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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 computationThu, 26 Nov 2015 19:17:25 +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/2015/Nov/26/t1448565465vymkgp542rz2yvr.htm/, Retrieved Tue, 14 May 2024 12:40:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284270, Retrieved Tue, 14 May 2024 12:40:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Ruben Ruys opgave...] [2015-11-26 19:17:25] [bcb0da8ff6be95621a49a67fe6a7b572] [Current]
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Dataseries X:
2754542000
2899512000
2928886000
3011252000
2932895000
3069307000
2863923000
2585491000
2993900000
3023542000
2491370000
2341705000
2126472000
2196705000
2368313000
2285174000
2163877000
2299241000
2275643000
2163091000
2416149000
2434553000
2281937000
2440464000
2255745000
2389872000
2863148000
2623516000
2558136000
2898129000
2537720000
2543469000
2779739000
2884779000
2711624000
2817771000
2884477000
3058996000
3285298000
2879617000
3220416000
3144280000
2940811000
2986507000
3153720000
2995806000
2990242000
2879837000
2848699000
3138385000
3532447000
3121872000
3309250000
3215022000
2966778000
3010284000
3083824000
3257727000
3180374000
3036414000
2966714000
3067677000
3339789000
3299861000
3193328000
3181266000
3193356000
2898282000
2929524000
3217311000
3126249000
3131083000
3008058000
2868318000
3207495000
3109336000
3070725000
2989963000
3287552000
2835238000
3368961000
3291689000
3008536000
2974109000




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284270&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284270&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284270&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 Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.476294261929898
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.476294261929898 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284270&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]0.476294261929898[/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=284270&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284270&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
alpha0.476294261929898
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
228995120002754542000144970000
329288860002823590379.15198105295620.848022
430112520002873742079.16824137509920.831763
529328950002939237265.41884-6342265.41884041
630693070002936216480.79221133090519.207789
728639230002999606731.40815-135683731.408152
825854910002934981348.70121-349490348.701212
929939000002768521101.01495225378898.985054
1030235420002875867777.36161147674222.638394
1124913700002946204162.23923-454834162.239231
1223417050002729569260.63499-387864260.634993
1321264720002544831738.88686-418359738.886864
1421967050002345569395.83256-148864395.83256
1523683130002274666138.2918593646861.708149
1622851740002319269601.17119-34095601.1711855
1721638770002303030061.9763-139153061.9763
1822992410002236752257.0270162488742.9729872
1922756430002266515286.740269127713.25974083
2021630910002270862764.19042-107771764.190415
2124161490002219531691.30846196617308.691542
2224345530002313179387.23434121373612.765661
2322819370002370988942.54432-89051942.5443249
2424404640002328574013.29675111889986.703248
2522557450002381866571.93092-126121571.930922
2623898720002321795590.9146468076409.0853553
2728631480002354219993.93479508928006.065208
2826235160002596619482.9590726896517.040925
2925581360002609430139.69157-51294139.6915674
3028981290002584999035.28584313129964.714157
3125377200002734141040.71751-196421040.717508
3225434690002640586826.10146-97117826.1014605
3327797390002594330162.79823185408837.201771
3428847790002682639328.06853202139671.931473
3527116240002778917293.91788-67293293.9178801
3628177710002746865884.1584370905115.841568
3728844770002780637583.97525103839416.024755
3830589960002830095701.98999228900298.010013
3932852980002939119600.4862346178399.5138
4028796170003104002385.7787-224385385.778699
4132204160002997128914.07138223287085.928622
4231442800003103479271.8622340800728.1377707
4329408110003122912424.55681-182101424.556811
4429865070003036178560.95114-49671560.9511423
4531537200003012520281.48901141199718.510988
4629958060003079772897.20191-83966897.2019129
4729902420003039779945.87258-49537945.8725843
4828798370003016185306.50568-136348306.505679
4928486990002951243390.49317-102544390.493165
5031383850002902402085.70817235982914.291828
5135324470003014799393.69886517647606.301135
5231218720003261351978.28184-139479978.281843
5333092500003194918464.97209114331535.027905
5432150220003249373919.06352-34351919.0635233
5529667780003233012297.12729-266234297.127287
5630102840003106206429.07662-95922429.0766211
5730838240003060519126.5170523304873.4829512
5832577270003071619104.03198186107895.968019
5931803740003160261226.9813920112773.0186052
6030364140003169840825.36166-133426825.361655
6129667140003106290394.05438-139576394.054377
6230676770003039810958.4654127866041.5345888
6333397890003053083394.15104286705605.848964
6432998610003189639629.08003110221370.919967
6531933280003242137435.59126-48809435.59126
6631812660003218889781.49111-37623781.491106
6731933560003200969790.25479-7613790.2547884
6828982820003197343385.6449-299061385.644895
6929295240003054902163.69743-125378163.697427
7032173110002995185263.75704222125736.242965
7131262490003100982477.3565125266522.6434865
7231310830003113016777.1105318066222.889472
7330080580003121621615.40753-113563615.40753
7428683180003067531917.02491-199213917.02491
7532074950002972647471.44937234847528.550633
7631093360003084504001.7264524831998.2735486
7730707250003096331340.0164-25606340.0163956
7829899630003084135187.19756-94172187.1975603
7932875520003039281514.80197248270485.198026
8028352380003157531322.30835-322293322.308346
8133689610003004024862.23456364936137.765442
8232916890003177841850.6231113847149.376903
8330085360003232066594.60839-223530594.608392
8429741090003125600255.03064-151491255.030637

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2899512000 & 2754542000 & 144970000 \tabularnewline
3 & 2928886000 & 2823590379.15198 & 105295620.848022 \tabularnewline
4 & 3011252000 & 2873742079.16824 & 137509920.831763 \tabularnewline
5 & 2932895000 & 2939237265.41884 & -6342265.41884041 \tabularnewline
6 & 3069307000 & 2936216480.79221 & 133090519.207789 \tabularnewline
7 & 2863923000 & 2999606731.40815 & -135683731.408152 \tabularnewline
8 & 2585491000 & 2934981348.70121 & -349490348.701212 \tabularnewline
9 & 2993900000 & 2768521101.01495 & 225378898.985054 \tabularnewline
10 & 3023542000 & 2875867777.36161 & 147674222.638394 \tabularnewline
11 & 2491370000 & 2946204162.23923 & -454834162.239231 \tabularnewline
12 & 2341705000 & 2729569260.63499 & -387864260.634993 \tabularnewline
13 & 2126472000 & 2544831738.88686 & -418359738.886864 \tabularnewline
14 & 2196705000 & 2345569395.83256 & -148864395.83256 \tabularnewline
15 & 2368313000 & 2274666138.29185 & 93646861.708149 \tabularnewline
16 & 2285174000 & 2319269601.17119 & -34095601.1711855 \tabularnewline
17 & 2163877000 & 2303030061.9763 & -139153061.9763 \tabularnewline
18 & 2299241000 & 2236752257.02701 & 62488742.9729872 \tabularnewline
19 & 2275643000 & 2266515286.74026 & 9127713.25974083 \tabularnewline
20 & 2163091000 & 2270862764.19042 & -107771764.190415 \tabularnewline
21 & 2416149000 & 2219531691.30846 & 196617308.691542 \tabularnewline
22 & 2434553000 & 2313179387.23434 & 121373612.765661 \tabularnewline
23 & 2281937000 & 2370988942.54432 & -89051942.5443249 \tabularnewline
24 & 2440464000 & 2328574013.29675 & 111889986.703248 \tabularnewline
25 & 2255745000 & 2381866571.93092 & -126121571.930922 \tabularnewline
26 & 2389872000 & 2321795590.91464 & 68076409.0853553 \tabularnewline
27 & 2863148000 & 2354219993.93479 & 508928006.065208 \tabularnewline
28 & 2623516000 & 2596619482.95907 & 26896517.040925 \tabularnewline
29 & 2558136000 & 2609430139.69157 & -51294139.6915674 \tabularnewline
30 & 2898129000 & 2584999035.28584 & 313129964.714157 \tabularnewline
31 & 2537720000 & 2734141040.71751 & -196421040.717508 \tabularnewline
32 & 2543469000 & 2640586826.10146 & -97117826.1014605 \tabularnewline
33 & 2779739000 & 2594330162.79823 & 185408837.201771 \tabularnewline
34 & 2884779000 & 2682639328.06853 & 202139671.931473 \tabularnewline
35 & 2711624000 & 2778917293.91788 & -67293293.9178801 \tabularnewline
36 & 2817771000 & 2746865884.15843 & 70905115.841568 \tabularnewline
37 & 2884477000 & 2780637583.97525 & 103839416.024755 \tabularnewline
38 & 3058996000 & 2830095701.98999 & 228900298.010013 \tabularnewline
39 & 3285298000 & 2939119600.4862 & 346178399.5138 \tabularnewline
40 & 2879617000 & 3104002385.7787 & -224385385.778699 \tabularnewline
41 & 3220416000 & 2997128914.07138 & 223287085.928622 \tabularnewline
42 & 3144280000 & 3103479271.86223 & 40800728.1377707 \tabularnewline
43 & 2940811000 & 3122912424.55681 & -182101424.556811 \tabularnewline
44 & 2986507000 & 3036178560.95114 & -49671560.9511423 \tabularnewline
45 & 3153720000 & 3012520281.48901 & 141199718.510988 \tabularnewline
46 & 2995806000 & 3079772897.20191 & -83966897.2019129 \tabularnewline
47 & 2990242000 & 3039779945.87258 & -49537945.8725843 \tabularnewline
48 & 2879837000 & 3016185306.50568 & -136348306.505679 \tabularnewline
49 & 2848699000 & 2951243390.49317 & -102544390.493165 \tabularnewline
50 & 3138385000 & 2902402085.70817 & 235982914.291828 \tabularnewline
51 & 3532447000 & 3014799393.69886 & 517647606.301135 \tabularnewline
52 & 3121872000 & 3261351978.28184 & -139479978.281843 \tabularnewline
53 & 3309250000 & 3194918464.97209 & 114331535.027905 \tabularnewline
54 & 3215022000 & 3249373919.06352 & -34351919.0635233 \tabularnewline
55 & 2966778000 & 3233012297.12729 & -266234297.127287 \tabularnewline
56 & 3010284000 & 3106206429.07662 & -95922429.0766211 \tabularnewline
57 & 3083824000 & 3060519126.51705 & 23304873.4829512 \tabularnewline
58 & 3257727000 & 3071619104.03198 & 186107895.968019 \tabularnewline
59 & 3180374000 & 3160261226.98139 & 20112773.0186052 \tabularnewline
60 & 3036414000 & 3169840825.36166 & -133426825.361655 \tabularnewline
61 & 2966714000 & 3106290394.05438 & -139576394.054377 \tabularnewline
62 & 3067677000 & 3039810958.46541 & 27866041.5345888 \tabularnewline
63 & 3339789000 & 3053083394.15104 & 286705605.848964 \tabularnewline
64 & 3299861000 & 3189639629.08003 & 110221370.919967 \tabularnewline
65 & 3193328000 & 3242137435.59126 & -48809435.59126 \tabularnewline
66 & 3181266000 & 3218889781.49111 & -37623781.491106 \tabularnewline
67 & 3193356000 & 3200969790.25479 & -7613790.2547884 \tabularnewline
68 & 2898282000 & 3197343385.6449 & -299061385.644895 \tabularnewline
69 & 2929524000 & 3054902163.69743 & -125378163.697427 \tabularnewline
70 & 3217311000 & 2995185263.75704 & 222125736.242965 \tabularnewline
71 & 3126249000 & 3100982477.35651 & 25266522.6434865 \tabularnewline
72 & 3131083000 & 3113016777.11053 & 18066222.889472 \tabularnewline
73 & 3008058000 & 3121621615.40753 & -113563615.40753 \tabularnewline
74 & 2868318000 & 3067531917.02491 & -199213917.02491 \tabularnewline
75 & 3207495000 & 2972647471.44937 & 234847528.550633 \tabularnewline
76 & 3109336000 & 3084504001.72645 & 24831998.2735486 \tabularnewline
77 & 3070725000 & 3096331340.0164 & -25606340.0163956 \tabularnewline
78 & 2989963000 & 3084135187.19756 & -94172187.1975603 \tabularnewline
79 & 3287552000 & 3039281514.80197 & 248270485.198026 \tabularnewline
80 & 2835238000 & 3157531322.30835 & -322293322.308346 \tabularnewline
81 & 3368961000 & 3004024862.23456 & 364936137.765442 \tabularnewline
82 & 3291689000 & 3177841850.6231 & 113847149.376903 \tabularnewline
83 & 3008536000 & 3232066594.60839 & -223530594.608392 \tabularnewline
84 & 2974109000 & 3125600255.03064 & -151491255.030637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284270&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]2899512000[/C][C]2754542000[/C][C]144970000[/C][/ROW]
[ROW][C]3[/C][C]2928886000[/C][C]2823590379.15198[/C][C]105295620.848022[/C][/ROW]
[ROW][C]4[/C][C]3011252000[/C][C]2873742079.16824[/C][C]137509920.831763[/C][/ROW]
[ROW][C]5[/C][C]2932895000[/C][C]2939237265.41884[/C][C]-6342265.41884041[/C][/ROW]
[ROW][C]6[/C][C]3069307000[/C][C]2936216480.79221[/C][C]133090519.207789[/C][/ROW]
[ROW][C]7[/C][C]2863923000[/C][C]2999606731.40815[/C][C]-135683731.408152[/C][/ROW]
[ROW][C]8[/C][C]2585491000[/C][C]2934981348.70121[/C][C]-349490348.701212[/C][/ROW]
[ROW][C]9[/C][C]2993900000[/C][C]2768521101.01495[/C][C]225378898.985054[/C][/ROW]
[ROW][C]10[/C][C]3023542000[/C][C]2875867777.36161[/C][C]147674222.638394[/C][/ROW]
[ROW][C]11[/C][C]2491370000[/C][C]2946204162.23923[/C][C]-454834162.239231[/C][/ROW]
[ROW][C]12[/C][C]2341705000[/C][C]2729569260.63499[/C][C]-387864260.634993[/C][/ROW]
[ROW][C]13[/C][C]2126472000[/C][C]2544831738.88686[/C][C]-418359738.886864[/C][/ROW]
[ROW][C]14[/C][C]2196705000[/C][C]2345569395.83256[/C][C]-148864395.83256[/C][/ROW]
[ROW][C]15[/C][C]2368313000[/C][C]2274666138.29185[/C][C]93646861.708149[/C][/ROW]
[ROW][C]16[/C][C]2285174000[/C][C]2319269601.17119[/C][C]-34095601.1711855[/C][/ROW]
[ROW][C]17[/C][C]2163877000[/C][C]2303030061.9763[/C][C]-139153061.9763[/C][/ROW]
[ROW][C]18[/C][C]2299241000[/C][C]2236752257.02701[/C][C]62488742.9729872[/C][/ROW]
[ROW][C]19[/C][C]2275643000[/C][C]2266515286.74026[/C][C]9127713.25974083[/C][/ROW]
[ROW][C]20[/C][C]2163091000[/C][C]2270862764.19042[/C][C]-107771764.190415[/C][/ROW]
[ROW][C]21[/C][C]2416149000[/C][C]2219531691.30846[/C][C]196617308.691542[/C][/ROW]
[ROW][C]22[/C][C]2434553000[/C][C]2313179387.23434[/C][C]121373612.765661[/C][/ROW]
[ROW][C]23[/C][C]2281937000[/C][C]2370988942.54432[/C][C]-89051942.5443249[/C][/ROW]
[ROW][C]24[/C][C]2440464000[/C][C]2328574013.29675[/C][C]111889986.703248[/C][/ROW]
[ROW][C]25[/C][C]2255745000[/C][C]2381866571.93092[/C][C]-126121571.930922[/C][/ROW]
[ROW][C]26[/C][C]2389872000[/C][C]2321795590.91464[/C][C]68076409.0853553[/C][/ROW]
[ROW][C]27[/C][C]2863148000[/C][C]2354219993.93479[/C][C]508928006.065208[/C][/ROW]
[ROW][C]28[/C][C]2623516000[/C][C]2596619482.95907[/C][C]26896517.040925[/C][/ROW]
[ROW][C]29[/C][C]2558136000[/C][C]2609430139.69157[/C][C]-51294139.6915674[/C][/ROW]
[ROW][C]30[/C][C]2898129000[/C][C]2584999035.28584[/C][C]313129964.714157[/C][/ROW]
[ROW][C]31[/C][C]2537720000[/C][C]2734141040.71751[/C][C]-196421040.717508[/C][/ROW]
[ROW][C]32[/C][C]2543469000[/C][C]2640586826.10146[/C][C]-97117826.1014605[/C][/ROW]
[ROW][C]33[/C][C]2779739000[/C][C]2594330162.79823[/C][C]185408837.201771[/C][/ROW]
[ROW][C]34[/C][C]2884779000[/C][C]2682639328.06853[/C][C]202139671.931473[/C][/ROW]
[ROW][C]35[/C][C]2711624000[/C][C]2778917293.91788[/C][C]-67293293.9178801[/C][/ROW]
[ROW][C]36[/C][C]2817771000[/C][C]2746865884.15843[/C][C]70905115.841568[/C][/ROW]
[ROW][C]37[/C][C]2884477000[/C][C]2780637583.97525[/C][C]103839416.024755[/C][/ROW]
[ROW][C]38[/C][C]3058996000[/C][C]2830095701.98999[/C][C]228900298.010013[/C][/ROW]
[ROW][C]39[/C][C]3285298000[/C][C]2939119600.4862[/C][C]346178399.5138[/C][/ROW]
[ROW][C]40[/C][C]2879617000[/C][C]3104002385.7787[/C][C]-224385385.778699[/C][/ROW]
[ROW][C]41[/C][C]3220416000[/C][C]2997128914.07138[/C][C]223287085.928622[/C][/ROW]
[ROW][C]42[/C][C]3144280000[/C][C]3103479271.86223[/C][C]40800728.1377707[/C][/ROW]
[ROW][C]43[/C][C]2940811000[/C][C]3122912424.55681[/C][C]-182101424.556811[/C][/ROW]
[ROW][C]44[/C][C]2986507000[/C][C]3036178560.95114[/C][C]-49671560.9511423[/C][/ROW]
[ROW][C]45[/C][C]3153720000[/C][C]3012520281.48901[/C][C]141199718.510988[/C][/ROW]
[ROW][C]46[/C][C]2995806000[/C][C]3079772897.20191[/C][C]-83966897.2019129[/C][/ROW]
[ROW][C]47[/C][C]2990242000[/C][C]3039779945.87258[/C][C]-49537945.8725843[/C][/ROW]
[ROW][C]48[/C][C]2879837000[/C][C]3016185306.50568[/C][C]-136348306.505679[/C][/ROW]
[ROW][C]49[/C][C]2848699000[/C][C]2951243390.49317[/C][C]-102544390.493165[/C][/ROW]
[ROW][C]50[/C][C]3138385000[/C][C]2902402085.70817[/C][C]235982914.291828[/C][/ROW]
[ROW][C]51[/C][C]3532447000[/C][C]3014799393.69886[/C][C]517647606.301135[/C][/ROW]
[ROW][C]52[/C][C]3121872000[/C][C]3261351978.28184[/C][C]-139479978.281843[/C][/ROW]
[ROW][C]53[/C][C]3309250000[/C][C]3194918464.97209[/C][C]114331535.027905[/C][/ROW]
[ROW][C]54[/C][C]3215022000[/C][C]3249373919.06352[/C][C]-34351919.0635233[/C][/ROW]
[ROW][C]55[/C][C]2966778000[/C][C]3233012297.12729[/C][C]-266234297.127287[/C][/ROW]
[ROW][C]56[/C][C]3010284000[/C][C]3106206429.07662[/C][C]-95922429.0766211[/C][/ROW]
[ROW][C]57[/C][C]3083824000[/C][C]3060519126.51705[/C][C]23304873.4829512[/C][/ROW]
[ROW][C]58[/C][C]3257727000[/C][C]3071619104.03198[/C][C]186107895.968019[/C][/ROW]
[ROW][C]59[/C][C]3180374000[/C][C]3160261226.98139[/C][C]20112773.0186052[/C][/ROW]
[ROW][C]60[/C][C]3036414000[/C][C]3169840825.36166[/C][C]-133426825.361655[/C][/ROW]
[ROW][C]61[/C][C]2966714000[/C][C]3106290394.05438[/C][C]-139576394.054377[/C][/ROW]
[ROW][C]62[/C][C]3067677000[/C][C]3039810958.46541[/C][C]27866041.5345888[/C][/ROW]
[ROW][C]63[/C][C]3339789000[/C][C]3053083394.15104[/C][C]286705605.848964[/C][/ROW]
[ROW][C]64[/C][C]3299861000[/C][C]3189639629.08003[/C][C]110221370.919967[/C][/ROW]
[ROW][C]65[/C][C]3193328000[/C][C]3242137435.59126[/C][C]-48809435.59126[/C][/ROW]
[ROW][C]66[/C][C]3181266000[/C][C]3218889781.49111[/C][C]-37623781.491106[/C][/ROW]
[ROW][C]67[/C][C]3193356000[/C][C]3200969790.25479[/C][C]-7613790.2547884[/C][/ROW]
[ROW][C]68[/C][C]2898282000[/C][C]3197343385.6449[/C][C]-299061385.644895[/C][/ROW]
[ROW][C]69[/C][C]2929524000[/C][C]3054902163.69743[/C][C]-125378163.697427[/C][/ROW]
[ROW][C]70[/C][C]3217311000[/C][C]2995185263.75704[/C][C]222125736.242965[/C][/ROW]
[ROW][C]71[/C][C]3126249000[/C][C]3100982477.35651[/C][C]25266522.6434865[/C][/ROW]
[ROW][C]72[/C][C]3131083000[/C][C]3113016777.11053[/C][C]18066222.889472[/C][/ROW]
[ROW][C]73[/C][C]3008058000[/C][C]3121621615.40753[/C][C]-113563615.40753[/C][/ROW]
[ROW][C]74[/C][C]2868318000[/C][C]3067531917.02491[/C][C]-199213917.02491[/C][/ROW]
[ROW][C]75[/C][C]3207495000[/C][C]2972647471.44937[/C][C]234847528.550633[/C][/ROW]
[ROW][C]76[/C][C]3109336000[/C][C]3084504001.72645[/C][C]24831998.2735486[/C][/ROW]
[ROW][C]77[/C][C]3070725000[/C][C]3096331340.0164[/C][C]-25606340.0163956[/C][/ROW]
[ROW][C]78[/C][C]2989963000[/C][C]3084135187.19756[/C][C]-94172187.1975603[/C][/ROW]
[ROW][C]79[/C][C]3287552000[/C][C]3039281514.80197[/C][C]248270485.198026[/C][/ROW]
[ROW][C]80[/C][C]2835238000[/C][C]3157531322.30835[/C][C]-322293322.308346[/C][/ROW]
[ROW][C]81[/C][C]3368961000[/C][C]3004024862.23456[/C][C]364936137.765442[/C][/ROW]
[ROW][C]82[/C][C]3291689000[/C][C]3177841850.6231[/C][C]113847149.376903[/C][/ROW]
[ROW][C]83[/C][C]3008536000[/C][C]3232066594.60839[/C][C]-223530594.608392[/C][/ROW]
[ROW][C]84[/C][C]2974109000[/C][C]3125600255.03064[/C][C]-151491255.030637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284270&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284270&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
228995120002754542000144970000
329288860002823590379.15198105295620.848022
430112520002873742079.16824137509920.831763
529328950002939237265.41884-6342265.41884041
630693070002936216480.79221133090519.207789
728639230002999606731.40815-135683731.408152
825854910002934981348.70121-349490348.701212
929939000002768521101.01495225378898.985054
1030235420002875867777.36161147674222.638394
1124913700002946204162.23923-454834162.239231
1223417050002729569260.63499-387864260.634993
1321264720002544831738.88686-418359738.886864
1421967050002345569395.83256-148864395.83256
1523683130002274666138.2918593646861.708149
1622851740002319269601.17119-34095601.1711855
1721638770002303030061.9763-139153061.9763
1822992410002236752257.0270162488742.9729872
1922756430002266515286.740269127713.25974083
2021630910002270862764.19042-107771764.190415
2124161490002219531691.30846196617308.691542
2224345530002313179387.23434121373612.765661
2322819370002370988942.54432-89051942.5443249
2424404640002328574013.29675111889986.703248
2522557450002381866571.93092-126121571.930922
2623898720002321795590.9146468076409.0853553
2728631480002354219993.93479508928006.065208
2826235160002596619482.9590726896517.040925
2925581360002609430139.69157-51294139.6915674
3028981290002584999035.28584313129964.714157
3125377200002734141040.71751-196421040.717508
3225434690002640586826.10146-97117826.1014605
3327797390002594330162.79823185408837.201771
3428847790002682639328.06853202139671.931473
3527116240002778917293.91788-67293293.9178801
3628177710002746865884.1584370905115.841568
3728844770002780637583.97525103839416.024755
3830589960002830095701.98999228900298.010013
3932852980002939119600.4862346178399.5138
4028796170003104002385.7787-224385385.778699
4132204160002997128914.07138223287085.928622
4231442800003103479271.8622340800728.1377707
4329408110003122912424.55681-182101424.556811
4429865070003036178560.95114-49671560.9511423
4531537200003012520281.48901141199718.510988
4629958060003079772897.20191-83966897.2019129
4729902420003039779945.87258-49537945.8725843
4828798370003016185306.50568-136348306.505679
4928486990002951243390.49317-102544390.493165
5031383850002902402085.70817235982914.291828
5135324470003014799393.69886517647606.301135
5231218720003261351978.28184-139479978.281843
5333092500003194918464.97209114331535.027905
5432150220003249373919.06352-34351919.0635233
5529667780003233012297.12729-266234297.127287
5630102840003106206429.07662-95922429.0766211
5730838240003060519126.5170523304873.4829512
5832577270003071619104.03198186107895.968019
5931803740003160261226.9813920112773.0186052
6030364140003169840825.36166-133426825.361655
6129667140003106290394.05438-139576394.054377
6230676770003039810958.4654127866041.5345888
6333397890003053083394.15104286705605.848964
6432998610003189639629.08003110221370.919967
6531933280003242137435.59126-48809435.59126
6631812660003218889781.49111-37623781.491106
6731933560003200969790.25479-7613790.2547884
6828982820003197343385.6449-299061385.644895
6929295240003054902163.69743-125378163.697427
7032173110002995185263.75704222125736.242965
7131262490003100982477.3565125266522.6434865
7231310830003113016777.1105318066222.889472
7330080580003121621615.40753-113563615.40753
7428683180003067531917.02491-199213917.02491
7532074950002972647471.44937234847528.550633
7631093360003084504001.7264524831998.2735486
7730707250003096331340.0164-25606340.0163956
7829899630003084135187.19756-94172187.1975603
7932875520003039281514.80197248270485.198026
8028352380003157531322.30835-322293322.308346
8133689610003004024862.23456364936137.765442
8232916890003177841850.6231113847149.376903
8330085360003232066594.60839-223530594.608392
8429741090003125600255.03064-151491255.030637







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
853053445839.526992671720285.317523435171393.73645
863053445839.526992630633094.912243476258584.14173
873053445839.526992593199345.481923513692333.57206
883053445839.526992558589240.548153548302438.50583
893053445839.526992526246378.38823580645300.66578
903053445839.526992495776143.293493611115535.76048
913053445839.526992466886628.219823640005050.83415
923053445839.526992439354700.817583667536978.23639
933053445839.526992413005252.966813693886426.08716
943053445839.526992387697866.803333719193812.25065
953053445839.526992363317893.811273743573785.2427
963053445839.526992339770283.178083767121395.87589

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 3053445839.52699 & 2671720285.31752 & 3435171393.73645 \tabularnewline
86 & 3053445839.52699 & 2630633094.91224 & 3476258584.14173 \tabularnewline
87 & 3053445839.52699 & 2593199345.48192 & 3513692333.57206 \tabularnewline
88 & 3053445839.52699 & 2558589240.54815 & 3548302438.50583 \tabularnewline
89 & 3053445839.52699 & 2526246378.3882 & 3580645300.66578 \tabularnewline
90 & 3053445839.52699 & 2495776143.29349 & 3611115535.76048 \tabularnewline
91 & 3053445839.52699 & 2466886628.21982 & 3640005050.83415 \tabularnewline
92 & 3053445839.52699 & 2439354700.81758 & 3667536978.23639 \tabularnewline
93 & 3053445839.52699 & 2413005252.96681 & 3693886426.08716 \tabularnewline
94 & 3053445839.52699 & 2387697866.80333 & 3719193812.25065 \tabularnewline
95 & 3053445839.52699 & 2363317893.81127 & 3743573785.2427 \tabularnewline
96 & 3053445839.52699 & 2339770283.17808 & 3767121395.87589 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284270&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]3053445839.52699[/C][C]2671720285.31752[/C][C]3435171393.73645[/C][/ROW]
[ROW][C]86[/C][C]3053445839.52699[/C][C]2630633094.91224[/C][C]3476258584.14173[/C][/ROW]
[ROW][C]87[/C][C]3053445839.52699[/C][C]2593199345.48192[/C][C]3513692333.57206[/C][/ROW]
[ROW][C]88[/C][C]3053445839.52699[/C][C]2558589240.54815[/C][C]3548302438.50583[/C][/ROW]
[ROW][C]89[/C][C]3053445839.52699[/C][C]2526246378.3882[/C][C]3580645300.66578[/C][/ROW]
[ROW][C]90[/C][C]3053445839.52699[/C][C]2495776143.29349[/C][C]3611115535.76048[/C][/ROW]
[ROW][C]91[/C][C]3053445839.52699[/C][C]2466886628.21982[/C][C]3640005050.83415[/C][/ROW]
[ROW][C]92[/C][C]3053445839.52699[/C][C]2439354700.81758[/C][C]3667536978.23639[/C][/ROW]
[ROW][C]93[/C][C]3053445839.52699[/C][C]2413005252.96681[/C][C]3693886426.08716[/C][/ROW]
[ROW][C]94[/C][C]3053445839.52699[/C][C]2387697866.80333[/C][C]3719193812.25065[/C][/ROW]
[ROW][C]95[/C][C]3053445839.52699[/C][C]2363317893.81127[/C][C]3743573785.2427[/C][/ROW]
[ROW][C]96[/C][C]3053445839.52699[/C][C]2339770283.17808[/C][C]3767121395.87589[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284270&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284270&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
853053445839.526992671720285.317523435171393.73645
863053445839.526992630633094.912243476258584.14173
873053445839.526992593199345.481923513692333.57206
883053445839.526992558589240.548153548302438.50583
893053445839.526992526246378.38823580645300.66578
903053445839.526992495776143.293493611115535.76048
913053445839.526992466886628.219823640005050.83415
923053445839.526992439354700.817583667536978.23639
933053445839.526992413005252.966813693886426.08716
943053445839.526992387697866.803333719193812.25065
953053445839.526992363317893.811273743573785.2427
963053445839.526992339770283.178083767121395.87589



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
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')