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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 18 May 2011 14:34:54 +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/2011/May/18/t13057290555s95ac4p5o03a65.htm/, Retrieved Tue, 14 May 2024 09:31:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121868, Retrieved Tue, 14 May 2024 09:31:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-05-18 14:34:54] [60509181c3aa3f51e201bae3996eda3b] [Current]
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Dataseries X:
31.900
31.815
31.075
31.070
31.300
31.410
30.310
31.440
31.355
31.380
31.975
31.905
32.565
32.780
32.850
32.910
32.910
33.755
34.130
34.330
34.120
33.600
33.715
33.535
33.745
34.295
33.940
34.245
34.395
33.640
33.890
33.905
33.930
33.975
33.880
33.800
33.165
33.660
33.545
33.590
33.810
33.720
33.660
33.915
34.265
34.175
33.735
33.855
34.210
33.950
33.130
32.195
33.160
33.255
32.260
31.795
31.875
31.985
31.835
32.200
32.275
32.515
32.700
32.680
32.135
31.460
30.755
31.090
31.270
31.110
30.835
31.025
30.800
30.790




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121868&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121868&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121868&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 time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.956867038068198
beta0.00845972160096074
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.956867038068198 \tabularnewline
beta & 0.00845972160096074 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121868&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]0.956867038068198[/C][/ROW]
[ROW][C]beta[/C][C]0.00845972160096074[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121868&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121868&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
alpha0.956867038068198
beta0.00845972160096074
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
331.07531.73-0.655000000000005
431.0731.01294997723330.057050022766699
531.330.97769896087230.322301039127687
631.4131.19886687059930.211133129400686
730.3131.3153709583438-1.00537095834381
831.4430.25970407711121.18029592288885
931.35531.30498408409890.0500159159011311
1031.3831.26914127888660.110858721113399
1131.97531.29241433084850.682585669151457
1231.90531.86827946826320.0367205317367691
1332.56531.82643479106450.738565208935519
1432.7832.46214071020880.317859289791251
1532.8532.69786001912150.152139980878481
1632.9132.77623953085560.133760469144356
1732.9132.8381150617270.0718849382730014
1833.75532.84136583290970.913634167090315
1934.1333.65745440759080.472545592409183
2034.3334.05530503993880.274694960061218
2134.1234.2660625323925-0.146062532392541
2233.634.0730286981104-0.473028698110383
2333.71533.56330263098370.151697369016318
2433.53533.6525843095367-0.117584309536703
2533.74533.48324740107710.261752598922882
2634.29533.67900431910870.615995680891338
2733.9434.2187111452878-0.278711145287815
2834.24533.90004638176940.34495361823064
2934.39534.1809382137330.21406178626701
3033.6434.3383167596403-0.698316759640278
3133.8933.61701759414490.272982405855096
3233.90533.82733233004270.0776676699573144
3333.9333.85138553959870.0786144604013046
3433.97533.87698107231680.0980189276831638
3533.8833.9219375466022-0.0419375466022345
3633.833.8326348066217-0.0326348066217079
3733.16533.7519693787213-0.586969378721328
3833.6633.13612805411420.523871945885752
3933.54533.5874548312372-0.0424548312371869
4033.5933.49653851796730.0934614820327297
4133.8133.5364325994930.273567400507019
4233.7233.7508785790267-0.0308785790267478
4333.6633.673760279063-0.0137602790629714
4433.91533.61291052897970.302089471020295
4534.26533.85673235626860.408267643731364
4634.17534.2054574338478-0.0304574338477721
4733.73534.1341343982063-0.399134398206314
4833.85533.70680560307290.14819439692706
4934.2133.80439729925330.405602700746726
5033.9534.1515778010873-0.201577801087261
5133.1333.9161355567788-0.78613555677876
5232.19533.1149856314946-0.91998563149459
5333.1632.17831185553140.981688144468627
5433.25533.06923363036260.185766369637413
5532.2633.200067840927-0.940067840927028
5631.79532.246018716886-0.451018716886004
5731.87531.75627366035920.118726339640805
5831.98531.81265993791280.172340062087159
5931.83531.9217424825531-0.0867424825531025
6032.231.78221531454650.417784685453455
6132.27532.1288354588990.146164541101015
6232.51532.21673441717490.298265582825053
6332.732.45258825754780.247411742452179
6432.6832.64178448999490.0382155100050952
6532.13532.6311170911344-0.496117091134444
6631.4632.105148455985-0.645148455985037
6730.75531.4313542539015-0.676354253901494
6831.0930.72222528053460.367774719465402
6931.2731.01516597864760.254834021352433
7031.1131.2021002832427-0.092100283242651
7130.83531.0563190513748-0.221319051374799
7231.02530.78510109976130.239898900238735
7330.830.9571493439271-0.157149343927085
7430.7930.74800311370030.0419968862996711

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 31.075 & 31.73 & -0.655000000000005 \tabularnewline
4 & 31.07 & 31.0129499772333 & 0.057050022766699 \tabularnewline
5 & 31.3 & 30.9776989608723 & 0.322301039127687 \tabularnewline
6 & 31.41 & 31.1988668705993 & 0.211133129400686 \tabularnewline
7 & 30.31 & 31.3153709583438 & -1.00537095834381 \tabularnewline
8 & 31.44 & 30.2597040771112 & 1.18029592288885 \tabularnewline
9 & 31.355 & 31.3049840840989 & 0.0500159159011311 \tabularnewline
10 & 31.38 & 31.2691412788866 & 0.110858721113399 \tabularnewline
11 & 31.975 & 31.2924143308485 & 0.682585669151457 \tabularnewline
12 & 31.905 & 31.8682794682632 & 0.0367205317367691 \tabularnewline
13 & 32.565 & 31.8264347910645 & 0.738565208935519 \tabularnewline
14 & 32.78 & 32.4621407102088 & 0.317859289791251 \tabularnewline
15 & 32.85 & 32.6978600191215 & 0.152139980878481 \tabularnewline
16 & 32.91 & 32.7762395308556 & 0.133760469144356 \tabularnewline
17 & 32.91 & 32.838115061727 & 0.0718849382730014 \tabularnewline
18 & 33.755 & 32.8413658329097 & 0.913634167090315 \tabularnewline
19 & 34.13 & 33.6574544075908 & 0.472545592409183 \tabularnewline
20 & 34.33 & 34.0553050399388 & 0.274694960061218 \tabularnewline
21 & 34.12 & 34.2660625323925 & -0.146062532392541 \tabularnewline
22 & 33.6 & 34.0730286981104 & -0.473028698110383 \tabularnewline
23 & 33.715 & 33.5633026309837 & 0.151697369016318 \tabularnewline
24 & 33.535 & 33.6525843095367 & -0.117584309536703 \tabularnewline
25 & 33.745 & 33.4832474010771 & 0.261752598922882 \tabularnewline
26 & 34.295 & 33.6790043191087 & 0.615995680891338 \tabularnewline
27 & 33.94 & 34.2187111452878 & -0.278711145287815 \tabularnewline
28 & 34.245 & 33.9000463817694 & 0.34495361823064 \tabularnewline
29 & 34.395 & 34.180938213733 & 0.21406178626701 \tabularnewline
30 & 33.64 & 34.3383167596403 & -0.698316759640278 \tabularnewline
31 & 33.89 & 33.6170175941449 & 0.272982405855096 \tabularnewline
32 & 33.905 & 33.8273323300427 & 0.0776676699573144 \tabularnewline
33 & 33.93 & 33.8513855395987 & 0.0786144604013046 \tabularnewline
34 & 33.975 & 33.8769810723168 & 0.0980189276831638 \tabularnewline
35 & 33.88 & 33.9219375466022 & -0.0419375466022345 \tabularnewline
36 & 33.8 & 33.8326348066217 & -0.0326348066217079 \tabularnewline
37 & 33.165 & 33.7519693787213 & -0.586969378721328 \tabularnewline
38 & 33.66 & 33.1361280541142 & 0.523871945885752 \tabularnewline
39 & 33.545 & 33.5874548312372 & -0.0424548312371869 \tabularnewline
40 & 33.59 & 33.4965385179673 & 0.0934614820327297 \tabularnewline
41 & 33.81 & 33.536432599493 & 0.273567400507019 \tabularnewline
42 & 33.72 & 33.7508785790267 & -0.0308785790267478 \tabularnewline
43 & 33.66 & 33.673760279063 & -0.0137602790629714 \tabularnewline
44 & 33.915 & 33.6129105289797 & 0.302089471020295 \tabularnewline
45 & 34.265 & 33.8567323562686 & 0.408267643731364 \tabularnewline
46 & 34.175 & 34.2054574338478 & -0.0304574338477721 \tabularnewline
47 & 33.735 & 34.1341343982063 & -0.399134398206314 \tabularnewline
48 & 33.855 & 33.7068056030729 & 0.14819439692706 \tabularnewline
49 & 34.21 & 33.8043972992533 & 0.405602700746726 \tabularnewline
50 & 33.95 & 34.1515778010873 & -0.201577801087261 \tabularnewline
51 & 33.13 & 33.9161355567788 & -0.78613555677876 \tabularnewline
52 & 32.195 & 33.1149856314946 & -0.91998563149459 \tabularnewline
53 & 33.16 & 32.1783118555314 & 0.981688144468627 \tabularnewline
54 & 33.255 & 33.0692336303626 & 0.185766369637413 \tabularnewline
55 & 32.26 & 33.200067840927 & -0.940067840927028 \tabularnewline
56 & 31.795 & 32.246018716886 & -0.451018716886004 \tabularnewline
57 & 31.875 & 31.7562736603592 & 0.118726339640805 \tabularnewline
58 & 31.985 & 31.8126599379128 & 0.172340062087159 \tabularnewline
59 & 31.835 & 31.9217424825531 & -0.0867424825531025 \tabularnewline
60 & 32.2 & 31.7822153145465 & 0.417784685453455 \tabularnewline
61 & 32.275 & 32.128835458899 & 0.146164541101015 \tabularnewline
62 & 32.515 & 32.2167344171749 & 0.298265582825053 \tabularnewline
63 & 32.7 & 32.4525882575478 & 0.247411742452179 \tabularnewline
64 & 32.68 & 32.6417844899949 & 0.0382155100050952 \tabularnewline
65 & 32.135 & 32.6311170911344 & -0.496117091134444 \tabularnewline
66 & 31.46 & 32.105148455985 & -0.645148455985037 \tabularnewline
67 & 30.755 & 31.4313542539015 & -0.676354253901494 \tabularnewline
68 & 31.09 & 30.7222252805346 & 0.367774719465402 \tabularnewline
69 & 31.27 & 31.0151659786476 & 0.254834021352433 \tabularnewline
70 & 31.11 & 31.2021002832427 & -0.092100283242651 \tabularnewline
71 & 30.835 & 31.0563190513748 & -0.221319051374799 \tabularnewline
72 & 31.025 & 30.7851010997613 & 0.239898900238735 \tabularnewline
73 & 30.8 & 30.9571493439271 & -0.157149343927085 \tabularnewline
74 & 30.79 & 30.7480031137003 & 0.0419968862996711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121868&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]31.075[/C][C]31.73[/C][C]-0.655000000000005[/C][/ROW]
[ROW][C]4[/C][C]31.07[/C][C]31.0129499772333[/C][C]0.057050022766699[/C][/ROW]
[ROW][C]5[/C][C]31.3[/C][C]30.9776989608723[/C][C]0.322301039127687[/C][/ROW]
[ROW][C]6[/C][C]31.41[/C][C]31.1988668705993[/C][C]0.211133129400686[/C][/ROW]
[ROW][C]7[/C][C]30.31[/C][C]31.3153709583438[/C][C]-1.00537095834381[/C][/ROW]
[ROW][C]8[/C][C]31.44[/C][C]30.2597040771112[/C][C]1.18029592288885[/C][/ROW]
[ROW][C]9[/C][C]31.355[/C][C]31.3049840840989[/C][C]0.0500159159011311[/C][/ROW]
[ROW][C]10[/C][C]31.38[/C][C]31.2691412788866[/C][C]0.110858721113399[/C][/ROW]
[ROW][C]11[/C][C]31.975[/C][C]31.2924143308485[/C][C]0.682585669151457[/C][/ROW]
[ROW][C]12[/C][C]31.905[/C][C]31.8682794682632[/C][C]0.0367205317367691[/C][/ROW]
[ROW][C]13[/C][C]32.565[/C][C]31.8264347910645[/C][C]0.738565208935519[/C][/ROW]
[ROW][C]14[/C][C]32.78[/C][C]32.4621407102088[/C][C]0.317859289791251[/C][/ROW]
[ROW][C]15[/C][C]32.85[/C][C]32.6978600191215[/C][C]0.152139980878481[/C][/ROW]
[ROW][C]16[/C][C]32.91[/C][C]32.7762395308556[/C][C]0.133760469144356[/C][/ROW]
[ROW][C]17[/C][C]32.91[/C][C]32.838115061727[/C][C]0.0718849382730014[/C][/ROW]
[ROW][C]18[/C][C]33.755[/C][C]32.8413658329097[/C][C]0.913634167090315[/C][/ROW]
[ROW][C]19[/C][C]34.13[/C][C]33.6574544075908[/C][C]0.472545592409183[/C][/ROW]
[ROW][C]20[/C][C]34.33[/C][C]34.0553050399388[/C][C]0.274694960061218[/C][/ROW]
[ROW][C]21[/C][C]34.12[/C][C]34.2660625323925[/C][C]-0.146062532392541[/C][/ROW]
[ROW][C]22[/C][C]33.6[/C][C]34.0730286981104[/C][C]-0.473028698110383[/C][/ROW]
[ROW][C]23[/C][C]33.715[/C][C]33.5633026309837[/C][C]0.151697369016318[/C][/ROW]
[ROW][C]24[/C][C]33.535[/C][C]33.6525843095367[/C][C]-0.117584309536703[/C][/ROW]
[ROW][C]25[/C][C]33.745[/C][C]33.4832474010771[/C][C]0.261752598922882[/C][/ROW]
[ROW][C]26[/C][C]34.295[/C][C]33.6790043191087[/C][C]0.615995680891338[/C][/ROW]
[ROW][C]27[/C][C]33.94[/C][C]34.2187111452878[/C][C]-0.278711145287815[/C][/ROW]
[ROW][C]28[/C][C]34.245[/C][C]33.9000463817694[/C][C]0.34495361823064[/C][/ROW]
[ROW][C]29[/C][C]34.395[/C][C]34.180938213733[/C][C]0.21406178626701[/C][/ROW]
[ROW][C]30[/C][C]33.64[/C][C]34.3383167596403[/C][C]-0.698316759640278[/C][/ROW]
[ROW][C]31[/C][C]33.89[/C][C]33.6170175941449[/C][C]0.272982405855096[/C][/ROW]
[ROW][C]32[/C][C]33.905[/C][C]33.8273323300427[/C][C]0.0776676699573144[/C][/ROW]
[ROW][C]33[/C][C]33.93[/C][C]33.8513855395987[/C][C]0.0786144604013046[/C][/ROW]
[ROW][C]34[/C][C]33.975[/C][C]33.8769810723168[/C][C]0.0980189276831638[/C][/ROW]
[ROW][C]35[/C][C]33.88[/C][C]33.9219375466022[/C][C]-0.0419375466022345[/C][/ROW]
[ROW][C]36[/C][C]33.8[/C][C]33.8326348066217[/C][C]-0.0326348066217079[/C][/ROW]
[ROW][C]37[/C][C]33.165[/C][C]33.7519693787213[/C][C]-0.586969378721328[/C][/ROW]
[ROW][C]38[/C][C]33.66[/C][C]33.1361280541142[/C][C]0.523871945885752[/C][/ROW]
[ROW][C]39[/C][C]33.545[/C][C]33.5874548312372[/C][C]-0.0424548312371869[/C][/ROW]
[ROW][C]40[/C][C]33.59[/C][C]33.4965385179673[/C][C]0.0934614820327297[/C][/ROW]
[ROW][C]41[/C][C]33.81[/C][C]33.536432599493[/C][C]0.273567400507019[/C][/ROW]
[ROW][C]42[/C][C]33.72[/C][C]33.7508785790267[/C][C]-0.0308785790267478[/C][/ROW]
[ROW][C]43[/C][C]33.66[/C][C]33.673760279063[/C][C]-0.0137602790629714[/C][/ROW]
[ROW][C]44[/C][C]33.915[/C][C]33.6129105289797[/C][C]0.302089471020295[/C][/ROW]
[ROW][C]45[/C][C]34.265[/C][C]33.8567323562686[/C][C]0.408267643731364[/C][/ROW]
[ROW][C]46[/C][C]34.175[/C][C]34.2054574338478[/C][C]-0.0304574338477721[/C][/ROW]
[ROW][C]47[/C][C]33.735[/C][C]34.1341343982063[/C][C]-0.399134398206314[/C][/ROW]
[ROW][C]48[/C][C]33.855[/C][C]33.7068056030729[/C][C]0.14819439692706[/C][/ROW]
[ROW][C]49[/C][C]34.21[/C][C]33.8043972992533[/C][C]0.405602700746726[/C][/ROW]
[ROW][C]50[/C][C]33.95[/C][C]34.1515778010873[/C][C]-0.201577801087261[/C][/ROW]
[ROW][C]51[/C][C]33.13[/C][C]33.9161355567788[/C][C]-0.78613555677876[/C][/ROW]
[ROW][C]52[/C][C]32.195[/C][C]33.1149856314946[/C][C]-0.91998563149459[/C][/ROW]
[ROW][C]53[/C][C]33.16[/C][C]32.1783118555314[/C][C]0.981688144468627[/C][/ROW]
[ROW][C]54[/C][C]33.255[/C][C]33.0692336303626[/C][C]0.185766369637413[/C][/ROW]
[ROW][C]55[/C][C]32.26[/C][C]33.200067840927[/C][C]-0.940067840927028[/C][/ROW]
[ROW][C]56[/C][C]31.795[/C][C]32.246018716886[/C][C]-0.451018716886004[/C][/ROW]
[ROW][C]57[/C][C]31.875[/C][C]31.7562736603592[/C][C]0.118726339640805[/C][/ROW]
[ROW][C]58[/C][C]31.985[/C][C]31.8126599379128[/C][C]0.172340062087159[/C][/ROW]
[ROW][C]59[/C][C]31.835[/C][C]31.9217424825531[/C][C]-0.0867424825531025[/C][/ROW]
[ROW][C]60[/C][C]32.2[/C][C]31.7822153145465[/C][C]0.417784685453455[/C][/ROW]
[ROW][C]61[/C][C]32.275[/C][C]32.128835458899[/C][C]0.146164541101015[/C][/ROW]
[ROW][C]62[/C][C]32.515[/C][C]32.2167344171749[/C][C]0.298265582825053[/C][/ROW]
[ROW][C]63[/C][C]32.7[/C][C]32.4525882575478[/C][C]0.247411742452179[/C][/ROW]
[ROW][C]64[/C][C]32.68[/C][C]32.6417844899949[/C][C]0.0382155100050952[/C][/ROW]
[ROW][C]65[/C][C]32.135[/C][C]32.6311170911344[/C][C]-0.496117091134444[/C][/ROW]
[ROW][C]66[/C][C]31.46[/C][C]32.105148455985[/C][C]-0.645148455985037[/C][/ROW]
[ROW][C]67[/C][C]30.755[/C][C]31.4313542539015[/C][C]-0.676354253901494[/C][/ROW]
[ROW][C]68[/C][C]31.09[/C][C]30.7222252805346[/C][C]0.367774719465402[/C][/ROW]
[ROW][C]69[/C][C]31.27[/C][C]31.0151659786476[/C][C]0.254834021352433[/C][/ROW]
[ROW][C]70[/C][C]31.11[/C][C]31.2021002832427[/C][C]-0.092100283242651[/C][/ROW]
[ROW][C]71[/C][C]30.835[/C][C]31.0563190513748[/C][C]-0.221319051374799[/C][/ROW]
[ROW][C]72[/C][C]31.025[/C][C]30.7851010997613[/C][C]0.239898900238735[/C][/ROW]
[ROW][C]73[/C][C]30.8[/C][C]30.9571493439271[/C][C]-0.157149343927085[/C][/ROW]
[ROW][C]74[/C][C]30.79[/C][C]30.7480031137003[/C][C]0.0419968862996711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121868&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121868&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
331.07531.73-0.655000000000005
431.0731.01294997723330.057050022766699
531.330.97769896087230.322301039127687
631.4131.19886687059930.211133129400686
730.3131.3153709583438-1.00537095834381
831.4430.25970407711121.18029592288885
931.35531.30498408409890.0500159159011311
1031.3831.26914127888660.110858721113399
1131.97531.29241433084850.682585669151457
1231.90531.86827946826320.0367205317367691
1332.56531.82643479106450.738565208935519
1432.7832.46214071020880.317859289791251
1532.8532.69786001912150.152139980878481
1632.9132.77623953085560.133760469144356
1732.9132.8381150617270.0718849382730014
1833.75532.84136583290970.913634167090315
1934.1333.65745440759080.472545592409183
2034.3334.05530503993880.274694960061218
2134.1234.2660625323925-0.146062532392541
2233.634.0730286981104-0.473028698110383
2333.71533.56330263098370.151697369016318
2433.53533.6525843095367-0.117584309536703
2533.74533.48324740107710.261752598922882
2634.29533.67900431910870.615995680891338
2733.9434.2187111452878-0.278711145287815
2834.24533.90004638176940.34495361823064
2934.39534.1809382137330.21406178626701
3033.6434.3383167596403-0.698316759640278
3133.8933.61701759414490.272982405855096
3233.90533.82733233004270.0776676699573144
3333.9333.85138553959870.0786144604013046
3433.97533.87698107231680.0980189276831638
3533.8833.9219375466022-0.0419375466022345
3633.833.8326348066217-0.0326348066217079
3733.16533.7519693787213-0.586969378721328
3833.6633.13612805411420.523871945885752
3933.54533.5874548312372-0.0424548312371869
4033.5933.49653851796730.0934614820327297
4133.8133.5364325994930.273567400507019
4233.7233.7508785790267-0.0308785790267478
4333.6633.673760279063-0.0137602790629714
4433.91533.61291052897970.302089471020295
4534.26533.85673235626860.408267643731364
4634.17534.2054574338478-0.0304574338477721
4733.73534.1341343982063-0.399134398206314
4833.85533.70680560307290.14819439692706
4934.2133.80439729925330.405602700746726
5033.9534.1515778010873-0.201577801087261
5133.1333.9161355567788-0.78613555677876
5232.19533.1149856314946-0.91998563149459
5333.1632.17831185553140.981688144468627
5433.25533.06923363036260.185766369637413
5532.2633.200067840927-0.940067840927028
5631.79532.246018716886-0.451018716886004
5731.87531.75627366035920.118726339640805
5831.98531.81265993791280.172340062087159
5931.83531.9217424825531-0.0867424825531025
6032.231.78221531454650.417784685453455
6132.27532.1288354588990.146164541101015
6232.51532.21673441717490.298265582825053
6332.732.45258825754780.247411742452179
6432.6832.64178448999490.0382155100050952
6532.13532.6311170911344-0.496117091134444
6631.4632.105148455985-0.645148455985037
6730.75531.4313542539015-0.676354253901494
6831.0930.72222528053460.367774719465402
6931.2731.01516597864760.254834021352433
7031.1131.2021002832427-0.092100283242651
7130.83531.0563190513748-0.221319051374799
7231.02530.78510109976130.239898900238735
7330.830.9571493439271-0.157149343927085
7430.7930.74800311370030.0419968862996711







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7530.729753304535829.876268686760831.5832379223107
7630.671318059169629.485265703461431.8573704148778
7730.612882813803429.164976725734532.0607889018723
7830.554447568437128.881824776443132.2270703604312
7930.496012323070928.622374004948732.3696506411932
8030.437577077704728.379644102182432.4955100532271
8130.379141832338528.149463554766132.6088201099109
8230.320706586972327.929107272767332.7123059011774
8330.262271341606127.716681082002932.8078616012093
8430.203836096239927.510806546628132.8968656458517
8530.145400850873727.3104444316432.9803572701074
8630.086965605507527.114788883849733.0591423271652

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
75 & 30.7297533045358 & 29.8762686867608 & 31.5832379223107 \tabularnewline
76 & 30.6713180591696 & 29.4852657034614 & 31.8573704148778 \tabularnewline
77 & 30.6128828138034 & 29.1649767257345 & 32.0607889018723 \tabularnewline
78 & 30.5544475684371 & 28.8818247764431 & 32.2270703604312 \tabularnewline
79 & 30.4960123230709 & 28.6223740049487 & 32.3696506411932 \tabularnewline
80 & 30.4375770777047 & 28.3796441021824 & 32.4955100532271 \tabularnewline
81 & 30.3791418323385 & 28.1494635547661 & 32.6088201099109 \tabularnewline
82 & 30.3207065869723 & 27.9291072727673 & 32.7123059011774 \tabularnewline
83 & 30.2622713416061 & 27.7166810820029 & 32.8078616012093 \tabularnewline
84 & 30.2038360962399 & 27.5108065466281 & 32.8968656458517 \tabularnewline
85 & 30.1454008508737 & 27.31044443164 & 32.9803572701074 \tabularnewline
86 & 30.0869656055075 & 27.1147888838497 & 33.0591423271652 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121868&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]75[/C][C]30.7297533045358[/C][C]29.8762686867608[/C][C]31.5832379223107[/C][/ROW]
[ROW][C]76[/C][C]30.6713180591696[/C][C]29.4852657034614[/C][C]31.8573704148778[/C][/ROW]
[ROW][C]77[/C][C]30.6128828138034[/C][C]29.1649767257345[/C][C]32.0607889018723[/C][/ROW]
[ROW][C]78[/C][C]30.5544475684371[/C][C]28.8818247764431[/C][C]32.2270703604312[/C][/ROW]
[ROW][C]79[/C][C]30.4960123230709[/C][C]28.6223740049487[/C][C]32.3696506411932[/C][/ROW]
[ROW][C]80[/C][C]30.4375770777047[/C][C]28.3796441021824[/C][C]32.4955100532271[/C][/ROW]
[ROW][C]81[/C][C]30.3791418323385[/C][C]28.1494635547661[/C][C]32.6088201099109[/C][/ROW]
[ROW][C]82[/C][C]30.3207065869723[/C][C]27.9291072727673[/C][C]32.7123059011774[/C][/ROW]
[ROW][C]83[/C][C]30.2622713416061[/C][C]27.7166810820029[/C][C]32.8078616012093[/C][/ROW]
[ROW][C]84[/C][C]30.2038360962399[/C][C]27.5108065466281[/C][C]32.8968656458517[/C][/ROW]
[ROW][C]85[/C][C]30.1454008508737[/C][C]27.31044443164[/C][C]32.9803572701074[/C][/ROW]
[ROW][C]86[/C][C]30.0869656055075[/C][C]27.1147888838497[/C][C]33.0591423271652[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121868&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121868&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
7530.729753304535829.876268686760831.5832379223107
7630.671318059169629.485265703461431.8573704148778
7730.612882813803429.164976725734532.0607889018723
7830.554447568437128.881824776443132.2270703604312
7930.496012323070928.622374004948732.3696506411932
8030.437577077704728.379644102182432.4955100532271
8130.379141832338528.149463554766132.6088201099109
8230.320706586972327.929107272767332.7123059011774
8330.262271341606127.716681082002932.8078616012093
8430.203836096239927.510806546628132.8968656458517
8530.145400850873727.3104444316432.9803572701074
8630.086965605507527.114788883849733.0591423271652



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')