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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 15:31:18 +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/25/t146159469540my89yg8hf2a81.htm/, Retrieved Mon, 06 May 2024 05:35:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294716, Retrieved Mon, 06 May 2024 05:35:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 14:31:18] [c0f67b4e93ea0adf92c2b9d3976edd70] [Current]
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Dataseries X:
87.5
87.3
87.8
88.1
88.0
87.8
87.0
87.2
87.0
89.4
89.1
87.8
87.8
88.0
86.5
84.1
84.3
84.7
85.7
86.4
86.0
86.9
89.1
90.7
89.8
89.4
88.6
86.8
86.8
89.5
88.5
91.2
92.3
92.0
92.8
92.9
92.7
94.2
94.0
94.3
94.8
94.7
95.1
97.0
97.9
97.3
96.5
98.1
99.3
99.9
99.9
99.9
99.8
99.5
99.9
100.1
100.1
100.2
100.6
100.8
100.8
100.5
101.0
100.5
99.0
97.9
97.6
97.2
96.5
96.3
96.3
96.2
95.6
93.5
93.2
93.6
94.6
96.1
98.4
99.6
99.4
99.7
100.1
99.9




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=294716&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=294716&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294716&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
alpha1
beta0.0485945014061319
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0485945014061319 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294716&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]0.0485945014061319[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294716&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294716&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
beta0.0485945014061319
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
387.887.10.700000000000003
488.187.63401615098430.465983849015714
58887.95666040379050.043339596209492
687.887.8587664698595-0.0587664698594637
78787.6559107425572-0.655910742557239
887.286.82403708705570.37596291294426
98787.0423068173575-0.0423068173574705
1089.486.84025093866192.5597490613381
1189.189.3646406680224-0.264640668022452
1287.889.0517805867081-1.25178058670811
1387.887.69095093322710.109049066772855
148887.69625011825580.303749881744224
1586.587.9110106923113-1.41101069231131
1684.186.3424433312397-2.24244333123973
1784.383.83347291562660.466527084373382
1884.784.05614356668420.643856433315804
1985.784.48743144903831.21256855096168
2086.485.54635561319310.853644386806948
218686.2878380365481-0.287838036548081
2286.985.87385069067631.0261493093237
2389.186.82371590473112.27628409526885
2490.789.13433079539941.56566920460057
2589.890.8104137097639-1.01041370976394
2689.489.861313159324-0.461313159324035
2788.689.4388958763546-0.838895876354613
2886.888.5981301495115-1.79813014951148
2986.886.71075091143260.0892490885673567
3089.586.71508792639252.78491207360747
3188.589.5504193400694-1.0504193400694
3291.288.49937473597142.70062526402863
3392.391.33061027416160.969389725838354
349292.477717284557-0.477717284556988
3592.892.15450285130080.64549714869915
3692.992.985870463401-0.0858704634009513
3792.793.0816976310465-0.381697631046478
3894.292.86314922497791.33685077502213
399494.4281128218445-0.428112821844479
4094.394.20730889272140.0926911072786254
4194.894.51181317086440.28818682913564
4294.795.025817466138-0.325817466138005
4395.194.90998452882160.190015471178356
449795.3192182359031.68078176409701
4597.997.30089498770180.599105012298196
4697.398.2300081970644-0.930008197064367
4796.597.5848149124244-1.08481491242439
4898.196.73209887263721.3679011273628
4999.398.39857134589430.901428654105729
5099.999.64237582189370.257624178106269
5199.9100.254894940379-0.354894940378983
5299.9100.2376489977-0.337648997699702
5399.8100.221241113006-0.421241113006218
5499.5100.100771111148-0.600771111147907
5599.999.77157693854250.128423061457539
56100.1100.177817593183-0.077817593183056
57100.1100.374036086042-0.27403608604169
58100.2100.360719439073-0.160719439073205
59100.6100.4529093580650.147090641934824
60100.8100.860057154471-0.0600571544714938
61100.8101.057138706994-0.257138706994084
62100.5101.044643179735-0.544643179735488
63101100.7181765159720.28182348402801
64100.5101.231871587663-0.73187158766288
6599100.696306652767-1.69630665276709
6697.999.113875476744-1.21387547674397
6797.697.9548878031825-0.354887803182478
6897.297.6376422073317-0.437642207331677
6996.597.2163752024721-0.716375202472136
7096.396.4815633066883-0.181563306688275
7196.396.27274032832610.0272596716738889
7296.296.2740649984796-0.0740649984795994
7395.696.1704658468068-0.57046584680684
7493.595.542744343412-2.04274434341202
7593.293.3434782005437-0.143478200543726
7693.693.03650594892570.563494051074329
7794.693.46388866138291.13611133861707
7896.194.51909742542491.58090257457512
7998.496.0959205978082.30407940219197
8099.698.50788618755771.09211381244229
8199.499.7609569137521-0.360956913752062
8299.799.54341639249920.156583607500806
83100.199.85102549483410.248974505165918
8499.9100.263124286775-0.363124286775431

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 87.8 & 87.1 & 0.700000000000003 \tabularnewline
4 & 88.1 & 87.6340161509843 & 0.465983849015714 \tabularnewline
5 & 88 & 87.9566604037905 & 0.043339596209492 \tabularnewline
6 & 87.8 & 87.8587664698595 & -0.0587664698594637 \tabularnewline
7 & 87 & 87.6559107425572 & -0.655910742557239 \tabularnewline
8 & 87.2 & 86.8240370870557 & 0.37596291294426 \tabularnewline
9 & 87 & 87.0423068173575 & -0.0423068173574705 \tabularnewline
10 & 89.4 & 86.8402509386619 & 2.5597490613381 \tabularnewline
11 & 89.1 & 89.3646406680224 & -0.264640668022452 \tabularnewline
12 & 87.8 & 89.0517805867081 & -1.25178058670811 \tabularnewline
13 & 87.8 & 87.6909509332271 & 0.109049066772855 \tabularnewline
14 & 88 & 87.6962501182558 & 0.303749881744224 \tabularnewline
15 & 86.5 & 87.9110106923113 & -1.41101069231131 \tabularnewline
16 & 84.1 & 86.3424433312397 & -2.24244333123973 \tabularnewline
17 & 84.3 & 83.8334729156266 & 0.466527084373382 \tabularnewline
18 & 84.7 & 84.0561435666842 & 0.643856433315804 \tabularnewline
19 & 85.7 & 84.4874314490383 & 1.21256855096168 \tabularnewline
20 & 86.4 & 85.5463556131931 & 0.853644386806948 \tabularnewline
21 & 86 & 86.2878380365481 & -0.287838036548081 \tabularnewline
22 & 86.9 & 85.8738506906763 & 1.0261493093237 \tabularnewline
23 & 89.1 & 86.8237159047311 & 2.27628409526885 \tabularnewline
24 & 90.7 & 89.1343307953994 & 1.56566920460057 \tabularnewline
25 & 89.8 & 90.8104137097639 & -1.01041370976394 \tabularnewline
26 & 89.4 & 89.861313159324 & -0.461313159324035 \tabularnewline
27 & 88.6 & 89.4388958763546 & -0.838895876354613 \tabularnewline
28 & 86.8 & 88.5981301495115 & -1.79813014951148 \tabularnewline
29 & 86.8 & 86.7107509114326 & 0.0892490885673567 \tabularnewline
30 & 89.5 & 86.7150879263925 & 2.78491207360747 \tabularnewline
31 & 88.5 & 89.5504193400694 & -1.0504193400694 \tabularnewline
32 & 91.2 & 88.4993747359714 & 2.70062526402863 \tabularnewline
33 & 92.3 & 91.3306102741616 & 0.969389725838354 \tabularnewline
34 & 92 & 92.477717284557 & -0.477717284556988 \tabularnewline
35 & 92.8 & 92.1545028513008 & 0.64549714869915 \tabularnewline
36 & 92.9 & 92.985870463401 & -0.0858704634009513 \tabularnewline
37 & 92.7 & 93.0816976310465 & -0.381697631046478 \tabularnewline
38 & 94.2 & 92.8631492249779 & 1.33685077502213 \tabularnewline
39 & 94 & 94.4281128218445 & -0.428112821844479 \tabularnewline
40 & 94.3 & 94.2073088927214 & 0.0926911072786254 \tabularnewline
41 & 94.8 & 94.5118131708644 & 0.28818682913564 \tabularnewline
42 & 94.7 & 95.025817466138 & -0.325817466138005 \tabularnewline
43 & 95.1 & 94.9099845288216 & 0.190015471178356 \tabularnewline
44 & 97 & 95.319218235903 & 1.68078176409701 \tabularnewline
45 & 97.9 & 97.3008949877018 & 0.599105012298196 \tabularnewline
46 & 97.3 & 98.2300081970644 & -0.930008197064367 \tabularnewline
47 & 96.5 & 97.5848149124244 & -1.08481491242439 \tabularnewline
48 & 98.1 & 96.7320988726372 & 1.3679011273628 \tabularnewline
49 & 99.3 & 98.3985713458943 & 0.901428654105729 \tabularnewline
50 & 99.9 & 99.6423758218937 & 0.257624178106269 \tabularnewline
51 & 99.9 & 100.254894940379 & -0.354894940378983 \tabularnewline
52 & 99.9 & 100.2376489977 & -0.337648997699702 \tabularnewline
53 & 99.8 & 100.221241113006 & -0.421241113006218 \tabularnewline
54 & 99.5 & 100.100771111148 & -0.600771111147907 \tabularnewline
55 & 99.9 & 99.7715769385425 & 0.128423061457539 \tabularnewline
56 & 100.1 & 100.177817593183 & -0.077817593183056 \tabularnewline
57 & 100.1 & 100.374036086042 & -0.27403608604169 \tabularnewline
58 & 100.2 & 100.360719439073 & -0.160719439073205 \tabularnewline
59 & 100.6 & 100.452909358065 & 0.147090641934824 \tabularnewline
60 & 100.8 & 100.860057154471 & -0.0600571544714938 \tabularnewline
61 & 100.8 & 101.057138706994 & -0.257138706994084 \tabularnewline
62 & 100.5 & 101.044643179735 & -0.544643179735488 \tabularnewline
63 & 101 & 100.718176515972 & 0.28182348402801 \tabularnewline
64 & 100.5 & 101.231871587663 & -0.73187158766288 \tabularnewline
65 & 99 & 100.696306652767 & -1.69630665276709 \tabularnewline
66 & 97.9 & 99.113875476744 & -1.21387547674397 \tabularnewline
67 & 97.6 & 97.9548878031825 & -0.354887803182478 \tabularnewline
68 & 97.2 & 97.6376422073317 & -0.437642207331677 \tabularnewline
69 & 96.5 & 97.2163752024721 & -0.716375202472136 \tabularnewline
70 & 96.3 & 96.4815633066883 & -0.181563306688275 \tabularnewline
71 & 96.3 & 96.2727403283261 & 0.0272596716738889 \tabularnewline
72 & 96.2 & 96.2740649984796 & -0.0740649984795994 \tabularnewline
73 & 95.6 & 96.1704658468068 & -0.57046584680684 \tabularnewline
74 & 93.5 & 95.542744343412 & -2.04274434341202 \tabularnewline
75 & 93.2 & 93.3434782005437 & -0.143478200543726 \tabularnewline
76 & 93.6 & 93.0365059489257 & 0.563494051074329 \tabularnewline
77 & 94.6 & 93.4638886613829 & 1.13611133861707 \tabularnewline
78 & 96.1 & 94.5190974254249 & 1.58090257457512 \tabularnewline
79 & 98.4 & 96.095920597808 & 2.30407940219197 \tabularnewline
80 & 99.6 & 98.5078861875577 & 1.09211381244229 \tabularnewline
81 & 99.4 & 99.7609569137521 & -0.360956913752062 \tabularnewline
82 & 99.7 & 99.5434163924992 & 0.156583607500806 \tabularnewline
83 & 100.1 & 99.8510254948341 & 0.248974505165918 \tabularnewline
84 & 99.9 & 100.263124286775 & -0.363124286775431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294716&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]87.8[/C][C]87.1[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]4[/C][C]88.1[/C][C]87.6340161509843[/C][C]0.465983849015714[/C][/ROW]
[ROW][C]5[/C][C]88[/C][C]87.9566604037905[/C][C]0.043339596209492[/C][/ROW]
[ROW][C]6[/C][C]87.8[/C][C]87.8587664698595[/C][C]-0.0587664698594637[/C][/ROW]
[ROW][C]7[/C][C]87[/C][C]87.6559107425572[/C][C]-0.655910742557239[/C][/ROW]
[ROW][C]8[/C][C]87.2[/C][C]86.8240370870557[/C][C]0.37596291294426[/C][/ROW]
[ROW][C]9[/C][C]87[/C][C]87.0423068173575[/C][C]-0.0423068173574705[/C][/ROW]
[ROW][C]10[/C][C]89.4[/C][C]86.8402509386619[/C][C]2.5597490613381[/C][/ROW]
[ROW][C]11[/C][C]89.1[/C][C]89.3646406680224[/C][C]-0.264640668022452[/C][/ROW]
[ROW][C]12[/C][C]87.8[/C][C]89.0517805867081[/C][C]-1.25178058670811[/C][/ROW]
[ROW][C]13[/C][C]87.8[/C][C]87.6909509332271[/C][C]0.109049066772855[/C][/ROW]
[ROW][C]14[/C][C]88[/C][C]87.6962501182558[/C][C]0.303749881744224[/C][/ROW]
[ROW][C]15[/C][C]86.5[/C][C]87.9110106923113[/C][C]-1.41101069231131[/C][/ROW]
[ROW][C]16[/C][C]84.1[/C][C]86.3424433312397[/C][C]-2.24244333123973[/C][/ROW]
[ROW][C]17[/C][C]84.3[/C][C]83.8334729156266[/C][C]0.466527084373382[/C][/ROW]
[ROW][C]18[/C][C]84.7[/C][C]84.0561435666842[/C][C]0.643856433315804[/C][/ROW]
[ROW][C]19[/C][C]85.7[/C][C]84.4874314490383[/C][C]1.21256855096168[/C][/ROW]
[ROW][C]20[/C][C]86.4[/C][C]85.5463556131931[/C][C]0.853644386806948[/C][/ROW]
[ROW][C]21[/C][C]86[/C][C]86.2878380365481[/C][C]-0.287838036548081[/C][/ROW]
[ROW][C]22[/C][C]86.9[/C][C]85.8738506906763[/C][C]1.0261493093237[/C][/ROW]
[ROW][C]23[/C][C]89.1[/C][C]86.8237159047311[/C][C]2.27628409526885[/C][/ROW]
[ROW][C]24[/C][C]90.7[/C][C]89.1343307953994[/C][C]1.56566920460057[/C][/ROW]
[ROW][C]25[/C][C]89.8[/C][C]90.8104137097639[/C][C]-1.01041370976394[/C][/ROW]
[ROW][C]26[/C][C]89.4[/C][C]89.861313159324[/C][C]-0.461313159324035[/C][/ROW]
[ROW][C]27[/C][C]88.6[/C][C]89.4388958763546[/C][C]-0.838895876354613[/C][/ROW]
[ROW][C]28[/C][C]86.8[/C][C]88.5981301495115[/C][C]-1.79813014951148[/C][/ROW]
[ROW][C]29[/C][C]86.8[/C][C]86.7107509114326[/C][C]0.0892490885673567[/C][/ROW]
[ROW][C]30[/C][C]89.5[/C][C]86.7150879263925[/C][C]2.78491207360747[/C][/ROW]
[ROW][C]31[/C][C]88.5[/C][C]89.5504193400694[/C][C]-1.0504193400694[/C][/ROW]
[ROW][C]32[/C][C]91.2[/C][C]88.4993747359714[/C][C]2.70062526402863[/C][/ROW]
[ROW][C]33[/C][C]92.3[/C][C]91.3306102741616[/C][C]0.969389725838354[/C][/ROW]
[ROW][C]34[/C][C]92[/C][C]92.477717284557[/C][C]-0.477717284556988[/C][/ROW]
[ROW][C]35[/C][C]92.8[/C][C]92.1545028513008[/C][C]0.64549714869915[/C][/ROW]
[ROW][C]36[/C][C]92.9[/C][C]92.985870463401[/C][C]-0.0858704634009513[/C][/ROW]
[ROW][C]37[/C][C]92.7[/C][C]93.0816976310465[/C][C]-0.381697631046478[/C][/ROW]
[ROW][C]38[/C][C]94.2[/C][C]92.8631492249779[/C][C]1.33685077502213[/C][/ROW]
[ROW][C]39[/C][C]94[/C][C]94.4281128218445[/C][C]-0.428112821844479[/C][/ROW]
[ROW][C]40[/C][C]94.3[/C][C]94.2073088927214[/C][C]0.0926911072786254[/C][/ROW]
[ROW][C]41[/C][C]94.8[/C][C]94.5118131708644[/C][C]0.28818682913564[/C][/ROW]
[ROW][C]42[/C][C]94.7[/C][C]95.025817466138[/C][C]-0.325817466138005[/C][/ROW]
[ROW][C]43[/C][C]95.1[/C][C]94.9099845288216[/C][C]0.190015471178356[/C][/ROW]
[ROW][C]44[/C][C]97[/C][C]95.319218235903[/C][C]1.68078176409701[/C][/ROW]
[ROW][C]45[/C][C]97.9[/C][C]97.3008949877018[/C][C]0.599105012298196[/C][/ROW]
[ROW][C]46[/C][C]97.3[/C][C]98.2300081970644[/C][C]-0.930008197064367[/C][/ROW]
[ROW][C]47[/C][C]96.5[/C][C]97.5848149124244[/C][C]-1.08481491242439[/C][/ROW]
[ROW][C]48[/C][C]98.1[/C][C]96.7320988726372[/C][C]1.3679011273628[/C][/ROW]
[ROW][C]49[/C][C]99.3[/C][C]98.3985713458943[/C][C]0.901428654105729[/C][/ROW]
[ROW][C]50[/C][C]99.9[/C][C]99.6423758218937[/C][C]0.257624178106269[/C][/ROW]
[ROW][C]51[/C][C]99.9[/C][C]100.254894940379[/C][C]-0.354894940378983[/C][/ROW]
[ROW][C]52[/C][C]99.9[/C][C]100.2376489977[/C][C]-0.337648997699702[/C][/ROW]
[ROW][C]53[/C][C]99.8[/C][C]100.221241113006[/C][C]-0.421241113006218[/C][/ROW]
[ROW][C]54[/C][C]99.5[/C][C]100.100771111148[/C][C]-0.600771111147907[/C][/ROW]
[ROW][C]55[/C][C]99.9[/C][C]99.7715769385425[/C][C]0.128423061457539[/C][/ROW]
[ROW][C]56[/C][C]100.1[/C][C]100.177817593183[/C][C]-0.077817593183056[/C][/ROW]
[ROW][C]57[/C][C]100.1[/C][C]100.374036086042[/C][C]-0.27403608604169[/C][/ROW]
[ROW][C]58[/C][C]100.2[/C][C]100.360719439073[/C][C]-0.160719439073205[/C][/ROW]
[ROW][C]59[/C][C]100.6[/C][C]100.452909358065[/C][C]0.147090641934824[/C][/ROW]
[ROW][C]60[/C][C]100.8[/C][C]100.860057154471[/C][C]-0.0600571544714938[/C][/ROW]
[ROW][C]61[/C][C]100.8[/C][C]101.057138706994[/C][C]-0.257138706994084[/C][/ROW]
[ROW][C]62[/C][C]100.5[/C][C]101.044643179735[/C][C]-0.544643179735488[/C][/ROW]
[ROW][C]63[/C][C]101[/C][C]100.718176515972[/C][C]0.28182348402801[/C][/ROW]
[ROW][C]64[/C][C]100.5[/C][C]101.231871587663[/C][C]-0.73187158766288[/C][/ROW]
[ROW][C]65[/C][C]99[/C][C]100.696306652767[/C][C]-1.69630665276709[/C][/ROW]
[ROW][C]66[/C][C]97.9[/C][C]99.113875476744[/C][C]-1.21387547674397[/C][/ROW]
[ROW][C]67[/C][C]97.6[/C][C]97.9548878031825[/C][C]-0.354887803182478[/C][/ROW]
[ROW][C]68[/C][C]97.2[/C][C]97.6376422073317[/C][C]-0.437642207331677[/C][/ROW]
[ROW][C]69[/C][C]96.5[/C][C]97.2163752024721[/C][C]-0.716375202472136[/C][/ROW]
[ROW][C]70[/C][C]96.3[/C][C]96.4815633066883[/C][C]-0.181563306688275[/C][/ROW]
[ROW][C]71[/C][C]96.3[/C][C]96.2727403283261[/C][C]0.0272596716738889[/C][/ROW]
[ROW][C]72[/C][C]96.2[/C][C]96.2740649984796[/C][C]-0.0740649984795994[/C][/ROW]
[ROW][C]73[/C][C]95.6[/C][C]96.1704658468068[/C][C]-0.57046584680684[/C][/ROW]
[ROW][C]74[/C][C]93.5[/C][C]95.542744343412[/C][C]-2.04274434341202[/C][/ROW]
[ROW][C]75[/C][C]93.2[/C][C]93.3434782005437[/C][C]-0.143478200543726[/C][/ROW]
[ROW][C]76[/C][C]93.6[/C][C]93.0365059489257[/C][C]0.563494051074329[/C][/ROW]
[ROW][C]77[/C][C]94.6[/C][C]93.4638886613829[/C][C]1.13611133861707[/C][/ROW]
[ROW][C]78[/C][C]96.1[/C][C]94.5190974254249[/C][C]1.58090257457512[/C][/ROW]
[ROW][C]79[/C][C]98.4[/C][C]96.095920597808[/C][C]2.30407940219197[/C][/ROW]
[ROW][C]80[/C][C]99.6[/C][C]98.5078861875577[/C][C]1.09211381244229[/C][/ROW]
[ROW][C]81[/C][C]99.4[/C][C]99.7609569137521[/C][C]-0.360956913752062[/C][/ROW]
[ROW][C]82[/C][C]99.7[/C][C]99.5434163924992[/C][C]0.156583607500806[/C][/ROW]
[ROW][C]83[/C][C]100.1[/C][C]99.8510254948341[/C][C]0.248974505165918[/C][/ROW]
[ROW][C]84[/C][C]99.9[/C][C]100.263124286775[/C][C]-0.363124286775431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294716&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294716&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
387.887.10.700000000000003
488.187.63401615098430.465983849015714
58887.95666040379050.043339596209492
687.887.8587664698595-0.0587664698594637
78787.6559107425572-0.655910742557239
887.286.82403708705570.37596291294426
98787.0423068173575-0.0423068173574705
1089.486.84025093866192.5597490613381
1189.189.3646406680224-0.264640668022452
1287.889.0517805867081-1.25178058670811
1387.887.69095093322710.109049066772855
148887.69625011825580.303749881744224
1586.587.9110106923113-1.41101069231131
1684.186.3424433312397-2.24244333123973
1784.383.83347291562660.466527084373382
1884.784.05614356668420.643856433315804
1985.784.48743144903831.21256855096168
2086.485.54635561319310.853644386806948
218686.2878380365481-0.287838036548081
2286.985.87385069067631.0261493093237
2389.186.82371590473112.27628409526885
2490.789.13433079539941.56566920460057
2589.890.8104137097639-1.01041370976394
2689.489.861313159324-0.461313159324035
2788.689.4388958763546-0.838895876354613
2886.888.5981301495115-1.79813014951148
2986.886.71075091143260.0892490885673567
3089.586.71508792639252.78491207360747
3188.589.5504193400694-1.0504193400694
3291.288.49937473597142.70062526402863
3392.391.33061027416160.969389725838354
349292.477717284557-0.477717284556988
3592.892.15450285130080.64549714869915
3692.992.985870463401-0.0858704634009513
3792.793.0816976310465-0.381697631046478
3894.292.86314922497791.33685077502213
399494.4281128218445-0.428112821844479
4094.394.20730889272140.0926911072786254
4194.894.51181317086440.28818682913564
4294.795.025817466138-0.325817466138005
4395.194.90998452882160.190015471178356
449795.3192182359031.68078176409701
4597.997.30089498770180.599105012298196
4697.398.2300081970644-0.930008197064367
4796.597.5848149124244-1.08481491242439
4898.196.73209887263721.3679011273628
4999.398.39857134589430.901428654105729
5099.999.64237582189370.257624178106269
5199.9100.254894940379-0.354894940378983
5299.9100.2376489977-0.337648997699702
5399.8100.221241113006-0.421241113006218
5499.5100.100771111148-0.600771111147907
5599.999.77157693854250.128423061457539
56100.1100.177817593183-0.077817593183056
57100.1100.374036086042-0.27403608604169
58100.2100.360719439073-0.160719439073205
59100.6100.4529093580650.147090641934824
60100.8100.860057154471-0.0600571544714938
61100.8101.057138706994-0.257138706994084
62100.5101.044643179735-0.544643179735488
63101100.7181765159720.28182348402801
64100.5101.231871587663-0.73187158766288
6599100.696306652767-1.69630665276709
6697.999.113875476744-1.21387547674397
6797.697.9548878031825-0.354887803182478
6897.297.6376422073317-0.437642207331677
6996.597.2163752024721-0.716375202472136
7096.396.4815633066883-0.181563306688275
7196.396.27274032832610.0272596716738889
7296.296.2740649984796-0.0740649984795994
7395.696.1704658468068-0.57046584680684
7493.595.542744343412-2.04274434341202
7593.293.3434782005437-0.143478200543726
7693.693.03650594892570.563494051074329
7794.693.46388866138291.13611133861707
7896.194.51909742542491.58090257457512
7998.496.0959205978082.30407940219197
8099.698.50788618755771.09211381244229
8199.499.7609569137521-0.360956913752062
8299.799.54341639249920.156583607500806
83100.199.85102549483410.248974505165918
8499.9100.263124286775-0.363124286775431







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85100.04547844311198.0562909402583102.034665945964
86100.19095688622297.3086589071633103.073254865281
87100.33643532933396.7210498935644103.951820765102
88100.48191377244596.2080788151512104.755748729738
89100.62739221555695.7375773404762105.517207090635
90100.77287065866795.2934936545086106.252247662825
91100.91834910177894.8665558585272106.970142345029
92101.06382754488994.4508959315993107.676759158179
93101.20930598894.0425599177044108.376052058296
94101.35478443111193.6387593342987109.070809527924
95101.50026287422393.2374586050231109.763067143422
96101.64574131733492.8371313124068110.454351322261

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 100.045478443111 & 98.0562909402583 & 102.034665945964 \tabularnewline
86 & 100.190956886222 & 97.3086589071633 & 103.073254865281 \tabularnewline
87 & 100.336435329333 & 96.7210498935644 & 103.951820765102 \tabularnewline
88 & 100.481913772445 & 96.2080788151512 & 104.755748729738 \tabularnewline
89 & 100.627392215556 & 95.7375773404762 & 105.517207090635 \tabularnewline
90 & 100.772870658667 & 95.2934936545086 & 106.252247662825 \tabularnewline
91 & 100.918349101778 & 94.8665558585272 & 106.970142345029 \tabularnewline
92 & 101.063827544889 & 94.4508959315993 & 107.676759158179 \tabularnewline
93 & 101.209305988 & 94.0425599177044 & 108.376052058296 \tabularnewline
94 & 101.354784431111 & 93.6387593342987 & 109.070809527924 \tabularnewline
95 & 101.500262874223 & 93.2374586050231 & 109.763067143422 \tabularnewline
96 & 101.645741317334 & 92.8371313124068 & 110.454351322261 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294716&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]100.045478443111[/C][C]98.0562909402583[/C][C]102.034665945964[/C][/ROW]
[ROW][C]86[/C][C]100.190956886222[/C][C]97.3086589071633[/C][C]103.073254865281[/C][/ROW]
[ROW][C]87[/C][C]100.336435329333[/C][C]96.7210498935644[/C][C]103.951820765102[/C][/ROW]
[ROW][C]88[/C][C]100.481913772445[/C][C]96.2080788151512[/C][C]104.755748729738[/C][/ROW]
[ROW][C]89[/C][C]100.627392215556[/C][C]95.7375773404762[/C][C]105.517207090635[/C][/ROW]
[ROW][C]90[/C][C]100.772870658667[/C][C]95.2934936545086[/C][C]106.252247662825[/C][/ROW]
[ROW][C]91[/C][C]100.918349101778[/C][C]94.8665558585272[/C][C]106.970142345029[/C][/ROW]
[ROW][C]92[/C][C]101.063827544889[/C][C]94.4508959315993[/C][C]107.676759158179[/C][/ROW]
[ROW][C]93[/C][C]101.209305988[/C][C]94.0425599177044[/C][C]108.376052058296[/C][/ROW]
[ROW][C]94[/C][C]101.354784431111[/C][C]93.6387593342987[/C][C]109.070809527924[/C][/ROW]
[ROW][C]95[/C][C]101.500262874223[/C][C]93.2374586050231[/C][C]109.763067143422[/C][/ROW]
[ROW][C]96[/C][C]101.645741317334[/C][C]92.8371313124068[/C][C]110.454351322261[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294716&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294716&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
85100.04547844311198.0562909402583102.034665945964
86100.19095688622297.3086589071633103.073254865281
87100.33643532933396.7210498935644103.951820765102
88100.48191377244596.2080788151512104.755748729738
89100.62739221555695.7375773404762105.517207090635
90100.77287065866795.2934936545086106.252247662825
91100.91834910177894.8665558585272106.970142345029
92101.06382754488994.4508959315993107.676759158179
93101.20930598894.0425599177044108.376052058296
94101.35478443111193.6387593342987109.070809527924
95101.50026287422393.2374586050231109.763067143422
96101.64574131733492.8371313124068110.454351322261



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')