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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 computationTue, 03 May 2016 10:13:08 +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/May/03/t1462266815fxtp6ie4ggplpho.htm/, Retrieved Mon, 29 Apr 2024 05:56:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295202, Retrieved Mon, 29 Apr 2024 05:56:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2016-04-25 10:39:09] [0fac179d48b12d87f452d447736804ac]
- R P     [Exponential Smoothing] [] [2016-05-03 09:13:08] [c1931050b1d666e3090788e81f04199e] [Current]
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Dataseries X:
4736
4840
4413
4571
4106
4801
3956
3829
4453
4027
4121
4798
3233
3554
3952
3951
3685
4312
3867
4140
4114
3818
3377
3453
3502
4017
5410
5184
5529
6434
4962
2980
2937
3023
2731
3163
3146
3173
3724
3224
4114
3450
2957
3882
4284
4181
3760
4457
4167
3962
5247
5157
3697
3514
3786
3297
3571
3871
3492
3051
3735
3645
4852
4232
3804
4464
4259
3373
4134
4488
3333
4772
4929
5555
7183
9266
4003
3051
3507
3273
3942
3216
3232
3593




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=295202&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=295202&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295202&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
alpha0.588167237735778
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.588167237735778 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295202&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]0.588167237735778[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295202&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295202&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
alpha0.588167237735778
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1332333532.69791666667-299.697916666668
1435543634.55989056264-80.5598905626366
1539523952.72833862175-0.728338621750481
1639513940.5177567367610.4822432632377
1736853686.77587183248-1.77587183247761
1843124366.15749856583-54.1574985658335
1938673463.77163526199403.228364738009
2041403656.53015175696483.469848243038
2141144604.06741329024-490.067413290242
2238183901.25195287464-83.2519528746384
2333773956.04535141322-579.045351413223
2434534296.7709829124-843.770982912401
2535022102.534916775851399.46508322415
2640173294.03711738799722.962882612009
2754104117.688583954681292.31141604532
2851844870.61850775906313.381492240944
2955294789.98374403821739.016255961791
3064345883.50256028324550.497439716762
3149625525.1214053174-563.121405317396
3229805182.55071867233-2202.55071867233
3329374149.32414327711-1212.32414327711
3430233189.24087184381-166.240871843805
3527312991.03894231711-260.038942317105
3631633410.37100421191-247.37100421191
3731462490.75597166104655.244028338956
3831732965.92596020063207.07403979937
3937243720.624890326433.37510967357139
4032243312.28929261132-88.2892926113163
4141143170.69527334359943.304726656411
4234504306.73165026537-856.731650265367
4329572662.03972352339294.960276476606
4438822148.993866754881733.00613324512
4542843838.34063971652445.659360283485
4641814284.24030901671-103.240309016705
4737604084.46412804575-324.464128045747
4844574471.12047835198-14.120478351977
4941674060.4222054132106.577794586801
5039624028.3136064637-66.3136064637047
5152474538.32498679189708.67501320811
5251574507.07328111971649.926718880285
5336975224.51794867361-1527.51794867361
5435144165.98342442782-651.983424427825
5537863116.02216357557669.977836424429
5632973415.78374659957-118.783746599575
5735713485.7968035651685.2031964348357
5838713493.63309963584377.366900364157
5934923485.427116972966.57288302704319
6030514194.59827417472-1143.59827417472
6137353169.28566912788565.714330872116
6236453336.02379520253308.976204797465
6348524385.93405113336466.065948866635
6442324187.7931699064644.2068300935371
6538043652.23019151481151.76980848519
6644643941.97151033846522.028489661541
6742594126.95255172812132.047448271881
6833733785.48324275363-412.483242753628
6941343766.76038455759367.239615442405
7044884060.8038473594427.196152640595
7133333929.2006739754-596.2006739754
7247723810.16200842783961.83799157217
7349294727.14896774357201.851032256434
7455554574.14145091814980.85854908186
7571836083.925592593551099.07440740645
7692666084.364141718723181.63585828128
7740037438.4320869367-3435.4320869367
7830515770.78343115067-2719.78343115067
7935073888.42994031111-381.429940311114
8032733020.6944754313252.305524568699
8139423714.09400868044227.90599131956
8232163950.87806498833-734.878064988329
8332322714.31256697985517.687433020151
8435933892.07775981751-299.077759817505

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3233 & 3532.69791666667 & -299.697916666668 \tabularnewline
14 & 3554 & 3634.55989056264 & -80.5598905626366 \tabularnewline
15 & 3952 & 3952.72833862175 & -0.728338621750481 \tabularnewline
16 & 3951 & 3940.51775673676 & 10.4822432632377 \tabularnewline
17 & 3685 & 3686.77587183248 & -1.77587183247761 \tabularnewline
18 & 4312 & 4366.15749856583 & -54.1574985658335 \tabularnewline
19 & 3867 & 3463.77163526199 & 403.228364738009 \tabularnewline
20 & 4140 & 3656.53015175696 & 483.469848243038 \tabularnewline
21 & 4114 & 4604.06741329024 & -490.067413290242 \tabularnewline
22 & 3818 & 3901.25195287464 & -83.2519528746384 \tabularnewline
23 & 3377 & 3956.04535141322 & -579.045351413223 \tabularnewline
24 & 3453 & 4296.7709829124 & -843.770982912401 \tabularnewline
25 & 3502 & 2102.53491677585 & 1399.46508322415 \tabularnewline
26 & 4017 & 3294.03711738799 & 722.962882612009 \tabularnewline
27 & 5410 & 4117.68858395468 & 1292.31141604532 \tabularnewline
28 & 5184 & 4870.61850775906 & 313.381492240944 \tabularnewline
29 & 5529 & 4789.98374403821 & 739.016255961791 \tabularnewline
30 & 6434 & 5883.50256028324 & 550.497439716762 \tabularnewline
31 & 4962 & 5525.1214053174 & -563.121405317396 \tabularnewline
32 & 2980 & 5182.55071867233 & -2202.55071867233 \tabularnewline
33 & 2937 & 4149.32414327711 & -1212.32414327711 \tabularnewline
34 & 3023 & 3189.24087184381 & -166.240871843805 \tabularnewline
35 & 2731 & 2991.03894231711 & -260.038942317105 \tabularnewline
36 & 3163 & 3410.37100421191 & -247.37100421191 \tabularnewline
37 & 3146 & 2490.75597166104 & 655.244028338956 \tabularnewline
38 & 3173 & 2965.92596020063 & 207.07403979937 \tabularnewline
39 & 3724 & 3720.62489032643 & 3.37510967357139 \tabularnewline
40 & 3224 & 3312.28929261132 & -88.2892926113163 \tabularnewline
41 & 4114 & 3170.69527334359 & 943.304726656411 \tabularnewline
42 & 3450 & 4306.73165026537 & -856.731650265367 \tabularnewline
43 & 2957 & 2662.03972352339 & 294.960276476606 \tabularnewline
44 & 3882 & 2148.99386675488 & 1733.00613324512 \tabularnewline
45 & 4284 & 3838.34063971652 & 445.659360283485 \tabularnewline
46 & 4181 & 4284.24030901671 & -103.240309016705 \tabularnewline
47 & 3760 & 4084.46412804575 & -324.464128045747 \tabularnewline
48 & 4457 & 4471.12047835198 & -14.120478351977 \tabularnewline
49 & 4167 & 4060.4222054132 & 106.577794586801 \tabularnewline
50 & 3962 & 4028.3136064637 & -66.3136064637047 \tabularnewline
51 & 5247 & 4538.32498679189 & 708.67501320811 \tabularnewline
52 & 5157 & 4507.07328111971 & 649.926718880285 \tabularnewline
53 & 3697 & 5224.51794867361 & -1527.51794867361 \tabularnewline
54 & 3514 & 4165.98342442782 & -651.983424427825 \tabularnewline
55 & 3786 & 3116.02216357557 & 669.977836424429 \tabularnewline
56 & 3297 & 3415.78374659957 & -118.783746599575 \tabularnewline
57 & 3571 & 3485.79680356516 & 85.2031964348357 \tabularnewline
58 & 3871 & 3493.63309963584 & 377.366900364157 \tabularnewline
59 & 3492 & 3485.42711697296 & 6.57288302704319 \tabularnewline
60 & 3051 & 4194.59827417472 & -1143.59827417472 \tabularnewline
61 & 3735 & 3169.28566912788 & 565.714330872116 \tabularnewline
62 & 3645 & 3336.02379520253 & 308.976204797465 \tabularnewline
63 & 4852 & 4385.93405113336 & 466.065948866635 \tabularnewline
64 & 4232 & 4187.79316990646 & 44.2068300935371 \tabularnewline
65 & 3804 & 3652.23019151481 & 151.76980848519 \tabularnewline
66 & 4464 & 3941.97151033846 & 522.028489661541 \tabularnewline
67 & 4259 & 4126.95255172812 & 132.047448271881 \tabularnewline
68 & 3373 & 3785.48324275363 & -412.483242753628 \tabularnewline
69 & 4134 & 3766.76038455759 & 367.239615442405 \tabularnewline
70 & 4488 & 4060.8038473594 & 427.196152640595 \tabularnewline
71 & 3333 & 3929.2006739754 & -596.2006739754 \tabularnewline
72 & 4772 & 3810.16200842783 & 961.83799157217 \tabularnewline
73 & 4929 & 4727.14896774357 & 201.851032256434 \tabularnewline
74 & 5555 & 4574.14145091814 & 980.85854908186 \tabularnewline
75 & 7183 & 6083.92559259355 & 1099.07440740645 \tabularnewline
76 & 9266 & 6084.36414171872 & 3181.63585828128 \tabularnewline
77 & 4003 & 7438.4320869367 & -3435.4320869367 \tabularnewline
78 & 3051 & 5770.78343115067 & -2719.78343115067 \tabularnewline
79 & 3507 & 3888.42994031111 & -381.429940311114 \tabularnewline
80 & 3273 & 3020.6944754313 & 252.305524568699 \tabularnewline
81 & 3942 & 3714.09400868044 & 227.90599131956 \tabularnewline
82 & 3216 & 3950.87806498833 & -734.878064988329 \tabularnewline
83 & 3232 & 2714.31256697985 & 517.687433020151 \tabularnewline
84 & 3593 & 3892.07775981751 & -299.077759817505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295202&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]3233[/C][C]3532.69791666667[/C][C]-299.697916666668[/C][/ROW]
[ROW][C]14[/C][C]3554[/C][C]3634.55989056264[/C][C]-80.5598905626366[/C][/ROW]
[ROW][C]15[/C][C]3952[/C][C]3952.72833862175[/C][C]-0.728338621750481[/C][/ROW]
[ROW][C]16[/C][C]3951[/C][C]3940.51775673676[/C][C]10.4822432632377[/C][/ROW]
[ROW][C]17[/C][C]3685[/C][C]3686.77587183248[/C][C]-1.77587183247761[/C][/ROW]
[ROW][C]18[/C][C]4312[/C][C]4366.15749856583[/C][C]-54.1574985658335[/C][/ROW]
[ROW][C]19[/C][C]3867[/C][C]3463.77163526199[/C][C]403.228364738009[/C][/ROW]
[ROW][C]20[/C][C]4140[/C][C]3656.53015175696[/C][C]483.469848243038[/C][/ROW]
[ROW][C]21[/C][C]4114[/C][C]4604.06741329024[/C][C]-490.067413290242[/C][/ROW]
[ROW][C]22[/C][C]3818[/C][C]3901.25195287464[/C][C]-83.2519528746384[/C][/ROW]
[ROW][C]23[/C][C]3377[/C][C]3956.04535141322[/C][C]-579.045351413223[/C][/ROW]
[ROW][C]24[/C][C]3453[/C][C]4296.7709829124[/C][C]-843.770982912401[/C][/ROW]
[ROW][C]25[/C][C]3502[/C][C]2102.53491677585[/C][C]1399.46508322415[/C][/ROW]
[ROW][C]26[/C][C]4017[/C][C]3294.03711738799[/C][C]722.962882612009[/C][/ROW]
[ROW][C]27[/C][C]5410[/C][C]4117.68858395468[/C][C]1292.31141604532[/C][/ROW]
[ROW][C]28[/C][C]5184[/C][C]4870.61850775906[/C][C]313.381492240944[/C][/ROW]
[ROW][C]29[/C][C]5529[/C][C]4789.98374403821[/C][C]739.016255961791[/C][/ROW]
[ROW][C]30[/C][C]6434[/C][C]5883.50256028324[/C][C]550.497439716762[/C][/ROW]
[ROW][C]31[/C][C]4962[/C][C]5525.1214053174[/C][C]-563.121405317396[/C][/ROW]
[ROW][C]32[/C][C]2980[/C][C]5182.55071867233[/C][C]-2202.55071867233[/C][/ROW]
[ROW][C]33[/C][C]2937[/C][C]4149.32414327711[/C][C]-1212.32414327711[/C][/ROW]
[ROW][C]34[/C][C]3023[/C][C]3189.24087184381[/C][C]-166.240871843805[/C][/ROW]
[ROW][C]35[/C][C]2731[/C][C]2991.03894231711[/C][C]-260.038942317105[/C][/ROW]
[ROW][C]36[/C][C]3163[/C][C]3410.37100421191[/C][C]-247.37100421191[/C][/ROW]
[ROW][C]37[/C][C]3146[/C][C]2490.75597166104[/C][C]655.244028338956[/C][/ROW]
[ROW][C]38[/C][C]3173[/C][C]2965.92596020063[/C][C]207.07403979937[/C][/ROW]
[ROW][C]39[/C][C]3724[/C][C]3720.62489032643[/C][C]3.37510967357139[/C][/ROW]
[ROW][C]40[/C][C]3224[/C][C]3312.28929261132[/C][C]-88.2892926113163[/C][/ROW]
[ROW][C]41[/C][C]4114[/C][C]3170.69527334359[/C][C]943.304726656411[/C][/ROW]
[ROW][C]42[/C][C]3450[/C][C]4306.73165026537[/C][C]-856.731650265367[/C][/ROW]
[ROW][C]43[/C][C]2957[/C][C]2662.03972352339[/C][C]294.960276476606[/C][/ROW]
[ROW][C]44[/C][C]3882[/C][C]2148.99386675488[/C][C]1733.00613324512[/C][/ROW]
[ROW][C]45[/C][C]4284[/C][C]3838.34063971652[/C][C]445.659360283485[/C][/ROW]
[ROW][C]46[/C][C]4181[/C][C]4284.24030901671[/C][C]-103.240309016705[/C][/ROW]
[ROW][C]47[/C][C]3760[/C][C]4084.46412804575[/C][C]-324.464128045747[/C][/ROW]
[ROW][C]48[/C][C]4457[/C][C]4471.12047835198[/C][C]-14.120478351977[/C][/ROW]
[ROW][C]49[/C][C]4167[/C][C]4060.4222054132[/C][C]106.577794586801[/C][/ROW]
[ROW][C]50[/C][C]3962[/C][C]4028.3136064637[/C][C]-66.3136064637047[/C][/ROW]
[ROW][C]51[/C][C]5247[/C][C]4538.32498679189[/C][C]708.67501320811[/C][/ROW]
[ROW][C]52[/C][C]5157[/C][C]4507.07328111971[/C][C]649.926718880285[/C][/ROW]
[ROW][C]53[/C][C]3697[/C][C]5224.51794867361[/C][C]-1527.51794867361[/C][/ROW]
[ROW][C]54[/C][C]3514[/C][C]4165.98342442782[/C][C]-651.983424427825[/C][/ROW]
[ROW][C]55[/C][C]3786[/C][C]3116.02216357557[/C][C]669.977836424429[/C][/ROW]
[ROW][C]56[/C][C]3297[/C][C]3415.78374659957[/C][C]-118.783746599575[/C][/ROW]
[ROW][C]57[/C][C]3571[/C][C]3485.79680356516[/C][C]85.2031964348357[/C][/ROW]
[ROW][C]58[/C][C]3871[/C][C]3493.63309963584[/C][C]377.366900364157[/C][/ROW]
[ROW][C]59[/C][C]3492[/C][C]3485.42711697296[/C][C]6.57288302704319[/C][/ROW]
[ROW][C]60[/C][C]3051[/C][C]4194.59827417472[/C][C]-1143.59827417472[/C][/ROW]
[ROW][C]61[/C][C]3735[/C][C]3169.28566912788[/C][C]565.714330872116[/C][/ROW]
[ROW][C]62[/C][C]3645[/C][C]3336.02379520253[/C][C]308.976204797465[/C][/ROW]
[ROW][C]63[/C][C]4852[/C][C]4385.93405113336[/C][C]466.065948866635[/C][/ROW]
[ROW][C]64[/C][C]4232[/C][C]4187.79316990646[/C][C]44.2068300935371[/C][/ROW]
[ROW][C]65[/C][C]3804[/C][C]3652.23019151481[/C][C]151.76980848519[/C][/ROW]
[ROW][C]66[/C][C]4464[/C][C]3941.97151033846[/C][C]522.028489661541[/C][/ROW]
[ROW][C]67[/C][C]4259[/C][C]4126.95255172812[/C][C]132.047448271881[/C][/ROW]
[ROW][C]68[/C][C]3373[/C][C]3785.48324275363[/C][C]-412.483242753628[/C][/ROW]
[ROW][C]69[/C][C]4134[/C][C]3766.76038455759[/C][C]367.239615442405[/C][/ROW]
[ROW][C]70[/C][C]4488[/C][C]4060.8038473594[/C][C]427.196152640595[/C][/ROW]
[ROW][C]71[/C][C]3333[/C][C]3929.2006739754[/C][C]-596.2006739754[/C][/ROW]
[ROW][C]72[/C][C]4772[/C][C]3810.16200842783[/C][C]961.83799157217[/C][/ROW]
[ROW][C]73[/C][C]4929[/C][C]4727.14896774357[/C][C]201.851032256434[/C][/ROW]
[ROW][C]74[/C][C]5555[/C][C]4574.14145091814[/C][C]980.85854908186[/C][/ROW]
[ROW][C]75[/C][C]7183[/C][C]6083.92559259355[/C][C]1099.07440740645[/C][/ROW]
[ROW][C]76[/C][C]9266[/C][C]6084.36414171872[/C][C]3181.63585828128[/C][/ROW]
[ROW][C]77[/C][C]4003[/C][C]7438.4320869367[/C][C]-3435.4320869367[/C][/ROW]
[ROW][C]78[/C][C]3051[/C][C]5770.78343115067[/C][C]-2719.78343115067[/C][/ROW]
[ROW][C]79[/C][C]3507[/C][C]3888.42994031111[/C][C]-381.429940311114[/C][/ROW]
[ROW][C]80[/C][C]3273[/C][C]3020.6944754313[/C][C]252.305524568699[/C][/ROW]
[ROW][C]81[/C][C]3942[/C][C]3714.09400868044[/C][C]227.90599131956[/C][/ROW]
[ROW][C]82[/C][C]3216[/C][C]3950.87806498833[/C][C]-734.878064988329[/C][/ROW]
[ROW][C]83[/C][C]3232[/C][C]2714.31256697985[/C][C]517.687433020151[/C][/ROW]
[ROW][C]84[/C][C]3593[/C][C]3892.07775981751[/C][C]-299.077759817505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295202&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295202&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
1332333532.69791666667-299.697916666668
1435543634.55989056264-80.5598905626366
1539523952.72833862175-0.728338621750481
1639513940.5177567367610.4822432632377
1736853686.77587183248-1.77587183247761
1843124366.15749856583-54.1574985658335
1938673463.77163526199403.228364738009
2041403656.53015175696483.469848243038
2141144604.06741329024-490.067413290242
2238183901.25195287464-83.2519528746384
2333773956.04535141322-579.045351413223
2434534296.7709829124-843.770982912401
2535022102.534916775851399.46508322415
2640173294.03711738799722.962882612009
2754104117.688583954681292.31141604532
2851844870.61850775906313.381492240944
2955294789.98374403821739.016255961791
3064345883.50256028324550.497439716762
3149625525.1214053174-563.121405317396
3229805182.55071867233-2202.55071867233
3329374149.32414327711-1212.32414327711
3430233189.24087184381-166.240871843805
3527312991.03894231711-260.038942317105
3631633410.37100421191-247.37100421191
3731462490.75597166104655.244028338956
3831732965.92596020063207.07403979937
3937243720.624890326433.37510967357139
4032243312.28929261132-88.2892926113163
4141143170.69527334359943.304726656411
4234504306.73165026537-856.731650265367
4329572662.03972352339294.960276476606
4438822148.993866754881733.00613324512
4542843838.34063971652445.659360283485
4641814284.24030901671-103.240309016705
4737604084.46412804575-324.464128045747
4844574471.12047835198-14.120478351977
4941674060.4222054132106.577794586801
5039624028.3136064637-66.3136064637047
5152474538.32498679189708.67501320811
5251574507.07328111971649.926718880285
5336975224.51794867361-1527.51794867361
5435144165.98342442782-651.983424427825
5537863116.02216357557669.977836424429
5632973415.78374659957-118.783746599575
5735713485.7968035651685.2031964348357
5838713493.63309963584377.366900364157
5934923485.427116972966.57288302704319
6030514194.59827417472-1143.59827417472
6137353169.28566912788565.714330872116
6236453336.02379520253308.976204797465
6348524385.93405113336466.065948866635
6442324187.7931699064644.2068300935371
6538043652.23019151481151.76980848519
6644643941.97151033846522.028489661541
6742594126.95255172812132.047448271881
6833733785.48324275363-412.483242753628
6941343766.76038455759367.239615442405
7044884060.8038473594427.196152640595
7133333929.2006739754-596.2006739754
7247723810.16200842783961.83799157217
7349294727.14896774357201.851032256434
7455554574.14145091814980.85854908186
7571836083.925592593551099.07440740645
7692666084.364141718723181.63585828128
7740037438.4320869367-3435.4320869367
7830515770.78343115067-2719.78343115067
7935073888.42994031111-381.429940311114
8032733020.6944754313252.305524568699
8139423714.09400868044227.90599131956
8232163950.87806498833-734.878064988329
8332322714.31256697985517.687433020151
8435933892.07775981751-299.077759817505







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
853754.447855881061950.880441611345558.01527015077
863803.538992458051711.135948927535895.94203598858
874785.099434187712439.157070160837131.0417982146
884996.765459941312422.131378349077571.39954153355
891754.37406094373-1030.232865151334538.98098703878
902402.06156888315-577.7590316927925381.8821694591
913082.40616326566-80.60282982573066245.41515635706
922700.00831981462-636.1452991210126036.16193875024
933234.96148243676-265.7835879586216735.70655283213
942941.19268399356-716.7454137136466599.13078170076
952652.70589650357-1155.942972244776461.35476525191
963189.61363636364-764.0051217083017143.23239443557

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 3754.44785588106 & 1950.88044161134 & 5558.01527015077 \tabularnewline
86 & 3803.53899245805 & 1711.13594892753 & 5895.94203598858 \tabularnewline
87 & 4785.09943418771 & 2439.15707016083 & 7131.0417982146 \tabularnewline
88 & 4996.76545994131 & 2422.13137834907 & 7571.39954153355 \tabularnewline
89 & 1754.37406094373 & -1030.23286515133 & 4538.98098703878 \tabularnewline
90 & 2402.06156888315 & -577.759031692792 & 5381.8821694591 \tabularnewline
91 & 3082.40616326566 & -80.6028298257306 & 6245.41515635706 \tabularnewline
92 & 2700.00831981462 & -636.145299121012 & 6036.16193875024 \tabularnewline
93 & 3234.96148243676 & -265.783587958621 & 6735.70655283213 \tabularnewline
94 & 2941.19268399356 & -716.745413713646 & 6599.13078170076 \tabularnewline
95 & 2652.70589650357 & -1155.94297224477 & 6461.35476525191 \tabularnewline
96 & 3189.61363636364 & -764.005121708301 & 7143.23239443557 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295202&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]85[/C][C]3754.44785588106[/C][C]1950.88044161134[/C][C]5558.01527015077[/C][/ROW]
[ROW][C]86[/C][C]3803.53899245805[/C][C]1711.13594892753[/C][C]5895.94203598858[/C][/ROW]
[ROW][C]87[/C][C]4785.09943418771[/C][C]2439.15707016083[/C][C]7131.0417982146[/C][/ROW]
[ROW][C]88[/C][C]4996.76545994131[/C][C]2422.13137834907[/C][C]7571.39954153355[/C][/ROW]
[ROW][C]89[/C][C]1754.37406094373[/C][C]-1030.23286515133[/C][C]4538.98098703878[/C][/ROW]
[ROW][C]90[/C][C]2402.06156888315[/C][C]-577.759031692792[/C][C]5381.8821694591[/C][/ROW]
[ROW][C]91[/C][C]3082.40616326566[/C][C]-80.6028298257306[/C][C]6245.41515635706[/C][/ROW]
[ROW][C]92[/C][C]2700.00831981462[/C][C]-636.145299121012[/C][C]6036.16193875024[/C][/ROW]
[ROW][C]93[/C][C]3234.96148243676[/C][C]-265.783587958621[/C][C]6735.70655283213[/C][/ROW]
[ROW][C]94[/C][C]2941.19268399356[/C][C]-716.745413713646[/C][C]6599.13078170076[/C][/ROW]
[ROW][C]95[/C][C]2652.70589650357[/C][C]-1155.94297224477[/C][C]6461.35476525191[/C][/ROW]
[ROW][C]96[/C][C]3189.61363636364[/C][C]-764.005121708301[/C][C]7143.23239443557[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295202&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295202&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
853754.447855881061950.880441611345558.01527015077
863803.538992458051711.135948927535895.94203598858
874785.099434187712439.157070160837131.0417982146
884996.765459941312422.131378349077571.39954153355
891754.37406094373-1030.232865151334538.98098703878
902402.06156888315-577.7590316927925381.8821694591
913082.40616326566-80.60282982573066245.41515635706
922700.00831981462-636.1452991210126036.16193875024
933234.96148243676-265.7835879586216735.70655283213
942941.19268399356-716.7454137136466599.13078170076
952652.70589650357-1155.942972244776461.35476525191
963189.61363636364-764.0051217083017143.23239443557



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')