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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 12 Dec 2014 11:51:49 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/12/t1418385163c15jjsxfeykvr9j.htm/, Retrieved Thu, 16 May 2024 03:38:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266562, Retrieved Thu, 16 May 2024 03:38:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact40
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-12 11:51:49] [345c72938773a86f996d724d064c8f2d] [Current]
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Dataseries X:
82303
79596
74472
73562
66618
69029
89899
93774
90305
83799
80320
82497
84420
84646
84186
83269
77793
81145
101691
107357
104253
95963
91432
94324
93855
92183
87600
83641
78195
79604
100846
105293
102518
93132
87479
85476
85460
82868
79941
76909
72613
72496
93244
99126
96748
89318
84724
83111
87497
86961
82319
79196
76898
77971
97335
106855
105401
99108
93456
92506
94602
93027
89722
87391
83030
83390
104501
110393
111017
103434
97817
96893




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266562&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266562&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266562&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'Sir Maurice George Kendall' @ kendall.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=266562&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=266562&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266562&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
27959682303-2707
37447279596.1789515444-5124.17895154438
47356274472.3387438999-910.338743899905
56661873562.0601797282-6944.06017972817
66902966618.45905071792410.54094928208
78989969028.840646462620870.1593535374
89377489897.62033718223876.3796628178
99030593773.7437443194-3468.74374431944
108379990305.2293081086-6506.22930810864
118032083799.4301070494-3479.43010704943
128249780320.23001455162176.76998544838
138442082496.85610035071923.14389964929
148464684419.8728668005226.12713319945
158418684645.9850514223-459.985051422336
168326984186.030408214-917.030408214021
177779383269.0606220938-5476.06062209376
188114577793.36200572793351.6379942721
1910169181144.778433396720546.2215666033
20107357101689.6417517255667.35824827502
21104253107356.625348167-3103.62534816732
2295963104253.205171241-8290.20517124094
239143295963.5480402729-4531.54804027286
249432491432.29956687122891.70043312883
259385594323.8088384712-468.808838471217
269218393855.0309915278-1672.03099152776
278760092183.1105328881-4583.11053288814
288364187600.3029755109-3959.30297551087
297819583641.2617374888-5446.26173748878
307960478195.36003581421408.63996418582
3110084679603.906879092321242.0931209077
32105293100844.5957497714448.40425022898
33102518105292.705929512-2774.70592951214
3493132102518.183427378-9386.18342737765
358747993132.6204920651-5653.62049206506
368547687479.3737436714-2003.37374367137
378546085476.1324369506-16.1324369506474
388286885460.0010664664-2592.00106646639
397994182868.1713493143-2927.17134931433
407690979941.1935064033-3032.19350640326
417261376909.2004490989-4296.20044909895
427249672613.2840087571-117.284008757051
439324472496.007753289420747.9922467106
449912693242.62841327845883.37158672158
459674899125.6110681819-2377.6110681819
468931896748.157176643-7430.157176643
478472489318.4911851133-4594.49118511332
488311184724.3037278512-1613.30372785121
498749783111.10665060724385.89334939282
508696187496.7100619179-535.710061917853
518231986961.0354141644-4642.03541416436
527919682319.3068708557-3123.30687085573
537689879196.2064723266-2298.20647232661
547797176898.15192744641072.84807255356
559733577970.929077273919364.0709227261
5610685597333.71990011199521.2800998881
57105401106854.370577104-1453.37057710442
5899108105401.096077913-6293.09607791257
599345699108.4160174592-5652.41601745921
609250693456.3736640472-950.37366404722
619460292506.06282631512095.93717368491
629302794601.8614439623-1574.86144396226
638972293027.1041093046-3305.10410930462
648739189722.2184903896-2331.21849038963
658303087391.1541097706-4361.15410977064
668339083030.2883026462359.711697353821
6710450183389.976220552721111.0237794473
68110393104499.6044143675893.39558563309
69111017110392.610405526624.389594474211
70103434111016.958723501-7582.95872350121
7197817103434.501286359-5617.50128635927
729689397817.3713559404-924.371355940442

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 79596 & 82303 & -2707 \tabularnewline
3 & 74472 & 79596.1789515444 & -5124.17895154438 \tabularnewline
4 & 73562 & 74472.3387438999 & -910.338743899905 \tabularnewline
5 & 66618 & 73562.0601797282 & -6944.06017972817 \tabularnewline
6 & 69029 & 66618.4590507179 & 2410.54094928208 \tabularnewline
7 & 89899 & 69028.8406464626 & 20870.1593535374 \tabularnewline
8 & 93774 & 89897.6203371822 & 3876.3796628178 \tabularnewline
9 & 90305 & 93773.7437443194 & -3468.74374431944 \tabularnewline
10 & 83799 & 90305.2293081086 & -6506.22930810864 \tabularnewline
11 & 80320 & 83799.4301070494 & -3479.43010704943 \tabularnewline
12 & 82497 & 80320.2300145516 & 2176.76998544838 \tabularnewline
13 & 84420 & 82496.8561003507 & 1923.14389964929 \tabularnewline
14 & 84646 & 84419.8728668005 & 226.12713319945 \tabularnewline
15 & 84186 & 84645.9850514223 & -459.985051422336 \tabularnewline
16 & 83269 & 84186.030408214 & -917.030408214021 \tabularnewline
17 & 77793 & 83269.0606220938 & -5476.06062209376 \tabularnewline
18 & 81145 & 77793.3620057279 & 3351.6379942721 \tabularnewline
19 & 101691 & 81144.7784333967 & 20546.2215666033 \tabularnewline
20 & 107357 & 101689.641751725 & 5667.35824827502 \tabularnewline
21 & 104253 & 107356.625348167 & -3103.62534816732 \tabularnewline
22 & 95963 & 104253.205171241 & -8290.20517124094 \tabularnewline
23 & 91432 & 95963.5480402729 & -4531.54804027286 \tabularnewline
24 & 94324 & 91432.2995668712 & 2891.70043312883 \tabularnewline
25 & 93855 & 94323.8088384712 & -468.808838471217 \tabularnewline
26 & 92183 & 93855.0309915278 & -1672.03099152776 \tabularnewline
27 & 87600 & 92183.1105328881 & -4583.11053288814 \tabularnewline
28 & 83641 & 87600.3029755109 & -3959.30297551087 \tabularnewline
29 & 78195 & 83641.2617374888 & -5446.26173748878 \tabularnewline
30 & 79604 & 78195.3600358142 & 1408.63996418582 \tabularnewline
31 & 100846 & 79603.9068790923 & 21242.0931209077 \tabularnewline
32 & 105293 & 100844.595749771 & 4448.40425022898 \tabularnewline
33 & 102518 & 105292.705929512 & -2774.70592951214 \tabularnewline
34 & 93132 & 102518.183427378 & -9386.18342737765 \tabularnewline
35 & 87479 & 93132.6204920651 & -5653.62049206506 \tabularnewline
36 & 85476 & 87479.3737436714 & -2003.37374367137 \tabularnewline
37 & 85460 & 85476.1324369506 & -16.1324369506474 \tabularnewline
38 & 82868 & 85460.0010664664 & -2592.00106646639 \tabularnewline
39 & 79941 & 82868.1713493143 & -2927.17134931433 \tabularnewline
40 & 76909 & 79941.1935064033 & -3032.19350640326 \tabularnewline
41 & 72613 & 76909.2004490989 & -4296.20044909895 \tabularnewline
42 & 72496 & 72613.2840087571 & -117.284008757051 \tabularnewline
43 & 93244 & 72496.0077532894 & 20747.9922467106 \tabularnewline
44 & 99126 & 93242.6284132784 & 5883.37158672158 \tabularnewline
45 & 96748 & 99125.6110681819 & -2377.6110681819 \tabularnewline
46 & 89318 & 96748.157176643 & -7430.157176643 \tabularnewline
47 & 84724 & 89318.4911851133 & -4594.49118511332 \tabularnewline
48 & 83111 & 84724.3037278512 & -1613.30372785121 \tabularnewline
49 & 87497 & 83111.1066506072 & 4385.89334939282 \tabularnewline
50 & 86961 & 87496.7100619179 & -535.710061917853 \tabularnewline
51 & 82319 & 86961.0354141644 & -4642.03541416436 \tabularnewline
52 & 79196 & 82319.3068708557 & -3123.30687085573 \tabularnewline
53 & 76898 & 79196.2064723266 & -2298.20647232661 \tabularnewline
54 & 77971 & 76898.1519274464 & 1072.84807255356 \tabularnewline
55 & 97335 & 77970.9290772739 & 19364.0709227261 \tabularnewline
56 & 106855 & 97333.7199001119 & 9521.2800998881 \tabularnewline
57 & 105401 & 106854.370577104 & -1453.37057710442 \tabularnewline
58 & 99108 & 105401.096077913 & -6293.09607791257 \tabularnewline
59 & 93456 & 99108.4160174592 & -5652.41601745921 \tabularnewline
60 & 92506 & 93456.3736640472 & -950.37366404722 \tabularnewline
61 & 94602 & 92506.0628263151 & 2095.93717368491 \tabularnewline
62 & 93027 & 94601.8614439623 & -1574.86144396226 \tabularnewline
63 & 89722 & 93027.1041093046 & -3305.10410930462 \tabularnewline
64 & 87391 & 89722.2184903896 & -2331.21849038963 \tabularnewline
65 & 83030 & 87391.1541097706 & -4361.15410977064 \tabularnewline
66 & 83390 & 83030.2883026462 & 359.711697353821 \tabularnewline
67 & 104501 & 83389.9762205527 & 21111.0237794473 \tabularnewline
68 & 110393 & 104499.604414367 & 5893.39558563309 \tabularnewline
69 & 111017 & 110392.610405526 & 624.389594474211 \tabularnewline
70 & 103434 & 111016.958723501 & -7582.95872350121 \tabularnewline
71 & 97817 & 103434.501286359 & -5617.50128635927 \tabularnewline
72 & 96893 & 97817.3713559404 & -924.371355940442 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266562&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]79596[/C][C]82303[/C][C]-2707[/C][/ROW]
[ROW][C]3[/C][C]74472[/C][C]79596.1789515444[/C][C]-5124.17895154438[/C][/ROW]
[ROW][C]4[/C][C]73562[/C][C]74472.3387438999[/C][C]-910.338743899905[/C][/ROW]
[ROW][C]5[/C][C]66618[/C][C]73562.0601797282[/C][C]-6944.06017972817[/C][/ROW]
[ROW][C]6[/C][C]69029[/C][C]66618.4590507179[/C][C]2410.54094928208[/C][/ROW]
[ROW][C]7[/C][C]89899[/C][C]69028.8406464626[/C][C]20870.1593535374[/C][/ROW]
[ROW][C]8[/C][C]93774[/C][C]89897.6203371822[/C][C]3876.3796628178[/C][/ROW]
[ROW][C]9[/C][C]90305[/C][C]93773.7437443194[/C][C]-3468.74374431944[/C][/ROW]
[ROW][C]10[/C][C]83799[/C][C]90305.2293081086[/C][C]-6506.22930810864[/C][/ROW]
[ROW][C]11[/C][C]80320[/C][C]83799.4301070494[/C][C]-3479.43010704943[/C][/ROW]
[ROW][C]12[/C][C]82497[/C][C]80320.2300145516[/C][C]2176.76998544838[/C][/ROW]
[ROW][C]13[/C][C]84420[/C][C]82496.8561003507[/C][C]1923.14389964929[/C][/ROW]
[ROW][C]14[/C][C]84646[/C][C]84419.8728668005[/C][C]226.12713319945[/C][/ROW]
[ROW][C]15[/C][C]84186[/C][C]84645.9850514223[/C][C]-459.985051422336[/C][/ROW]
[ROW][C]16[/C][C]83269[/C][C]84186.030408214[/C][C]-917.030408214021[/C][/ROW]
[ROW][C]17[/C][C]77793[/C][C]83269.0606220938[/C][C]-5476.06062209376[/C][/ROW]
[ROW][C]18[/C][C]81145[/C][C]77793.3620057279[/C][C]3351.6379942721[/C][/ROW]
[ROW][C]19[/C][C]101691[/C][C]81144.7784333967[/C][C]20546.2215666033[/C][/ROW]
[ROW][C]20[/C][C]107357[/C][C]101689.641751725[/C][C]5667.35824827502[/C][/ROW]
[ROW][C]21[/C][C]104253[/C][C]107356.625348167[/C][C]-3103.62534816732[/C][/ROW]
[ROW][C]22[/C][C]95963[/C][C]104253.205171241[/C][C]-8290.20517124094[/C][/ROW]
[ROW][C]23[/C][C]91432[/C][C]95963.5480402729[/C][C]-4531.54804027286[/C][/ROW]
[ROW][C]24[/C][C]94324[/C][C]91432.2995668712[/C][C]2891.70043312883[/C][/ROW]
[ROW][C]25[/C][C]93855[/C][C]94323.8088384712[/C][C]-468.808838471217[/C][/ROW]
[ROW][C]26[/C][C]92183[/C][C]93855.0309915278[/C][C]-1672.03099152776[/C][/ROW]
[ROW][C]27[/C][C]87600[/C][C]92183.1105328881[/C][C]-4583.11053288814[/C][/ROW]
[ROW][C]28[/C][C]83641[/C][C]87600.3029755109[/C][C]-3959.30297551087[/C][/ROW]
[ROW][C]29[/C][C]78195[/C][C]83641.2617374888[/C][C]-5446.26173748878[/C][/ROW]
[ROW][C]30[/C][C]79604[/C][C]78195.3600358142[/C][C]1408.63996418582[/C][/ROW]
[ROW][C]31[/C][C]100846[/C][C]79603.9068790923[/C][C]21242.0931209077[/C][/ROW]
[ROW][C]32[/C][C]105293[/C][C]100844.595749771[/C][C]4448.40425022898[/C][/ROW]
[ROW][C]33[/C][C]102518[/C][C]105292.705929512[/C][C]-2774.70592951214[/C][/ROW]
[ROW][C]34[/C][C]93132[/C][C]102518.183427378[/C][C]-9386.18342737765[/C][/ROW]
[ROW][C]35[/C][C]87479[/C][C]93132.6204920651[/C][C]-5653.62049206506[/C][/ROW]
[ROW][C]36[/C][C]85476[/C][C]87479.3737436714[/C][C]-2003.37374367137[/C][/ROW]
[ROW][C]37[/C][C]85460[/C][C]85476.1324369506[/C][C]-16.1324369506474[/C][/ROW]
[ROW][C]38[/C][C]82868[/C][C]85460.0010664664[/C][C]-2592.00106646639[/C][/ROW]
[ROW][C]39[/C][C]79941[/C][C]82868.1713493143[/C][C]-2927.17134931433[/C][/ROW]
[ROW][C]40[/C][C]76909[/C][C]79941.1935064033[/C][C]-3032.19350640326[/C][/ROW]
[ROW][C]41[/C][C]72613[/C][C]76909.2004490989[/C][C]-4296.20044909895[/C][/ROW]
[ROW][C]42[/C][C]72496[/C][C]72613.2840087571[/C][C]-117.284008757051[/C][/ROW]
[ROW][C]43[/C][C]93244[/C][C]72496.0077532894[/C][C]20747.9922467106[/C][/ROW]
[ROW][C]44[/C][C]99126[/C][C]93242.6284132784[/C][C]5883.37158672158[/C][/ROW]
[ROW][C]45[/C][C]96748[/C][C]99125.6110681819[/C][C]-2377.6110681819[/C][/ROW]
[ROW][C]46[/C][C]89318[/C][C]96748.157176643[/C][C]-7430.157176643[/C][/ROW]
[ROW][C]47[/C][C]84724[/C][C]89318.4911851133[/C][C]-4594.49118511332[/C][/ROW]
[ROW][C]48[/C][C]83111[/C][C]84724.3037278512[/C][C]-1613.30372785121[/C][/ROW]
[ROW][C]49[/C][C]87497[/C][C]83111.1066506072[/C][C]4385.89334939282[/C][/ROW]
[ROW][C]50[/C][C]86961[/C][C]87496.7100619179[/C][C]-535.710061917853[/C][/ROW]
[ROW][C]51[/C][C]82319[/C][C]86961.0354141644[/C][C]-4642.03541416436[/C][/ROW]
[ROW][C]52[/C][C]79196[/C][C]82319.3068708557[/C][C]-3123.30687085573[/C][/ROW]
[ROW][C]53[/C][C]76898[/C][C]79196.2064723266[/C][C]-2298.20647232661[/C][/ROW]
[ROW][C]54[/C][C]77971[/C][C]76898.1519274464[/C][C]1072.84807255356[/C][/ROW]
[ROW][C]55[/C][C]97335[/C][C]77970.9290772739[/C][C]19364.0709227261[/C][/ROW]
[ROW][C]56[/C][C]106855[/C][C]97333.7199001119[/C][C]9521.2800998881[/C][/ROW]
[ROW][C]57[/C][C]105401[/C][C]106854.370577104[/C][C]-1453.37057710442[/C][/ROW]
[ROW][C]58[/C][C]99108[/C][C]105401.096077913[/C][C]-6293.09607791257[/C][/ROW]
[ROW][C]59[/C][C]93456[/C][C]99108.4160174592[/C][C]-5652.41601745921[/C][/ROW]
[ROW][C]60[/C][C]92506[/C][C]93456.3736640472[/C][C]-950.37366404722[/C][/ROW]
[ROW][C]61[/C][C]94602[/C][C]92506.0628263151[/C][C]2095.93717368491[/C][/ROW]
[ROW][C]62[/C][C]93027[/C][C]94601.8614439623[/C][C]-1574.86144396226[/C][/ROW]
[ROW][C]63[/C][C]89722[/C][C]93027.1041093046[/C][C]-3305.10410930462[/C][/ROW]
[ROW][C]64[/C][C]87391[/C][C]89722.2184903896[/C][C]-2331.21849038963[/C][/ROW]
[ROW][C]65[/C][C]83030[/C][C]87391.1541097706[/C][C]-4361.15410977064[/C][/ROW]
[ROW][C]66[/C][C]83390[/C][C]83030.2883026462[/C][C]359.711697353821[/C][/ROW]
[ROW][C]67[/C][C]104501[/C][C]83389.9762205527[/C][C]21111.0237794473[/C][/ROW]
[ROW][C]68[/C][C]110393[/C][C]104499.604414367[/C][C]5893.39558563309[/C][/ROW]
[ROW][C]69[/C][C]111017[/C][C]110392.610405526[/C][C]624.389594474211[/C][/ROW]
[ROW][C]70[/C][C]103434[/C][C]111016.958723501[/C][C]-7582.95872350121[/C][/ROW]
[ROW][C]71[/C][C]97817[/C][C]103434.501286359[/C][C]-5617.50128635927[/C][/ROW]
[ROW][C]72[/C][C]96893[/C][C]97817.3713559404[/C][C]-924.371355940442[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266562&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266562&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
27959682303-2707
37447279596.1789515444-5124.17895154438
47356274472.3387438999-910.338743899905
56661873562.0601797282-6944.06017972817
66902966618.45905071792410.54094928208
78989969028.840646462620870.1593535374
89377489897.62033718223876.3796628178
99030593773.7437443194-3468.74374431944
108379990305.2293081086-6506.22930810864
118032083799.4301070494-3479.43010704943
128249780320.23001455162176.76998544838
138442082496.85610035071923.14389964929
148464684419.8728668005226.12713319945
158418684645.9850514223-459.985051422336
168326984186.030408214-917.030408214021
177779383269.0606220938-5476.06062209376
188114577793.36200572793351.6379942721
1910169181144.778433396720546.2215666033
20107357101689.6417517255667.35824827502
21104253107356.625348167-3103.62534816732
2295963104253.205171241-8290.20517124094
239143295963.5480402729-4531.54804027286
249432491432.29956687122891.70043312883
259385594323.8088384712-468.808838471217
269218393855.0309915278-1672.03099152776
278760092183.1105328881-4583.11053288814
288364187600.3029755109-3959.30297551087
297819583641.2617374888-5446.26173748878
307960478195.36003581421408.63996418582
3110084679603.906879092321242.0931209077
32105293100844.5957497714448.40425022898
33102518105292.705929512-2774.70592951214
3493132102518.183427378-9386.18342737765
358747993132.6204920651-5653.62049206506
368547687479.3737436714-2003.37374367137
378546085476.1324369506-16.1324369506474
388286885460.0010664664-2592.00106646639
397994182868.1713493143-2927.17134931433
407690979941.1935064033-3032.19350640326
417261376909.2004490989-4296.20044909895
427249672613.2840087571-117.284008757051
439324472496.007753289420747.9922467106
449912693242.62841327845883.37158672158
459674899125.6110681819-2377.6110681819
468931896748.157176643-7430.157176643
478472489318.4911851133-4594.49118511332
488311184724.3037278512-1613.30372785121
498749783111.10665060724385.89334939282
508696187496.7100619179-535.710061917853
518231986961.0354141644-4642.03541416436
527919682319.3068708557-3123.30687085573
537689879196.2064723266-2298.20647232661
547797176898.15192744641072.84807255356
559733577970.929077273919364.0709227261
5610685597333.71990011199521.2800998881
57105401106854.370577104-1453.37057710442
5899108105401.096077913-6293.09607791257
599345699108.4160174592-5652.41601745921
609250693456.3736640472-950.37366404722
619460292506.06282631512095.93717368491
629302794601.8614439623-1574.86144396226
638972293027.1041093046-3305.10410930462
648739189722.2184903896-2331.21849038963
658303087391.1541097706-4361.15410977064
668339083030.2883026462359.711697353821
6710450183389.976220552721111.0237794473
68110393104499.6044143675893.39558563309
69111017110392.610405526624.389594474211
70103434111016.958723501-7582.95872350121
7197817103434.501286359-5617.50128635927
729689397817.3713559404-924.371355940442







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7396893.061107381582658.8084746418111127.313740121
7496893.061107381576763.4533485129117022.66886625
7596893.061107381572239.6988815278121546.423333235
7696893.061107381568425.967305021125360.154909742
7796893.061107381565065.9878824423128720.134332321
7896893.061107381562028.3260506098131757.796164153
7996893.061107381559234.902481499134551.219733264
8096893.061107381556634.8436654061137151.278549357
8196893.061107381554192.8124884493139593.309726314
8296893.061107381551883.0800739277141903.042140835
8396893.061107381549686.2231159939144099.899098769
8496893.061107381547587.1515867332146198.97062803

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 96893.0611073815 & 82658.8084746418 & 111127.313740121 \tabularnewline
74 & 96893.0611073815 & 76763.4533485129 & 117022.66886625 \tabularnewline
75 & 96893.0611073815 & 72239.6988815278 & 121546.423333235 \tabularnewline
76 & 96893.0611073815 & 68425.967305021 & 125360.154909742 \tabularnewline
77 & 96893.0611073815 & 65065.9878824423 & 128720.134332321 \tabularnewline
78 & 96893.0611073815 & 62028.3260506098 & 131757.796164153 \tabularnewline
79 & 96893.0611073815 & 59234.902481499 & 134551.219733264 \tabularnewline
80 & 96893.0611073815 & 56634.8436654061 & 137151.278549357 \tabularnewline
81 & 96893.0611073815 & 54192.8124884493 & 139593.309726314 \tabularnewline
82 & 96893.0611073815 & 51883.0800739277 & 141903.042140835 \tabularnewline
83 & 96893.0611073815 & 49686.2231159939 & 144099.899098769 \tabularnewline
84 & 96893.0611073815 & 47587.1515867332 & 146198.97062803 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266562&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]73[/C][C]96893.0611073815[/C][C]82658.8084746418[/C][C]111127.313740121[/C][/ROW]
[ROW][C]74[/C][C]96893.0611073815[/C][C]76763.4533485129[/C][C]117022.66886625[/C][/ROW]
[ROW][C]75[/C][C]96893.0611073815[/C][C]72239.6988815278[/C][C]121546.423333235[/C][/ROW]
[ROW][C]76[/C][C]96893.0611073815[/C][C]68425.967305021[/C][C]125360.154909742[/C][/ROW]
[ROW][C]77[/C][C]96893.0611073815[/C][C]65065.9878824423[/C][C]128720.134332321[/C][/ROW]
[ROW][C]78[/C][C]96893.0611073815[/C][C]62028.3260506098[/C][C]131757.796164153[/C][/ROW]
[ROW][C]79[/C][C]96893.0611073815[/C][C]59234.902481499[/C][C]134551.219733264[/C][/ROW]
[ROW][C]80[/C][C]96893.0611073815[/C][C]56634.8436654061[/C][C]137151.278549357[/C][/ROW]
[ROW][C]81[/C][C]96893.0611073815[/C][C]54192.8124884493[/C][C]139593.309726314[/C][/ROW]
[ROW][C]82[/C][C]96893.0611073815[/C][C]51883.0800739277[/C][C]141903.042140835[/C][/ROW]
[ROW][C]83[/C][C]96893.0611073815[/C][C]49686.2231159939[/C][C]144099.899098769[/C][/ROW]
[ROW][C]84[/C][C]96893.0611073815[/C][C]47587.1515867332[/C][C]146198.97062803[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266562&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266562&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
7396893.061107381582658.8084746418111127.313740121
7496893.061107381576763.4533485129117022.66886625
7596893.061107381572239.6988815278121546.423333235
7696893.061107381568425.967305021125360.154909742
7796893.061107381565065.9878824423128720.134332321
7896893.061107381562028.3260506098131757.796164153
7996893.061107381559234.902481499134551.219733264
8096893.061107381556634.8436654061137151.278549357
8196893.061107381554192.8124884493139593.309726314
8296893.061107381551883.0800739277141903.042140835
8396893.061107381549686.2231159939144099.899098769
8496893.061107381547587.1515867332146198.97062803



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')