2117124.516194.7805486265929.719451373508
2217659.416776.5543898899882.845610110126
231781517380.0403582851434.959641714926
2416165.617775.9669009152-1610.36690091519
2517416.617037.4785056226379.121494377428
2616823.917340.8474202562-516.947420256183
2719171.217157.0041660482014.19583395197
2816806.818378.1342955878-1571.33429558781
2918112.817675.5237643045437.276235695514
3018485.518027.6120723865457.887927613538
311766818414.0425382147-746.04253821473
3216324.318143.1989818305-1818.89898183049
3317877.517226.7745891539650.725410846106
3420136.717612.98833523282523.7116647672
351930719092.4470645379214.552935462059
3617776.319396.5987280605-1620.29872806046
3719861.318673.96141426681187.33858573324
381875719455.4675847789-698.467584778908
3919879.319231.8225661367647.477433863296
4021068.419733.30522704121335.0947729588
411935820657.3381058305-1299.33810583051
4220639.220160.409513168478.790486832004
4320008.120601.9125223475-593.812522347464
4418150.120461.5136374514-2311.41363745144
4521180.419318.71853761021861.68146238985
4620428.920416.613770770212.286229229765
4717241.220564.9344364699-3323.73443646987
4815969.318826.8094148131-2857.50941481314
4914972.417180.0017854173-2207.60178541728
5014488.315752.5995012781-1264.29950127812
5115885.114744.27934474961140.82065525043
5214305.315030.8779459877-725.577945987656
5313891.514320.890597947-429.390597946993
5415431.613740.8094121991690.790587801
5514199.314337.7749872446-138.47498724463
5613542.613987.6881185531-445.088118553094
5716226.313456.97665668992769.32334331007
5816786.114721.46967404762064.63032595242
5916034.315730.9924951227303.307504877297
6016744.515851.2881061028893.211893897238
6115896.516321.0076860332-424.507686033223
6215781.816091.6677809018-309.867780901843
6318590.315905.15567591672685.14432408331
6417416.817396.754930481520.0450695184954
651698317520.0766203237-537.076620323725
6618829.417329.29171354821500.10828645178
6716748.618263.0191758983-1514.41917589835
6816502.817569.3372183359-1066.53721833592
6918616.617050.45089562241566.14910437764
7019136.417965.46891826291170.93108173708
7119523.918738.1650330444785.734966955599
7218970.219353.7072351661-383.50723516606
7320118.219348.6038466389769.596153361108
7420125.419975.8815240685149.518475931498
7523117.820292.32171555792825.4782844421
7620014.622130.2249928765-2115.62499287651
7722228.521319.6656258201908.834374179874
7820819.122110.2052408722-1291.1052408722
7919208.921703.4513513509-2494.55135135087
8019953.320548.9721605564-595.672160556402
8121041.320339.2303050653702.069694934711
8220006.820832.6813925692-825.88139256919
8321045.120498.2364866471546.863513352899
8420496.320897.4698043793-401.169804379326
8520873.520788.797565500684.7024344993661
8621304.220934.1583005208370.041699479243
8723137.821245.32032931371892.47967068631
8820514.222436.8732290214-1922.67322902143
8921343.521568.4812525988-224.981252598809
9020967.221560.686218355-593.486218354985
9120024.421332.7689807624-1308.36898076244
9219602.720669.6790026768-1066.9790026768
9319804.120075.2669879532-271.166987953198
9422173.919875.67380499232298.22619500768
9521802.621115.4401313897687.159868610324
9619452.221563.0919517894-2110.8919517894

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 16686.2 & 15362.1 & 1324.1 \tabularnewline
4 & 15232.4 & 16815.5021384009 & -1583.10213840088 \tabularnewline
5 & 15014.1 & 16693.0753988116 & -1678.97539881158 \tabularnewline
6 & 16688.6 & 16434.2961182923 & 254.30388170771 \tabularnewline
7 & 13969.6 & 17182.0194833285 & -3212.41948332849 \tabularnewline
8 & 14546.8 & 15981.9168598607 & -1435.11685986069 \tabularnewline
9 & 16292 & 15620.5416259991 & 671.4583740009 \tabularnewline
10 & 15039 & 16376.3468000802 & -1337.3468000802 \tabularnewline
11 & 17433.8 & 16030.6639009164 & 1403.13609908358 \tabularnewline
12 & 17798.4 & 17165.8148483332 & 632.585151666844 \tabularnewline
13 & 16870.9 & 17937.8737904645 & -1066.97379046451 \tabularnewline
14 & 16659.3 & 17781.3591581323 & -1122.05915813225 \tabularnewline
15 & 19620.4 & 17538.3374750985 & 2082.06252490148 \tabularnewline
16 & 15953.5 & 19049.583245266 & -3096.083245266 \tabularnewline
17 & 17420.9 & 17739.7157185222 & -318.815718522208 \tabularnewline
18 & 17647.5 & 17840.2592813822 & -192.759281382172 \tabularnewline
19 & 15200.8 & 17995.571164832 & -2794.77116483199 \tabularnewline
20 & 15637.3 & 16669.0069770679 & -1031.70697706792 \tabularnewline
21 & 17124.5 & 16194.7805486265 & 929.719451373508 \tabularnewline
22 & 17659.4 & 16776.5543898899 & 882.845610110126 \tabularnewline
23 & 17815 & 17380.0403582851 & 434.959641714926 \tabularnewline
24 & 16165.6 & 17775.9669009152 & -1610.36690091519 \tabularnewline
25 & 17416.6 & 17037.4785056226 & 379.121494377428 \tabularnewline
26 & 16823.9 & 17340.8474202562 & -516.947420256183 \tabularnewline
27 & 19171.2 & 17157.004166048 & 2014.19583395197 \tabularnewline
28 & 16806.8 & 18378.1342955878 & -1571.33429558781 \tabularnewline
29 & 18112.8 & 17675.5237643045 & 437.276235695514 \tabularnewline
30 & 18485.5 & 18027.6120723865 & 457.887927613538 \tabularnewline
31 & 17668 & 18414.0425382147 & -746.04253821473 \tabularnewline
32 & 16324.3 & 18143.1989818305 & -1818.89898183049 \tabularnewline
33 & 17877.5 & 17226.7745891539 & 650.725410846106 \tabularnewline
34 & 20136.7 & 17612.9883352328 & 2523.7116647672 \tabularnewline
35 & 19307 & 19092.4470645379 & 214.552935462059 \tabularnewline
36 & 17776.3 & 19396.5987280605 & -1620.29872806046 \tabularnewline
37 & 19861.3 & 18673.9614142668 & 1187.33858573324 \tabularnewline
38 & 18757 & 19455.4675847789 & -698.467584778908 \tabularnewline
39 & 19879.3 & 19231.8225661367 & 647.477433863296 \tabularnewline
40 & 21068.4 & 19733.3052270412 & 1335.0947729588 \tabularnewline
41 & 19358 & 20657.3381058305 & -1299.33810583051 \tabularnewline
42 & 20639.2 & 20160.409513168 & 478.790486832004 \tabularnewline
43 & 20008.1 & 20601.9125223475 & -593.812522347464 \tabularnewline
44 & 18150.1 & 20461.5136374514 & -2311.41363745144 \tabularnewline
45 & 21180.4 & 19318.7185376102 & 1861.68146238985 \tabularnewline
46 & 20428.9 & 20416.6137707702 & 12.286229229765 \tabularnewline
47 & 17241.2 & 20564.9344364699 & -3323.73443646987 \tabularnewline
48 & 15969.3 & 18826.8094148131 & -2857.50941481314 \tabularnewline
49 & 14972.4 & 17180.0017854173 & -2207.60178541728 \tabularnewline
50 & 14488.3 & 15752.5995012781 & -1264.29950127812 \tabularnewline
51 & 15885.1 & 14744.2793447496 & 1140.82065525043 \tabularnewline
52 & 14305.3 & 15030.8779459877 & -725.577945987656 \tabularnewline
53 & 13891.5 & 14320.890597947 & -429.390597946993 \tabularnewline
54 & 15431.6 & 13740.809412199 & 1690.790587801 \tabularnewline
55 & 14199.3 & 14337.7749872446 & -138.47498724463 \tabularnewline
56 & 13542.6 & 13987.6881185531 & -445.088118553094 \tabularnewline
57 & 16226.3 & 13456.9766566899 & 2769.32334331007 \tabularnewline
58 & 16786.1 & 14721.4696740476 & 2064.63032595242 \tabularnewline
59 & 16034.3 & 15730.9924951227 & 303.307504877297 \tabularnewline
60 & 16744.5 & 15851.2881061028 & 893.211893897238 \tabularnewline
61 & 15896.5 & 16321.0076860332 & -424.507686033223 \tabularnewline
62 & 15781.8 & 16091.6677809018 & -309.867780901843 \tabularnewline
63 & 18590.3 & 15905.1556759167 & 2685.14432408331 \tabularnewline
64 & 17416.8 & 17396.7549304815 & 20.0450695184954 \tabularnewline
65 & 16983 & 17520.0766203237 & -537.076620323725 \tabularnewline
66 & 18829.4 & 17329.2917135482 & 1500.10828645178 \tabularnewline
67 & 16748.6 & 18263.0191758983 & -1514.41917589835 \tabularnewline
68 & 16502.8 & 17569.3372183359 & -1066.53721833592 \tabularnewline
69 & 18616.6 & 17050.4508956224 & 1566.14910437764 \tabularnewline
70 & 19136.4 & 17965.4689182629 & 1170.93108173708 \tabularnewline
71 & 19523.9 & 18738.1650330444 & 785.734966955599 \tabularnewline
72 & 18970.2 & 19353.7072351661 & -383.50723516606 \tabularnewline
73 & 20118.2 & 19348.6038466389 & 769.596153361108 \tabularnewline
74 & 20125.4 & 19975.8815240685 & 149.518475931498 \tabularnewline
75 & 23117.8 & 20292.3217155579 & 2825.4782844421 \tabularnewline
76 & 20014.6 & 22130.2249928765 & -2115.62499287651 \tabularnewline
77 & 22228.5 & 21319.6656258201 & 908.834374179874 \tabularnewline
78 & 20819.1 & 22110.2052408722 & -1291.1052408722 \tabularnewline
79 & 19208.9 & 21703.4513513509 & -2494.55135135087 \tabularnewline
80 & 19953.3 & 20548.9721605564 & -595.672160556402 \tabularnewline
81 & 21041.3 & 20339.2303050653 & 702.069694934711 \tabularnewline
82 & 20006.8 & 20832.6813925692 & -825.88139256919 \tabularnewline
83 & 21045.1 & 20498.2364866471 & 546.863513352899 \tabularnewline
84 & 20496.3 & 20897.4698043793 & -401.169804379326 \tabularnewline
85 & 20873.5 & 20788.7975655006 & 84.7024344993661 \tabularnewline
86 & 21304.2 & 20934.1583005208 & 370.041699479243 \tabularnewline
87 & 23137.8 & 21245.3203293137 & 1892.47967068631 \tabularnewline
88 & 20514.2 & 22436.8732290214 & -1922.67322902143 \tabularnewline
89 & 21343.5 & 21568.4812525988 & -224.981252598809 \tabularnewline
90 & 20967.2 & 21560.686218355 & -593.486218354985 \tabularnewline
91 & 20024.4 & 21332.7689807624 & -1308.36898076244 \tabularnewline
92 & 19602.7 & 20669.6790026768 & -1066.9790026768 \tabularnewline
93 & 19804.1 & 20075.2669879532 & -271.166987953198 \tabularnewline
94 & 22173.9 & 19875.6738049923 & 2298.22619500768 \tabularnewline
95 & 21802.6 & 21115.4401313897 & 687.159868610324 \tabularnewline
96 & 19452.2 & 21563.0919517894 & -2110.8919517894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232287&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]16686.2[/C][C]15362.1[/C][C]1324.1[/C][/ROW]
[ROW][C]4[/C][C]15232.4[/C][C]16815.5021384009[/C][C]-1583.10213840088[/C][/ROW]
[ROW][C]5[/C][C]15014.1[/C][C]16693.0753988116[/C][C]-1678.97539881158[/C][/ROW]
[ROW][C]6[/C][C]16688.6[/C][C]16434.2961182923[/C][C]254.30388170771[/C][/ROW]
[ROW][C]7[/C][C]13969.6[/C][C]17182.0194833285[/C][C]-3212.41948332849[/C][/ROW]
[ROW][C]8[/C][C]14546.8[/C][C]15981.9168598607[/C][C]-1435.11685986069[/C][/ROW]
[ROW][C]9[/C][C]16292[/C][C]15620.5416259991[/C][C]671.4583740009[/C][/ROW]
[ROW][C]10[/C][C]15039[/C][C]16376.3468000802[/C][C]-1337.3468000802[/C][/ROW]
[ROW][C]11[/C][C]17433.8[/C][C]16030.6639009164[/C][C]1403.13609908358[/C][/ROW]
[ROW][C]12[/C][C]17798.4[/C][C]17165.8148483332[/C][C]632.585151666844[/C][/ROW]
[ROW][C]13[/C][C]16870.9[/C][C]17937.8737904645[/C][C]-1066.97379046451[/C][/ROW]
[ROW][C]14[/C][C]16659.3[/C][C]17781.3591581323[/C][C]-1122.05915813225[/C][/ROW]
[ROW][C]15[/C][C]19620.4[/C][C]17538.3374750985[/C][C]2082.06252490148[/C][/ROW]
[ROW][C]16[/C][C]15953.5[/C][C]19049.583245266[/C][C]-3096.083245266[/C][/ROW]
[ROW][C]17[/C][C]17420.9[/C][C]17739.7157185222[/C][C]-318.815718522208[/C][/ROW]
[ROW][C]18[/C][C]17647.5[/C][C]17840.2592813822[/C][C]-192.759281382172[/C][/ROW]
[ROW][C]19[/C][C]15200.8[/C][C]17995.571164832[/C][C]-2794.77116483199[/C][/ROW]
[ROW][C]20[/C][C]15637.3[/C][C]16669.0069770679[/C][C]-1031.70697706792[/C][/ROW]
[ROW][C]21[/C][C]17124.5[/C][C]16194.7805486265[/C][C]929.719451373508[/C][/ROW]
[ROW][C]22[/C][C]17659.4[/C][C]16776.5543898899[/C][C]882.845610110126[/C][/ROW]
[ROW][C]23[/C][C]17815[/C][C]17380.0403582851[/C][C]434.959641714926[/C][/ROW]
[ROW][C]24[/C][C]16165.6[/C][C]17775.9669009152[/C][C]-1610.36690091519[/C][/ROW]
[ROW][C]25[/C][C]17416.6[/C][C]17037.4785056226[/C][C]379.121494377428[/C][/ROW]
[ROW][C]26[/C][C]16823.9[/C][C]17340.8474202562[/C][C]-516.947420256183[/C][/ROW]
[ROW][C]27[/C][C]19171.2[/C][C]17157.004166048[/C][C]2014.19583395197[/C][/ROW]
[ROW][C]28[/C][C]16806.8[/C][C]18378.1342955878[/C][C]-1571.33429558781[/C][/ROW]
[ROW][C]29[/C][C]18112.8[/C][C]17675.5237643045[/C][C]437.276235695514[/C][/ROW]
[ROW][C]30[/C][C]18485.5[/C][C]18027.6120723865[/C][C]457.887927613538[/C][/ROW]
[ROW][C]31[/C][C]17668[/C][C]18414.0425382147[/C][C]-746.04253821473[/C][/ROW]
[ROW][C]32[/C][C]16324.3[/C][C]18143.1989818305[/C][C]-1818.89898183049[/C][/ROW]
[ROW][C]33[/C][C]17877.5[/C][C]17226.7745891539[/C][C]650.725410846106[/C][/ROW]
[ROW][C]34[/C][C]20136.7[/C][C]17612.9883352328[/C][C]2523.7116647672[/C][/ROW]
[ROW][C]35[/C][C]19307[/C][C]19092.4470645379[/C][C]214.552935462059[/C][/ROW]
[ROW][C]36[/C][C]17776.3[/C][C]19396.5987280605[/C][C]-1620.29872806046[/C][/ROW]
[ROW][C]37[/C][C]19861.3[/C][C]18673.9614142668[/C][C]1187.33858573324[/C][/ROW]
[ROW][C]38[/C][C]18757[/C][C]19455.4675847789[/C][C]-698.467584778908[/C][/ROW]
[ROW][C]39[/C][C]19879.3[/C][C]19231.8225661367[/C][C]647.477433863296[/C][/ROW]
[ROW][C]40[/C][C]21068.4[/C][C]19733.3052270412[/C][C]1335.0947729588[/C][/ROW]
[ROW][C]41[/C][C]19358[/C][C]20657.3381058305[/C][C]-1299.33810583051[/C][/ROW]
[ROW][C]42[/C][C]20639.2[/C][C]20160.409513168[/C][C]478.790486832004[/C][/ROW]
[ROW][C]43[/C][C]20008.1[/C][C]20601.9125223475[/C][C]-593.812522347464[/C][/ROW]
[ROW][C]44[/C][C]18150.1[/C][C]20461.5136374514[/C][C]-2311.41363745144[/C][/ROW]
[ROW][C]45[/C][C]21180.4[/C][C]19318.7185376102[/C][C]1861.68146238985[/C][/ROW]
[ROW][C]46[/C][C]20428.9[/C][C]20416.6137707702[/C][C]12.286229229765[/C][/ROW]
[ROW][C]47[/C][C]17241.2[/C][C]20564.9344364699[/C][C]-3323.73443646987[/C][/ROW]
[ROW][C]48[/C][C]15969.3[/C][C]18826.8094148131[/C][C]-2857.50941481314[/C][/ROW]
[ROW][C]49[/C][C]14972.4[/C][C]17180.0017854173[/C][C]-2207.60178541728[/C][/ROW]
[ROW][C]50[/C][C]14488.3[/C][C]15752.5995012781[/C][C]-1264.29950127812[/C][/ROW]
[ROW][C]51[/C][C]15885.1[/C][C]14744.2793447496[/C][C]1140.82065525043[/C][/ROW]
[ROW][C]52[/C][C]14305.3[/C][C]15030.8779459877[/C][C]-725.577945987656[/C][/ROW]
[ROW][C]53[/C][C]13891.5[/C][C]14320.890597947[/C][C]-429.390597946993[/C][/ROW]
[ROW][C]54[/C][C]15431.6[/C][C]13740.809412199[/C][C]1690.790587801[/C][/ROW]
[ROW][C]55[/C][C]14199.3[/C][C]14337.7749872446[/C][C]-138.47498724463[/C][/ROW]
[ROW][C]56[/C][C]13542.6[/C][C]13987.6881185531[/C][C]-445.088118553094[/C][/ROW]
[ROW][C]57[/C][C]16226.3[/C][C]13456.9766566899[/C][C]2769.32334331007[/C][/ROW]
[ROW][C]58[/C][C]16786.1[/C][C]14721.4696740476[/C][C]2064.63032595242[/C][/ROW]
[ROW][C]59[/C][C]16034.3[/C][C]15730.9924951227[/C][C]303.307504877297[/C][/ROW]
[ROW][C]60[/C][C]16744.5[/C][C]15851.2881061028[/C][C]893.211893897238[/C][/ROW]
[ROW][C]61[/C][C]15896.5[/C][C]16321.0076860332[/C][C]-424.507686033223[/C][/ROW]
[ROW][C]62[/C][C]15781.8[/C][C]16091.6677809018[/C][C]-309.867780901843[/C][/ROW]
[ROW][C]63[/C][C]18590.3[/C][C]15905.1556759167[/C][C]2685.14432408331[/C][/ROW]
[ROW][C]64[/C][C]17416.8[/C][C]17396.7549304815[/C][C]20.0450695184954[/C][/ROW]
[ROW][C]65[/C][C]16983[/C][C]17520.0766203237[/C][C]-537.076620323725[/C][/ROW]
[ROW][C]66[/C][C]18829.4[/C][C]17329.2917135482[/C][C]1500.10828645178[/C][/ROW]
[ROW][C]67[/C][C]16748.6[/C][C]18263.0191758983[/C][C]-1514.41917589835[/C][/ROW]
[ROW][C]68[/C][C]16502.8[/C][C]17569.3372183359[/C][C]-1066.53721833592[/C][/ROW]
[ROW][C]69[/C][C]18616.6[/C][C]17050.4508956224[/C][C]1566.14910437764[/C][/ROW]
[ROW][C]70[/C][C]19136.4[/C][C]17965.4689182629[/C][C]1170.93108173708[/C][/ROW]
[ROW][C]71[/C][C]19523.9[/C][C]18738.1650330444[/C][C]785.734966955599[/C][/ROW]
[ROW][C]72[/C][C]18970.2[/C][C]19353.7072351661[/C][C]-383.50723516606[/C][/ROW]
[ROW][C]73[/C][C]20118.2[/C][C]19348.6038466389[/C][C]769.596153361108[/C][/ROW]
[ROW][C]74[/C][C]20125.4[/C][C]19975.8815240685[/C][C]149.518475931498[/C][/ROW]
[ROW][C]75[/C][C]23117.8[/C][C]20292.3217155579[/C][C]2825.4782844421[/C][/ROW]
[ROW][C]76[/C][C]20014.6[/C][C]22130.2249928765[/C][C]-2115.62499287651[/C][/ROW]
[ROW][C]77[/C][C]22228.5[/C][C]21319.6656258201[/C][C]908.834374179874[/C][/ROW]
[ROW][C]78[/C][C]20819.1[/C][C]22110.2052408722[/C][C]-1291.1052408722[/C][/ROW]
[ROW][C]79[/C][C]19208.9[/C][C]21703.4513513509[/C][C]-2494.55135135087[/C][/ROW]
[ROW][C]80[/C][C]19953.3[/C][C]20548.9721605564[/C][C]-595.672160556402[/C][/ROW]
[ROW][C]81[/C][C]21041.3[/C][C]20339.2303050653[/C][C]702.069694934711[/C][/ROW]
[ROW][C]82[/C][C]20006.8[/C][C]20832.6813925692[/C][C]-825.88139256919[/C][/ROW]
[ROW][C]83[/C][C]21045.1[/C][C]20498.2364866471[/C][C]546.863513352899[/C][/ROW]
[ROW][C]84[/C][C]20496.3[/C][C]20897.4698043793[/C][C]-401.169804379326[/C][/ROW]
[ROW][C]85[/C][C]20873.5[/C][C]20788.7975655006[/C][C]84.7024344993661[/C][/ROW]
[ROW][C]86[/C][C]21304.2[/C][C]20934.1583005208[/C][C]370.041699479243[/C][/ROW]
[ROW][C]87[/C][C]23137.8[/C][C]21245.3203293137[/C][C]1892.47967068631[/C][/ROW]
[ROW][C]88[/C][C]20514.2[/C][C]22436.8732290214[/C][C]-1922.67322902143[/C][/ROW]
[ROW][C]89[/C][C]21343.5[/C][C]21568.4812525988[/C][C]-224.981252598809[/C][/ROW]
[ROW][C]90[/C][C]20967.2[/C][C]21560.686218355[/C][C]-593.486218354985[/C][/ROW]
[ROW][C]91[/C][C]20024.4[/C][C]21332.7689807624[/C][C]-1308.36898076244[/C][/ROW]
[ROW][C]92[/C][C]19602.7[/C][C]20669.6790026768[/C][C]-1066.9790026768[/C][/ROW]
[ROW][C]93[/C][C]19804.1[/C][C]20075.2669879532[/C][C]-271.166987953198[/C][/ROW]
[ROW][C]94[/C][C]22173.9[/C][C]19875.6738049923[/C][C]2298.22619500768[/C][/ROW]
[ROW][C]95[/C][C]21802.6[/C][C]21115.4401313897[/C][C]687.159868610324[/C][/ROW]
[ROW][C]96[/C][C]19452.2[/C][C]21563.0919517894[/C][C]-2110.8919517894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232287&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232287&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
316686.215362.11324.1
415232.416815.5021384009-1583.10213840088
515014.116693.0753988116-1678.97539881158
616688.616434.2961182923254.30388170771
713969.617182.0194833285-3212.41948332849
814546.815981.9168598607-1435.11685986069
91629215620.5416259991671.4583740009
101503916376.3468000802-1337.3468000802
1117433.816030.66390091641403.13609908358
1217798.417165.8148483332632.585151666844
1316870.917937.8737904645-1066.97379046451
1416659.317781.3591581323-1122.05915813225
1519620.417538.33747509852082.06252490148
1615953.519049.583245266-3096.083245266
1717420.917739.7157185222-318.815718522208
1817647.517840.2592813822-192.759281382172
1915200.817995.571164832-2794.77116483199
2015637.316669.0069770679-1031.70697706792
2117124.516194.7805486265929.719451373508
2217659.416776.5543898899882.845610110126
231781517380.0403582851434.959641714926
2416165.617775.9669009152-1610.36690091519
2517416.617037.4785056226379.121494377428
2616823.917340.8474202562-516.947420256183
2719171.217157.0041660482014.19583395197
2816806.818378.1342955878-1571.33429558781
2918112.817675.5237643045437.276235695514
3018485.518027.6120723865457.887927613538
311766818414.0425382147-746.04253821473
3216324.318143.1989818305-1818.89898183049
3317877.517226.7745891539650.725410846106
3420136.717612.98833523282523.7116647672
351930719092.4470645379214.552935462059
3617776.319396.5987280605-1620.29872806046
3719861.318673.96141426681187.33858573324
381875719455.4675847789-698.467584778908
3919879.319231.8225661367647.477433863296
4021068.419733.30522704121335.0947729588
411935820657.3381058305-1299.33810583051
4220639.220160.409513168478.790486832004
4320008.120601.9125223475-593.812522347464
4418150.120461.5136374514-2311.41363745144
4521180.419318.71853761021861.68146238985
4620428.920416.613770770212.286229229765
4717241.220564.9344364699-3323.73443646987
4815969.318826.8094148131-2857.50941481314
4914972.417180.0017854173-2207.60178541728
5014488.315752.5995012781-1264.29950127812
5115885.114744.27934474961140.82065525043
5214305.315030.8779459877-725.577945987656
5313891.514320.890597947-429.390597946993
5415431.613740.8094121991690.790587801
5514199.314337.7749872446-138.47498724463
5613542.613987.6881185531-445.088118553094
5716226.313456.97665668992769.32334331007
5816786.114721.46967404762064.63032595242
5916034.315730.9924951227303.307504877297
6016744.515851.2881061028893.211893897238
6115896.516321.0076860332-424.507686033223
6215781.816091.6677809018-309.867780901843
6318590.315905.15567591672685.14432408331
6417416.817396.754930481520.0450695184954
651698317520.0766203237-537.076620323725
6618829.417329.29171354821500.10828645178
6716748.618263.0191758983-1514.41917589835
6816502.817569.3372183359-1066.53721833592
6918616.617050.45089562241566.14910437764
7019136.417965.46891826291170.93108173708
7119523.918738.1650330444785.734966955599
7218970.219353.7072351661-383.50723516606
7320118.219348.6038466389769.596153361108
7420125.419975.8815240685149.518475931498
7523117.820292.32171555792825.4782844421
7620014.622130.2249928765-2115.62499287651
7722228.521319.6656258201908.834374179874
7820819.122110.2052408722-1291.1052408722
7919208.921703.4513513509-2494.55135135087
8019953.320548.9721605564-595.672160556402
8121041.320339.2303050653702.069694934711
8220006.820832.6813925692-825.88139256919
8321045.120498.2364866471546.863513352899
8420496.320897.4698043793-401.169804379326
8520873.520788.797565500684.7024344993661
8621304.220934.1583005208370.041699479243
8723137.821245.32032931371892.47967068631
8820514.222436.8732290214-1922.67322902143
8921343.521568.4812525988-224.981252598809
9020967.221560.686218355-593.486218354985
9120024.421332.7689807624-1308.36898076244
9219602.720669.6790026768-1066.9790026768
9319804.120075.2669879532-271.166987953198
9422173.919875.67380499232298.22619500768
9521802.621115.4401313897687.159868610324
9619452.221563.0919517894-2110.8919517894







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9720463.617929047117632.348970990823294.8868871035
9820448.711765822417195.854476772923701.5690548718
9920433.805602597616740.828970781424126.7822344137
10020418.899439372816267.970539129624569.828339616
10120403.99327614815777.912561386125030.0739909099
10220389.087112923215271.230942771525506.9432830749
10320374.180949698414748.451043913225999.9108554837
10420359.274786473714210.053892383326508.4956805641
10520344.368623248913656.481594138527032.2556523592
10620329.462460024113088.141990407627570.7829296405
10720314.556296799312505.412647568828123.6999460298
10820299.650133574511908.644274477328690.6559926717

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 20463.6179290471 & 17632.3489709908 & 23294.8868871035 \tabularnewline
98 & 20448.7117658224 & 17195.8544767729 & 23701.5690548718 \tabularnewline
99 & 20433.8056025976 & 16740.8289707814 & 24126.7822344137 \tabularnewline
100 & 20418.8994393728 & 16267.9705391296 & 24569.828339616 \tabularnewline
101 & 20403.993276148 & 15777.9125613861 & 25030.0739909099 \tabularnewline
102 & 20389.0871129232 & 15271.2309427715 & 25506.9432830749 \tabularnewline
103 & 20374.1809496984 & 14748.4510439132 & 25999.9108554837 \tabularnewline
104 & 20359.2747864737 & 14210.0538923833 & 26508.4956805641 \tabularnewline
105 & 20344.3686232489 & 13656.4815941385 & 27032.2556523592 \tabularnewline
106 & 20329.4624600241 & 13088.1419904076 & 27570.7829296405 \tabularnewline
107 & 20314.5562967993 & 12505.4126475688 & 28123.6999460298 \tabularnewline
108 & 20299.6501335745 & 11908.6442744773 & 28690.6559926717 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232287&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]20463.6179290471[/C][C]17632.3489709908[/C][C]23294.8868871035[/C][/ROW]
[ROW][C]98[/C][C]20448.7117658224[/C][C]17195.8544767729[/C][C]23701.5690548718[/C][/ROW]
[ROW][C]99[/C][C]20433.8056025976[/C][C]16740.8289707814[/C][C]24126.7822344137[/C][/ROW]
[ROW][C]100[/C][C]20418.8994393728[/C][C]16267.9705391296[/C][C]24569.828339616[/C][/ROW]
[ROW][C]101[/C][C]20403.993276148[/C][C]15777.9125613861[/C][C]25030.0739909099[/C][/ROW]
[ROW][C]102[/C][C]20389.0871129232[/C][C]15271.2309427715[/C][C]25506.9432830749[/C][/ROW]
[ROW][C]103[/C][C]20374.1809496984[/C][C]14748.4510439132[/C][C]25999.9108554837[/C][/ROW]
[ROW][C]104[/C][C]20359.2747864737[/C][C]14210.0538923833[/C][C]26508.4956805641[/C][/ROW]
[ROW][C]105[/C][C]20344.3686232489[/C][C]13656.4815941385[/C][C]27032.2556523592[/C][/ROW]
[ROW][C]106[/C][C]20329.4624600241[/C][C]13088.1419904076[/C][C]27570.7829296405[/C][/ROW]
[ROW][C]107[/C][C]20314.5562967993[/C][C]12505.4126475688[/C][C]28123.6999460298[/C][/ROW]
[ROW][C]108[/C][C]20299.6501335745[/C][C]11908.6442744773[/C][C]28690.6559926717[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232287&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232287&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
9720463.617929047117632.348970990823294.8868871035
9820448.711765822417195.854476772923701.5690548718
9920433.805602597616740.828970781424126.7822344137
10020418.899439372816267.970539129624569.828339616
10120403.99327614815777.912561386125030.0739909099
10220389.087112923215271.230942771525506.9432830749
10320374.180949698414748.451043913225999.9108554837
10420359.274786473714210.053892383326508.4956805641
10520344.368623248913656.481594138527032.2556523592
10620329.462460024113088.141990407627570.7829296405
10720314.556296799312505.412647568828123.6999460298
10820299.650133574511908.644274477328690.6559926717



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=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')