Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 25 Nov 2016 10:12:51 +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/2016/Nov/25/t148006878750g86buolxelp0p.htm/, Retrieved Sun, 19 May 2024 05:43:39 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 19 May 2024 05:43:39 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
726
784
884
696
893
674
703
799
793
799
1022
758
1021
944
915
864
1022
891
1087
822
890
1092
967
833
1104
1063
1103
1039
1185
1047
1155
878
879
1133
920
943
938
900
781
1040
792
653
866
679
799
760
699
762
671
679
862
624
516
650
583
444
562
540
524
683




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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.338628509793376
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.338628509793376 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.338628509793376[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.338628509793376
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
278472658
3884745.640453568016138.359546431984
4696792.492940591966-96.4929405919661
5893759.817679913728133.182320086272
6674804.917010495367-130.917010495367
7703760.584778324717-57.5847783247169
8799741.08493065383657.9150693461638
9793760.69662428110832.3033757188923
10799771.63546826209227.3645317379082
111022780.901878865693241.098121134307
12758862.544576339386-104.544576339386
131021827.1428022466193.8571977534
14944892.78837623455451.2116237654463
15915910.1300920743464.86990792565416
16864911.779181738041-47.7791817380411
171022895.599788626941126.400211373059
18891938.402503841768-47.4025038417678
191087922.350664605355164.649335394645
20822978.105623688514-156.105623688514
21890925.243808968507-35.2438089685066
221092913.309250458059178.690749541941
23967973.819032689308-6.81903268930773
24833971.509913811495-138.509913811495
251104924.6065081059179.3934918941
261063985.35425893262977.6457410673711
2711031011.6473205220891.3526794779249
2810391042.58194223932-3.58194223931673
2911851041.36899447665143.631005523349
3010471090.00654783715-43.0065478371469
3111551075.443304631779.5566953683037
328781102.38346982835-224.383469828351
338791026.40082981811-147.400829818109
341133976.486706474496156.513293525504
359201029.48656982389-109.48656982389
36943992.411295842038-49.411295842038
37938975.679222364089-37.679222364089
38900962.919963444764-62.9199634447643
39781941.61346998721-160.61346998721
401040887.225169992698152.774830007302
41792938.959083012007-146.959083012007
42653889.19454773105-236.19454773105
43866809.21234001156456.787659988436
44679828.442260688101-149.442260688101
45799777.83685065113621.1631493488638
46760785.003296377677-25.0032963776766
47699776.536467385382-77.5364673853819
48762750.28040898002711.7195910199727
49671754.248996622508-83.2489966225085
50679726.058512954435-47.0585129544346
51862710.123158839582151.876841160418
52624761.55298723386-137.55298723386
53516714.973624149231-198.973624149231
54650647.5954823153892.40451768461071
55583648.409720555701-65.4097205557008
56444626.260124357923-182.260124357923
57562564.541650051844-2.54165005184393
58540563.680974882372-23.6809748823717
59524555.6619216475-31.6619216474999
60683544.940292302812138.059707697188

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 784 & 726 & 58 \tabularnewline
3 & 884 & 745.640453568016 & 138.359546431984 \tabularnewline
4 & 696 & 792.492940591966 & -96.4929405919661 \tabularnewline
5 & 893 & 759.817679913728 & 133.182320086272 \tabularnewline
6 & 674 & 804.917010495367 & -130.917010495367 \tabularnewline
7 & 703 & 760.584778324717 & -57.5847783247169 \tabularnewline
8 & 799 & 741.084930653836 & 57.9150693461638 \tabularnewline
9 & 793 & 760.696624281108 & 32.3033757188923 \tabularnewline
10 & 799 & 771.635468262092 & 27.3645317379082 \tabularnewline
11 & 1022 & 780.901878865693 & 241.098121134307 \tabularnewline
12 & 758 & 862.544576339386 & -104.544576339386 \tabularnewline
13 & 1021 & 827.1428022466 & 193.8571977534 \tabularnewline
14 & 944 & 892.788376234554 & 51.2116237654463 \tabularnewline
15 & 915 & 910.130092074346 & 4.86990792565416 \tabularnewline
16 & 864 & 911.779181738041 & -47.7791817380411 \tabularnewline
17 & 1022 & 895.599788626941 & 126.400211373059 \tabularnewline
18 & 891 & 938.402503841768 & -47.4025038417678 \tabularnewline
19 & 1087 & 922.350664605355 & 164.649335394645 \tabularnewline
20 & 822 & 978.105623688514 & -156.105623688514 \tabularnewline
21 & 890 & 925.243808968507 & -35.2438089685066 \tabularnewline
22 & 1092 & 913.309250458059 & 178.690749541941 \tabularnewline
23 & 967 & 973.819032689308 & -6.81903268930773 \tabularnewline
24 & 833 & 971.509913811495 & -138.509913811495 \tabularnewline
25 & 1104 & 924.6065081059 & 179.3934918941 \tabularnewline
26 & 1063 & 985.354258932629 & 77.6457410673711 \tabularnewline
27 & 1103 & 1011.64732052208 & 91.3526794779249 \tabularnewline
28 & 1039 & 1042.58194223932 & -3.58194223931673 \tabularnewline
29 & 1185 & 1041.36899447665 & 143.631005523349 \tabularnewline
30 & 1047 & 1090.00654783715 & -43.0065478371469 \tabularnewline
31 & 1155 & 1075.4433046317 & 79.5566953683037 \tabularnewline
32 & 878 & 1102.38346982835 & -224.383469828351 \tabularnewline
33 & 879 & 1026.40082981811 & -147.400829818109 \tabularnewline
34 & 1133 & 976.486706474496 & 156.513293525504 \tabularnewline
35 & 920 & 1029.48656982389 & -109.48656982389 \tabularnewline
36 & 943 & 992.411295842038 & -49.411295842038 \tabularnewline
37 & 938 & 975.679222364089 & -37.679222364089 \tabularnewline
38 & 900 & 962.919963444764 & -62.9199634447643 \tabularnewline
39 & 781 & 941.61346998721 & -160.61346998721 \tabularnewline
40 & 1040 & 887.225169992698 & 152.774830007302 \tabularnewline
41 & 792 & 938.959083012007 & -146.959083012007 \tabularnewline
42 & 653 & 889.19454773105 & -236.19454773105 \tabularnewline
43 & 866 & 809.212340011564 & 56.787659988436 \tabularnewline
44 & 679 & 828.442260688101 & -149.442260688101 \tabularnewline
45 & 799 & 777.836850651136 & 21.1631493488638 \tabularnewline
46 & 760 & 785.003296377677 & -25.0032963776766 \tabularnewline
47 & 699 & 776.536467385382 & -77.5364673853819 \tabularnewline
48 & 762 & 750.280408980027 & 11.7195910199727 \tabularnewline
49 & 671 & 754.248996622508 & -83.2489966225085 \tabularnewline
50 & 679 & 726.058512954435 & -47.0585129544346 \tabularnewline
51 & 862 & 710.123158839582 & 151.876841160418 \tabularnewline
52 & 624 & 761.55298723386 & -137.55298723386 \tabularnewline
53 & 516 & 714.973624149231 & -198.973624149231 \tabularnewline
54 & 650 & 647.595482315389 & 2.40451768461071 \tabularnewline
55 & 583 & 648.409720555701 & -65.4097205557008 \tabularnewline
56 & 444 & 626.260124357923 & -182.260124357923 \tabularnewline
57 & 562 & 564.541650051844 & -2.54165005184393 \tabularnewline
58 & 540 & 563.680974882372 & -23.6809748823717 \tabularnewline
59 & 524 & 555.6619216475 & -31.6619216474999 \tabularnewline
60 & 683 & 544.940292302812 & 138.059707697188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]784[/C][C]726[/C][C]58[/C][/ROW]
[ROW][C]3[/C][C]884[/C][C]745.640453568016[/C][C]138.359546431984[/C][/ROW]
[ROW][C]4[/C][C]696[/C][C]792.492940591966[/C][C]-96.4929405919661[/C][/ROW]
[ROW][C]5[/C][C]893[/C][C]759.817679913728[/C][C]133.182320086272[/C][/ROW]
[ROW][C]6[/C][C]674[/C][C]804.917010495367[/C][C]-130.917010495367[/C][/ROW]
[ROW][C]7[/C][C]703[/C][C]760.584778324717[/C][C]-57.5847783247169[/C][/ROW]
[ROW][C]8[/C][C]799[/C][C]741.084930653836[/C][C]57.9150693461638[/C][/ROW]
[ROW][C]9[/C][C]793[/C][C]760.696624281108[/C][C]32.3033757188923[/C][/ROW]
[ROW][C]10[/C][C]799[/C][C]771.635468262092[/C][C]27.3645317379082[/C][/ROW]
[ROW][C]11[/C][C]1022[/C][C]780.901878865693[/C][C]241.098121134307[/C][/ROW]
[ROW][C]12[/C][C]758[/C][C]862.544576339386[/C][C]-104.544576339386[/C][/ROW]
[ROW][C]13[/C][C]1021[/C][C]827.1428022466[/C][C]193.8571977534[/C][/ROW]
[ROW][C]14[/C][C]944[/C][C]892.788376234554[/C][C]51.2116237654463[/C][/ROW]
[ROW][C]15[/C][C]915[/C][C]910.130092074346[/C][C]4.86990792565416[/C][/ROW]
[ROW][C]16[/C][C]864[/C][C]911.779181738041[/C][C]-47.7791817380411[/C][/ROW]
[ROW][C]17[/C][C]1022[/C][C]895.599788626941[/C][C]126.400211373059[/C][/ROW]
[ROW][C]18[/C][C]891[/C][C]938.402503841768[/C][C]-47.4025038417678[/C][/ROW]
[ROW][C]19[/C][C]1087[/C][C]922.350664605355[/C][C]164.649335394645[/C][/ROW]
[ROW][C]20[/C][C]822[/C][C]978.105623688514[/C][C]-156.105623688514[/C][/ROW]
[ROW][C]21[/C][C]890[/C][C]925.243808968507[/C][C]-35.2438089685066[/C][/ROW]
[ROW][C]22[/C][C]1092[/C][C]913.309250458059[/C][C]178.690749541941[/C][/ROW]
[ROW][C]23[/C][C]967[/C][C]973.819032689308[/C][C]-6.81903268930773[/C][/ROW]
[ROW][C]24[/C][C]833[/C][C]971.509913811495[/C][C]-138.509913811495[/C][/ROW]
[ROW][C]25[/C][C]1104[/C][C]924.6065081059[/C][C]179.3934918941[/C][/ROW]
[ROW][C]26[/C][C]1063[/C][C]985.354258932629[/C][C]77.6457410673711[/C][/ROW]
[ROW][C]27[/C][C]1103[/C][C]1011.64732052208[/C][C]91.3526794779249[/C][/ROW]
[ROW][C]28[/C][C]1039[/C][C]1042.58194223932[/C][C]-3.58194223931673[/C][/ROW]
[ROW][C]29[/C][C]1185[/C][C]1041.36899447665[/C][C]143.631005523349[/C][/ROW]
[ROW][C]30[/C][C]1047[/C][C]1090.00654783715[/C][C]-43.0065478371469[/C][/ROW]
[ROW][C]31[/C][C]1155[/C][C]1075.4433046317[/C][C]79.5566953683037[/C][/ROW]
[ROW][C]32[/C][C]878[/C][C]1102.38346982835[/C][C]-224.383469828351[/C][/ROW]
[ROW][C]33[/C][C]879[/C][C]1026.40082981811[/C][C]-147.400829818109[/C][/ROW]
[ROW][C]34[/C][C]1133[/C][C]976.486706474496[/C][C]156.513293525504[/C][/ROW]
[ROW][C]35[/C][C]920[/C][C]1029.48656982389[/C][C]-109.48656982389[/C][/ROW]
[ROW][C]36[/C][C]943[/C][C]992.411295842038[/C][C]-49.411295842038[/C][/ROW]
[ROW][C]37[/C][C]938[/C][C]975.679222364089[/C][C]-37.679222364089[/C][/ROW]
[ROW][C]38[/C][C]900[/C][C]962.919963444764[/C][C]-62.9199634447643[/C][/ROW]
[ROW][C]39[/C][C]781[/C][C]941.61346998721[/C][C]-160.61346998721[/C][/ROW]
[ROW][C]40[/C][C]1040[/C][C]887.225169992698[/C][C]152.774830007302[/C][/ROW]
[ROW][C]41[/C][C]792[/C][C]938.959083012007[/C][C]-146.959083012007[/C][/ROW]
[ROW][C]42[/C][C]653[/C][C]889.19454773105[/C][C]-236.19454773105[/C][/ROW]
[ROW][C]43[/C][C]866[/C][C]809.212340011564[/C][C]56.787659988436[/C][/ROW]
[ROW][C]44[/C][C]679[/C][C]828.442260688101[/C][C]-149.442260688101[/C][/ROW]
[ROW][C]45[/C][C]799[/C][C]777.836850651136[/C][C]21.1631493488638[/C][/ROW]
[ROW][C]46[/C][C]760[/C][C]785.003296377677[/C][C]-25.0032963776766[/C][/ROW]
[ROW][C]47[/C][C]699[/C][C]776.536467385382[/C][C]-77.5364673853819[/C][/ROW]
[ROW][C]48[/C][C]762[/C][C]750.280408980027[/C][C]11.7195910199727[/C][/ROW]
[ROW][C]49[/C][C]671[/C][C]754.248996622508[/C][C]-83.2489966225085[/C][/ROW]
[ROW][C]50[/C][C]679[/C][C]726.058512954435[/C][C]-47.0585129544346[/C][/ROW]
[ROW][C]51[/C][C]862[/C][C]710.123158839582[/C][C]151.876841160418[/C][/ROW]
[ROW][C]52[/C][C]624[/C][C]761.55298723386[/C][C]-137.55298723386[/C][/ROW]
[ROW][C]53[/C][C]516[/C][C]714.973624149231[/C][C]-198.973624149231[/C][/ROW]
[ROW][C]54[/C][C]650[/C][C]647.595482315389[/C][C]2.40451768461071[/C][/ROW]
[ROW][C]55[/C][C]583[/C][C]648.409720555701[/C][C]-65.4097205557008[/C][/ROW]
[ROW][C]56[/C][C]444[/C][C]626.260124357923[/C][C]-182.260124357923[/C][/ROW]
[ROW][C]57[/C][C]562[/C][C]564.541650051844[/C][C]-2.54165005184393[/C][/ROW]
[ROW][C]58[/C][C]540[/C][C]563.680974882372[/C][C]-23.6809748823717[/C][/ROW]
[ROW][C]59[/C][C]524[/C][C]555.6619216475[/C][C]-31.6619216474999[/C][/ROW]
[ROW][C]60[/C][C]683[/C][C]544.940292302812[/C][C]138.059707697188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
278472658
3884745.640453568016138.359546431984
4696792.492940591966-96.4929405919661
5893759.817679913728133.182320086272
6674804.917010495367-130.917010495367
7703760.584778324717-57.5847783247169
8799741.08493065383657.9150693461638
9793760.69662428110832.3033757188923
10799771.63546826209227.3645317379082
111022780.901878865693241.098121134307
12758862.544576339386-104.544576339386
131021827.1428022466193.8571977534
14944892.78837623455451.2116237654463
15915910.1300920743464.86990792565416
16864911.779181738041-47.7791817380411
171022895.599788626941126.400211373059
18891938.402503841768-47.4025038417678
191087922.350664605355164.649335394645
20822978.105623688514-156.105623688514
21890925.243808968507-35.2438089685066
221092913.309250458059178.690749541941
23967973.819032689308-6.81903268930773
24833971.509913811495-138.509913811495
251104924.6065081059179.3934918941
261063985.35425893262977.6457410673711
2711031011.6473205220891.3526794779249
2810391042.58194223932-3.58194223931673
2911851041.36899447665143.631005523349
3010471090.00654783715-43.0065478371469
3111551075.443304631779.5566953683037
328781102.38346982835-224.383469828351
338791026.40082981811-147.400829818109
341133976.486706474496156.513293525504
359201029.48656982389-109.48656982389
36943992.411295842038-49.411295842038
37938975.679222364089-37.679222364089
38900962.919963444764-62.9199634447643
39781941.61346998721-160.61346998721
401040887.225169992698152.774830007302
41792938.959083012007-146.959083012007
42653889.19454773105-236.19454773105
43866809.21234001156456.787659988436
44679828.442260688101-149.442260688101
45799777.83685065113621.1631493488638
46760785.003296377677-25.0032963776766
47699776.536467385382-77.5364673853819
48762750.28040898002711.7195910199727
49671754.248996622508-83.2489966225085
50679726.058512954435-47.0585129544346
51862710.123158839582151.876841160418
52624761.55298723386-137.55298723386
53516714.973624149231-198.973624149231
54650647.5954823153892.40451768461071
55583648.409720555701-65.4097205557008
56444626.260124357923-182.260124357923
57562564.541650051844-2.54165005184393
58540563.680974882372-23.6809748823717
59524555.6619216475-31.6619216474999
60683544.940292302812138.059707697188







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61591.69124538282360.632157432704822.750333332937
62591.69124538282347.743915760745835.638575004895
63591.69124538282335.503234080294847.879256685346
64591.69124538282323.821324263362859.561166502279
65591.69124538282312.628004976731870.754485788909
66591.69124538282301.866661105799881.515829659842
67591.69124538282291.490833729621891.891657036019
68591.69124538282281.461838875068901.920651890572
69591.69124538282271.747059363518911.635431402122
70591.69124538282262.318690859898921.063799905743
71591.69124538282253.152802693726930.229688071915
72591.69124538282244.228621948646939.153868816995

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 591.69124538282 & 360.632157432704 & 822.750333332937 \tabularnewline
62 & 591.69124538282 & 347.743915760745 & 835.638575004895 \tabularnewline
63 & 591.69124538282 & 335.503234080294 & 847.879256685346 \tabularnewline
64 & 591.69124538282 & 323.821324263362 & 859.561166502279 \tabularnewline
65 & 591.69124538282 & 312.628004976731 & 870.754485788909 \tabularnewline
66 & 591.69124538282 & 301.866661105799 & 881.515829659842 \tabularnewline
67 & 591.69124538282 & 291.490833729621 & 891.891657036019 \tabularnewline
68 & 591.69124538282 & 281.461838875068 & 901.920651890572 \tabularnewline
69 & 591.69124538282 & 271.747059363518 & 911.635431402122 \tabularnewline
70 & 591.69124538282 & 262.318690859898 & 921.063799905743 \tabularnewline
71 & 591.69124538282 & 253.152802693726 & 930.229688071915 \tabularnewline
72 & 591.69124538282 & 244.228621948646 & 939.153868816995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]61[/C][C]591.69124538282[/C][C]360.632157432704[/C][C]822.750333332937[/C][/ROW]
[ROW][C]62[/C][C]591.69124538282[/C][C]347.743915760745[/C][C]835.638575004895[/C][/ROW]
[ROW][C]63[/C][C]591.69124538282[/C][C]335.503234080294[/C][C]847.879256685346[/C][/ROW]
[ROW][C]64[/C][C]591.69124538282[/C][C]323.821324263362[/C][C]859.561166502279[/C][/ROW]
[ROW][C]65[/C][C]591.69124538282[/C][C]312.628004976731[/C][C]870.754485788909[/C][/ROW]
[ROW][C]66[/C][C]591.69124538282[/C][C]301.866661105799[/C][C]881.515829659842[/C][/ROW]
[ROW][C]67[/C][C]591.69124538282[/C][C]291.490833729621[/C][C]891.891657036019[/C][/ROW]
[ROW][C]68[/C][C]591.69124538282[/C][C]281.461838875068[/C][C]901.920651890572[/C][/ROW]
[ROW][C]69[/C][C]591.69124538282[/C][C]271.747059363518[/C][C]911.635431402122[/C][/ROW]
[ROW][C]70[/C][C]591.69124538282[/C][C]262.318690859898[/C][C]921.063799905743[/C][/ROW]
[ROW][C]71[/C][C]591.69124538282[/C][C]253.152802693726[/C][C]930.229688071915[/C][/ROW]
[ROW][C]72[/C][C]591.69124538282[/C][C]244.228621948646[/C][C]939.153868816995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61591.69124538282360.632157432704822.750333332937
62591.69124538282347.743915760745835.638575004895
63591.69124538282335.503234080294847.879256685346
64591.69124538282323.821324263362859.561166502279
65591.69124538282312.628004976731870.754485788909
66591.69124538282301.866661105799881.515829659842
67591.69124538282291.490833729621891.891657036019
68591.69124538282281.461838875068901.920651890572
69591.69124538282271.747059363518911.635431402122
70591.69124538282262.318690859898921.063799905743
71591.69124538282253.152802693726930.229688071915
72591.69124538282244.228621948646939.153868816995



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')