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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Dec 2016 11:49:46 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/07/t14811078292av7s6x5q027wzu.htm/, Retrieved Fri, 01 Nov 2024 03:43:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298000, Retrieved Fri, 01 Nov 2024 03:43:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-07 10:49:46] [aed32bb2e1132335210cb15bafce0db8] [Current]
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Dataseries X:
1418.7
1344.1
1574.6
1621.6
1887.2
2055.3
1606.8
1494.8
1636
1485.7
1369.7
1333.8
1614.9
1297.3
1226.2
1098.5
1258.5
1065.2
1000.4
1820.2
1224.8
1428.4
1144
1166.9
1902.3
1949.4
1784.5
1671.5
1923.8
1882.8
2165
1826.9
1511.2
2063.1
2169.6
2495.3
2936.9
3076.9
3365.7
3846
3436.2
3561.1
3328
2762.9
2923
2731.1
2571.5
3282.4
4606.5
4698.7
5093.3
4477.3
3850.1
4275.2
3975
4495.9
4042.4
5221.3
2555
2694.6
2757.7
2760.9
3872.9
2888.7
2529.2
3458.3
2882.8
2958.5
2652.4
2869.8
2501.7
2576.1
3347.5
3036.1
3345.2
3223.2
4087
4157.2
3368
3957.5
3469
4501.6
3181.4
3464.5
4186.9
3064.7
4011.7
3537.1
4879.5
4488.7
4632.9
4405.8
2615.2
3338
2825.2
3012.7
4537.5
5676.7
5575.4
6643.4
5590.6
4697.6
5078.1
5769.9
5561.4
7268.8
6496.7
6489.3
10883.5
7998.6
7340
7814.4
5729.6
6463.5
6315.4
5357.1




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298000&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298000&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298000&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.710850707357125
beta0.00434277932328067
gamma0.786543691830047

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.710850707357125 \tabularnewline
beta & 0.00434277932328067 \tabularnewline
gamma & 0.786543691830047 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298000&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]0.710850707357125[/C][/ROW]
[ROW][C]beta[/C][C]0.00434277932328067[/C][/ROW]
[ROW][C]gamma[/C][C]0.786543691830047[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298000&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298000&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
alpha0.710850707357125
beta0.00434277932328067
gamma0.786543691830047







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131614.91983.56999834078-368.669998340777
141297.31362.43484458459-65.1348445845897
151226.21216.239260037439.96073996257405
161098.51083.9574164152114.5425835847871
171258.51232.435851754326.0641482456981
181065.21044.4176229967820.7823770032167
191000.41268.27117446981-267.871174469807
201820.2966.326326022022853.873673977978
211224.81707.03392666744-482.233926667437
221428.41236.25154030761192.148459692391
2311441276.68575055831-132.685750558308
241166.91175.29507473474-8.39507473474464
251902.31375.79265952103526.507340478967
261949.41443.85101886625505.548981133748
271784.51704.1443302203580.3556697796523
281671.51578.3744273385793.1255726614263
291923.81876.061472521147.7385274789031
301882.81612.56811467702270.231885322984
3121652057.46825852298107.531741477022
321826.92325.1238496601-498.223849660103
331511.21756.33112670988-245.131126709877
342063.11620.31558961511442.784410384887
352169.61713.62654084178455.973459158219
362495.32104.46393950385390.83606049615
372936.93049.92480270014-113.024802700143
383076.92463.71613265654613.183867343457
393365.72622.22282343377743.477176566231
4038462856.55054878408989.449451215925
413436.24075.42510038238-639.225100382379
423561.13173.21643695269387.883563047313
4333283878.36183814906-550.361838149056
442762.93564.87127462987-801.971274629874
4529232753.94814895076169.051851049245
462731.13245.69507411871-514.595074118712
472571.52563.178263293778.32173670622615
483282.42627.24715980598655.152840194022
494606.53796.84450672016809.655493279839
504698.73855.45670362101843.243296378986
515093.34067.920019443121025.37998055688
524477.34403.9586063020973.3413936979105
533850.14612.49124224806-762.391242248065
544275.23817.78733066807457.412669331933
5539754386.2842448854-411.284244885395
564495.94084.93387965297410.96612034703
574042.44363.14671671307-320.746716713069
585221.34437.02276002657784.277239973432
5925554665.19545582078-2110.19545582078
602694.63399.56966370608-704.969663706077
612757.73533.8270624894-776.127062489395
622760.92619.19859518982141.701404810181
633872.92482.7429489241390.157051076
642888.73041.21157405128-152.511574051276
652529.22885.5312039118-356.331203911802
663458.32633.91388033369824.386119666306
672882.83242.69770757026-359.897707570261
682958.53107.56723935627-149.067239356273
692652.42868.16214404103-215.762144041033
702869.83060.15026848175-190.350268481749
712501.72226.51653746646275.183462533535
722576.12894.61163703136-318.511637031364
733347.53240.02560541349107.474394586513
743036.13141.12113820282-105.021138202816
753345.23023.90676277154321.29323722846
763223.22577.46903232878645.730967671218
7740872932.591616559251154.40838344075
784157.24116.9925916356340.2074083643693
7933683844.57461734582-476.574617345825
803957.53715.53515449374241.964845506259
8134693699.67936992657-230.679369926568
824501.64011.20531348339490.394686516608
833181.43470.85240432849-289.452404328493
843464.53711.28607369972-246.786073699721
854186.94461.57039878406-274.670398784058
863064.73991.39074692718-926.690746927175
874011.73391.26525069022620.434749309783
883537.13119.62688372336417.473116276645
894879.53370.490444422271509.00955557773
904488.74569.429288122-80.7292881220019
914632.94049.31314048425583.586859515745
924405.84962.0252991703-556.225299170303
932615.24227.07163832125-1611.87163832125
9433383635.88607774795-297.886077747949
952825.22598.80286488617226.397135113826
963012.73147.16815498278-134.468154982779
974537.53851.54252410724685.957475892758
985676.73861.265120310971815.43487968903
995575.45828.46451321883-253.064513218827
1006643.44572.037683912592071.36231608741
1015590.66274.32260202256-683.722602022555
1024697.65510.57899577234-812.978995772338
1035078.14580.42885541035497.671144589655
1045769.95181.40908707733588.490912922667
1055561.44703.89204621893857.50795378107
1067268.87008.22455866925260.575441330749
1076496.75704.28235532735792.417644672646
1086489.36982.66262177522-493.362621775219
10910883.58806.06597735512077.4340226449
1107998.69587.42470823461-1588.82470823461
11173408788.42710793777-1448.42710793777
1127814.46852.20099469242962.199005307578
1135729.67067.17673262355-1337.57673262355
1146463.55761.9649184496701.535081550395
1156315.46187.78428113384127.615718866159
1165357.16606.70676857828-1249.60676857828

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1614.9 & 1983.56999834078 & -368.669998340777 \tabularnewline
14 & 1297.3 & 1362.43484458459 & -65.1348445845897 \tabularnewline
15 & 1226.2 & 1216.23926003743 & 9.96073996257405 \tabularnewline
16 & 1098.5 & 1083.95741641521 & 14.5425835847871 \tabularnewline
17 & 1258.5 & 1232.4358517543 & 26.0641482456981 \tabularnewline
18 & 1065.2 & 1044.41762299678 & 20.7823770032167 \tabularnewline
19 & 1000.4 & 1268.27117446981 & -267.871174469807 \tabularnewline
20 & 1820.2 & 966.326326022022 & 853.873673977978 \tabularnewline
21 & 1224.8 & 1707.03392666744 & -482.233926667437 \tabularnewline
22 & 1428.4 & 1236.25154030761 & 192.148459692391 \tabularnewline
23 & 1144 & 1276.68575055831 & -132.685750558308 \tabularnewline
24 & 1166.9 & 1175.29507473474 & -8.39507473474464 \tabularnewline
25 & 1902.3 & 1375.79265952103 & 526.507340478967 \tabularnewline
26 & 1949.4 & 1443.85101886625 & 505.548981133748 \tabularnewline
27 & 1784.5 & 1704.14433022035 & 80.3556697796523 \tabularnewline
28 & 1671.5 & 1578.37442733857 & 93.1255726614263 \tabularnewline
29 & 1923.8 & 1876.0614725211 & 47.7385274789031 \tabularnewline
30 & 1882.8 & 1612.56811467702 & 270.231885322984 \tabularnewline
31 & 2165 & 2057.46825852298 & 107.531741477022 \tabularnewline
32 & 1826.9 & 2325.1238496601 & -498.223849660103 \tabularnewline
33 & 1511.2 & 1756.33112670988 & -245.131126709877 \tabularnewline
34 & 2063.1 & 1620.31558961511 & 442.784410384887 \tabularnewline
35 & 2169.6 & 1713.62654084178 & 455.973459158219 \tabularnewline
36 & 2495.3 & 2104.46393950385 & 390.83606049615 \tabularnewline
37 & 2936.9 & 3049.92480270014 & -113.024802700143 \tabularnewline
38 & 3076.9 & 2463.71613265654 & 613.183867343457 \tabularnewline
39 & 3365.7 & 2622.22282343377 & 743.477176566231 \tabularnewline
40 & 3846 & 2856.55054878408 & 989.449451215925 \tabularnewline
41 & 3436.2 & 4075.42510038238 & -639.225100382379 \tabularnewline
42 & 3561.1 & 3173.21643695269 & 387.883563047313 \tabularnewline
43 & 3328 & 3878.36183814906 & -550.361838149056 \tabularnewline
44 & 2762.9 & 3564.87127462987 & -801.971274629874 \tabularnewline
45 & 2923 & 2753.94814895076 & 169.051851049245 \tabularnewline
46 & 2731.1 & 3245.69507411871 & -514.595074118712 \tabularnewline
47 & 2571.5 & 2563.17826329377 & 8.32173670622615 \tabularnewline
48 & 3282.4 & 2627.24715980598 & 655.152840194022 \tabularnewline
49 & 4606.5 & 3796.84450672016 & 809.655493279839 \tabularnewline
50 & 4698.7 & 3855.45670362101 & 843.243296378986 \tabularnewline
51 & 5093.3 & 4067.92001944312 & 1025.37998055688 \tabularnewline
52 & 4477.3 & 4403.95860630209 & 73.3413936979105 \tabularnewline
53 & 3850.1 & 4612.49124224806 & -762.391242248065 \tabularnewline
54 & 4275.2 & 3817.78733066807 & 457.412669331933 \tabularnewline
55 & 3975 & 4386.2842448854 & -411.284244885395 \tabularnewline
56 & 4495.9 & 4084.93387965297 & 410.96612034703 \tabularnewline
57 & 4042.4 & 4363.14671671307 & -320.746716713069 \tabularnewline
58 & 5221.3 & 4437.02276002657 & 784.277239973432 \tabularnewline
59 & 2555 & 4665.19545582078 & -2110.19545582078 \tabularnewline
60 & 2694.6 & 3399.56966370608 & -704.969663706077 \tabularnewline
61 & 2757.7 & 3533.8270624894 & -776.127062489395 \tabularnewline
62 & 2760.9 & 2619.19859518982 & 141.701404810181 \tabularnewline
63 & 3872.9 & 2482.742948924 & 1390.157051076 \tabularnewline
64 & 2888.7 & 3041.21157405128 & -152.511574051276 \tabularnewline
65 & 2529.2 & 2885.5312039118 & -356.331203911802 \tabularnewline
66 & 3458.3 & 2633.91388033369 & 824.386119666306 \tabularnewline
67 & 2882.8 & 3242.69770757026 & -359.897707570261 \tabularnewline
68 & 2958.5 & 3107.56723935627 & -149.067239356273 \tabularnewline
69 & 2652.4 & 2868.16214404103 & -215.762144041033 \tabularnewline
70 & 2869.8 & 3060.15026848175 & -190.350268481749 \tabularnewline
71 & 2501.7 & 2226.51653746646 & 275.183462533535 \tabularnewline
72 & 2576.1 & 2894.61163703136 & -318.511637031364 \tabularnewline
73 & 3347.5 & 3240.02560541349 & 107.474394586513 \tabularnewline
74 & 3036.1 & 3141.12113820282 & -105.021138202816 \tabularnewline
75 & 3345.2 & 3023.90676277154 & 321.29323722846 \tabularnewline
76 & 3223.2 & 2577.46903232878 & 645.730967671218 \tabularnewline
77 & 4087 & 2932.59161655925 & 1154.40838344075 \tabularnewline
78 & 4157.2 & 4116.99259163563 & 40.2074083643693 \tabularnewline
79 & 3368 & 3844.57461734582 & -476.574617345825 \tabularnewline
80 & 3957.5 & 3715.53515449374 & 241.964845506259 \tabularnewline
81 & 3469 & 3699.67936992657 & -230.679369926568 \tabularnewline
82 & 4501.6 & 4011.20531348339 & 490.394686516608 \tabularnewline
83 & 3181.4 & 3470.85240432849 & -289.452404328493 \tabularnewline
84 & 3464.5 & 3711.28607369972 & -246.786073699721 \tabularnewline
85 & 4186.9 & 4461.57039878406 & -274.670398784058 \tabularnewline
86 & 3064.7 & 3991.39074692718 & -926.690746927175 \tabularnewline
87 & 4011.7 & 3391.26525069022 & 620.434749309783 \tabularnewline
88 & 3537.1 & 3119.62688372336 & 417.473116276645 \tabularnewline
89 & 4879.5 & 3370.49044442227 & 1509.00955557773 \tabularnewline
90 & 4488.7 & 4569.429288122 & -80.7292881220019 \tabularnewline
91 & 4632.9 & 4049.31314048425 & 583.586859515745 \tabularnewline
92 & 4405.8 & 4962.0252991703 & -556.225299170303 \tabularnewline
93 & 2615.2 & 4227.07163832125 & -1611.87163832125 \tabularnewline
94 & 3338 & 3635.88607774795 & -297.886077747949 \tabularnewline
95 & 2825.2 & 2598.80286488617 & 226.397135113826 \tabularnewline
96 & 3012.7 & 3147.16815498278 & -134.468154982779 \tabularnewline
97 & 4537.5 & 3851.54252410724 & 685.957475892758 \tabularnewline
98 & 5676.7 & 3861.26512031097 & 1815.43487968903 \tabularnewline
99 & 5575.4 & 5828.46451321883 & -253.064513218827 \tabularnewline
100 & 6643.4 & 4572.03768391259 & 2071.36231608741 \tabularnewline
101 & 5590.6 & 6274.32260202256 & -683.722602022555 \tabularnewline
102 & 4697.6 & 5510.57899577234 & -812.978995772338 \tabularnewline
103 & 5078.1 & 4580.42885541035 & 497.671144589655 \tabularnewline
104 & 5769.9 & 5181.40908707733 & 588.490912922667 \tabularnewline
105 & 5561.4 & 4703.89204621893 & 857.50795378107 \tabularnewline
106 & 7268.8 & 7008.22455866925 & 260.575441330749 \tabularnewline
107 & 6496.7 & 5704.28235532735 & 792.417644672646 \tabularnewline
108 & 6489.3 & 6982.66262177522 & -493.362621775219 \tabularnewline
109 & 10883.5 & 8806.0659773551 & 2077.4340226449 \tabularnewline
110 & 7998.6 & 9587.42470823461 & -1588.82470823461 \tabularnewline
111 & 7340 & 8788.42710793777 & -1448.42710793777 \tabularnewline
112 & 7814.4 & 6852.20099469242 & 962.199005307578 \tabularnewline
113 & 5729.6 & 7067.17673262355 & -1337.57673262355 \tabularnewline
114 & 6463.5 & 5761.9649184496 & 701.535081550395 \tabularnewline
115 & 6315.4 & 6187.78428113384 & 127.615718866159 \tabularnewline
116 & 5357.1 & 6606.70676857828 & -1249.60676857828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298000&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]1614.9[/C][C]1983.56999834078[/C][C]-368.669998340777[/C][/ROW]
[ROW][C]14[/C][C]1297.3[/C][C]1362.43484458459[/C][C]-65.1348445845897[/C][/ROW]
[ROW][C]15[/C][C]1226.2[/C][C]1216.23926003743[/C][C]9.96073996257405[/C][/ROW]
[ROW][C]16[/C][C]1098.5[/C][C]1083.95741641521[/C][C]14.5425835847871[/C][/ROW]
[ROW][C]17[/C][C]1258.5[/C][C]1232.4358517543[/C][C]26.0641482456981[/C][/ROW]
[ROW][C]18[/C][C]1065.2[/C][C]1044.41762299678[/C][C]20.7823770032167[/C][/ROW]
[ROW][C]19[/C][C]1000.4[/C][C]1268.27117446981[/C][C]-267.871174469807[/C][/ROW]
[ROW][C]20[/C][C]1820.2[/C][C]966.326326022022[/C][C]853.873673977978[/C][/ROW]
[ROW][C]21[/C][C]1224.8[/C][C]1707.03392666744[/C][C]-482.233926667437[/C][/ROW]
[ROW][C]22[/C][C]1428.4[/C][C]1236.25154030761[/C][C]192.148459692391[/C][/ROW]
[ROW][C]23[/C][C]1144[/C][C]1276.68575055831[/C][C]-132.685750558308[/C][/ROW]
[ROW][C]24[/C][C]1166.9[/C][C]1175.29507473474[/C][C]-8.39507473474464[/C][/ROW]
[ROW][C]25[/C][C]1902.3[/C][C]1375.79265952103[/C][C]526.507340478967[/C][/ROW]
[ROW][C]26[/C][C]1949.4[/C][C]1443.85101886625[/C][C]505.548981133748[/C][/ROW]
[ROW][C]27[/C][C]1784.5[/C][C]1704.14433022035[/C][C]80.3556697796523[/C][/ROW]
[ROW][C]28[/C][C]1671.5[/C][C]1578.37442733857[/C][C]93.1255726614263[/C][/ROW]
[ROW][C]29[/C][C]1923.8[/C][C]1876.0614725211[/C][C]47.7385274789031[/C][/ROW]
[ROW][C]30[/C][C]1882.8[/C][C]1612.56811467702[/C][C]270.231885322984[/C][/ROW]
[ROW][C]31[/C][C]2165[/C][C]2057.46825852298[/C][C]107.531741477022[/C][/ROW]
[ROW][C]32[/C][C]1826.9[/C][C]2325.1238496601[/C][C]-498.223849660103[/C][/ROW]
[ROW][C]33[/C][C]1511.2[/C][C]1756.33112670988[/C][C]-245.131126709877[/C][/ROW]
[ROW][C]34[/C][C]2063.1[/C][C]1620.31558961511[/C][C]442.784410384887[/C][/ROW]
[ROW][C]35[/C][C]2169.6[/C][C]1713.62654084178[/C][C]455.973459158219[/C][/ROW]
[ROW][C]36[/C][C]2495.3[/C][C]2104.46393950385[/C][C]390.83606049615[/C][/ROW]
[ROW][C]37[/C][C]2936.9[/C][C]3049.92480270014[/C][C]-113.024802700143[/C][/ROW]
[ROW][C]38[/C][C]3076.9[/C][C]2463.71613265654[/C][C]613.183867343457[/C][/ROW]
[ROW][C]39[/C][C]3365.7[/C][C]2622.22282343377[/C][C]743.477176566231[/C][/ROW]
[ROW][C]40[/C][C]3846[/C][C]2856.55054878408[/C][C]989.449451215925[/C][/ROW]
[ROW][C]41[/C][C]3436.2[/C][C]4075.42510038238[/C][C]-639.225100382379[/C][/ROW]
[ROW][C]42[/C][C]3561.1[/C][C]3173.21643695269[/C][C]387.883563047313[/C][/ROW]
[ROW][C]43[/C][C]3328[/C][C]3878.36183814906[/C][C]-550.361838149056[/C][/ROW]
[ROW][C]44[/C][C]2762.9[/C][C]3564.87127462987[/C][C]-801.971274629874[/C][/ROW]
[ROW][C]45[/C][C]2923[/C][C]2753.94814895076[/C][C]169.051851049245[/C][/ROW]
[ROW][C]46[/C][C]2731.1[/C][C]3245.69507411871[/C][C]-514.595074118712[/C][/ROW]
[ROW][C]47[/C][C]2571.5[/C][C]2563.17826329377[/C][C]8.32173670622615[/C][/ROW]
[ROW][C]48[/C][C]3282.4[/C][C]2627.24715980598[/C][C]655.152840194022[/C][/ROW]
[ROW][C]49[/C][C]4606.5[/C][C]3796.84450672016[/C][C]809.655493279839[/C][/ROW]
[ROW][C]50[/C][C]4698.7[/C][C]3855.45670362101[/C][C]843.243296378986[/C][/ROW]
[ROW][C]51[/C][C]5093.3[/C][C]4067.92001944312[/C][C]1025.37998055688[/C][/ROW]
[ROW][C]52[/C][C]4477.3[/C][C]4403.95860630209[/C][C]73.3413936979105[/C][/ROW]
[ROW][C]53[/C][C]3850.1[/C][C]4612.49124224806[/C][C]-762.391242248065[/C][/ROW]
[ROW][C]54[/C][C]4275.2[/C][C]3817.78733066807[/C][C]457.412669331933[/C][/ROW]
[ROW][C]55[/C][C]3975[/C][C]4386.2842448854[/C][C]-411.284244885395[/C][/ROW]
[ROW][C]56[/C][C]4495.9[/C][C]4084.93387965297[/C][C]410.96612034703[/C][/ROW]
[ROW][C]57[/C][C]4042.4[/C][C]4363.14671671307[/C][C]-320.746716713069[/C][/ROW]
[ROW][C]58[/C][C]5221.3[/C][C]4437.02276002657[/C][C]784.277239973432[/C][/ROW]
[ROW][C]59[/C][C]2555[/C][C]4665.19545582078[/C][C]-2110.19545582078[/C][/ROW]
[ROW][C]60[/C][C]2694.6[/C][C]3399.56966370608[/C][C]-704.969663706077[/C][/ROW]
[ROW][C]61[/C][C]2757.7[/C][C]3533.8270624894[/C][C]-776.127062489395[/C][/ROW]
[ROW][C]62[/C][C]2760.9[/C][C]2619.19859518982[/C][C]141.701404810181[/C][/ROW]
[ROW][C]63[/C][C]3872.9[/C][C]2482.742948924[/C][C]1390.157051076[/C][/ROW]
[ROW][C]64[/C][C]2888.7[/C][C]3041.21157405128[/C][C]-152.511574051276[/C][/ROW]
[ROW][C]65[/C][C]2529.2[/C][C]2885.5312039118[/C][C]-356.331203911802[/C][/ROW]
[ROW][C]66[/C][C]3458.3[/C][C]2633.91388033369[/C][C]824.386119666306[/C][/ROW]
[ROW][C]67[/C][C]2882.8[/C][C]3242.69770757026[/C][C]-359.897707570261[/C][/ROW]
[ROW][C]68[/C][C]2958.5[/C][C]3107.56723935627[/C][C]-149.067239356273[/C][/ROW]
[ROW][C]69[/C][C]2652.4[/C][C]2868.16214404103[/C][C]-215.762144041033[/C][/ROW]
[ROW][C]70[/C][C]2869.8[/C][C]3060.15026848175[/C][C]-190.350268481749[/C][/ROW]
[ROW][C]71[/C][C]2501.7[/C][C]2226.51653746646[/C][C]275.183462533535[/C][/ROW]
[ROW][C]72[/C][C]2576.1[/C][C]2894.61163703136[/C][C]-318.511637031364[/C][/ROW]
[ROW][C]73[/C][C]3347.5[/C][C]3240.02560541349[/C][C]107.474394586513[/C][/ROW]
[ROW][C]74[/C][C]3036.1[/C][C]3141.12113820282[/C][C]-105.021138202816[/C][/ROW]
[ROW][C]75[/C][C]3345.2[/C][C]3023.90676277154[/C][C]321.29323722846[/C][/ROW]
[ROW][C]76[/C][C]3223.2[/C][C]2577.46903232878[/C][C]645.730967671218[/C][/ROW]
[ROW][C]77[/C][C]4087[/C][C]2932.59161655925[/C][C]1154.40838344075[/C][/ROW]
[ROW][C]78[/C][C]4157.2[/C][C]4116.99259163563[/C][C]40.2074083643693[/C][/ROW]
[ROW][C]79[/C][C]3368[/C][C]3844.57461734582[/C][C]-476.574617345825[/C][/ROW]
[ROW][C]80[/C][C]3957.5[/C][C]3715.53515449374[/C][C]241.964845506259[/C][/ROW]
[ROW][C]81[/C][C]3469[/C][C]3699.67936992657[/C][C]-230.679369926568[/C][/ROW]
[ROW][C]82[/C][C]4501.6[/C][C]4011.20531348339[/C][C]490.394686516608[/C][/ROW]
[ROW][C]83[/C][C]3181.4[/C][C]3470.85240432849[/C][C]-289.452404328493[/C][/ROW]
[ROW][C]84[/C][C]3464.5[/C][C]3711.28607369972[/C][C]-246.786073699721[/C][/ROW]
[ROW][C]85[/C][C]4186.9[/C][C]4461.57039878406[/C][C]-274.670398784058[/C][/ROW]
[ROW][C]86[/C][C]3064.7[/C][C]3991.39074692718[/C][C]-926.690746927175[/C][/ROW]
[ROW][C]87[/C][C]4011.7[/C][C]3391.26525069022[/C][C]620.434749309783[/C][/ROW]
[ROW][C]88[/C][C]3537.1[/C][C]3119.62688372336[/C][C]417.473116276645[/C][/ROW]
[ROW][C]89[/C][C]4879.5[/C][C]3370.49044442227[/C][C]1509.00955557773[/C][/ROW]
[ROW][C]90[/C][C]4488.7[/C][C]4569.429288122[/C][C]-80.7292881220019[/C][/ROW]
[ROW][C]91[/C][C]4632.9[/C][C]4049.31314048425[/C][C]583.586859515745[/C][/ROW]
[ROW][C]92[/C][C]4405.8[/C][C]4962.0252991703[/C][C]-556.225299170303[/C][/ROW]
[ROW][C]93[/C][C]2615.2[/C][C]4227.07163832125[/C][C]-1611.87163832125[/C][/ROW]
[ROW][C]94[/C][C]3338[/C][C]3635.88607774795[/C][C]-297.886077747949[/C][/ROW]
[ROW][C]95[/C][C]2825.2[/C][C]2598.80286488617[/C][C]226.397135113826[/C][/ROW]
[ROW][C]96[/C][C]3012.7[/C][C]3147.16815498278[/C][C]-134.468154982779[/C][/ROW]
[ROW][C]97[/C][C]4537.5[/C][C]3851.54252410724[/C][C]685.957475892758[/C][/ROW]
[ROW][C]98[/C][C]5676.7[/C][C]3861.26512031097[/C][C]1815.43487968903[/C][/ROW]
[ROW][C]99[/C][C]5575.4[/C][C]5828.46451321883[/C][C]-253.064513218827[/C][/ROW]
[ROW][C]100[/C][C]6643.4[/C][C]4572.03768391259[/C][C]2071.36231608741[/C][/ROW]
[ROW][C]101[/C][C]5590.6[/C][C]6274.32260202256[/C][C]-683.722602022555[/C][/ROW]
[ROW][C]102[/C][C]4697.6[/C][C]5510.57899577234[/C][C]-812.978995772338[/C][/ROW]
[ROW][C]103[/C][C]5078.1[/C][C]4580.42885541035[/C][C]497.671144589655[/C][/ROW]
[ROW][C]104[/C][C]5769.9[/C][C]5181.40908707733[/C][C]588.490912922667[/C][/ROW]
[ROW][C]105[/C][C]5561.4[/C][C]4703.89204621893[/C][C]857.50795378107[/C][/ROW]
[ROW][C]106[/C][C]7268.8[/C][C]7008.22455866925[/C][C]260.575441330749[/C][/ROW]
[ROW][C]107[/C][C]6496.7[/C][C]5704.28235532735[/C][C]792.417644672646[/C][/ROW]
[ROW][C]108[/C][C]6489.3[/C][C]6982.66262177522[/C][C]-493.362621775219[/C][/ROW]
[ROW][C]109[/C][C]10883.5[/C][C]8806.0659773551[/C][C]2077.4340226449[/C][/ROW]
[ROW][C]110[/C][C]7998.6[/C][C]9587.42470823461[/C][C]-1588.82470823461[/C][/ROW]
[ROW][C]111[/C][C]7340[/C][C]8788.42710793777[/C][C]-1448.42710793777[/C][/ROW]
[ROW][C]112[/C][C]7814.4[/C][C]6852.20099469242[/C][C]962.199005307578[/C][/ROW]
[ROW][C]113[/C][C]5729.6[/C][C]7067.17673262355[/C][C]-1337.57673262355[/C][/ROW]
[ROW][C]114[/C][C]6463.5[/C][C]5761.9649184496[/C][C]701.535081550395[/C][/ROW]
[ROW][C]115[/C][C]6315.4[/C][C]6187.78428113384[/C][C]127.615718866159[/C][/ROW]
[ROW][C]116[/C][C]5357.1[/C][C]6606.70676857828[/C][C]-1249.60676857828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298000&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298000&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
131614.91983.56999834078-368.669998340777
141297.31362.43484458459-65.1348445845897
151226.21216.239260037439.96073996257405
161098.51083.9574164152114.5425835847871
171258.51232.435851754326.0641482456981
181065.21044.4176229967820.7823770032167
191000.41268.27117446981-267.871174469807
201820.2966.326326022022853.873673977978
211224.81707.03392666744-482.233926667437
221428.41236.25154030761192.148459692391
2311441276.68575055831-132.685750558308
241166.91175.29507473474-8.39507473474464
251902.31375.79265952103526.507340478967
261949.41443.85101886625505.548981133748
271784.51704.1443302203580.3556697796523
281671.51578.3744273385793.1255726614263
291923.81876.061472521147.7385274789031
301882.81612.56811467702270.231885322984
3121652057.46825852298107.531741477022
321826.92325.1238496601-498.223849660103
331511.21756.33112670988-245.131126709877
342063.11620.31558961511442.784410384887
352169.61713.62654084178455.973459158219
362495.32104.46393950385390.83606049615
372936.93049.92480270014-113.024802700143
383076.92463.71613265654613.183867343457
393365.72622.22282343377743.477176566231
4038462856.55054878408989.449451215925
413436.24075.42510038238-639.225100382379
423561.13173.21643695269387.883563047313
4333283878.36183814906-550.361838149056
442762.93564.87127462987-801.971274629874
4529232753.94814895076169.051851049245
462731.13245.69507411871-514.595074118712
472571.52563.178263293778.32173670622615
483282.42627.24715980598655.152840194022
494606.53796.84450672016809.655493279839
504698.73855.45670362101843.243296378986
515093.34067.920019443121025.37998055688
524477.34403.9586063020973.3413936979105
533850.14612.49124224806-762.391242248065
544275.23817.78733066807457.412669331933
5539754386.2842448854-411.284244885395
564495.94084.93387965297410.96612034703
574042.44363.14671671307-320.746716713069
585221.34437.02276002657784.277239973432
5925554665.19545582078-2110.19545582078
602694.63399.56966370608-704.969663706077
612757.73533.8270624894-776.127062489395
622760.92619.19859518982141.701404810181
633872.92482.7429489241390.157051076
642888.73041.21157405128-152.511574051276
652529.22885.5312039118-356.331203911802
663458.32633.91388033369824.386119666306
672882.83242.69770757026-359.897707570261
682958.53107.56723935627-149.067239356273
692652.42868.16214404103-215.762144041033
702869.83060.15026848175-190.350268481749
712501.72226.51653746646275.183462533535
722576.12894.61163703136-318.511637031364
733347.53240.02560541349107.474394586513
743036.13141.12113820282-105.021138202816
753345.23023.90676277154321.29323722846
763223.22577.46903232878645.730967671218
7740872932.591616559251154.40838344075
784157.24116.9925916356340.2074083643693
7933683844.57461734582-476.574617345825
803957.53715.53515449374241.964845506259
8134693699.67936992657-230.679369926568
824501.64011.20531348339490.394686516608
833181.43470.85240432849-289.452404328493
843464.53711.28607369972-246.786073699721
854186.94461.57039878406-274.670398784058
863064.73991.39074692718-926.690746927175
874011.73391.26525069022620.434749309783
883537.13119.62688372336417.473116276645
894879.53370.490444422271509.00955557773
904488.74569.429288122-80.7292881220019
914632.94049.31314048425583.586859515745
924405.84962.0252991703-556.225299170303
932615.24227.07163832125-1611.87163832125
9433383635.88607774795-297.886077747949
952825.22598.80286488617226.397135113826
963012.73147.16815498278-134.468154982779
974537.53851.54252410724685.957475892758
985676.73861.265120310971815.43487968903
995575.45828.46451321883-253.064513218827
1006643.44572.037683912592071.36231608741
1015590.66274.32260202256-683.722602022555
1024697.65510.57899577234-812.978995772338
1035078.14580.42885541035497.671144589655
1045769.95181.40908707733588.490912922667
1055561.44703.89204621893857.50795378107
1067268.87008.22455866925260.575441330749
1076496.75704.28235532735792.417644672646
1086489.36982.66262177522-493.362621775219
10910883.58806.06597735512077.4340226449
1107998.69587.42470823461-1588.82470823461
11173408788.42710793777-1448.42710793777
1127814.46852.20099469242962.199005307578
1135729.67067.17673262355-1337.57673262355
1146463.55761.9649184496701.535081550395
1156315.46187.78428113384127.615718866159
1165357.16606.70676857828-1249.60676857828







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1174863.626050187043528.000460813826199.25163956027
1186234.985029088414368.32623353958101.64382463733
1195041.155846145783148.090145033246934.22154725832
1205360.865036955333122.387196584317599.34287732634
1217566.507310245954350.7305534774110782.2840670145
1226446.766064506973478.232908730469415.29922028347
1236693.439857343693444.586498173549942.29321651385
1246349.566824903683079.924783637979619.2088661694
1255493.510864806722444.760518668518542.26121094492
1265583.467247559292313.523256198768853.41123891982
1275402.700869155262058.966271617288746.43546669323
1285373.862960562712137.689685711968610.03623541346

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 4863.62605018704 & 3528.00046081382 & 6199.25163956027 \tabularnewline
118 & 6234.98502908841 & 4368.3262335395 & 8101.64382463733 \tabularnewline
119 & 5041.15584614578 & 3148.09014503324 & 6934.22154725832 \tabularnewline
120 & 5360.86503695533 & 3122.38719658431 & 7599.34287732634 \tabularnewline
121 & 7566.50731024595 & 4350.73055347741 & 10782.2840670145 \tabularnewline
122 & 6446.76606450697 & 3478.23290873046 & 9415.29922028347 \tabularnewline
123 & 6693.43985734369 & 3444.58649817354 & 9942.29321651385 \tabularnewline
124 & 6349.56682490368 & 3079.92478363797 & 9619.2088661694 \tabularnewline
125 & 5493.51086480672 & 2444.76051866851 & 8542.26121094492 \tabularnewline
126 & 5583.46724755929 & 2313.52325619876 & 8853.41123891982 \tabularnewline
127 & 5402.70086915526 & 2058.96627161728 & 8746.43546669323 \tabularnewline
128 & 5373.86296056271 & 2137.68968571196 & 8610.03623541346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298000&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]117[/C][C]4863.62605018704[/C][C]3528.00046081382[/C][C]6199.25163956027[/C][/ROW]
[ROW][C]118[/C][C]6234.98502908841[/C][C]4368.3262335395[/C][C]8101.64382463733[/C][/ROW]
[ROW][C]119[/C][C]5041.15584614578[/C][C]3148.09014503324[/C][C]6934.22154725832[/C][/ROW]
[ROW][C]120[/C][C]5360.86503695533[/C][C]3122.38719658431[/C][C]7599.34287732634[/C][/ROW]
[ROW][C]121[/C][C]7566.50731024595[/C][C]4350.73055347741[/C][C]10782.2840670145[/C][/ROW]
[ROW][C]122[/C][C]6446.76606450697[/C][C]3478.23290873046[/C][C]9415.29922028347[/C][/ROW]
[ROW][C]123[/C][C]6693.43985734369[/C][C]3444.58649817354[/C][C]9942.29321651385[/C][/ROW]
[ROW][C]124[/C][C]6349.56682490368[/C][C]3079.92478363797[/C][C]9619.2088661694[/C][/ROW]
[ROW][C]125[/C][C]5493.51086480672[/C][C]2444.76051866851[/C][C]8542.26121094492[/C][/ROW]
[ROW][C]126[/C][C]5583.46724755929[/C][C]2313.52325619876[/C][C]8853.41123891982[/C][/ROW]
[ROW][C]127[/C][C]5402.70086915526[/C][C]2058.96627161728[/C][C]8746.43546669323[/C][/ROW]
[ROW][C]128[/C][C]5373.86296056271[/C][C]2137.68968571196[/C][C]8610.03623541346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298000&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298000&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
1174863.626050187043528.000460813826199.25163956027
1186234.985029088414368.32623353958101.64382463733
1195041.155846145783148.090145033246934.22154725832
1205360.865036955333122.387196584317599.34287732634
1217566.507310245954350.7305534774110782.2840670145
1226446.766064506973478.232908730469415.29922028347
1236693.439857343693444.586498173549942.29321651385
1246349.566824903683079.924783637979619.2088661694
1255493.510864806722444.760518668518542.26121094492
1265583.467247559292313.523256198768853.41123891982
1275402.700869155262058.966271617288746.43546669323
1285373.862960562712137.689685711968610.03623541346



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')