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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, 19 May 2014 06:21:01 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/19/t1400494976n2l1ibhwfvk8pap.htm/, Retrieved Sun, 19 May 2024 12:57:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234927, Retrieved Sun, 19 May 2024 12:57:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [] [2014-04-28 08:46:31] [81aa55046b9483ad574c1beb765d747c]
- RMP     [Exponential Smoothing] [] [2014-05-19 10:21:01] [67026c9811d097a2c582f1dcce4b8e60] [Current]
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Dataseries X:
-2
0
1
-3
-3
-5
-7
-7
-5
-13
-16
-20
-18
-21
-20
-16
-14
-12
-10
-3
-4
-4
-1
-8
-10
-11
-7
-2
-6
-4
0
2
2
5
8
8
5
10
6
6
9
5
5
-4
-5
-1
-8
-8
-13
-18
-8
-8
-6
-5
-11
-14
-12
-13
-19
-21
-22
-13
-21
-17
-15
-14
-11
-8
-3
-2
-1
1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234927&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234927&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.916836741801242
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.916836741801242 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234927&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]0.916836741801242[/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=234927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234927&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
alpha0.916836741801242
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
20-22
31-0.1663265163975161.16632651639752
4-30.903004486772775-3.90300448677278
5-3-2.6754134301156-0.324586569884396
6-5-2.97300632328085-2.02699367671915
7-7-4.83142860149576-2.16857139850424
8-7-6.81965453686375-0.18034546313625
9-5-6.985001883684231.98500188368423
10-13-5.16507922417785-7.83492077582215
11-16-12.3484224605535-3.65157753944651
12-20-15.6963229142542-4.30367708574578
13-18-19.6420921913141.64209219131405
14-21-18.1365617368924-2.86343826310759
15-20-20.7618671443890.76186714438898
16-16-20.0633593540424.06335935404197
17-14-16.33792220311452.33792220311453
18-12-14.19442922782622.19442922782622
19-10-12.18249588447262.18249588447261
20-3-10.18150346875817.18150346875812
21-4-3.59723722722761-0.402762772772391
22-4-3.96650493553508-0.0334950644649181
23-1-3.997214441305522.99721444130552
24-8-1.24925811845934-6.75074188154066
25-10-7.43858630987226-2.56141369012774
26-11-9.78698449193407-1.21301550806593
27-7-10.89912167810363.89912167810362
28-2-7.324263662864515.32426366286451
29-6-2.44278311371307-3.55721688628693
30-4-5.704170253616741.70417025361674
310-4.141724350816174.14172435081617
322-0.3444392915750092.34443929157501
3321.805028789863430.194971210136566
3451.983785558910093.01621444108991
3584.749161779652823.25083822034718
3687.729649701718880.270350298281124
3757.97751678833994-2.97751678833994
38105.247619997459854.75238000254015
3969.60477659479014-3.60477659479014
4066.29978496670137-0.299784966701372
4196.024931094589892.97506890541011
4258.75258357646028-3.75258357646028
4355.31207707688159-0.312077076881586
44-45.02595334652262-9.02595334652262
45-5-3.24937231135319-1.75062768864681
46-1-4.854412097519173.85441209751917
47-8-1.3205454684704-6.6794545315296
48-8-7.44451479816754-0.555485201832461
49-13-7.95380404073442-5.04619595926558
50-18-12.5803419025181-5.41965809748193
51-8-17.54928357429019.54928357429012
52-8-8.794149535501850.79414953550185
53-6-8.066044062869362.06604406286936
54-5-6.171818955850421.17181895585042
55-11-5.09745228238759-5.90254771761241
56-14-10.5091249001297-3.49087509987029
57-12-13.70968745272991.70968745272987
58-13-12.1421831790706-0.857816820929449
59-19-12.9286611582338-6.07133884176619
60-21-18.49508768029-2.50491231970995
61-22-20.7916833299907-1.20831667000929
62-13-21.89951244878628.89951244878615
63-21-13.7401124516215-7.25988754837853
64-17-20.39624409732023.39624409732025
65-15-17.28244272477152.28244272477145
66-14-15.1898153736441.18981537364404
67-11-14.09894892312723.09894892312721
68-8-11.25771868943883.25771868943879
69-3-8.270922500508725.27092250050872
70-2-3.438347088855451.43834708885545
71-1-2.119617630329921.11961763032992
721-1.093111050075012.09311105007501

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 0 & -2 & 2 \tabularnewline
3 & 1 & -0.166326516397516 & 1.16632651639752 \tabularnewline
4 & -3 & 0.903004486772775 & -3.90300448677278 \tabularnewline
5 & -3 & -2.6754134301156 & -0.324586569884396 \tabularnewline
6 & -5 & -2.97300632328085 & -2.02699367671915 \tabularnewline
7 & -7 & -4.83142860149576 & -2.16857139850424 \tabularnewline
8 & -7 & -6.81965453686375 & -0.18034546313625 \tabularnewline
9 & -5 & -6.98500188368423 & 1.98500188368423 \tabularnewline
10 & -13 & -5.16507922417785 & -7.83492077582215 \tabularnewline
11 & -16 & -12.3484224605535 & -3.65157753944651 \tabularnewline
12 & -20 & -15.6963229142542 & -4.30367708574578 \tabularnewline
13 & -18 & -19.642092191314 & 1.64209219131405 \tabularnewline
14 & -21 & -18.1365617368924 & -2.86343826310759 \tabularnewline
15 & -20 & -20.761867144389 & 0.76186714438898 \tabularnewline
16 & -16 & -20.063359354042 & 4.06335935404197 \tabularnewline
17 & -14 & -16.3379222031145 & 2.33792220311453 \tabularnewline
18 & -12 & -14.1944292278262 & 2.19442922782622 \tabularnewline
19 & -10 & -12.1824958844726 & 2.18249588447261 \tabularnewline
20 & -3 & -10.1815034687581 & 7.18150346875812 \tabularnewline
21 & -4 & -3.59723722722761 & -0.402762772772391 \tabularnewline
22 & -4 & -3.96650493553508 & -0.0334950644649181 \tabularnewline
23 & -1 & -3.99721444130552 & 2.99721444130552 \tabularnewline
24 & -8 & -1.24925811845934 & -6.75074188154066 \tabularnewline
25 & -10 & -7.43858630987226 & -2.56141369012774 \tabularnewline
26 & -11 & -9.78698449193407 & -1.21301550806593 \tabularnewline
27 & -7 & -10.8991216781036 & 3.89912167810362 \tabularnewline
28 & -2 & -7.32426366286451 & 5.32426366286451 \tabularnewline
29 & -6 & -2.44278311371307 & -3.55721688628693 \tabularnewline
30 & -4 & -5.70417025361674 & 1.70417025361674 \tabularnewline
31 & 0 & -4.14172435081617 & 4.14172435081617 \tabularnewline
32 & 2 & -0.344439291575009 & 2.34443929157501 \tabularnewline
33 & 2 & 1.80502878986343 & 0.194971210136566 \tabularnewline
34 & 5 & 1.98378555891009 & 3.01621444108991 \tabularnewline
35 & 8 & 4.74916177965282 & 3.25083822034718 \tabularnewline
36 & 8 & 7.72964970171888 & 0.270350298281124 \tabularnewline
37 & 5 & 7.97751678833994 & -2.97751678833994 \tabularnewline
38 & 10 & 5.24761999745985 & 4.75238000254015 \tabularnewline
39 & 6 & 9.60477659479014 & -3.60477659479014 \tabularnewline
40 & 6 & 6.29978496670137 & -0.299784966701372 \tabularnewline
41 & 9 & 6.02493109458989 & 2.97506890541011 \tabularnewline
42 & 5 & 8.75258357646028 & -3.75258357646028 \tabularnewline
43 & 5 & 5.31207707688159 & -0.312077076881586 \tabularnewline
44 & -4 & 5.02595334652262 & -9.02595334652262 \tabularnewline
45 & -5 & -3.24937231135319 & -1.75062768864681 \tabularnewline
46 & -1 & -4.85441209751917 & 3.85441209751917 \tabularnewline
47 & -8 & -1.3205454684704 & -6.6794545315296 \tabularnewline
48 & -8 & -7.44451479816754 & -0.555485201832461 \tabularnewline
49 & -13 & -7.95380404073442 & -5.04619595926558 \tabularnewline
50 & -18 & -12.5803419025181 & -5.41965809748193 \tabularnewline
51 & -8 & -17.5492835742901 & 9.54928357429012 \tabularnewline
52 & -8 & -8.79414953550185 & 0.79414953550185 \tabularnewline
53 & -6 & -8.06604406286936 & 2.06604406286936 \tabularnewline
54 & -5 & -6.17181895585042 & 1.17181895585042 \tabularnewline
55 & -11 & -5.09745228238759 & -5.90254771761241 \tabularnewline
56 & -14 & -10.5091249001297 & -3.49087509987029 \tabularnewline
57 & -12 & -13.7096874527299 & 1.70968745272987 \tabularnewline
58 & -13 & -12.1421831790706 & -0.857816820929449 \tabularnewline
59 & -19 & -12.9286611582338 & -6.07133884176619 \tabularnewline
60 & -21 & -18.49508768029 & -2.50491231970995 \tabularnewline
61 & -22 & -20.7916833299907 & -1.20831667000929 \tabularnewline
62 & -13 & -21.8995124487862 & 8.89951244878615 \tabularnewline
63 & -21 & -13.7401124516215 & -7.25988754837853 \tabularnewline
64 & -17 & -20.3962440973202 & 3.39624409732025 \tabularnewline
65 & -15 & -17.2824427247715 & 2.28244272477145 \tabularnewline
66 & -14 & -15.189815373644 & 1.18981537364404 \tabularnewline
67 & -11 & -14.0989489231272 & 3.09894892312721 \tabularnewline
68 & -8 & -11.2577186894388 & 3.25771868943879 \tabularnewline
69 & -3 & -8.27092250050872 & 5.27092250050872 \tabularnewline
70 & -2 & -3.43834708885545 & 1.43834708885545 \tabularnewline
71 & -1 & -2.11961763032992 & 1.11961763032992 \tabularnewline
72 & 1 & -1.09311105007501 & 2.09311105007501 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234927&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]0[/C][C]-2[/C][C]2[/C][/ROW]
[ROW][C]3[/C][C]1[/C][C]-0.166326516397516[/C][C]1.16632651639752[/C][/ROW]
[ROW][C]4[/C][C]-3[/C][C]0.903004486772775[/C][C]-3.90300448677278[/C][/ROW]
[ROW][C]5[/C][C]-3[/C][C]-2.6754134301156[/C][C]-0.324586569884396[/C][/ROW]
[ROW][C]6[/C][C]-5[/C][C]-2.97300632328085[/C][C]-2.02699367671915[/C][/ROW]
[ROW][C]7[/C][C]-7[/C][C]-4.83142860149576[/C][C]-2.16857139850424[/C][/ROW]
[ROW][C]8[/C][C]-7[/C][C]-6.81965453686375[/C][C]-0.18034546313625[/C][/ROW]
[ROW][C]9[/C][C]-5[/C][C]-6.98500188368423[/C][C]1.98500188368423[/C][/ROW]
[ROW][C]10[/C][C]-13[/C][C]-5.16507922417785[/C][C]-7.83492077582215[/C][/ROW]
[ROW][C]11[/C][C]-16[/C][C]-12.3484224605535[/C][C]-3.65157753944651[/C][/ROW]
[ROW][C]12[/C][C]-20[/C][C]-15.6963229142542[/C][C]-4.30367708574578[/C][/ROW]
[ROW][C]13[/C][C]-18[/C][C]-19.642092191314[/C][C]1.64209219131405[/C][/ROW]
[ROW][C]14[/C][C]-21[/C][C]-18.1365617368924[/C][C]-2.86343826310759[/C][/ROW]
[ROW][C]15[/C][C]-20[/C][C]-20.761867144389[/C][C]0.76186714438898[/C][/ROW]
[ROW][C]16[/C][C]-16[/C][C]-20.063359354042[/C][C]4.06335935404197[/C][/ROW]
[ROW][C]17[/C][C]-14[/C][C]-16.3379222031145[/C][C]2.33792220311453[/C][/ROW]
[ROW][C]18[/C][C]-12[/C][C]-14.1944292278262[/C][C]2.19442922782622[/C][/ROW]
[ROW][C]19[/C][C]-10[/C][C]-12.1824958844726[/C][C]2.18249588447261[/C][/ROW]
[ROW][C]20[/C][C]-3[/C][C]-10.1815034687581[/C][C]7.18150346875812[/C][/ROW]
[ROW][C]21[/C][C]-4[/C][C]-3.59723722722761[/C][C]-0.402762772772391[/C][/ROW]
[ROW][C]22[/C][C]-4[/C][C]-3.96650493553508[/C][C]-0.0334950644649181[/C][/ROW]
[ROW][C]23[/C][C]-1[/C][C]-3.99721444130552[/C][C]2.99721444130552[/C][/ROW]
[ROW][C]24[/C][C]-8[/C][C]-1.24925811845934[/C][C]-6.75074188154066[/C][/ROW]
[ROW][C]25[/C][C]-10[/C][C]-7.43858630987226[/C][C]-2.56141369012774[/C][/ROW]
[ROW][C]26[/C][C]-11[/C][C]-9.78698449193407[/C][C]-1.21301550806593[/C][/ROW]
[ROW][C]27[/C][C]-7[/C][C]-10.8991216781036[/C][C]3.89912167810362[/C][/ROW]
[ROW][C]28[/C][C]-2[/C][C]-7.32426366286451[/C][C]5.32426366286451[/C][/ROW]
[ROW][C]29[/C][C]-6[/C][C]-2.44278311371307[/C][C]-3.55721688628693[/C][/ROW]
[ROW][C]30[/C][C]-4[/C][C]-5.70417025361674[/C][C]1.70417025361674[/C][/ROW]
[ROW][C]31[/C][C]0[/C][C]-4.14172435081617[/C][C]4.14172435081617[/C][/ROW]
[ROW][C]32[/C][C]2[/C][C]-0.344439291575009[/C][C]2.34443929157501[/C][/ROW]
[ROW][C]33[/C][C]2[/C][C]1.80502878986343[/C][C]0.194971210136566[/C][/ROW]
[ROW][C]34[/C][C]5[/C][C]1.98378555891009[/C][C]3.01621444108991[/C][/ROW]
[ROW][C]35[/C][C]8[/C][C]4.74916177965282[/C][C]3.25083822034718[/C][/ROW]
[ROW][C]36[/C][C]8[/C][C]7.72964970171888[/C][C]0.270350298281124[/C][/ROW]
[ROW][C]37[/C][C]5[/C][C]7.97751678833994[/C][C]-2.97751678833994[/C][/ROW]
[ROW][C]38[/C][C]10[/C][C]5.24761999745985[/C][C]4.75238000254015[/C][/ROW]
[ROW][C]39[/C][C]6[/C][C]9.60477659479014[/C][C]-3.60477659479014[/C][/ROW]
[ROW][C]40[/C][C]6[/C][C]6.29978496670137[/C][C]-0.299784966701372[/C][/ROW]
[ROW][C]41[/C][C]9[/C][C]6.02493109458989[/C][C]2.97506890541011[/C][/ROW]
[ROW][C]42[/C][C]5[/C][C]8.75258357646028[/C][C]-3.75258357646028[/C][/ROW]
[ROW][C]43[/C][C]5[/C][C]5.31207707688159[/C][C]-0.312077076881586[/C][/ROW]
[ROW][C]44[/C][C]-4[/C][C]5.02595334652262[/C][C]-9.02595334652262[/C][/ROW]
[ROW][C]45[/C][C]-5[/C][C]-3.24937231135319[/C][C]-1.75062768864681[/C][/ROW]
[ROW][C]46[/C][C]-1[/C][C]-4.85441209751917[/C][C]3.85441209751917[/C][/ROW]
[ROW][C]47[/C][C]-8[/C][C]-1.3205454684704[/C][C]-6.6794545315296[/C][/ROW]
[ROW][C]48[/C][C]-8[/C][C]-7.44451479816754[/C][C]-0.555485201832461[/C][/ROW]
[ROW][C]49[/C][C]-13[/C][C]-7.95380404073442[/C][C]-5.04619595926558[/C][/ROW]
[ROW][C]50[/C][C]-18[/C][C]-12.5803419025181[/C][C]-5.41965809748193[/C][/ROW]
[ROW][C]51[/C][C]-8[/C][C]-17.5492835742901[/C][C]9.54928357429012[/C][/ROW]
[ROW][C]52[/C][C]-8[/C][C]-8.79414953550185[/C][C]0.79414953550185[/C][/ROW]
[ROW][C]53[/C][C]-6[/C][C]-8.06604406286936[/C][C]2.06604406286936[/C][/ROW]
[ROW][C]54[/C][C]-5[/C][C]-6.17181895585042[/C][C]1.17181895585042[/C][/ROW]
[ROW][C]55[/C][C]-11[/C][C]-5.09745228238759[/C][C]-5.90254771761241[/C][/ROW]
[ROW][C]56[/C][C]-14[/C][C]-10.5091249001297[/C][C]-3.49087509987029[/C][/ROW]
[ROW][C]57[/C][C]-12[/C][C]-13.7096874527299[/C][C]1.70968745272987[/C][/ROW]
[ROW][C]58[/C][C]-13[/C][C]-12.1421831790706[/C][C]-0.857816820929449[/C][/ROW]
[ROW][C]59[/C][C]-19[/C][C]-12.9286611582338[/C][C]-6.07133884176619[/C][/ROW]
[ROW][C]60[/C][C]-21[/C][C]-18.49508768029[/C][C]-2.50491231970995[/C][/ROW]
[ROW][C]61[/C][C]-22[/C][C]-20.7916833299907[/C][C]-1.20831667000929[/C][/ROW]
[ROW][C]62[/C][C]-13[/C][C]-21.8995124487862[/C][C]8.89951244878615[/C][/ROW]
[ROW][C]63[/C][C]-21[/C][C]-13.7401124516215[/C][C]-7.25988754837853[/C][/ROW]
[ROW][C]64[/C][C]-17[/C][C]-20.3962440973202[/C][C]3.39624409732025[/C][/ROW]
[ROW][C]65[/C][C]-15[/C][C]-17.2824427247715[/C][C]2.28244272477145[/C][/ROW]
[ROW][C]66[/C][C]-14[/C][C]-15.189815373644[/C][C]1.18981537364404[/C][/ROW]
[ROW][C]67[/C][C]-11[/C][C]-14.0989489231272[/C][C]3.09894892312721[/C][/ROW]
[ROW][C]68[/C][C]-8[/C][C]-11.2577186894388[/C][C]3.25771868943879[/C][/ROW]
[ROW][C]69[/C][C]-3[/C][C]-8.27092250050872[/C][C]5.27092250050872[/C][/ROW]
[ROW][C]70[/C][C]-2[/C][C]-3.43834708885545[/C][C]1.43834708885545[/C][/ROW]
[ROW][C]71[/C][C]-1[/C][C]-2.11961763032992[/C][C]1.11961763032992[/C][/ROW]
[ROW][C]72[/C][C]1[/C][C]-1.09311105007501[/C][C]2.09311105007501[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234927&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234927&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
20-22
31-0.1663265163975161.16632651639752
4-30.903004486772775-3.90300448677278
5-3-2.6754134301156-0.324586569884396
6-5-2.97300632328085-2.02699367671915
7-7-4.83142860149576-2.16857139850424
8-7-6.81965453686375-0.18034546313625
9-5-6.985001883684231.98500188368423
10-13-5.16507922417785-7.83492077582215
11-16-12.3484224605535-3.65157753944651
12-20-15.6963229142542-4.30367708574578
13-18-19.6420921913141.64209219131405
14-21-18.1365617368924-2.86343826310759
15-20-20.7618671443890.76186714438898
16-16-20.0633593540424.06335935404197
17-14-16.33792220311452.33792220311453
18-12-14.19442922782622.19442922782622
19-10-12.18249588447262.18249588447261
20-3-10.18150346875817.18150346875812
21-4-3.59723722722761-0.402762772772391
22-4-3.96650493553508-0.0334950644649181
23-1-3.997214441305522.99721444130552
24-8-1.24925811845934-6.75074188154066
25-10-7.43858630987226-2.56141369012774
26-11-9.78698449193407-1.21301550806593
27-7-10.89912167810363.89912167810362
28-2-7.324263662864515.32426366286451
29-6-2.44278311371307-3.55721688628693
30-4-5.704170253616741.70417025361674
310-4.141724350816174.14172435081617
322-0.3444392915750092.34443929157501
3321.805028789863430.194971210136566
3451.983785558910093.01621444108991
3584.749161779652823.25083822034718
3687.729649701718880.270350298281124
3757.97751678833994-2.97751678833994
38105.247619997459854.75238000254015
3969.60477659479014-3.60477659479014
4066.29978496670137-0.299784966701372
4196.024931094589892.97506890541011
4258.75258357646028-3.75258357646028
4355.31207707688159-0.312077076881586
44-45.02595334652262-9.02595334652262
45-5-3.24937231135319-1.75062768864681
46-1-4.854412097519173.85441209751917
47-8-1.3205454684704-6.6794545315296
48-8-7.44451479816754-0.555485201832461
49-13-7.95380404073442-5.04619595926558
50-18-12.5803419025181-5.41965809748193
51-8-17.54928357429019.54928357429012
52-8-8.794149535501850.79414953550185
53-6-8.066044062869362.06604406286936
54-5-6.171818955850421.17181895585042
55-11-5.09745228238759-5.90254771761241
56-14-10.5091249001297-3.49087509987029
57-12-13.70968745272991.70968745272987
58-13-12.1421831790706-0.857816820929449
59-19-12.9286611582338-6.07133884176619
60-21-18.49508768029-2.50491231970995
61-22-20.7916833299907-1.20831667000929
62-13-21.89951244878628.89951244878615
63-21-13.7401124516215-7.25988754837853
64-17-20.39624409732023.39624409732025
65-15-17.28244272477152.28244272477145
66-14-15.1898153736441.18981537364404
67-11-14.09894892312723.09894892312721
68-8-11.25771868943883.25771868943879
69-3-8.270922500508725.27092250050872
70-2-3.438347088855451.43834708885545
71-1-2.119617630329921.11961763032992
721-1.093111050075012.09311105007501







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
730.825930065303938-6.767544889371218.41940501997908
740.825930065303938-9.4760106915515911.1278708221595
750.825930065303938-11.607858771098413.2597189017063
760.825930065303938-13.424270856041915.0761309866498
770.825930065303938-15.033998931044316.6858590616522
780.825930065303938-16.494764760241918.1466248908498
790.825930065303938-17.841570857695219.4934309883031
800.825930065303938-19.097541323504220.749401454112
810.825930065303938-20.278899563270121.930759693878
820.825930065303938-21.397547500586123.049407631194
830.825930065303938-22.46252365305424.1143837836619
840.825930065303938-23.480883754334925.1327438849428

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.825930065303938 & -6.76754488937121 & 8.41940501997908 \tabularnewline
74 & 0.825930065303938 & -9.47601069155159 & 11.1278708221595 \tabularnewline
75 & 0.825930065303938 & -11.6078587710984 & 13.2597189017063 \tabularnewline
76 & 0.825930065303938 & -13.4242708560419 & 15.0761309866498 \tabularnewline
77 & 0.825930065303938 & -15.0339989310443 & 16.6858590616522 \tabularnewline
78 & 0.825930065303938 & -16.4947647602419 & 18.1466248908498 \tabularnewline
79 & 0.825930065303938 & -17.8415708576952 & 19.4934309883031 \tabularnewline
80 & 0.825930065303938 & -19.0975413235042 & 20.749401454112 \tabularnewline
81 & 0.825930065303938 & -20.2788995632701 & 21.930759693878 \tabularnewline
82 & 0.825930065303938 & -21.3975475005861 & 23.049407631194 \tabularnewline
83 & 0.825930065303938 & -22.462523653054 & 24.1143837836619 \tabularnewline
84 & 0.825930065303938 & -23.4808837543349 & 25.1327438849428 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234927&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]73[/C][C]0.825930065303938[/C][C]-6.76754488937121[/C][C]8.41940501997908[/C][/ROW]
[ROW][C]74[/C][C]0.825930065303938[/C][C]-9.47601069155159[/C][C]11.1278708221595[/C][/ROW]
[ROW][C]75[/C][C]0.825930065303938[/C][C]-11.6078587710984[/C][C]13.2597189017063[/C][/ROW]
[ROW][C]76[/C][C]0.825930065303938[/C][C]-13.4242708560419[/C][C]15.0761309866498[/C][/ROW]
[ROW][C]77[/C][C]0.825930065303938[/C][C]-15.0339989310443[/C][C]16.6858590616522[/C][/ROW]
[ROW][C]78[/C][C]0.825930065303938[/C][C]-16.4947647602419[/C][C]18.1466248908498[/C][/ROW]
[ROW][C]79[/C][C]0.825930065303938[/C][C]-17.8415708576952[/C][C]19.4934309883031[/C][/ROW]
[ROW][C]80[/C][C]0.825930065303938[/C][C]-19.0975413235042[/C][C]20.749401454112[/C][/ROW]
[ROW][C]81[/C][C]0.825930065303938[/C][C]-20.2788995632701[/C][C]21.930759693878[/C][/ROW]
[ROW][C]82[/C][C]0.825930065303938[/C][C]-21.3975475005861[/C][C]23.049407631194[/C][/ROW]
[ROW][C]83[/C][C]0.825930065303938[/C][C]-22.462523653054[/C][C]24.1143837836619[/C][/ROW]
[ROW][C]84[/C][C]0.825930065303938[/C][C]-23.4808837543349[/C][C]25.1327438849428[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234927&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234927&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
730.825930065303938-6.767544889371218.41940501997908
740.825930065303938-9.4760106915515911.1278708221595
750.825930065303938-11.607858771098413.2597189017063
760.825930065303938-13.424270856041915.0761309866498
770.825930065303938-15.033998931044316.6858590616522
780.825930065303938-16.494764760241918.1466248908498
790.825930065303938-17.841570857695219.4934309883031
800.825930065303938-19.097541323504220.749401454112
810.825930065303938-20.278899563270121.930759693878
820.825930065303938-21.397547500586123.049407631194
830.825930065303938-22.46252365305424.1143837836619
840.825930065303938-23.480883754334925.1327438849428



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')