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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 28 Apr 2016 15:13:49 +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/Apr/28/t1461852853t1fg71cg7m4ofcs.htm/, Retrieved Sat, 04 May 2024 10:14:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295054, Retrieved Sat, 04 May 2024 10:14:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-28 14:13:49] [b94c13d84d922b33c8d74b1e5b1d38c1] [Current]
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Dataseries X:
83,8
86,62
83,98
82,59
82,3
81,64
81,66
81,63
85,54
85,62
85,89
86,38
87,59
87,68
88,07
87,66
88,36
88,08
94,35
99,07
100,39
102,1
102,89
103,05
102,78
102,53
101,6
100,78
100,54
100,19
100,07
100,18
100,08
99,66
99,92
99,51
101,77
102,49
101,91
100,57
100,23
99,99
99,2
99,07
98,79
99,31
98,98
97,69
98,9
98,75
99,7
100,18
100,14
100,13
99,85
99,38
98,87
97,79
97,32
97,29
96,73
97,22
96,66
96,58
96,47
96,7
97,91
97,97
98,26
97,8
97,33
97,56




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295054&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295054&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295054&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999931958746635
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999931958746635 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295054&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]0.999931958746635[/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=295054&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295054&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
alpha0.999931958746635
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
286.6283.82.82000000000001
383.9886.6198081236655-2.6398081236655
482.5983.9801796158534-1.39017961585337
582.382.5900945895635-0.290094589563466
681.6482.3000197383995-0.66001973839947
781.6681.64004490857020.0199550914297504
881.6381.6599986422306-0.0299986422305665
985.5481.63000204114523.90999795885479
1085.6285.53973395883820.0802660411617779
1185.8985.6199945385980.270005461402036
1286.3885.889981628490.490018371510004
1387.5986.37996665853581.21003334146417
1487.6887.58991766781480.090082332185176
1588.0787.67999387068520.39000612931477
1687.6688.0699734634941-0.40997346349414
1788.3687.66002789510830.6999721048917
1888.0888.3599523730207-0.279952373020663
1994.3588.08001904831036.26998095168966
2099.0794.34957338263754.72042661736252
21100.3999.06967881625651.32032118374347
22102.1100.3899101636921.71008983630819
23102.89102.0998836433440.790116356655844
24103.05102.8899462394930.160053760507196
25102.78103.049989109742-0.269989109741516
26102.53102.780018370397-0.250018370397413
27101.6102.530017011563-0.930017011563294
28100.78101.600063279523-0.820063279523112
29100.54100.780055798133-0.240055798133369
30100.19100.540016333697-0.350016333697397
31100.07100.19002381555-0.120023815550056
32100.18100.0700081665710.109991833429163
33100.08100.179992516018-0.0999925160177924
3499.66100.080006803616-0.420006803616118
3599.9299.66002857778930.259971422210668
3699.5199.9199823112186-0.409982311218599
37101.7799.51002789571032.25997210428967
38102.49101.7698462286650.720153771334552
39101.91102.489950999835-0.579950999834779
40100.57101.910039460593-1.34003946059292
41100.23100.570091177964-0.340091177964439
4299.99100.23002314023-0.240023140230022
4399.299.9900163314753-0.790016331475286
4499.0799.2000537537014-0.130053753701389
4598.7999.0700088490204-0.28000884902039
4699.3198.7900190521530.51998094784696
4798.9899.3099646198446-0.329964619844574
4897.6998.9800224512063-1.29002245120631
4998.997.69008777474451.20991222525555
5098.7598.8999176760557-0.149917676055736
5199.798.75001020058660.949989799413416
52100.1899.69993536150340.480064638496643
53100.14100.1799673358-0.0399673358002985
54100.13100.140002719428-0.010002719427618
5599.85100.130000680598-0.280000680597567
5699.3899.8500190515972-0.470019051597248
5798.8799.3800319806854-0.510031980685355
5897.7998.8700347032152-1.08003470321522
5997.3297.7900734869149-0.470073486914885
6097.2997.3200319843892-0.0300319843892112
6196.7397.2900020434139-0.56000204341386
6297.2296.73003810324090.48996189675907
6396.6697.2199666623784-0.559966662378443
6496.5896.6600381008335-0.0800381008335478
6596.4796.5800054458927-0.110005445892696
6696.796.47000748490840.229992515091581
6797.9196.6999843510211.21001564897898
6897.9797.90991766901860.0600823309813592
6998.2697.96999591192290.290004088077112
7097.898.2599802677584-0.459980267758368
7197.3397.8000312976339-0.470031297633938
7297.5697.33003198151860.229968018481401

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 86.62 & 83.8 & 2.82000000000001 \tabularnewline
3 & 83.98 & 86.6198081236655 & -2.6398081236655 \tabularnewline
4 & 82.59 & 83.9801796158534 & -1.39017961585337 \tabularnewline
5 & 82.3 & 82.5900945895635 & -0.290094589563466 \tabularnewline
6 & 81.64 & 82.3000197383995 & -0.66001973839947 \tabularnewline
7 & 81.66 & 81.6400449085702 & 0.0199550914297504 \tabularnewline
8 & 81.63 & 81.6599986422306 & -0.0299986422305665 \tabularnewline
9 & 85.54 & 81.6300020411452 & 3.90999795885479 \tabularnewline
10 & 85.62 & 85.5397339588382 & 0.0802660411617779 \tabularnewline
11 & 85.89 & 85.619994538598 & 0.270005461402036 \tabularnewline
12 & 86.38 & 85.88998162849 & 0.490018371510004 \tabularnewline
13 & 87.59 & 86.3799666585358 & 1.21003334146417 \tabularnewline
14 & 87.68 & 87.5899176678148 & 0.090082332185176 \tabularnewline
15 & 88.07 & 87.6799938706852 & 0.39000612931477 \tabularnewline
16 & 87.66 & 88.0699734634941 & -0.40997346349414 \tabularnewline
17 & 88.36 & 87.6600278951083 & 0.6999721048917 \tabularnewline
18 & 88.08 & 88.3599523730207 & -0.279952373020663 \tabularnewline
19 & 94.35 & 88.0800190483103 & 6.26998095168966 \tabularnewline
20 & 99.07 & 94.3495733826375 & 4.72042661736252 \tabularnewline
21 & 100.39 & 99.0696788162565 & 1.32032118374347 \tabularnewline
22 & 102.1 & 100.389910163692 & 1.71008983630819 \tabularnewline
23 & 102.89 & 102.099883643344 & 0.790116356655844 \tabularnewline
24 & 103.05 & 102.889946239493 & 0.160053760507196 \tabularnewline
25 & 102.78 & 103.049989109742 & -0.269989109741516 \tabularnewline
26 & 102.53 & 102.780018370397 & -0.250018370397413 \tabularnewline
27 & 101.6 & 102.530017011563 & -0.930017011563294 \tabularnewline
28 & 100.78 & 101.600063279523 & -0.820063279523112 \tabularnewline
29 & 100.54 & 100.780055798133 & -0.240055798133369 \tabularnewline
30 & 100.19 & 100.540016333697 & -0.350016333697397 \tabularnewline
31 & 100.07 & 100.19002381555 & -0.120023815550056 \tabularnewline
32 & 100.18 & 100.070008166571 & 0.109991833429163 \tabularnewline
33 & 100.08 & 100.179992516018 & -0.0999925160177924 \tabularnewline
34 & 99.66 & 100.080006803616 & -0.420006803616118 \tabularnewline
35 & 99.92 & 99.6600285777893 & 0.259971422210668 \tabularnewline
36 & 99.51 & 99.9199823112186 & -0.409982311218599 \tabularnewline
37 & 101.77 & 99.5100278957103 & 2.25997210428967 \tabularnewline
38 & 102.49 & 101.769846228665 & 0.720153771334552 \tabularnewline
39 & 101.91 & 102.489950999835 & -0.579950999834779 \tabularnewline
40 & 100.57 & 101.910039460593 & -1.34003946059292 \tabularnewline
41 & 100.23 & 100.570091177964 & -0.340091177964439 \tabularnewline
42 & 99.99 & 100.23002314023 & -0.240023140230022 \tabularnewline
43 & 99.2 & 99.9900163314753 & -0.790016331475286 \tabularnewline
44 & 99.07 & 99.2000537537014 & -0.130053753701389 \tabularnewline
45 & 98.79 & 99.0700088490204 & -0.28000884902039 \tabularnewline
46 & 99.31 & 98.790019052153 & 0.51998094784696 \tabularnewline
47 & 98.98 & 99.3099646198446 & -0.329964619844574 \tabularnewline
48 & 97.69 & 98.9800224512063 & -1.29002245120631 \tabularnewline
49 & 98.9 & 97.6900877747445 & 1.20991222525555 \tabularnewline
50 & 98.75 & 98.8999176760557 & -0.149917676055736 \tabularnewline
51 & 99.7 & 98.7500102005866 & 0.949989799413416 \tabularnewline
52 & 100.18 & 99.6999353615034 & 0.480064638496643 \tabularnewline
53 & 100.14 & 100.1799673358 & -0.0399673358002985 \tabularnewline
54 & 100.13 & 100.140002719428 & -0.010002719427618 \tabularnewline
55 & 99.85 & 100.130000680598 & -0.280000680597567 \tabularnewline
56 & 99.38 & 99.8500190515972 & -0.470019051597248 \tabularnewline
57 & 98.87 & 99.3800319806854 & -0.510031980685355 \tabularnewline
58 & 97.79 & 98.8700347032152 & -1.08003470321522 \tabularnewline
59 & 97.32 & 97.7900734869149 & -0.470073486914885 \tabularnewline
60 & 97.29 & 97.3200319843892 & -0.0300319843892112 \tabularnewline
61 & 96.73 & 97.2900020434139 & -0.56000204341386 \tabularnewline
62 & 97.22 & 96.7300381032409 & 0.48996189675907 \tabularnewline
63 & 96.66 & 97.2199666623784 & -0.559966662378443 \tabularnewline
64 & 96.58 & 96.6600381008335 & -0.0800381008335478 \tabularnewline
65 & 96.47 & 96.5800054458927 & -0.110005445892696 \tabularnewline
66 & 96.7 & 96.4700074849084 & 0.229992515091581 \tabularnewline
67 & 97.91 & 96.699984351021 & 1.21001564897898 \tabularnewline
68 & 97.97 & 97.9099176690186 & 0.0600823309813592 \tabularnewline
69 & 98.26 & 97.9699959119229 & 0.290004088077112 \tabularnewline
70 & 97.8 & 98.2599802677584 & -0.459980267758368 \tabularnewline
71 & 97.33 & 97.8000312976339 & -0.470031297633938 \tabularnewline
72 & 97.56 & 97.3300319815186 & 0.229968018481401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295054&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]86.62[/C][C]83.8[/C][C]2.82000000000001[/C][/ROW]
[ROW][C]3[/C][C]83.98[/C][C]86.6198081236655[/C][C]-2.6398081236655[/C][/ROW]
[ROW][C]4[/C][C]82.59[/C][C]83.9801796158534[/C][C]-1.39017961585337[/C][/ROW]
[ROW][C]5[/C][C]82.3[/C][C]82.5900945895635[/C][C]-0.290094589563466[/C][/ROW]
[ROW][C]6[/C][C]81.64[/C][C]82.3000197383995[/C][C]-0.66001973839947[/C][/ROW]
[ROW][C]7[/C][C]81.66[/C][C]81.6400449085702[/C][C]0.0199550914297504[/C][/ROW]
[ROW][C]8[/C][C]81.63[/C][C]81.6599986422306[/C][C]-0.0299986422305665[/C][/ROW]
[ROW][C]9[/C][C]85.54[/C][C]81.6300020411452[/C][C]3.90999795885479[/C][/ROW]
[ROW][C]10[/C][C]85.62[/C][C]85.5397339588382[/C][C]0.0802660411617779[/C][/ROW]
[ROW][C]11[/C][C]85.89[/C][C]85.619994538598[/C][C]0.270005461402036[/C][/ROW]
[ROW][C]12[/C][C]86.38[/C][C]85.88998162849[/C][C]0.490018371510004[/C][/ROW]
[ROW][C]13[/C][C]87.59[/C][C]86.3799666585358[/C][C]1.21003334146417[/C][/ROW]
[ROW][C]14[/C][C]87.68[/C][C]87.5899176678148[/C][C]0.090082332185176[/C][/ROW]
[ROW][C]15[/C][C]88.07[/C][C]87.6799938706852[/C][C]0.39000612931477[/C][/ROW]
[ROW][C]16[/C][C]87.66[/C][C]88.0699734634941[/C][C]-0.40997346349414[/C][/ROW]
[ROW][C]17[/C][C]88.36[/C][C]87.6600278951083[/C][C]0.6999721048917[/C][/ROW]
[ROW][C]18[/C][C]88.08[/C][C]88.3599523730207[/C][C]-0.279952373020663[/C][/ROW]
[ROW][C]19[/C][C]94.35[/C][C]88.0800190483103[/C][C]6.26998095168966[/C][/ROW]
[ROW][C]20[/C][C]99.07[/C][C]94.3495733826375[/C][C]4.72042661736252[/C][/ROW]
[ROW][C]21[/C][C]100.39[/C][C]99.0696788162565[/C][C]1.32032118374347[/C][/ROW]
[ROW][C]22[/C][C]102.1[/C][C]100.389910163692[/C][C]1.71008983630819[/C][/ROW]
[ROW][C]23[/C][C]102.89[/C][C]102.099883643344[/C][C]0.790116356655844[/C][/ROW]
[ROW][C]24[/C][C]103.05[/C][C]102.889946239493[/C][C]0.160053760507196[/C][/ROW]
[ROW][C]25[/C][C]102.78[/C][C]103.049989109742[/C][C]-0.269989109741516[/C][/ROW]
[ROW][C]26[/C][C]102.53[/C][C]102.780018370397[/C][C]-0.250018370397413[/C][/ROW]
[ROW][C]27[/C][C]101.6[/C][C]102.530017011563[/C][C]-0.930017011563294[/C][/ROW]
[ROW][C]28[/C][C]100.78[/C][C]101.600063279523[/C][C]-0.820063279523112[/C][/ROW]
[ROW][C]29[/C][C]100.54[/C][C]100.780055798133[/C][C]-0.240055798133369[/C][/ROW]
[ROW][C]30[/C][C]100.19[/C][C]100.540016333697[/C][C]-0.350016333697397[/C][/ROW]
[ROW][C]31[/C][C]100.07[/C][C]100.19002381555[/C][C]-0.120023815550056[/C][/ROW]
[ROW][C]32[/C][C]100.18[/C][C]100.070008166571[/C][C]0.109991833429163[/C][/ROW]
[ROW][C]33[/C][C]100.08[/C][C]100.179992516018[/C][C]-0.0999925160177924[/C][/ROW]
[ROW][C]34[/C][C]99.66[/C][C]100.080006803616[/C][C]-0.420006803616118[/C][/ROW]
[ROW][C]35[/C][C]99.92[/C][C]99.6600285777893[/C][C]0.259971422210668[/C][/ROW]
[ROW][C]36[/C][C]99.51[/C][C]99.9199823112186[/C][C]-0.409982311218599[/C][/ROW]
[ROW][C]37[/C][C]101.77[/C][C]99.5100278957103[/C][C]2.25997210428967[/C][/ROW]
[ROW][C]38[/C][C]102.49[/C][C]101.769846228665[/C][C]0.720153771334552[/C][/ROW]
[ROW][C]39[/C][C]101.91[/C][C]102.489950999835[/C][C]-0.579950999834779[/C][/ROW]
[ROW][C]40[/C][C]100.57[/C][C]101.910039460593[/C][C]-1.34003946059292[/C][/ROW]
[ROW][C]41[/C][C]100.23[/C][C]100.570091177964[/C][C]-0.340091177964439[/C][/ROW]
[ROW][C]42[/C][C]99.99[/C][C]100.23002314023[/C][C]-0.240023140230022[/C][/ROW]
[ROW][C]43[/C][C]99.2[/C][C]99.9900163314753[/C][C]-0.790016331475286[/C][/ROW]
[ROW][C]44[/C][C]99.07[/C][C]99.2000537537014[/C][C]-0.130053753701389[/C][/ROW]
[ROW][C]45[/C][C]98.79[/C][C]99.0700088490204[/C][C]-0.28000884902039[/C][/ROW]
[ROW][C]46[/C][C]99.31[/C][C]98.790019052153[/C][C]0.51998094784696[/C][/ROW]
[ROW][C]47[/C][C]98.98[/C][C]99.3099646198446[/C][C]-0.329964619844574[/C][/ROW]
[ROW][C]48[/C][C]97.69[/C][C]98.9800224512063[/C][C]-1.29002245120631[/C][/ROW]
[ROW][C]49[/C][C]98.9[/C][C]97.6900877747445[/C][C]1.20991222525555[/C][/ROW]
[ROW][C]50[/C][C]98.75[/C][C]98.8999176760557[/C][C]-0.149917676055736[/C][/ROW]
[ROW][C]51[/C][C]99.7[/C][C]98.7500102005866[/C][C]0.949989799413416[/C][/ROW]
[ROW][C]52[/C][C]100.18[/C][C]99.6999353615034[/C][C]0.480064638496643[/C][/ROW]
[ROW][C]53[/C][C]100.14[/C][C]100.1799673358[/C][C]-0.0399673358002985[/C][/ROW]
[ROW][C]54[/C][C]100.13[/C][C]100.140002719428[/C][C]-0.010002719427618[/C][/ROW]
[ROW][C]55[/C][C]99.85[/C][C]100.130000680598[/C][C]-0.280000680597567[/C][/ROW]
[ROW][C]56[/C][C]99.38[/C][C]99.8500190515972[/C][C]-0.470019051597248[/C][/ROW]
[ROW][C]57[/C][C]98.87[/C][C]99.3800319806854[/C][C]-0.510031980685355[/C][/ROW]
[ROW][C]58[/C][C]97.79[/C][C]98.8700347032152[/C][C]-1.08003470321522[/C][/ROW]
[ROW][C]59[/C][C]97.32[/C][C]97.7900734869149[/C][C]-0.470073486914885[/C][/ROW]
[ROW][C]60[/C][C]97.29[/C][C]97.3200319843892[/C][C]-0.0300319843892112[/C][/ROW]
[ROW][C]61[/C][C]96.73[/C][C]97.2900020434139[/C][C]-0.56000204341386[/C][/ROW]
[ROW][C]62[/C][C]97.22[/C][C]96.7300381032409[/C][C]0.48996189675907[/C][/ROW]
[ROW][C]63[/C][C]96.66[/C][C]97.2199666623784[/C][C]-0.559966662378443[/C][/ROW]
[ROW][C]64[/C][C]96.58[/C][C]96.6600381008335[/C][C]-0.0800381008335478[/C][/ROW]
[ROW][C]65[/C][C]96.47[/C][C]96.5800054458927[/C][C]-0.110005445892696[/C][/ROW]
[ROW][C]66[/C][C]96.7[/C][C]96.4700074849084[/C][C]0.229992515091581[/C][/ROW]
[ROW][C]67[/C][C]97.91[/C][C]96.699984351021[/C][C]1.21001564897898[/C][/ROW]
[ROW][C]68[/C][C]97.97[/C][C]97.9099176690186[/C][C]0.0600823309813592[/C][/ROW]
[ROW][C]69[/C][C]98.26[/C][C]97.9699959119229[/C][C]0.290004088077112[/C][/ROW]
[ROW][C]70[/C][C]97.8[/C][C]98.2599802677584[/C][C]-0.459980267758368[/C][/ROW]
[ROW][C]71[/C][C]97.33[/C][C]97.8000312976339[/C][C]-0.470031297633938[/C][/ROW]
[ROW][C]72[/C][C]97.56[/C][C]97.3300319815186[/C][C]0.229968018481401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295054&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295054&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
286.6283.82.82000000000001
383.9886.6198081236655-2.6398081236655
482.5983.9801796158534-1.39017961585337
582.382.5900945895635-0.290094589563466
681.6482.3000197383995-0.66001973839947
781.6681.64004490857020.0199550914297504
881.6381.6599986422306-0.0299986422305665
985.5481.63000204114523.90999795885479
1085.6285.53973395883820.0802660411617779
1185.8985.6199945385980.270005461402036
1286.3885.889981628490.490018371510004
1387.5986.37996665853581.21003334146417
1487.6887.58991766781480.090082332185176
1588.0787.67999387068520.39000612931477
1687.6688.0699734634941-0.40997346349414
1788.3687.66002789510830.6999721048917
1888.0888.3599523730207-0.279952373020663
1994.3588.08001904831036.26998095168966
2099.0794.34957338263754.72042661736252
21100.3999.06967881625651.32032118374347
22102.1100.3899101636921.71008983630819
23102.89102.0998836433440.790116356655844
24103.05102.8899462394930.160053760507196
25102.78103.049989109742-0.269989109741516
26102.53102.780018370397-0.250018370397413
27101.6102.530017011563-0.930017011563294
28100.78101.600063279523-0.820063279523112
29100.54100.780055798133-0.240055798133369
30100.19100.540016333697-0.350016333697397
31100.07100.19002381555-0.120023815550056
32100.18100.0700081665710.109991833429163
33100.08100.179992516018-0.0999925160177924
3499.66100.080006803616-0.420006803616118
3599.9299.66002857778930.259971422210668
3699.5199.9199823112186-0.409982311218599
37101.7799.51002789571032.25997210428967
38102.49101.7698462286650.720153771334552
39101.91102.489950999835-0.579950999834779
40100.57101.910039460593-1.34003946059292
41100.23100.570091177964-0.340091177964439
4299.99100.23002314023-0.240023140230022
4399.299.9900163314753-0.790016331475286
4499.0799.2000537537014-0.130053753701389
4598.7999.0700088490204-0.28000884902039
4699.3198.7900190521530.51998094784696
4798.9899.3099646198446-0.329964619844574
4897.6998.9800224512063-1.29002245120631
4998.997.69008777474451.20991222525555
5098.7598.8999176760557-0.149917676055736
5199.798.75001020058660.949989799413416
52100.1899.69993536150340.480064638496643
53100.14100.1799673358-0.0399673358002985
54100.13100.140002719428-0.010002719427618
5599.85100.130000680598-0.280000680597567
5699.3899.8500190515972-0.470019051597248
5798.8799.3800319806854-0.510031980685355
5897.7998.8700347032152-1.08003470321522
5997.3297.7900734869149-0.470073486914885
6097.2997.3200319843892-0.0300319843892112
6196.7397.2900020434139-0.56000204341386
6297.2296.73003810324090.48996189675907
6396.6697.2199666623784-0.559966662378443
6496.5896.6600381008335-0.0800381008335478
6596.4796.5800054458927-0.110005445892696
6696.796.47000748490840.229992515091581
6797.9196.6999843510211.21001564897898
6897.9797.90991766901860.0600823309813592
6998.2697.96999591192290.290004088077112
7097.898.2599802677584-0.459980267758368
7197.3397.8000312976339-0.470031297633938
7297.5697.33003198151860.229968018481401







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7397.559984352687894.9924091146885100.127559590687
7497.559984352687893.9290081588826101.190960546493
7597.559984352687893.1130153133114102.006953392064
7697.559984352687892.4250959260163102.694872779359
7797.559984352687891.8190240957658103.30094460961
7897.559984352687891.2710917483614103.848876957014
7997.559984352687890.7672149832816104.352753722094
8097.559984352687890.2982172658737104.821751439502
8197.559984352687889.8577245063616105.262244199014
8297.559984352687889.4410957429382105.678872962437
8397.559984352687889.044827409054106.075141296322
8497.559984352687888.6661975724739106.453771132902

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 97.5599843526878 & 94.9924091146885 & 100.127559590687 \tabularnewline
74 & 97.5599843526878 & 93.9290081588826 & 101.190960546493 \tabularnewline
75 & 97.5599843526878 & 93.1130153133114 & 102.006953392064 \tabularnewline
76 & 97.5599843526878 & 92.4250959260163 & 102.694872779359 \tabularnewline
77 & 97.5599843526878 & 91.8190240957658 & 103.30094460961 \tabularnewline
78 & 97.5599843526878 & 91.2710917483614 & 103.848876957014 \tabularnewline
79 & 97.5599843526878 & 90.7672149832816 & 104.352753722094 \tabularnewline
80 & 97.5599843526878 & 90.2982172658737 & 104.821751439502 \tabularnewline
81 & 97.5599843526878 & 89.8577245063616 & 105.262244199014 \tabularnewline
82 & 97.5599843526878 & 89.4410957429382 & 105.678872962437 \tabularnewline
83 & 97.5599843526878 & 89.044827409054 & 106.075141296322 \tabularnewline
84 & 97.5599843526878 & 88.6661975724739 & 106.453771132902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295054&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]97.5599843526878[/C][C]94.9924091146885[/C][C]100.127559590687[/C][/ROW]
[ROW][C]74[/C][C]97.5599843526878[/C][C]93.9290081588826[/C][C]101.190960546493[/C][/ROW]
[ROW][C]75[/C][C]97.5599843526878[/C][C]93.1130153133114[/C][C]102.006953392064[/C][/ROW]
[ROW][C]76[/C][C]97.5599843526878[/C][C]92.4250959260163[/C][C]102.694872779359[/C][/ROW]
[ROW][C]77[/C][C]97.5599843526878[/C][C]91.8190240957658[/C][C]103.30094460961[/C][/ROW]
[ROW][C]78[/C][C]97.5599843526878[/C][C]91.2710917483614[/C][C]103.848876957014[/C][/ROW]
[ROW][C]79[/C][C]97.5599843526878[/C][C]90.7672149832816[/C][C]104.352753722094[/C][/ROW]
[ROW][C]80[/C][C]97.5599843526878[/C][C]90.2982172658737[/C][C]104.821751439502[/C][/ROW]
[ROW][C]81[/C][C]97.5599843526878[/C][C]89.8577245063616[/C][C]105.262244199014[/C][/ROW]
[ROW][C]82[/C][C]97.5599843526878[/C][C]89.4410957429382[/C][C]105.678872962437[/C][/ROW]
[ROW][C]83[/C][C]97.5599843526878[/C][C]89.044827409054[/C][C]106.075141296322[/C][/ROW]
[ROW][C]84[/C][C]97.5599843526878[/C][C]88.6661975724739[/C][C]106.453771132902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295054&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295054&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
7397.559984352687894.9924091146885100.127559590687
7497.559984352687893.9290081588826101.190960546493
7597.559984352687893.1130153133114102.006953392064
7697.559984352687892.4250959260163102.694872779359
7797.559984352687891.8190240957658103.30094460961
7897.559984352687891.2710917483614103.848876957014
7997.559984352687890.7672149832816104.352753722094
8097.559984352687890.2982172658737104.821751439502
8197.559984352687889.8577245063616105.262244199014
8297.559984352687889.4410957429382105.678872962437
8397.559984352687889.044827409054106.075141296322
8497.559984352687888.6661975724739106.453771132902



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')