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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 10 May 2013 08:50:54 -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/2013/May/10/t1368190317rdhkc1e7lrqndzx.htm/, Retrieved Mon, 29 Apr 2024 17:48:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208875, Retrieved Mon, 29 Apr 2024 17:48:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2013-05-10 12:50:54] [38b7061a49f7215900abdc4599fce3db] [Current]
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Dataseries X:
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394
20.148
20.108
18.584
18.441
18.391
19.178
18.079
18.483
19.644
19.195
19.650
20.830
23.595
22.937
21.814
21.928
21.777
21.383
21.467
22.052
22.680
24.320
24.977
25.204
25.739
26.434
27.525
30.695
32.436
30.160
30.236
31.293
31.077
32.226
33.865
32.810
32.242
32.700
32.819
33.947
34.148
35.261
39.506
41.591
39.148
41.216
40.225




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208875&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208875&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208875&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0.390555699717276

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.390555699717276 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208875&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[/C][/ROW]
[ROW][C]gamma[/C][C]0.390555699717276[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208875&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208875&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
gamma0.390555699717276







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315.57915.45480899225990.124191007740077
1416.34816.4202003344058-0.0722003344058351
1515.92815.92395789432380.00404210567620922
1616.17116.0720325188880.0989674811120338
1715.93715.80957244025820.127427559741818
1815.71315.5742003464080.138799653591967
1915.59416.8367734825685-1.24277348256845
2015.68315.33262108787710.35037891212286
2116.43814.93228462815211.50571537184791
2217.03216.22888977240110.803110227598886
2317.69617.9113593373384-0.215359337338423
2417.74517.37748455029510.367515449704918
2519.39418.10180191642421.2921980835758
2620.14820.4300272021554-0.282027202155398
2720.10819.6150954564790.492904543521036
2818.58420.2781339945216-1.6941339945216
2918.44118.16215660590060.278843394099372
3018.39118.01454355281090.376456447189117
3119.17819.698587106943-0.52058710694298
3218.07918.8463499802461-0.767349980246134
3318.48317.20715650532581.27584349467424
3419.64418.2427139304671.40128606953296
3519.19520.6515420777206-1.45654207772061
3619.6518.84589221521510.804107784784897
3720.8320.04044839555950.789551604440515
3823.59521.93936177151011.65563822848985
3922.93722.9633457661497-0.0263457661497206
4021.81423.1247993233655-1.31079932336552
4121.92821.31128501660310.616714983396893
4221.77721.41289689175930.364103108240737
4321.38323.3169967156555-1.93399671565551
4421.46721.00811677926220.458883220737789
4522.05220.4238785086081.62812149139196
4622.6821.75730484495960.922695155040408
4724.3223.83653242986470.483467570135307
4824.97723.86629867466481.11070132533521
4925.20425.4615349017819-0.257534901781895
5025.73926.5367360099208-0.79773600992079
5126.43425.04592443279731.38807556720273
5227.52526.64363589281310.881364107186915
5330.69526.87929503317333.81570496682665
5432.43629.95702184804272.47897815195727
5530.1634.7076133781679-4.54761337816786
5630.23629.61302707176290.622972928237058
5731.29328.74956777861462.54343222138536
5831.07730.85742662720270.219573372797289
5932.22632.6456114769509-0.419611476950934
6033.86531.61094910752512.25405089247486
6132.8134.5065164800257-1.6965164800257
6232.24234.5311640980212-2.28916409802123
6332.731.36262642403281.33737357596718
6432.81932.9487631287749-0.12976312877489
6533.94732.04074574718541.90625425281459
6634.14833.12634936690141.02165063309862
6735.26136.5371223120473-1.27612231204731
6839.50634.61401230613074.89198769386925
6941.59137.55092934013384.04007065986624
7039.14840.9984345390672-1.85043453906719
7141.21641.11269221876740.103307781232587
7240.22540.4174767310281-0.192476731028108

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15.579 & 15.4548089922599 & 0.124191007740077 \tabularnewline
14 & 16.348 & 16.4202003344058 & -0.0722003344058351 \tabularnewline
15 & 15.928 & 15.9239578943238 & 0.00404210567620922 \tabularnewline
16 & 16.171 & 16.072032518888 & 0.0989674811120338 \tabularnewline
17 & 15.937 & 15.8095724402582 & 0.127427559741818 \tabularnewline
18 & 15.713 & 15.574200346408 & 0.138799653591967 \tabularnewline
19 & 15.594 & 16.8367734825685 & -1.24277348256845 \tabularnewline
20 & 15.683 & 15.3326210878771 & 0.35037891212286 \tabularnewline
21 & 16.438 & 14.9322846281521 & 1.50571537184791 \tabularnewline
22 & 17.032 & 16.2288897724011 & 0.803110227598886 \tabularnewline
23 & 17.696 & 17.9113593373384 & -0.215359337338423 \tabularnewline
24 & 17.745 & 17.3774845502951 & 0.367515449704918 \tabularnewline
25 & 19.394 & 18.1018019164242 & 1.2921980835758 \tabularnewline
26 & 20.148 & 20.4300272021554 & -0.282027202155398 \tabularnewline
27 & 20.108 & 19.615095456479 & 0.492904543521036 \tabularnewline
28 & 18.584 & 20.2781339945216 & -1.6941339945216 \tabularnewline
29 & 18.441 & 18.1621566059006 & 0.278843394099372 \tabularnewline
30 & 18.391 & 18.0145435528109 & 0.376456447189117 \tabularnewline
31 & 19.178 & 19.698587106943 & -0.52058710694298 \tabularnewline
32 & 18.079 & 18.8463499802461 & -0.767349980246134 \tabularnewline
33 & 18.483 & 17.2071565053258 & 1.27584349467424 \tabularnewline
34 & 19.644 & 18.242713930467 & 1.40128606953296 \tabularnewline
35 & 19.195 & 20.6515420777206 & -1.45654207772061 \tabularnewline
36 & 19.65 & 18.8458922152151 & 0.804107784784897 \tabularnewline
37 & 20.83 & 20.0404483955595 & 0.789551604440515 \tabularnewline
38 & 23.595 & 21.9393617715101 & 1.65563822848985 \tabularnewline
39 & 22.937 & 22.9633457661497 & -0.0263457661497206 \tabularnewline
40 & 21.814 & 23.1247993233655 & -1.31079932336552 \tabularnewline
41 & 21.928 & 21.3112850166031 & 0.616714983396893 \tabularnewline
42 & 21.777 & 21.4128968917593 & 0.364103108240737 \tabularnewline
43 & 21.383 & 23.3169967156555 & -1.93399671565551 \tabularnewline
44 & 21.467 & 21.0081167792622 & 0.458883220737789 \tabularnewline
45 & 22.052 & 20.423878508608 & 1.62812149139196 \tabularnewline
46 & 22.68 & 21.7573048449596 & 0.922695155040408 \tabularnewline
47 & 24.32 & 23.8365324298647 & 0.483467570135307 \tabularnewline
48 & 24.977 & 23.8662986746648 & 1.11070132533521 \tabularnewline
49 & 25.204 & 25.4615349017819 & -0.257534901781895 \tabularnewline
50 & 25.739 & 26.5367360099208 & -0.79773600992079 \tabularnewline
51 & 26.434 & 25.0459244327973 & 1.38807556720273 \tabularnewline
52 & 27.525 & 26.6436358928131 & 0.881364107186915 \tabularnewline
53 & 30.695 & 26.8792950331733 & 3.81570496682665 \tabularnewline
54 & 32.436 & 29.9570218480427 & 2.47897815195727 \tabularnewline
55 & 30.16 & 34.7076133781679 & -4.54761337816786 \tabularnewline
56 & 30.236 & 29.6130270717629 & 0.622972928237058 \tabularnewline
57 & 31.293 & 28.7495677786146 & 2.54343222138536 \tabularnewline
58 & 31.077 & 30.8574266272027 & 0.219573372797289 \tabularnewline
59 & 32.226 & 32.6456114769509 & -0.419611476950934 \tabularnewline
60 & 33.865 & 31.6109491075251 & 2.25405089247486 \tabularnewline
61 & 32.81 & 34.5065164800257 & -1.6965164800257 \tabularnewline
62 & 32.242 & 34.5311640980212 & -2.28916409802123 \tabularnewline
63 & 32.7 & 31.3626264240328 & 1.33737357596718 \tabularnewline
64 & 32.819 & 32.9487631287749 & -0.12976312877489 \tabularnewline
65 & 33.947 & 32.0407457471854 & 1.90625425281459 \tabularnewline
66 & 34.148 & 33.1263493669014 & 1.02165063309862 \tabularnewline
67 & 35.261 & 36.5371223120473 & -1.27612231204731 \tabularnewline
68 & 39.506 & 34.6140123061307 & 4.89198769386925 \tabularnewline
69 & 41.591 & 37.5509293401338 & 4.04007065986624 \tabularnewline
70 & 39.148 & 40.9984345390672 & -1.85043453906719 \tabularnewline
71 & 41.216 & 41.1126922187674 & 0.103307781232587 \tabularnewline
72 & 40.225 & 40.4174767310281 & -0.192476731028108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208875&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]13[/C][C]15.579[/C][C]15.4548089922599[/C][C]0.124191007740077[/C][/ROW]
[ROW][C]14[/C][C]16.348[/C][C]16.4202003344058[/C][C]-0.0722003344058351[/C][/ROW]
[ROW][C]15[/C][C]15.928[/C][C]15.9239578943238[/C][C]0.00404210567620922[/C][/ROW]
[ROW][C]16[/C][C]16.171[/C][C]16.072032518888[/C][C]0.0989674811120338[/C][/ROW]
[ROW][C]17[/C][C]15.937[/C][C]15.8095724402582[/C][C]0.127427559741818[/C][/ROW]
[ROW][C]18[/C][C]15.713[/C][C]15.574200346408[/C][C]0.138799653591967[/C][/ROW]
[ROW][C]19[/C][C]15.594[/C][C]16.8367734825685[/C][C]-1.24277348256845[/C][/ROW]
[ROW][C]20[/C][C]15.683[/C][C]15.3326210878771[/C][C]0.35037891212286[/C][/ROW]
[ROW][C]21[/C][C]16.438[/C][C]14.9322846281521[/C][C]1.50571537184791[/C][/ROW]
[ROW][C]22[/C][C]17.032[/C][C]16.2288897724011[/C][C]0.803110227598886[/C][/ROW]
[ROW][C]23[/C][C]17.696[/C][C]17.9113593373384[/C][C]-0.215359337338423[/C][/ROW]
[ROW][C]24[/C][C]17.745[/C][C]17.3774845502951[/C][C]0.367515449704918[/C][/ROW]
[ROW][C]25[/C][C]19.394[/C][C]18.1018019164242[/C][C]1.2921980835758[/C][/ROW]
[ROW][C]26[/C][C]20.148[/C][C]20.4300272021554[/C][C]-0.282027202155398[/C][/ROW]
[ROW][C]27[/C][C]20.108[/C][C]19.615095456479[/C][C]0.492904543521036[/C][/ROW]
[ROW][C]28[/C][C]18.584[/C][C]20.2781339945216[/C][C]-1.6941339945216[/C][/ROW]
[ROW][C]29[/C][C]18.441[/C][C]18.1621566059006[/C][C]0.278843394099372[/C][/ROW]
[ROW][C]30[/C][C]18.391[/C][C]18.0145435528109[/C][C]0.376456447189117[/C][/ROW]
[ROW][C]31[/C][C]19.178[/C][C]19.698587106943[/C][C]-0.52058710694298[/C][/ROW]
[ROW][C]32[/C][C]18.079[/C][C]18.8463499802461[/C][C]-0.767349980246134[/C][/ROW]
[ROW][C]33[/C][C]18.483[/C][C]17.2071565053258[/C][C]1.27584349467424[/C][/ROW]
[ROW][C]34[/C][C]19.644[/C][C]18.242713930467[/C][C]1.40128606953296[/C][/ROW]
[ROW][C]35[/C][C]19.195[/C][C]20.6515420777206[/C][C]-1.45654207772061[/C][/ROW]
[ROW][C]36[/C][C]19.65[/C][C]18.8458922152151[/C][C]0.804107784784897[/C][/ROW]
[ROW][C]37[/C][C]20.83[/C][C]20.0404483955595[/C][C]0.789551604440515[/C][/ROW]
[ROW][C]38[/C][C]23.595[/C][C]21.9393617715101[/C][C]1.65563822848985[/C][/ROW]
[ROW][C]39[/C][C]22.937[/C][C]22.9633457661497[/C][C]-0.0263457661497206[/C][/ROW]
[ROW][C]40[/C][C]21.814[/C][C]23.1247993233655[/C][C]-1.31079932336552[/C][/ROW]
[ROW][C]41[/C][C]21.928[/C][C]21.3112850166031[/C][C]0.616714983396893[/C][/ROW]
[ROW][C]42[/C][C]21.777[/C][C]21.4128968917593[/C][C]0.364103108240737[/C][/ROW]
[ROW][C]43[/C][C]21.383[/C][C]23.3169967156555[/C][C]-1.93399671565551[/C][/ROW]
[ROW][C]44[/C][C]21.467[/C][C]21.0081167792622[/C][C]0.458883220737789[/C][/ROW]
[ROW][C]45[/C][C]22.052[/C][C]20.423878508608[/C][C]1.62812149139196[/C][/ROW]
[ROW][C]46[/C][C]22.68[/C][C]21.7573048449596[/C][C]0.922695155040408[/C][/ROW]
[ROW][C]47[/C][C]24.32[/C][C]23.8365324298647[/C][C]0.483467570135307[/C][/ROW]
[ROW][C]48[/C][C]24.977[/C][C]23.8662986746648[/C][C]1.11070132533521[/C][/ROW]
[ROW][C]49[/C][C]25.204[/C][C]25.4615349017819[/C][C]-0.257534901781895[/C][/ROW]
[ROW][C]50[/C][C]25.739[/C][C]26.5367360099208[/C][C]-0.79773600992079[/C][/ROW]
[ROW][C]51[/C][C]26.434[/C][C]25.0459244327973[/C][C]1.38807556720273[/C][/ROW]
[ROW][C]52[/C][C]27.525[/C][C]26.6436358928131[/C][C]0.881364107186915[/C][/ROW]
[ROW][C]53[/C][C]30.695[/C][C]26.8792950331733[/C][C]3.81570496682665[/C][/ROW]
[ROW][C]54[/C][C]32.436[/C][C]29.9570218480427[/C][C]2.47897815195727[/C][/ROW]
[ROW][C]55[/C][C]30.16[/C][C]34.7076133781679[/C][C]-4.54761337816786[/C][/ROW]
[ROW][C]56[/C][C]30.236[/C][C]29.6130270717629[/C][C]0.622972928237058[/C][/ROW]
[ROW][C]57[/C][C]31.293[/C][C]28.7495677786146[/C][C]2.54343222138536[/C][/ROW]
[ROW][C]58[/C][C]31.077[/C][C]30.8574266272027[/C][C]0.219573372797289[/C][/ROW]
[ROW][C]59[/C][C]32.226[/C][C]32.6456114769509[/C][C]-0.419611476950934[/C][/ROW]
[ROW][C]60[/C][C]33.865[/C][C]31.6109491075251[/C][C]2.25405089247486[/C][/ROW]
[ROW][C]61[/C][C]32.81[/C][C]34.5065164800257[/C][C]-1.6965164800257[/C][/ROW]
[ROW][C]62[/C][C]32.242[/C][C]34.5311640980212[/C][C]-2.28916409802123[/C][/ROW]
[ROW][C]63[/C][C]32.7[/C][C]31.3626264240328[/C][C]1.33737357596718[/C][/ROW]
[ROW][C]64[/C][C]32.819[/C][C]32.9487631287749[/C][C]-0.12976312877489[/C][/ROW]
[ROW][C]65[/C][C]33.947[/C][C]32.0407457471854[/C][C]1.90625425281459[/C][/ROW]
[ROW][C]66[/C][C]34.148[/C][C]33.1263493669014[/C][C]1.02165063309862[/C][/ROW]
[ROW][C]67[/C][C]35.261[/C][C]36.5371223120473[/C][C]-1.27612231204731[/C][/ROW]
[ROW][C]68[/C][C]39.506[/C][C]34.6140123061307[/C][C]4.89198769386925[/C][/ROW]
[ROW][C]69[/C][C]41.591[/C][C]37.5509293401338[/C][C]4.04007065986624[/C][/ROW]
[ROW][C]70[/C][C]39.148[/C][C]40.9984345390672[/C][C]-1.85043453906719[/C][/ROW]
[ROW][C]71[/C][C]41.216[/C][C]41.1126922187674[/C][C]0.103307781232587[/C][/ROW]
[ROW][C]72[/C][C]40.225[/C][C]40.4174767310281[/C][C]-0.192476731028108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208875&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208875&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
1315.57915.45480899225990.124191007740077
1416.34816.4202003344058-0.0722003344058351
1515.92815.92395789432380.00404210567620922
1616.17116.0720325188880.0989674811120338
1715.93715.80957244025820.127427559741818
1815.71315.5742003464080.138799653591967
1915.59416.8367734825685-1.24277348256845
2015.68315.33262108787710.35037891212286
2116.43814.93228462815211.50571537184791
2217.03216.22888977240110.803110227598886
2317.69617.9113593373384-0.215359337338423
2417.74517.37748455029510.367515449704918
2519.39418.10180191642421.2921980835758
2620.14820.4300272021554-0.282027202155398
2720.10819.6150954564790.492904543521036
2818.58420.2781339945216-1.6941339945216
2918.44118.16215660590060.278843394099372
3018.39118.01454355281090.376456447189117
3119.17819.698587106943-0.52058710694298
3218.07918.8463499802461-0.767349980246134
3318.48317.20715650532581.27584349467424
3419.64418.2427139304671.40128606953296
3519.19520.6515420777206-1.45654207772061
3619.6518.84589221521510.804107784784897
3720.8320.04044839555950.789551604440515
3823.59521.93936177151011.65563822848985
3922.93722.9633457661497-0.0263457661497206
4021.81423.1247993233655-1.31079932336552
4121.92821.31128501660310.616714983396893
4221.77721.41289689175930.364103108240737
4321.38323.3169967156555-1.93399671565551
4421.46721.00811677926220.458883220737789
4522.05220.4238785086081.62812149139196
4622.6821.75730484495960.922695155040408
4724.3223.83653242986470.483467570135307
4824.97723.86629867466481.11070132533521
4925.20425.4615349017819-0.257534901781895
5025.73926.5367360099208-0.79773600992079
5126.43425.04592443279731.38807556720273
5227.52526.64363589281310.881364107186915
5330.69526.87929503317333.81570496682665
5432.43629.95702184804272.47897815195727
5530.1634.7076133781679-4.54761337816786
5630.23629.61302707176290.622972928237058
5731.29328.74956777861462.54343222138536
5831.07730.85742662720270.219573372797289
5932.22632.6456114769509-0.419611476950934
6033.86531.61094910752512.25405089247486
6132.8134.5065164800257-1.6965164800257
6232.24234.5311640980212-2.28916409802123
6332.731.36262642403281.33737357596718
6432.81932.9487631287749-0.12976312877489
6533.94732.04074574718541.90625425281459
6634.14833.12634936690141.02165063309862
6735.26136.5371223120473-1.27612231204731
6839.50634.61401230613074.89198769386925
6941.59137.55092934013384.04007065986624
7039.14840.9984345390672-1.85043453906719
7141.21641.11269221876740.103307781232587
7240.22540.4174767310281-0.192476731028108







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7340.978848032414437.954413273113444.0032827917154
7443.117184102985438.729412695366747.5049555106041
7541.926258144528136.700126643756447.1523896452999
7642.232633462812436.166183161411648.2990837642131
7741.218684009006534.575700217806847.8616678002062
7840.213172318373933.067456914237547.3588877225103
7943.01859832956134.805283535277151.2319131238449
8042.21950822855633.617975006866450.8210414502455
8140.127258036970731.418526254225148.8359898197162
8239.557007191231930.463359307711748.650655074752
8341.54177125632731.533915517068751.5496269955853
8440.7365994860656-27.8335770469334109.306776019065

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 40.9788480324144 & 37.9544132731134 & 44.0032827917154 \tabularnewline
74 & 43.1171841029854 & 38.7294126953667 & 47.5049555106041 \tabularnewline
75 & 41.9262581445281 & 36.7001266437564 & 47.1523896452999 \tabularnewline
76 & 42.2326334628124 & 36.1661831614116 & 48.2990837642131 \tabularnewline
77 & 41.2186840090065 & 34.5757002178068 & 47.8616678002062 \tabularnewline
78 & 40.2131723183739 & 33.0674569142375 & 47.3588877225103 \tabularnewline
79 & 43.018598329561 & 34.8052835352771 & 51.2319131238449 \tabularnewline
80 & 42.219508228556 & 33.6179750068664 & 50.8210414502455 \tabularnewline
81 & 40.1272580369707 & 31.4185262542251 & 48.8359898197162 \tabularnewline
82 & 39.5570071912319 & 30.4633593077117 & 48.650655074752 \tabularnewline
83 & 41.541771256327 & 31.5339155170687 & 51.5496269955853 \tabularnewline
84 & 40.7365994860656 & -27.8335770469334 & 109.306776019065 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208875&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]40.9788480324144[/C][C]37.9544132731134[/C][C]44.0032827917154[/C][/ROW]
[ROW][C]74[/C][C]43.1171841029854[/C][C]38.7294126953667[/C][C]47.5049555106041[/C][/ROW]
[ROW][C]75[/C][C]41.9262581445281[/C][C]36.7001266437564[/C][C]47.1523896452999[/C][/ROW]
[ROW][C]76[/C][C]42.2326334628124[/C][C]36.1661831614116[/C][C]48.2990837642131[/C][/ROW]
[ROW][C]77[/C][C]41.2186840090065[/C][C]34.5757002178068[/C][C]47.8616678002062[/C][/ROW]
[ROW][C]78[/C][C]40.2131723183739[/C][C]33.0674569142375[/C][C]47.3588877225103[/C][/ROW]
[ROW][C]79[/C][C]43.018598329561[/C][C]34.8052835352771[/C][C]51.2319131238449[/C][/ROW]
[ROW][C]80[/C][C]42.219508228556[/C][C]33.6179750068664[/C][C]50.8210414502455[/C][/ROW]
[ROW][C]81[/C][C]40.1272580369707[/C][C]31.4185262542251[/C][C]48.8359898197162[/C][/ROW]
[ROW][C]82[/C][C]39.5570071912319[/C][C]30.4633593077117[/C][C]48.650655074752[/C][/ROW]
[ROW][C]83[/C][C]41.541771256327[/C][C]31.5339155170687[/C][C]51.5496269955853[/C][/ROW]
[ROW][C]84[/C][C]40.7365994860656[/C][C]-27.8335770469334[/C][C]109.306776019065[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208875&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208875&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
7340.978848032414437.954413273113444.0032827917154
7443.117184102985438.729412695366747.5049555106041
7541.926258144528136.700126643756447.1523896452999
7642.232633462812436.166183161411648.2990837642131
7741.218684009006534.575700217806847.8616678002062
7840.213172318373933.067456914237547.3588877225103
7943.01859832956134.805283535277151.2319131238449
8042.21950822855633.617975006866450.8210414502455
8140.127258036970731.418526254225148.8359898197162
8239.557007191231930.463359307711748.650655074752
8341.54177125632731.533915517068751.5496269955853
8440.7365994860656-27.8335770469334109.306776019065



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')