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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 15:14:42 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/19/t1305817834qes68n6oyk2jauj.htm/, Retrieved Sat, 11 May 2024 09:04:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122090, Retrieved Sat, 11 May 2024 09:04:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-05-19 15:14:42] [f0cd0ad4d4cb2a25864ed1f6cd7bfd87] [Current]
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Dataseries X:
7989
41102
9123
22109
47115
9105
5496
23102
6994
84101
5884
6383
6292
36109
49127
26116
63120
60115
77117
18110
3999
79105
2286
7487
7789
3788
83108
52100
93102
598
8983
3488
2780
7974
9171
3071
4166
7968
6580
7183
2779
5273
1568
1860
9853
6757
6745
5144
9444
2248
7349
8149
7949
3545
1043
4038
4335
5432
8027
8626
24
4829
931
232
9034
1337
5138
9736
7730
7133
8126
424




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122090&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122090&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122090&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.130272576604942
beta0
gamma0.756196503879971

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.130272576604942 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.756196503879971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122090&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]0.130272576604942[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.756196503879971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122090&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122090&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
alpha0.130272576604942
beta0
gamma0.756196503879971







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1362923969.895182234532322.10481776547
143610924218.994151326511890.0058486735
154912737503.280438528711623.7195614713
162611622073.25666506774042.74333493228
176312057952.24850692665167.75149307344
186011558656.18572391981458.81427608016
19771179000.8577964150668116.142203585
201811077741.508506714-59631.508506714
21399920338.4378290079-16339.4378290079
2279105208355.093671417-129250.093671417
23228613327.3391535333-11041.3391535333
24748712001.2948668556-4514.29486685558
25778913376.7178792542-5587.71787925417
26378866467.1031031926-62679.1031031926
278310875982.29710368287125.70289631725
285210039835.998368987412264.0016310126
299310298687.992310571-5585.992310571
3059892585.4502551047-91987.4502551047
31898342059.566646475-33076.566646475
32348820870.6444833256-17382.6444833256
3327805119.41688566289-2339.41688566289
34797475784.64362913-67810.64362913
3591713311.837126605385859.16287339462
3630717850.61766997836-4779.61766997836
3741668163.82272799007-3997.82272799007
38796816670.7621802862-8702.7621802862
39658073579.1865338919-66999.1865338919
40718338136.3750859982-30953.3750859982
41277966325.4788897944-63546.4788897944
42527314475.6405510821-9202.64055108208
43156811966.8807954418-10398.8807954418
4418605432.85327309944-3572.85327309944
4598532452.379683693457400.62031630655
46675726344.8634434983-19587.8634434983
4767456841.41442528839-96.414425288388
4851443841.186475057791302.81352494221
4994445262.203403812634181.79659618737
50224812136.3145672137-9888.3145672137
51734925980.0288444426-18631.0288444426
52814917335.7305034508-9186.73050345076
53794921665.7055815168-13716.7055815168
5435459551.71632794744-6006.71632794744
5510435120.4980987671-4077.4980987671
5640383450.25478430826587.745215691737
5743357901.08376871055-3566.08376871055
58543210890.7115911266-5458.7115911266
5980276341.707652627411685.29234737259
6086264526.406157078744099.59384292126
61248050.75015126546-8026.75015126546
6248294006.12339519448822.876604805523
6393111822.1852087524-10891.1852087524
6423210015.9619410109-9783.96194101088
65903410302.9809753101-1268.98097531013
6613374914.04300285116-3577.04300285116
6751381971.264446163373166.73555383663
6897364743.137179226734992.86282077327
6977307372.833264847357.166735153004
70713310141.4695586494-3008.46955864941
71812610818.5795433004-2692.5795433004
724249370.53568691316-8946.53568691316

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6292 & 3969.89518223453 & 2322.10481776547 \tabularnewline
14 & 36109 & 24218.9941513265 & 11890.0058486735 \tabularnewline
15 & 49127 & 37503.2804385287 & 11623.7195614713 \tabularnewline
16 & 26116 & 22073.2566650677 & 4042.74333493228 \tabularnewline
17 & 63120 & 57952.2485069266 & 5167.75149307344 \tabularnewline
18 & 60115 & 58656.1857239198 & 1458.81427608016 \tabularnewline
19 & 77117 & 9000.85779641506 & 68116.142203585 \tabularnewline
20 & 18110 & 77741.508506714 & -59631.508506714 \tabularnewline
21 & 3999 & 20338.4378290079 & -16339.4378290079 \tabularnewline
22 & 79105 & 208355.093671417 & -129250.093671417 \tabularnewline
23 & 2286 & 13327.3391535333 & -11041.3391535333 \tabularnewline
24 & 7487 & 12001.2948668556 & -4514.29486685558 \tabularnewline
25 & 7789 & 13376.7178792542 & -5587.71787925417 \tabularnewline
26 & 3788 & 66467.1031031926 & -62679.1031031926 \tabularnewline
27 & 83108 & 75982.2971036828 & 7125.70289631725 \tabularnewline
28 & 52100 & 39835.9983689874 & 12264.0016310126 \tabularnewline
29 & 93102 & 98687.992310571 & -5585.992310571 \tabularnewline
30 & 598 & 92585.4502551047 & -91987.4502551047 \tabularnewline
31 & 8983 & 42059.566646475 & -33076.566646475 \tabularnewline
32 & 3488 & 20870.6444833256 & -17382.6444833256 \tabularnewline
33 & 2780 & 5119.41688566289 & -2339.41688566289 \tabularnewline
34 & 7974 & 75784.64362913 & -67810.64362913 \tabularnewline
35 & 9171 & 3311.83712660538 & 5859.16287339462 \tabularnewline
36 & 3071 & 7850.61766997836 & -4779.61766997836 \tabularnewline
37 & 4166 & 8163.82272799007 & -3997.82272799007 \tabularnewline
38 & 7968 & 16670.7621802862 & -8702.7621802862 \tabularnewline
39 & 6580 & 73579.1865338919 & -66999.1865338919 \tabularnewline
40 & 7183 & 38136.3750859982 & -30953.3750859982 \tabularnewline
41 & 2779 & 66325.4788897944 & -63546.4788897944 \tabularnewline
42 & 5273 & 14475.6405510821 & -9202.64055108208 \tabularnewline
43 & 1568 & 11966.8807954418 & -10398.8807954418 \tabularnewline
44 & 1860 & 5432.85327309944 & -3572.85327309944 \tabularnewline
45 & 9853 & 2452.37968369345 & 7400.62031630655 \tabularnewline
46 & 6757 & 26344.8634434983 & -19587.8634434983 \tabularnewline
47 & 6745 & 6841.41442528839 & -96.414425288388 \tabularnewline
48 & 5144 & 3841.18647505779 & 1302.81352494221 \tabularnewline
49 & 9444 & 5262.20340381263 & 4181.79659618737 \tabularnewline
50 & 2248 & 12136.3145672137 & -9888.3145672137 \tabularnewline
51 & 7349 & 25980.0288444426 & -18631.0288444426 \tabularnewline
52 & 8149 & 17335.7305034508 & -9186.73050345076 \tabularnewline
53 & 7949 & 21665.7055815168 & -13716.7055815168 \tabularnewline
54 & 3545 & 9551.71632794744 & -6006.71632794744 \tabularnewline
55 & 1043 & 5120.4980987671 & -4077.4980987671 \tabularnewline
56 & 4038 & 3450.25478430826 & 587.745215691737 \tabularnewline
57 & 4335 & 7901.08376871055 & -3566.08376871055 \tabularnewline
58 & 5432 & 10890.7115911266 & -5458.7115911266 \tabularnewline
59 & 8027 & 6341.70765262741 & 1685.29234737259 \tabularnewline
60 & 8626 & 4526.40615707874 & 4099.59384292126 \tabularnewline
61 & 24 & 8050.75015126546 & -8026.75015126546 \tabularnewline
62 & 4829 & 4006.12339519448 & 822.876604805523 \tabularnewline
63 & 931 & 11822.1852087524 & -10891.1852087524 \tabularnewline
64 & 232 & 10015.9619410109 & -9783.96194101088 \tabularnewline
65 & 9034 & 10302.9809753101 & -1268.98097531013 \tabularnewline
66 & 1337 & 4914.04300285116 & -3577.04300285116 \tabularnewline
67 & 5138 & 1971.26444616337 & 3166.73555383663 \tabularnewline
68 & 9736 & 4743.13717922673 & 4992.86282077327 \tabularnewline
69 & 7730 & 7372.833264847 & 357.166735153004 \tabularnewline
70 & 7133 & 10141.4695586494 & -3008.46955864941 \tabularnewline
71 & 8126 & 10818.5795433004 & -2692.5795433004 \tabularnewline
72 & 424 & 9370.53568691316 & -8946.53568691316 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122090&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]6292[/C][C]3969.89518223453[/C][C]2322.10481776547[/C][/ROW]
[ROW][C]14[/C][C]36109[/C][C]24218.9941513265[/C][C]11890.0058486735[/C][/ROW]
[ROW][C]15[/C][C]49127[/C][C]37503.2804385287[/C][C]11623.7195614713[/C][/ROW]
[ROW][C]16[/C][C]26116[/C][C]22073.2566650677[/C][C]4042.74333493228[/C][/ROW]
[ROW][C]17[/C][C]63120[/C][C]57952.2485069266[/C][C]5167.75149307344[/C][/ROW]
[ROW][C]18[/C][C]60115[/C][C]58656.1857239198[/C][C]1458.81427608016[/C][/ROW]
[ROW][C]19[/C][C]77117[/C][C]9000.85779641506[/C][C]68116.142203585[/C][/ROW]
[ROW][C]20[/C][C]18110[/C][C]77741.508506714[/C][C]-59631.508506714[/C][/ROW]
[ROW][C]21[/C][C]3999[/C][C]20338.4378290079[/C][C]-16339.4378290079[/C][/ROW]
[ROW][C]22[/C][C]79105[/C][C]208355.093671417[/C][C]-129250.093671417[/C][/ROW]
[ROW][C]23[/C][C]2286[/C][C]13327.3391535333[/C][C]-11041.3391535333[/C][/ROW]
[ROW][C]24[/C][C]7487[/C][C]12001.2948668556[/C][C]-4514.29486685558[/C][/ROW]
[ROW][C]25[/C][C]7789[/C][C]13376.7178792542[/C][C]-5587.71787925417[/C][/ROW]
[ROW][C]26[/C][C]3788[/C][C]66467.1031031926[/C][C]-62679.1031031926[/C][/ROW]
[ROW][C]27[/C][C]83108[/C][C]75982.2971036828[/C][C]7125.70289631725[/C][/ROW]
[ROW][C]28[/C][C]52100[/C][C]39835.9983689874[/C][C]12264.0016310126[/C][/ROW]
[ROW][C]29[/C][C]93102[/C][C]98687.992310571[/C][C]-5585.992310571[/C][/ROW]
[ROW][C]30[/C][C]598[/C][C]92585.4502551047[/C][C]-91987.4502551047[/C][/ROW]
[ROW][C]31[/C][C]8983[/C][C]42059.566646475[/C][C]-33076.566646475[/C][/ROW]
[ROW][C]32[/C][C]3488[/C][C]20870.6444833256[/C][C]-17382.6444833256[/C][/ROW]
[ROW][C]33[/C][C]2780[/C][C]5119.41688566289[/C][C]-2339.41688566289[/C][/ROW]
[ROW][C]34[/C][C]7974[/C][C]75784.64362913[/C][C]-67810.64362913[/C][/ROW]
[ROW][C]35[/C][C]9171[/C][C]3311.83712660538[/C][C]5859.16287339462[/C][/ROW]
[ROW][C]36[/C][C]3071[/C][C]7850.61766997836[/C][C]-4779.61766997836[/C][/ROW]
[ROW][C]37[/C][C]4166[/C][C]8163.82272799007[/C][C]-3997.82272799007[/C][/ROW]
[ROW][C]38[/C][C]7968[/C][C]16670.7621802862[/C][C]-8702.7621802862[/C][/ROW]
[ROW][C]39[/C][C]6580[/C][C]73579.1865338919[/C][C]-66999.1865338919[/C][/ROW]
[ROW][C]40[/C][C]7183[/C][C]38136.3750859982[/C][C]-30953.3750859982[/C][/ROW]
[ROW][C]41[/C][C]2779[/C][C]66325.4788897944[/C][C]-63546.4788897944[/C][/ROW]
[ROW][C]42[/C][C]5273[/C][C]14475.6405510821[/C][C]-9202.64055108208[/C][/ROW]
[ROW][C]43[/C][C]1568[/C][C]11966.8807954418[/C][C]-10398.8807954418[/C][/ROW]
[ROW][C]44[/C][C]1860[/C][C]5432.85327309944[/C][C]-3572.85327309944[/C][/ROW]
[ROW][C]45[/C][C]9853[/C][C]2452.37968369345[/C][C]7400.62031630655[/C][/ROW]
[ROW][C]46[/C][C]6757[/C][C]26344.8634434983[/C][C]-19587.8634434983[/C][/ROW]
[ROW][C]47[/C][C]6745[/C][C]6841.41442528839[/C][C]-96.414425288388[/C][/ROW]
[ROW][C]48[/C][C]5144[/C][C]3841.18647505779[/C][C]1302.81352494221[/C][/ROW]
[ROW][C]49[/C][C]9444[/C][C]5262.20340381263[/C][C]4181.79659618737[/C][/ROW]
[ROW][C]50[/C][C]2248[/C][C]12136.3145672137[/C][C]-9888.3145672137[/C][/ROW]
[ROW][C]51[/C][C]7349[/C][C]25980.0288444426[/C][C]-18631.0288444426[/C][/ROW]
[ROW][C]52[/C][C]8149[/C][C]17335.7305034508[/C][C]-9186.73050345076[/C][/ROW]
[ROW][C]53[/C][C]7949[/C][C]21665.7055815168[/C][C]-13716.7055815168[/C][/ROW]
[ROW][C]54[/C][C]3545[/C][C]9551.71632794744[/C][C]-6006.71632794744[/C][/ROW]
[ROW][C]55[/C][C]1043[/C][C]5120.4980987671[/C][C]-4077.4980987671[/C][/ROW]
[ROW][C]56[/C][C]4038[/C][C]3450.25478430826[/C][C]587.745215691737[/C][/ROW]
[ROW][C]57[/C][C]4335[/C][C]7901.08376871055[/C][C]-3566.08376871055[/C][/ROW]
[ROW][C]58[/C][C]5432[/C][C]10890.7115911266[/C][C]-5458.7115911266[/C][/ROW]
[ROW][C]59[/C][C]8027[/C][C]6341.70765262741[/C][C]1685.29234737259[/C][/ROW]
[ROW][C]60[/C][C]8626[/C][C]4526.40615707874[/C][C]4099.59384292126[/C][/ROW]
[ROW][C]61[/C][C]24[/C][C]8050.75015126546[/C][C]-8026.75015126546[/C][/ROW]
[ROW][C]62[/C][C]4829[/C][C]4006.12339519448[/C][C]822.876604805523[/C][/ROW]
[ROW][C]63[/C][C]931[/C][C]11822.1852087524[/C][C]-10891.1852087524[/C][/ROW]
[ROW][C]64[/C][C]232[/C][C]10015.9619410109[/C][C]-9783.96194101088[/C][/ROW]
[ROW][C]65[/C][C]9034[/C][C]10302.9809753101[/C][C]-1268.98097531013[/C][/ROW]
[ROW][C]66[/C][C]1337[/C][C]4914.04300285116[/C][C]-3577.04300285116[/C][/ROW]
[ROW][C]67[/C][C]5138[/C][C]1971.26444616337[/C][C]3166.73555383663[/C][/ROW]
[ROW][C]68[/C][C]9736[/C][C]4743.13717922673[/C][C]4992.86282077327[/C][/ROW]
[ROW][C]69[/C][C]7730[/C][C]7372.833264847[/C][C]357.166735153004[/C][/ROW]
[ROW][C]70[/C][C]7133[/C][C]10141.4695586494[/C][C]-3008.46955864941[/C][/ROW]
[ROW][C]71[/C][C]8126[/C][C]10818.5795433004[/C][C]-2692.5795433004[/C][/ROW]
[ROW][C]72[/C][C]424[/C][C]9370.53568691316[/C][C]-8946.53568691316[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122090&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122090&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
1362923969.895182234532322.10481776547
143610924218.994151326511890.0058486735
154912737503.280438528711623.7195614713
162611622073.25666506774042.74333493228
176312057952.24850692665167.75149307344
186011558656.18572391981458.81427608016
19771179000.8577964150668116.142203585
201811077741.508506714-59631.508506714
21399920338.4378290079-16339.4378290079
2279105208355.093671417-129250.093671417
23228613327.3391535333-11041.3391535333
24748712001.2948668556-4514.29486685558
25778913376.7178792542-5587.71787925417
26378866467.1031031926-62679.1031031926
278310875982.29710368287125.70289631725
285210039835.998368987412264.0016310126
299310298687.992310571-5585.992310571
3059892585.4502551047-91987.4502551047
31898342059.566646475-33076.566646475
32348820870.6444833256-17382.6444833256
3327805119.41688566289-2339.41688566289
34797475784.64362913-67810.64362913
3591713311.837126605385859.16287339462
3630717850.61766997836-4779.61766997836
3741668163.82272799007-3997.82272799007
38796816670.7621802862-8702.7621802862
39658073579.1865338919-66999.1865338919
40718338136.3750859982-30953.3750859982
41277966325.4788897944-63546.4788897944
42527314475.6405510821-9202.64055108208
43156811966.8807954418-10398.8807954418
4418605432.85327309944-3572.85327309944
4598532452.379683693457400.62031630655
46675726344.8634434983-19587.8634434983
4767456841.41442528839-96.414425288388
4851443841.186475057791302.81352494221
4994445262.203403812634181.79659618737
50224812136.3145672137-9888.3145672137
51734925980.0288444426-18631.0288444426
52814917335.7305034508-9186.73050345076
53794921665.7055815168-13716.7055815168
5435459551.71632794744-6006.71632794744
5510435120.4980987671-4077.4980987671
5640383450.25478430826587.745215691737
5743357901.08376871055-3566.08376871055
58543210890.7115911266-5458.7115911266
5980276341.707652627411685.29234737259
6086264526.406157078744099.59384292126
61248050.75015126546-8026.75015126546
6248294006.12339519448822.876604805523
6393111822.1852087524-10891.1852087524
6423210015.9619410109-9783.96194101088
65903410302.9809753101-1268.98097531013
6613374914.04300285116-3577.04300285116
6751381971.264446163373166.73555383663
6897364743.137179226734992.86282077327
6977307372.833264847357.166735153004
70713310141.4695586494-3008.46955864941
71812610818.5795433004-2692.5795433004
724249370.53568691316-8946.53568691316







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
732094.44494119407-41922.156115890646111.0459982788
745464.74013895725-42242.713665813753172.1939437282
754300.82807973095-42235.204698159650836.8608576215
763474.69829651008-42464.349866045149413.7464590653
7714041.2414442036-59580.274396786287662.7572851935
783445.71919191919-42801.527871458349692.9662552966
795970.33200457656-45610.021339598657550.6853487517
8010111.1696160544-53516.742245060573739.0814771693
818826.03055893003-50364.07537310568016.1364909651
829285.47075522608-51059.529592554569630.4711030067
8310689.7387909515-53767.007440636175146.4850225392
843240.56676757367-10861.743757979117342.8772931264

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 2094.44494119407 & -41922.1561158906 & 46111.0459982788 \tabularnewline
74 & 5464.74013895725 & -42242.7136658137 & 53172.1939437282 \tabularnewline
75 & 4300.82807973095 & -42235.2046981596 & 50836.8608576215 \tabularnewline
76 & 3474.69829651008 & -42464.3498660451 & 49413.7464590653 \tabularnewline
77 & 14041.2414442036 & -59580.2743967862 & 87662.7572851935 \tabularnewline
78 & 3445.71919191919 & -42801.5278714583 & 49692.9662552966 \tabularnewline
79 & 5970.33200457656 & -45610.0213395986 & 57550.6853487517 \tabularnewline
80 & 10111.1696160544 & -53516.7422450605 & 73739.0814771693 \tabularnewline
81 & 8826.03055893003 & -50364.075373105 & 68016.1364909651 \tabularnewline
82 & 9285.47075522608 & -51059.5295925545 & 69630.4711030067 \tabularnewline
83 & 10689.7387909515 & -53767.0074406361 & 75146.4850225392 \tabularnewline
84 & 3240.56676757367 & -10861.7437579791 & 17342.8772931264 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122090&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]2094.44494119407[/C][C]-41922.1561158906[/C][C]46111.0459982788[/C][/ROW]
[ROW][C]74[/C][C]5464.74013895725[/C][C]-42242.7136658137[/C][C]53172.1939437282[/C][/ROW]
[ROW][C]75[/C][C]4300.82807973095[/C][C]-42235.2046981596[/C][C]50836.8608576215[/C][/ROW]
[ROW][C]76[/C][C]3474.69829651008[/C][C]-42464.3498660451[/C][C]49413.7464590653[/C][/ROW]
[ROW][C]77[/C][C]14041.2414442036[/C][C]-59580.2743967862[/C][C]87662.7572851935[/C][/ROW]
[ROW][C]78[/C][C]3445.71919191919[/C][C]-42801.5278714583[/C][C]49692.9662552966[/C][/ROW]
[ROW][C]79[/C][C]5970.33200457656[/C][C]-45610.0213395986[/C][C]57550.6853487517[/C][/ROW]
[ROW][C]80[/C][C]10111.1696160544[/C][C]-53516.7422450605[/C][C]73739.0814771693[/C][/ROW]
[ROW][C]81[/C][C]8826.03055893003[/C][C]-50364.075373105[/C][C]68016.1364909651[/C][/ROW]
[ROW][C]82[/C][C]9285.47075522608[/C][C]-51059.5295925545[/C][C]69630.4711030067[/C][/ROW]
[ROW][C]83[/C][C]10689.7387909515[/C][C]-53767.0074406361[/C][C]75146.4850225392[/C][/ROW]
[ROW][C]84[/C][C]3240.56676757367[/C][C]-10861.7437579791[/C][C]17342.8772931264[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122090&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122090&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
732094.44494119407-41922.156115890646111.0459982788
745464.74013895725-42242.713665813753172.1939437282
754300.82807973095-42235.204698159650836.8608576215
763474.69829651008-42464.349866045149413.7464590653
7714041.2414442036-59580.274396786287662.7572851935
783445.71919191919-42801.527871458349692.9662552966
795970.33200457656-45610.021339598657550.6853487517
8010111.1696160544-53516.742245060573739.0814771693
818826.03055893003-50364.07537310568016.1364909651
829285.47075522608-51059.529592554569630.4711030067
8310689.7387909515-53767.007440636175146.4850225392
843240.56676757367-10861.743757979117342.8772931264



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')