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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 computationMon, 23 May 2016 22:21:33 +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/23/t1464038526v4hkt1o959yynlq.htm/, Retrieved Tue, 07 May 2024 12:46:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295533, Retrieved Tue, 07 May 2024 12:46:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Verhuur en handel...] [2016-05-23 21:21:33] [38f93cf143127a30e50d4675c70fea9c] [Current]
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Dataseries X:
16,8
17,2
17,4
17,6
17,7
17,7
17,6
17,6
17,5
17,5
17,6
17,6
17,9
18,2
18,4
18,5
19
19,5
19,7
19,9
19,7
19,5
19,7
19,7
19,7
19,9
20,1
20,1
20,1
20,1
20,2
20,3
20,8
21,1
21,2
21,3
21,6
21,7
21,8
22
21,9
21,9
22
22,1
21
19,7
19,8
19,9
19,8
20
20,2
20,3
20,7
20,9
21
21,2
23,7
23,7
23,7
23,8
24
24
24,1
24,3
24,4
24,4
24,5
24,6
24,7
24,6
24,6
24,6
24,7
24,7
24,8
24,9
25
25,1
25,2
25,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295533&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]2 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=295533&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295533&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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.166695979301405
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.166695979301405 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295533&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.166695979301405[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295533&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295533&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
alpha1
beta0.166695979301405
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
317.417.6-0.199999999999999
417.617.7666608041397-0.166660804139713
517.717.9388791181825-0.238879118182492
617.717.9990589296424-0.299058929642403
717.617.9492070084968-0.34920700849683
817.617.7909956042365-0.190995604236537
917.517.7591574049461-0.259157404946066
1017.517.6159569075354-0.11595690753537
1117.617.5966273572770.0033726427230043
1217.617.6971895632585-0.0971895632585422
1317.917.68098845383330.219011546166712
1418.218.01749679799990.182503202000142
1518.418.34791934798290.0520806520170822
1618.518.5566009832736-0.0566009832735581
171918.64716582693730.35283417306265
1819.519.2059818649470.294018135052969
1919.719.7549935059021-0.0549935059020576
2019.919.9458263095805-0.045826309580498
2119.720.1381872480272-0.438187248027205
2219.519.8651431955999-0.365143195599924
2319.719.60427529302410.0957247069758509
2419.719.8202322167968-0.120232216796829
2519.719.8001899896743-0.100189989674302
2619.919.78348872122930.116511278770652
2720.120.00291068294370.097089317056323
2820.120.2190950817301-0.119095081730087
2920.120.1992424104511-0.0992424104511116
3020.120.1826990996527-0.0826990996527321
3120.220.16891349224880.0310865077512226
3220.320.27409548810140.0259045118985775
3320.820.37841366608070.421586333919318
3421.120.94869041287350.151309587126548
3521.221.2739131126772-0.0739131126772072
3621.321.3615920939763-0.0615920939762624
3721.621.45132493955370.148675060446337
3821.721.7761084743525-0.0761084743524663
3921.821.8634214976871-0.0634214976871412
402221.95284938902140.0471506109785764
4121.922.1607092062932-0.260709206293157
4221.922.0172500298372-0.117250029837226
432221.99770492129040.00229507870961143
4422.122.09808750168350.00191249831653906
452122.1984063074633-1.19840630746325
4619.720.8986367944397-1.19863679443968
4719.819.39882886016390.401171139836141
4819.919.56570247618630.334297523813689
4919.819.72142852929650.0785714707035368
502019.63452607755050.365473922449457
5120.219.89544911096240.304550889037618
5220.320.14621651965760.15378348034238
5320.720.27185160751370.428148392486325
5420.920.74322222308550.156777776914495
552120.9693564481410.0306435518590398
5621.221.07446460502740.125535394972619
5723.721.29539085062932.40460914937067
5823.724.1962295276208-0.496229527620791
5923.724.1135100605558-0.413510060555769
6023.824.0445795960604-0.24457959606044
612424.103809160778-0.103809160778006
622424.2865045910617-0.286504591061657
6324.124.2387454276803-0.138745427680284
6424.324.3156171227395-0.0156171227395312
6524.424.5130138111706-0.113013811170596
6624.424.5941748632429-0.194174863242928
6724.524.5618066942589-0.0618066942589302
6824.624.6515037668321-0.0515037668320559
6924.724.7429182959823-0.0429182959822789
7024.624.8357639886036-0.235763988603559
7124.624.6964630796393-0.0964630796392854
7224.624.6803830721124-0.0803830721123866
7324.724.66698353718740.0330164628126433
7424.724.772487248789-0.0724872487889776
7524.824.76040391586520.039596084134768
7624.924.86700442388660.032995576113418
772524.97250465375940.0274953462405811
7825.125.07708801742720.0229119825727757
7925.225.18090735279990.0190926472000683
8025.325.28409002032240.0159099796775983

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 17.4 & 17.6 & -0.199999999999999 \tabularnewline
4 & 17.6 & 17.7666608041397 & -0.166660804139713 \tabularnewline
5 & 17.7 & 17.9388791181825 & -0.238879118182492 \tabularnewline
6 & 17.7 & 17.9990589296424 & -0.299058929642403 \tabularnewline
7 & 17.6 & 17.9492070084968 & -0.34920700849683 \tabularnewline
8 & 17.6 & 17.7909956042365 & -0.190995604236537 \tabularnewline
9 & 17.5 & 17.7591574049461 & -0.259157404946066 \tabularnewline
10 & 17.5 & 17.6159569075354 & -0.11595690753537 \tabularnewline
11 & 17.6 & 17.596627357277 & 0.0033726427230043 \tabularnewline
12 & 17.6 & 17.6971895632585 & -0.0971895632585422 \tabularnewline
13 & 17.9 & 17.6809884538333 & 0.219011546166712 \tabularnewline
14 & 18.2 & 18.0174967979999 & 0.182503202000142 \tabularnewline
15 & 18.4 & 18.3479193479829 & 0.0520806520170822 \tabularnewline
16 & 18.5 & 18.5566009832736 & -0.0566009832735581 \tabularnewline
17 & 19 & 18.6471658269373 & 0.35283417306265 \tabularnewline
18 & 19.5 & 19.205981864947 & 0.294018135052969 \tabularnewline
19 & 19.7 & 19.7549935059021 & -0.0549935059020576 \tabularnewline
20 & 19.9 & 19.9458263095805 & -0.045826309580498 \tabularnewline
21 & 19.7 & 20.1381872480272 & -0.438187248027205 \tabularnewline
22 & 19.5 & 19.8651431955999 & -0.365143195599924 \tabularnewline
23 & 19.7 & 19.6042752930241 & 0.0957247069758509 \tabularnewline
24 & 19.7 & 19.8202322167968 & -0.120232216796829 \tabularnewline
25 & 19.7 & 19.8001899896743 & -0.100189989674302 \tabularnewline
26 & 19.9 & 19.7834887212293 & 0.116511278770652 \tabularnewline
27 & 20.1 & 20.0029106829437 & 0.097089317056323 \tabularnewline
28 & 20.1 & 20.2190950817301 & -0.119095081730087 \tabularnewline
29 & 20.1 & 20.1992424104511 & -0.0992424104511116 \tabularnewline
30 & 20.1 & 20.1826990996527 & -0.0826990996527321 \tabularnewline
31 & 20.2 & 20.1689134922488 & 0.0310865077512226 \tabularnewline
32 & 20.3 & 20.2740954881014 & 0.0259045118985775 \tabularnewline
33 & 20.8 & 20.3784136660807 & 0.421586333919318 \tabularnewline
34 & 21.1 & 20.9486904128735 & 0.151309587126548 \tabularnewline
35 & 21.2 & 21.2739131126772 & -0.0739131126772072 \tabularnewline
36 & 21.3 & 21.3615920939763 & -0.0615920939762624 \tabularnewline
37 & 21.6 & 21.4513249395537 & 0.148675060446337 \tabularnewline
38 & 21.7 & 21.7761084743525 & -0.0761084743524663 \tabularnewline
39 & 21.8 & 21.8634214976871 & -0.0634214976871412 \tabularnewline
40 & 22 & 21.9528493890214 & 0.0471506109785764 \tabularnewline
41 & 21.9 & 22.1607092062932 & -0.260709206293157 \tabularnewline
42 & 21.9 & 22.0172500298372 & -0.117250029837226 \tabularnewline
43 & 22 & 21.9977049212904 & 0.00229507870961143 \tabularnewline
44 & 22.1 & 22.0980875016835 & 0.00191249831653906 \tabularnewline
45 & 21 & 22.1984063074633 & -1.19840630746325 \tabularnewline
46 & 19.7 & 20.8986367944397 & -1.19863679443968 \tabularnewline
47 & 19.8 & 19.3988288601639 & 0.401171139836141 \tabularnewline
48 & 19.9 & 19.5657024761863 & 0.334297523813689 \tabularnewline
49 & 19.8 & 19.7214285292965 & 0.0785714707035368 \tabularnewline
50 & 20 & 19.6345260775505 & 0.365473922449457 \tabularnewline
51 & 20.2 & 19.8954491109624 & 0.304550889037618 \tabularnewline
52 & 20.3 & 20.1462165196576 & 0.15378348034238 \tabularnewline
53 & 20.7 & 20.2718516075137 & 0.428148392486325 \tabularnewline
54 & 20.9 & 20.7432222230855 & 0.156777776914495 \tabularnewline
55 & 21 & 20.969356448141 & 0.0306435518590398 \tabularnewline
56 & 21.2 & 21.0744646050274 & 0.125535394972619 \tabularnewline
57 & 23.7 & 21.2953908506293 & 2.40460914937067 \tabularnewline
58 & 23.7 & 24.1962295276208 & -0.496229527620791 \tabularnewline
59 & 23.7 & 24.1135100605558 & -0.413510060555769 \tabularnewline
60 & 23.8 & 24.0445795960604 & -0.24457959606044 \tabularnewline
61 & 24 & 24.103809160778 & -0.103809160778006 \tabularnewline
62 & 24 & 24.2865045910617 & -0.286504591061657 \tabularnewline
63 & 24.1 & 24.2387454276803 & -0.138745427680284 \tabularnewline
64 & 24.3 & 24.3156171227395 & -0.0156171227395312 \tabularnewline
65 & 24.4 & 24.5130138111706 & -0.113013811170596 \tabularnewline
66 & 24.4 & 24.5941748632429 & -0.194174863242928 \tabularnewline
67 & 24.5 & 24.5618066942589 & -0.0618066942589302 \tabularnewline
68 & 24.6 & 24.6515037668321 & -0.0515037668320559 \tabularnewline
69 & 24.7 & 24.7429182959823 & -0.0429182959822789 \tabularnewline
70 & 24.6 & 24.8357639886036 & -0.235763988603559 \tabularnewline
71 & 24.6 & 24.6964630796393 & -0.0964630796392854 \tabularnewline
72 & 24.6 & 24.6803830721124 & -0.0803830721123866 \tabularnewline
73 & 24.7 & 24.6669835371874 & 0.0330164628126433 \tabularnewline
74 & 24.7 & 24.772487248789 & -0.0724872487889776 \tabularnewline
75 & 24.8 & 24.7604039158652 & 0.039596084134768 \tabularnewline
76 & 24.9 & 24.8670044238866 & 0.032995576113418 \tabularnewline
77 & 25 & 24.9725046537594 & 0.0274953462405811 \tabularnewline
78 & 25.1 & 25.0770880174272 & 0.0229119825727757 \tabularnewline
79 & 25.2 & 25.1809073527999 & 0.0190926472000683 \tabularnewline
80 & 25.3 & 25.2840900203224 & 0.0159099796775983 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295533&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]17.4[/C][C]17.6[/C][C]-0.199999999999999[/C][/ROW]
[ROW][C]4[/C][C]17.6[/C][C]17.7666608041397[/C][C]-0.166660804139713[/C][/ROW]
[ROW][C]5[/C][C]17.7[/C][C]17.9388791181825[/C][C]-0.238879118182492[/C][/ROW]
[ROW][C]6[/C][C]17.7[/C][C]17.9990589296424[/C][C]-0.299058929642403[/C][/ROW]
[ROW][C]7[/C][C]17.6[/C][C]17.9492070084968[/C][C]-0.34920700849683[/C][/ROW]
[ROW][C]8[/C][C]17.6[/C][C]17.7909956042365[/C][C]-0.190995604236537[/C][/ROW]
[ROW][C]9[/C][C]17.5[/C][C]17.7591574049461[/C][C]-0.259157404946066[/C][/ROW]
[ROW][C]10[/C][C]17.5[/C][C]17.6159569075354[/C][C]-0.11595690753537[/C][/ROW]
[ROW][C]11[/C][C]17.6[/C][C]17.596627357277[/C][C]0.0033726427230043[/C][/ROW]
[ROW][C]12[/C][C]17.6[/C][C]17.6971895632585[/C][C]-0.0971895632585422[/C][/ROW]
[ROW][C]13[/C][C]17.9[/C][C]17.6809884538333[/C][C]0.219011546166712[/C][/ROW]
[ROW][C]14[/C][C]18.2[/C][C]18.0174967979999[/C][C]0.182503202000142[/C][/ROW]
[ROW][C]15[/C][C]18.4[/C][C]18.3479193479829[/C][C]0.0520806520170822[/C][/ROW]
[ROW][C]16[/C][C]18.5[/C][C]18.5566009832736[/C][C]-0.0566009832735581[/C][/ROW]
[ROW][C]17[/C][C]19[/C][C]18.6471658269373[/C][C]0.35283417306265[/C][/ROW]
[ROW][C]18[/C][C]19.5[/C][C]19.205981864947[/C][C]0.294018135052969[/C][/ROW]
[ROW][C]19[/C][C]19.7[/C][C]19.7549935059021[/C][C]-0.0549935059020576[/C][/ROW]
[ROW][C]20[/C][C]19.9[/C][C]19.9458263095805[/C][C]-0.045826309580498[/C][/ROW]
[ROW][C]21[/C][C]19.7[/C][C]20.1381872480272[/C][C]-0.438187248027205[/C][/ROW]
[ROW][C]22[/C][C]19.5[/C][C]19.8651431955999[/C][C]-0.365143195599924[/C][/ROW]
[ROW][C]23[/C][C]19.7[/C][C]19.6042752930241[/C][C]0.0957247069758509[/C][/ROW]
[ROW][C]24[/C][C]19.7[/C][C]19.8202322167968[/C][C]-0.120232216796829[/C][/ROW]
[ROW][C]25[/C][C]19.7[/C][C]19.8001899896743[/C][C]-0.100189989674302[/C][/ROW]
[ROW][C]26[/C][C]19.9[/C][C]19.7834887212293[/C][C]0.116511278770652[/C][/ROW]
[ROW][C]27[/C][C]20.1[/C][C]20.0029106829437[/C][C]0.097089317056323[/C][/ROW]
[ROW][C]28[/C][C]20.1[/C][C]20.2190950817301[/C][C]-0.119095081730087[/C][/ROW]
[ROW][C]29[/C][C]20.1[/C][C]20.1992424104511[/C][C]-0.0992424104511116[/C][/ROW]
[ROW][C]30[/C][C]20.1[/C][C]20.1826990996527[/C][C]-0.0826990996527321[/C][/ROW]
[ROW][C]31[/C][C]20.2[/C][C]20.1689134922488[/C][C]0.0310865077512226[/C][/ROW]
[ROW][C]32[/C][C]20.3[/C][C]20.2740954881014[/C][C]0.0259045118985775[/C][/ROW]
[ROW][C]33[/C][C]20.8[/C][C]20.3784136660807[/C][C]0.421586333919318[/C][/ROW]
[ROW][C]34[/C][C]21.1[/C][C]20.9486904128735[/C][C]0.151309587126548[/C][/ROW]
[ROW][C]35[/C][C]21.2[/C][C]21.2739131126772[/C][C]-0.0739131126772072[/C][/ROW]
[ROW][C]36[/C][C]21.3[/C][C]21.3615920939763[/C][C]-0.0615920939762624[/C][/ROW]
[ROW][C]37[/C][C]21.6[/C][C]21.4513249395537[/C][C]0.148675060446337[/C][/ROW]
[ROW][C]38[/C][C]21.7[/C][C]21.7761084743525[/C][C]-0.0761084743524663[/C][/ROW]
[ROW][C]39[/C][C]21.8[/C][C]21.8634214976871[/C][C]-0.0634214976871412[/C][/ROW]
[ROW][C]40[/C][C]22[/C][C]21.9528493890214[/C][C]0.0471506109785764[/C][/ROW]
[ROW][C]41[/C][C]21.9[/C][C]22.1607092062932[/C][C]-0.260709206293157[/C][/ROW]
[ROW][C]42[/C][C]21.9[/C][C]22.0172500298372[/C][C]-0.117250029837226[/C][/ROW]
[ROW][C]43[/C][C]22[/C][C]21.9977049212904[/C][C]0.00229507870961143[/C][/ROW]
[ROW][C]44[/C][C]22.1[/C][C]22.0980875016835[/C][C]0.00191249831653906[/C][/ROW]
[ROW][C]45[/C][C]21[/C][C]22.1984063074633[/C][C]-1.19840630746325[/C][/ROW]
[ROW][C]46[/C][C]19.7[/C][C]20.8986367944397[/C][C]-1.19863679443968[/C][/ROW]
[ROW][C]47[/C][C]19.8[/C][C]19.3988288601639[/C][C]0.401171139836141[/C][/ROW]
[ROW][C]48[/C][C]19.9[/C][C]19.5657024761863[/C][C]0.334297523813689[/C][/ROW]
[ROW][C]49[/C][C]19.8[/C][C]19.7214285292965[/C][C]0.0785714707035368[/C][/ROW]
[ROW][C]50[/C][C]20[/C][C]19.6345260775505[/C][C]0.365473922449457[/C][/ROW]
[ROW][C]51[/C][C]20.2[/C][C]19.8954491109624[/C][C]0.304550889037618[/C][/ROW]
[ROW][C]52[/C][C]20.3[/C][C]20.1462165196576[/C][C]0.15378348034238[/C][/ROW]
[ROW][C]53[/C][C]20.7[/C][C]20.2718516075137[/C][C]0.428148392486325[/C][/ROW]
[ROW][C]54[/C][C]20.9[/C][C]20.7432222230855[/C][C]0.156777776914495[/C][/ROW]
[ROW][C]55[/C][C]21[/C][C]20.969356448141[/C][C]0.0306435518590398[/C][/ROW]
[ROW][C]56[/C][C]21.2[/C][C]21.0744646050274[/C][C]0.125535394972619[/C][/ROW]
[ROW][C]57[/C][C]23.7[/C][C]21.2953908506293[/C][C]2.40460914937067[/C][/ROW]
[ROW][C]58[/C][C]23.7[/C][C]24.1962295276208[/C][C]-0.496229527620791[/C][/ROW]
[ROW][C]59[/C][C]23.7[/C][C]24.1135100605558[/C][C]-0.413510060555769[/C][/ROW]
[ROW][C]60[/C][C]23.8[/C][C]24.0445795960604[/C][C]-0.24457959606044[/C][/ROW]
[ROW][C]61[/C][C]24[/C][C]24.103809160778[/C][C]-0.103809160778006[/C][/ROW]
[ROW][C]62[/C][C]24[/C][C]24.2865045910617[/C][C]-0.286504591061657[/C][/ROW]
[ROW][C]63[/C][C]24.1[/C][C]24.2387454276803[/C][C]-0.138745427680284[/C][/ROW]
[ROW][C]64[/C][C]24.3[/C][C]24.3156171227395[/C][C]-0.0156171227395312[/C][/ROW]
[ROW][C]65[/C][C]24.4[/C][C]24.5130138111706[/C][C]-0.113013811170596[/C][/ROW]
[ROW][C]66[/C][C]24.4[/C][C]24.5941748632429[/C][C]-0.194174863242928[/C][/ROW]
[ROW][C]67[/C][C]24.5[/C][C]24.5618066942589[/C][C]-0.0618066942589302[/C][/ROW]
[ROW][C]68[/C][C]24.6[/C][C]24.6515037668321[/C][C]-0.0515037668320559[/C][/ROW]
[ROW][C]69[/C][C]24.7[/C][C]24.7429182959823[/C][C]-0.0429182959822789[/C][/ROW]
[ROW][C]70[/C][C]24.6[/C][C]24.8357639886036[/C][C]-0.235763988603559[/C][/ROW]
[ROW][C]71[/C][C]24.6[/C][C]24.6964630796393[/C][C]-0.0964630796392854[/C][/ROW]
[ROW][C]72[/C][C]24.6[/C][C]24.6803830721124[/C][C]-0.0803830721123866[/C][/ROW]
[ROW][C]73[/C][C]24.7[/C][C]24.6669835371874[/C][C]0.0330164628126433[/C][/ROW]
[ROW][C]74[/C][C]24.7[/C][C]24.772487248789[/C][C]-0.0724872487889776[/C][/ROW]
[ROW][C]75[/C][C]24.8[/C][C]24.7604039158652[/C][C]0.039596084134768[/C][/ROW]
[ROW][C]76[/C][C]24.9[/C][C]24.8670044238866[/C][C]0.032995576113418[/C][/ROW]
[ROW][C]77[/C][C]25[/C][C]24.9725046537594[/C][C]0.0274953462405811[/C][/ROW]
[ROW][C]78[/C][C]25.1[/C][C]25.0770880174272[/C][C]0.0229119825727757[/C][/ROW]
[ROW][C]79[/C][C]25.2[/C][C]25.1809073527999[/C][C]0.0190926472000683[/C][/ROW]
[ROW][C]80[/C][C]25.3[/C][C]25.2840900203224[/C][C]0.0159099796775983[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295533&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295533&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
317.417.6-0.199999999999999
417.617.7666608041397-0.166660804139713
517.717.9388791181825-0.238879118182492
617.717.9990589296424-0.299058929642403
717.617.9492070084968-0.34920700849683
817.617.7909956042365-0.190995604236537
917.517.7591574049461-0.259157404946066
1017.517.6159569075354-0.11595690753537
1117.617.5966273572770.0033726427230043
1217.617.6971895632585-0.0971895632585422
1317.917.68098845383330.219011546166712
1418.218.01749679799990.182503202000142
1518.418.34791934798290.0520806520170822
1618.518.5566009832736-0.0566009832735581
171918.64716582693730.35283417306265
1819.519.2059818649470.294018135052969
1919.719.7549935059021-0.0549935059020576
2019.919.9458263095805-0.045826309580498
2119.720.1381872480272-0.438187248027205
2219.519.8651431955999-0.365143195599924
2319.719.60427529302410.0957247069758509
2419.719.8202322167968-0.120232216796829
2519.719.8001899896743-0.100189989674302
2619.919.78348872122930.116511278770652
2720.120.00291068294370.097089317056323
2820.120.2190950817301-0.119095081730087
2920.120.1992424104511-0.0992424104511116
3020.120.1826990996527-0.0826990996527321
3120.220.16891349224880.0310865077512226
3220.320.27409548810140.0259045118985775
3320.820.37841366608070.421586333919318
3421.120.94869041287350.151309587126548
3521.221.2739131126772-0.0739131126772072
3621.321.3615920939763-0.0615920939762624
3721.621.45132493955370.148675060446337
3821.721.7761084743525-0.0761084743524663
3921.821.8634214976871-0.0634214976871412
402221.95284938902140.0471506109785764
4121.922.1607092062932-0.260709206293157
4221.922.0172500298372-0.117250029837226
432221.99770492129040.00229507870961143
4422.122.09808750168350.00191249831653906
452122.1984063074633-1.19840630746325
4619.720.8986367944397-1.19863679443968
4719.819.39882886016390.401171139836141
4819.919.56570247618630.334297523813689
4919.819.72142852929650.0785714707035368
502019.63452607755050.365473922449457
5120.219.89544911096240.304550889037618
5220.320.14621651965760.15378348034238
5320.720.27185160751370.428148392486325
5420.920.74322222308550.156777776914495
552120.9693564481410.0306435518590398
5621.221.07446460502740.125535394972619
5723.721.29539085062932.40460914937067
5823.724.1962295276208-0.496229527620791
5923.724.1135100605558-0.413510060555769
6023.824.0445795960604-0.24457959606044
612424.103809160778-0.103809160778006
622424.2865045910617-0.286504591061657
6324.124.2387454276803-0.138745427680284
6424.324.3156171227395-0.0156171227395312
6524.424.5130138111706-0.113013811170596
6624.424.5941748632429-0.194174863242928
6724.524.5618066942589-0.0618066942589302
6824.624.6515037668321-0.0515037668320559
6924.724.7429182959823-0.0429182959822789
7024.624.8357639886036-0.235763988603559
7124.624.6964630796393-0.0964630796392854
7224.624.6803830721124-0.0803830721123866
7324.724.66698353718740.0330164628126433
7424.724.772487248789-0.0724872487889776
7524.824.76040391586520.039596084134768
7624.924.86700442388660.032995576113418
772524.97250465375940.0274953462405811
7825.125.07708801742720.0229119825727757
7925.225.18090735279990.0190926472000683
8025.325.28409002032240.0159099796775983







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8125.386742149965424.626012274544226.1474720253866
8225.473484299930924.30453688477426.6424317150877
8325.560226449896324.012535844334927.1079170554576
8425.646968599861723.724055117878427.569882081845
8525.733710749827123.430376195802328.037045303852
8625.820452899792623.127727607700928.5131781918842
8725.90719504975822.814297312308429.0000927872076
8825.993937199723422.489190036641729.4986843628051
8926.080679349688822.151984891028630.0093738083491
9026.167421499654321.802522795919230.5323202033893
9126.254163649619721.440795164595731.0675321346437
9226.340905799585121.066881866364731.6149297328056

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 25.3867421499654 & 24.6260122745442 & 26.1474720253866 \tabularnewline
82 & 25.4734842999309 & 24.304536884774 & 26.6424317150877 \tabularnewline
83 & 25.5602264498963 & 24.0125358443349 & 27.1079170554576 \tabularnewline
84 & 25.6469685998617 & 23.7240551178784 & 27.569882081845 \tabularnewline
85 & 25.7337107498271 & 23.4303761958023 & 28.037045303852 \tabularnewline
86 & 25.8204528997926 & 23.1277276077009 & 28.5131781918842 \tabularnewline
87 & 25.907195049758 & 22.8142973123084 & 29.0000927872076 \tabularnewline
88 & 25.9939371997234 & 22.4891900366417 & 29.4986843628051 \tabularnewline
89 & 26.0806793496888 & 22.1519848910286 & 30.0093738083491 \tabularnewline
90 & 26.1674214996543 & 21.8025227959192 & 30.5323202033893 \tabularnewline
91 & 26.2541636496197 & 21.4407951645957 & 31.0675321346437 \tabularnewline
92 & 26.3409057995851 & 21.0668818663647 & 31.6149297328056 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295533&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]81[/C][C]25.3867421499654[/C][C]24.6260122745442[/C][C]26.1474720253866[/C][/ROW]
[ROW][C]82[/C][C]25.4734842999309[/C][C]24.304536884774[/C][C]26.6424317150877[/C][/ROW]
[ROW][C]83[/C][C]25.5602264498963[/C][C]24.0125358443349[/C][C]27.1079170554576[/C][/ROW]
[ROW][C]84[/C][C]25.6469685998617[/C][C]23.7240551178784[/C][C]27.569882081845[/C][/ROW]
[ROW][C]85[/C][C]25.7337107498271[/C][C]23.4303761958023[/C][C]28.037045303852[/C][/ROW]
[ROW][C]86[/C][C]25.8204528997926[/C][C]23.1277276077009[/C][C]28.5131781918842[/C][/ROW]
[ROW][C]87[/C][C]25.907195049758[/C][C]22.8142973123084[/C][C]29.0000927872076[/C][/ROW]
[ROW][C]88[/C][C]25.9939371997234[/C][C]22.4891900366417[/C][C]29.4986843628051[/C][/ROW]
[ROW][C]89[/C][C]26.0806793496888[/C][C]22.1519848910286[/C][C]30.0093738083491[/C][/ROW]
[ROW][C]90[/C][C]26.1674214996543[/C][C]21.8025227959192[/C][C]30.5323202033893[/C][/ROW]
[ROW][C]91[/C][C]26.2541636496197[/C][C]21.4407951645957[/C][C]31.0675321346437[/C][/ROW]
[ROW][C]92[/C][C]26.3409057995851[/C][C]21.0668818663647[/C][C]31.6149297328056[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295533&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295533&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
8125.386742149965424.626012274544226.1474720253866
8225.473484299930924.30453688477426.6424317150877
8325.560226449896324.012535844334927.1079170554576
8425.646968599861723.724055117878427.569882081845
8525.733710749827123.430376195802328.037045303852
8625.820452899792623.127727607700928.5131781918842
8725.90719504975822.814297312308429.0000927872076
8825.993937199723422.489190036641729.4986843628051
8926.080679349688822.151984891028630.0093738083491
9026.167421499654321.802522795919230.5323202033893
9126.254163649619721.440795164595731.0675321346437
9226.340905799585121.066881866364731.6149297328056



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')