Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 15:58:37 +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/26/t1461682879jo1xmj0tyl4rhds.htm/, Retrieved Mon, 13 May 2024 03:11:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294895, Retrieved Mon, 13 May 2024 03:11:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 14:58:37] [f8975010d6e80ebfdd11eb899305ce74] [Current]
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Dataseries X:
38552
33618
31499
33892
37134
32710
32520
33419
35003
34417
32359
35703
38632
33577
33277
35001
38296
34179
32791
35261
36789
35036
33004
35548
38485
34675
33081
36114
37524
34600
33795
36017
37009
32877
32505
34162
38591
33550
30753
33508
36327
33230
32971
32844
35124
32243
30840
34815
36308
33138
31425
34265
37612
31846
31065
33712
36031
32909
32204
34914
34888
33242
32316
35295
37800
34540
32614
35859
39866
34609
32375
34395
35348
33221
33892
36762





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
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=294895&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]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=294895&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294895&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
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.143960413964627
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.143960413964627 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294895&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]0.143960413964627[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294895&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294895&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
beta0.143960413964627
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
331499286842815
43389226970.24856531046921.75143468958
53713430359.70676720866774.29323279142
63271034576.936825319-1866.936825319
73252029884.17182710032635.82817289972
83341930073.62674201053345.37325798946
93500331454.22806109693548.7719389031
103441733549.1107384874867.889261512559
113235933088.0524358502-729.052435850244
123570330925.09774538334777.90225461668
133863234956.92653184053675.07346815954
143357738414.9916296671-4837.99162966712
153327732663.5123519028613.487648097154
163500132451.83028768512549.1697123149
173829634542.8098147363753.19018526396
183417938378.1206274946-4199.12062749461
193279133656.6134836731-865.613483673085
203526132143.99940823013117.00059176985
213678935062.72410374931726.27589625068
223503636839.2394963907-1803.23949639072
233300434826.644392013-1822.64439201295
243554832532.25575082853015.74424917154
253848535510.40354135062974.59645864936
263467538875.6276789155-4200.62767891551
273308134460.9035793476-1379.90357934756
283611432668.25208883343445.74791116658
293752436197.30338454271326.69661545729
303460037798.2951785094-3198.29517850941
313379534413.8672806301-618.867280630126
323601733519.77489072142497.22510927855
333700936101.2764512161907.72354878395
343287737223.9527090644-4346.95270906443
353250532466.163597582938.8364024171424
363416232099.75450215172062.24549784827
373859134053.63621771874537.36378228135
383355039135.836986124-5585.83698612398
393075333290.6975812626-2537.69758126265
403350830128.3695869473379.63041305295
413632733369.90258025762957.09741974241
423323036614.6075489374-3384.60754893743
433297133030.3580450846-59.3580450846057
443284432762.812836342181.1871636579053
453512432647.50057403092476.4994259691
463224335284.0184565766-3041.01845657657
473084031965.2321806937-1125.23218069374
483481530400.24329015474414.75670984525
493630835010.79349365721297.20650634282
503313836690.5398793079-3552.5398793079
513142533009.1147676569-1584.11476765689
523426531068.06494993753196.93505006247
533761234368.29704316253243.70295683746
543184638182.2618636071-6336.26186360715
553106531504.090982734-439.090982733986
563371230659.87926309153052.12073690853
573603133746.26382784682284.73617215316
583290936394.17539299-3485.17539298996
593220432770.4481006758-566.4481006758
603491431983.9019976132930.09800238696
613488835115.7201189936-227.720118993588
623324235056.9374363952-1814.9374363952
633231633149.6582917318-833.658291731845
643529532103.64449894913191.35550105091
653780035542.07335798872257.92664201133
663454038372.1254120744-3832.12541207438
673261434560.4510513878-1946.45105138778
683585932354.23915226813504.76084773189
693986636103.78597475463762.21402524539
703460940652.3958632525-6043.39586325246
713237534525.3860930265-2150.38609302653
723439531981.81562089072413.18437910935
733534834349.2186430802998.781356919797
743322135446.0036206825-2225.00362068253
753389232998.6911783763893.308821623723
763676233798.29228613552963.70771386452

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 31499 & 28684 & 2815 \tabularnewline
4 & 33892 & 26970.2485653104 & 6921.75143468958 \tabularnewline
5 & 37134 & 30359.7067672086 & 6774.29323279142 \tabularnewline
6 & 32710 & 34576.936825319 & -1866.936825319 \tabularnewline
7 & 32520 & 29884.1718271003 & 2635.82817289972 \tabularnewline
8 & 33419 & 30073.6267420105 & 3345.37325798946 \tabularnewline
9 & 35003 & 31454.2280610969 & 3548.7719389031 \tabularnewline
10 & 34417 & 33549.1107384874 & 867.889261512559 \tabularnewline
11 & 32359 & 33088.0524358502 & -729.052435850244 \tabularnewline
12 & 35703 & 30925.0977453833 & 4777.90225461668 \tabularnewline
13 & 38632 & 34956.9265318405 & 3675.07346815954 \tabularnewline
14 & 33577 & 38414.9916296671 & -4837.99162966712 \tabularnewline
15 & 33277 & 32663.5123519028 & 613.487648097154 \tabularnewline
16 & 35001 & 32451.8302876851 & 2549.1697123149 \tabularnewline
17 & 38296 & 34542.809814736 & 3753.19018526396 \tabularnewline
18 & 34179 & 38378.1206274946 & -4199.12062749461 \tabularnewline
19 & 32791 & 33656.6134836731 & -865.613483673085 \tabularnewline
20 & 35261 & 32143.9994082301 & 3117.00059176985 \tabularnewline
21 & 36789 & 35062.7241037493 & 1726.27589625068 \tabularnewline
22 & 35036 & 36839.2394963907 & -1803.23949639072 \tabularnewline
23 & 33004 & 34826.644392013 & -1822.64439201295 \tabularnewline
24 & 35548 & 32532.2557508285 & 3015.74424917154 \tabularnewline
25 & 38485 & 35510.4035413506 & 2974.59645864936 \tabularnewline
26 & 34675 & 38875.6276789155 & -4200.62767891551 \tabularnewline
27 & 33081 & 34460.9035793476 & -1379.90357934756 \tabularnewline
28 & 36114 & 32668.2520888334 & 3445.74791116658 \tabularnewline
29 & 37524 & 36197.3033845427 & 1326.69661545729 \tabularnewline
30 & 34600 & 37798.2951785094 & -3198.29517850941 \tabularnewline
31 & 33795 & 34413.8672806301 & -618.867280630126 \tabularnewline
32 & 36017 & 33519.7748907214 & 2497.22510927855 \tabularnewline
33 & 37009 & 36101.2764512161 & 907.72354878395 \tabularnewline
34 & 32877 & 37223.9527090644 & -4346.95270906443 \tabularnewline
35 & 32505 & 32466.1635975829 & 38.8364024171424 \tabularnewline
36 & 34162 & 32099.7545021517 & 2062.24549784827 \tabularnewline
37 & 38591 & 34053.6362177187 & 4537.36378228135 \tabularnewline
38 & 33550 & 39135.836986124 & -5585.83698612398 \tabularnewline
39 & 30753 & 33290.6975812626 & -2537.69758126265 \tabularnewline
40 & 33508 & 30128.369586947 & 3379.63041305295 \tabularnewline
41 & 36327 & 33369.9025802576 & 2957.09741974241 \tabularnewline
42 & 33230 & 36614.6075489374 & -3384.60754893743 \tabularnewline
43 & 32971 & 33030.3580450846 & -59.3580450846057 \tabularnewline
44 & 32844 & 32762.8128363421 & 81.1871636579053 \tabularnewline
45 & 35124 & 32647.5005740309 & 2476.4994259691 \tabularnewline
46 & 32243 & 35284.0184565766 & -3041.01845657657 \tabularnewline
47 & 30840 & 31965.2321806937 & -1125.23218069374 \tabularnewline
48 & 34815 & 30400.2432901547 & 4414.75670984525 \tabularnewline
49 & 36308 & 35010.7934936572 & 1297.20650634282 \tabularnewline
50 & 33138 & 36690.5398793079 & -3552.5398793079 \tabularnewline
51 & 31425 & 33009.1147676569 & -1584.11476765689 \tabularnewline
52 & 34265 & 31068.0649499375 & 3196.93505006247 \tabularnewline
53 & 37612 & 34368.2970431625 & 3243.70295683746 \tabularnewline
54 & 31846 & 38182.2618636071 & -6336.26186360715 \tabularnewline
55 & 31065 & 31504.090982734 & -439.090982733986 \tabularnewline
56 & 33712 & 30659.8792630915 & 3052.12073690853 \tabularnewline
57 & 36031 & 33746.2638278468 & 2284.73617215316 \tabularnewline
58 & 32909 & 36394.17539299 & -3485.17539298996 \tabularnewline
59 & 32204 & 32770.4481006758 & -566.4481006758 \tabularnewline
60 & 34914 & 31983.901997613 & 2930.09800238696 \tabularnewline
61 & 34888 & 35115.7201189936 & -227.720118993588 \tabularnewline
62 & 33242 & 35056.9374363952 & -1814.9374363952 \tabularnewline
63 & 32316 & 33149.6582917318 & -833.658291731845 \tabularnewline
64 & 35295 & 32103.6444989491 & 3191.35550105091 \tabularnewline
65 & 37800 & 35542.0733579887 & 2257.92664201133 \tabularnewline
66 & 34540 & 38372.1254120744 & -3832.12541207438 \tabularnewline
67 & 32614 & 34560.4510513878 & -1946.45105138778 \tabularnewline
68 & 35859 & 32354.2391522681 & 3504.76084773189 \tabularnewline
69 & 39866 & 36103.7859747546 & 3762.21402524539 \tabularnewline
70 & 34609 & 40652.3958632525 & -6043.39586325246 \tabularnewline
71 & 32375 & 34525.3860930265 & -2150.38609302653 \tabularnewline
72 & 34395 & 31981.8156208907 & 2413.18437910935 \tabularnewline
73 & 35348 & 34349.2186430802 & 998.781356919797 \tabularnewline
74 & 33221 & 35446.0036206825 & -2225.00362068253 \tabularnewline
75 & 33892 & 32998.6911783763 & 893.308821623723 \tabularnewline
76 & 36762 & 33798.2922861355 & 2963.70771386452 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294895&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]31499[/C][C]28684[/C][C]2815[/C][/ROW]
[ROW][C]4[/C][C]33892[/C][C]26970.2485653104[/C][C]6921.75143468958[/C][/ROW]
[ROW][C]5[/C][C]37134[/C][C]30359.7067672086[/C][C]6774.29323279142[/C][/ROW]
[ROW][C]6[/C][C]32710[/C][C]34576.936825319[/C][C]-1866.936825319[/C][/ROW]
[ROW][C]7[/C][C]32520[/C][C]29884.1718271003[/C][C]2635.82817289972[/C][/ROW]
[ROW][C]8[/C][C]33419[/C][C]30073.6267420105[/C][C]3345.37325798946[/C][/ROW]
[ROW][C]9[/C][C]35003[/C][C]31454.2280610969[/C][C]3548.7719389031[/C][/ROW]
[ROW][C]10[/C][C]34417[/C][C]33549.1107384874[/C][C]867.889261512559[/C][/ROW]
[ROW][C]11[/C][C]32359[/C][C]33088.0524358502[/C][C]-729.052435850244[/C][/ROW]
[ROW][C]12[/C][C]35703[/C][C]30925.0977453833[/C][C]4777.90225461668[/C][/ROW]
[ROW][C]13[/C][C]38632[/C][C]34956.9265318405[/C][C]3675.07346815954[/C][/ROW]
[ROW][C]14[/C][C]33577[/C][C]38414.9916296671[/C][C]-4837.99162966712[/C][/ROW]
[ROW][C]15[/C][C]33277[/C][C]32663.5123519028[/C][C]613.487648097154[/C][/ROW]
[ROW][C]16[/C][C]35001[/C][C]32451.8302876851[/C][C]2549.1697123149[/C][/ROW]
[ROW][C]17[/C][C]38296[/C][C]34542.809814736[/C][C]3753.19018526396[/C][/ROW]
[ROW][C]18[/C][C]34179[/C][C]38378.1206274946[/C][C]-4199.12062749461[/C][/ROW]
[ROW][C]19[/C][C]32791[/C][C]33656.6134836731[/C][C]-865.613483673085[/C][/ROW]
[ROW][C]20[/C][C]35261[/C][C]32143.9994082301[/C][C]3117.00059176985[/C][/ROW]
[ROW][C]21[/C][C]36789[/C][C]35062.7241037493[/C][C]1726.27589625068[/C][/ROW]
[ROW][C]22[/C][C]35036[/C][C]36839.2394963907[/C][C]-1803.23949639072[/C][/ROW]
[ROW][C]23[/C][C]33004[/C][C]34826.644392013[/C][C]-1822.64439201295[/C][/ROW]
[ROW][C]24[/C][C]35548[/C][C]32532.2557508285[/C][C]3015.74424917154[/C][/ROW]
[ROW][C]25[/C][C]38485[/C][C]35510.4035413506[/C][C]2974.59645864936[/C][/ROW]
[ROW][C]26[/C][C]34675[/C][C]38875.6276789155[/C][C]-4200.62767891551[/C][/ROW]
[ROW][C]27[/C][C]33081[/C][C]34460.9035793476[/C][C]-1379.90357934756[/C][/ROW]
[ROW][C]28[/C][C]36114[/C][C]32668.2520888334[/C][C]3445.74791116658[/C][/ROW]
[ROW][C]29[/C][C]37524[/C][C]36197.3033845427[/C][C]1326.69661545729[/C][/ROW]
[ROW][C]30[/C][C]34600[/C][C]37798.2951785094[/C][C]-3198.29517850941[/C][/ROW]
[ROW][C]31[/C][C]33795[/C][C]34413.8672806301[/C][C]-618.867280630126[/C][/ROW]
[ROW][C]32[/C][C]36017[/C][C]33519.7748907214[/C][C]2497.22510927855[/C][/ROW]
[ROW][C]33[/C][C]37009[/C][C]36101.2764512161[/C][C]907.72354878395[/C][/ROW]
[ROW][C]34[/C][C]32877[/C][C]37223.9527090644[/C][C]-4346.95270906443[/C][/ROW]
[ROW][C]35[/C][C]32505[/C][C]32466.1635975829[/C][C]38.8364024171424[/C][/ROW]
[ROW][C]36[/C][C]34162[/C][C]32099.7545021517[/C][C]2062.24549784827[/C][/ROW]
[ROW][C]37[/C][C]38591[/C][C]34053.6362177187[/C][C]4537.36378228135[/C][/ROW]
[ROW][C]38[/C][C]33550[/C][C]39135.836986124[/C][C]-5585.83698612398[/C][/ROW]
[ROW][C]39[/C][C]30753[/C][C]33290.6975812626[/C][C]-2537.69758126265[/C][/ROW]
[ROW][C]40[/C][C]33508[/C][C]30128.369586947[/C][C]3379.63041305295[/C][/ROW]
[ROW][C]41[/C][C]36327[/C][C]33369.9025802576[/C][C]2957.09741974241[/C][/ROW]
[ROW][C]42[/C][C]33230[/C][C]36614.6075489374[/C][C]-3384.60754893743[/C][/ROW]
[ROW][C]43[/C][C]32971[/C][C]33030.3580450846[/C][C]-59.3580450846057[/C][/ROW]
[ROW][C]44[/C][C]32844[/C][C]32762.8128363421[/C][C]81.1871636579053[/C][/ROW]
[ROW][C]45[/C][C]35124[/C][C]32647.5005740309[/C][C]2476.4994259691[/C][/ROW]
[ROW][C]46[/C][C]32243[/C][C]35284.0184565766[/C][C]-3041.01845657657[/C][/ROW]
[ROW][C]47[/C][C]30840[/C][C]31965.2321806937[/C][C]-1125.23218069374[/C][/ROW]
[ROW][C]48[/C][C]34815[/C][C]30400.2432901547[/C][C]4414.75670984525[/C][/ROW]
[ROW][C]49[/C][C]36308[/C][C]35010.7934936572[/C][C]1297.20650634282[/C][/ROW]
[ROW][C]50[/C][C]33138[/C][C]36690.5398793079[/C][C]-3552.5398793079[/C][/ROW]
[ROW][C]51[/C][C]31425[/C][C]33009.1147676569[/C][C]-1584.11476765689[/C][/ROW]
[ROW][C]52[/C][C]34265[/C][C]31068.0649499375[/C][C]3196.93505006247[/C][/ROW]
[ROW][C]53[/C][C]37612[/C][C]34368.2970431625[/C][C]3243.70295683746[/C][/ROW]
[ROW][C]54[/C][C]31846[/C][C]38182.2618636071[/C][C]-6336.26186360715[/C][/ROW]
[ROW][C]55[/C][C]31065[/C][C]31504.090982734[/C][C]-439.090982733986[/C][/ROW]
[ROW][C]56[/C][C]33712[/C][C]30659.8792630915[/C][C]3052.12073690853[/C][/ROW]
[ROW][C]57[/C][C]36031[/C][C]33746.2638278468[/C][C]2284.73617215316[/C][/ROW]
[ROW][C]58[/C][C]32909[/C][C]36394.17539299[/C][C]-3485.17539298996[/C][/ROW]
[ROW][C]59[/C][C]32204[/C][C]32770.4481006758[/C][C]-566.4481006758[/C][/ROW]
[ROW][C]60[/C][C]34914[/C][C]31983.901997613[/C][C]2930.09800238696[/C][/ROW]
[ROW][C]61[/C][C]34888[/C][C]35115.7201189936[/C][C]-227.720118993588[/C][/ROW]
[ROW][C]62[/C][C]33242[/C][C]35056.9374363952[/C][C]-1814.9374363952[/C][/ROW]
[ROW][C]63[/C][C]32316[/C][C]33149.6582917318[/C][C]-833.658291731845[/C][/ROW]
[ROW][C]64[/C][C]35295[/C][C]32103.6444989491[/C][C]3191.35550105091[/C][/ROW]
[ROW][C]65[/C][C]37800[/C][C]35542.0733579887[/C][C]2257.92664201133[/C][/ROW]
[ROW][C]66[/C][C]34540[/C][C]38372.1254120744[/C][C]-3832.12541207438[/C][/ROW]
[ROW][C]67[/C][C]32614[/C][C]34560.4510513878[/C][C]-1946.45105138778[/C][/ROW]
[ROW][C]68[/C][C]35859[/C][C]32354.2391522681[/C][C]3504.76084773189[/C][/ROW]
[ROW][C]69[/C][C]39866[/C][C]36103.7859747546[/C][C]3762.21402524539[/C][/ROW]
[ROW][C]70[/C][C]34609[/C][C]40652.3958632525[/C][C]-6043.39586325246[/C][/ROW]
[ROW][C]71[/C][C]32375[/C][C]34525.3860930265[/C][C]-2150.38609302653[/C][/ROW]
[ROW][C]72[/C][C]34395[/C][C]31981.8156208907[/C][C]2413.18437910935[/C][/ROW]
[ROW][C]73[/C][C]35348[/C][C]34349.2186430802[/C][C]998.781356919797[/C][/ROW]
[ROW][C]74[/C][C]33221[/C][C]35446.0036206825[/C][C]-2225.00362068253[/C][/ROW]
[ROW][C]75[/C][C]33892[/C][C]32998.6911783763[/C][C]893.308821623723[/C][/ROW]
[ROW][C]76[/C][C]36762[/C][C]33798.2922861355[/C][C]2963.70771386452[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294895&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294895&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
331499286842815
43389226970.24856531046921.75143468958
53713430359.70676720866774.29323279142
63271034576.936825319-1866.936825319
73252029884.17182710032635.82817289972
83341930073.62674201053345.37325798946
93500331454.22806109693548.7719389031
103441733549.1107384874867.889261512559
113235933088.0524358502-729.052435850244
123570330925.09774538334777.90225461668
133863234956.92653184053675.07346815954
143357738414.9916296671-4837.99162966712
153327732663.5123519028613.487648097154
163500132451.83028768512549.1697123149
173829634542.8098147363753.19018526396
183417938378.1206274946-4199.12062749461
193279133656.6134836731-865.613483673085
203526132143.99940823013117.00059176985
213678935062.72410374931726.27589625068
223503636839.2394963907-1803.23949639072
233300434826.644392013-1822.64439201295
243554832532.25575082853015.74424917154
253848535510.40354135062974.59645864936
263467538875.6276789155-4200.62767891551
273308134460.9035793476-1379.90357934756
283611432668.25208883343445.74791116658
293752436197.30338454271326.69661545729
303460037798.2951785094-3198.29517850941
313379534413.8672806301-618.867280630126
323601733519.77489072142497.22510927855
333700936101.2764512161907.72354878395
343287737223.9527090644-4346.95270906443
353250532466.163597582938.8364024171424
363416232099.75450215172062.24549784827
373859134053.63621771874537.36378228135
383355039135.836986124-5585.83698612398
393075333290.6975812626-2537.69758126265
403350830128.3695869473379.63041305295
413632733369.90258025762957.09741974241
423323036614.6075489374-3384.60754893743
433297133030.3580450846-59.3580450846057
443284432762.812836342181.1871636579053
453512432647.50057403092476.4994259691
463224335284.0184565766-3041.01845657657
473084031965.2321806937-1125.23218069374
483481530400.24329015474414.75670984525
493630835010.79349365721297.20650634282
503313836690.5398793079-3552.5398793079
513142533009.1147676569-1584.11476765689
523426531068.06494993753196.93505006247
533761234368.29704316253243.70295683746
543184638182.2618636071-6336.26186360715
553106531504.090982734-439.090982733986
563371230659.87926309153052.12073690853
573603133746.26382784682284.73617215316
583290936394.17539299-3485.17539298996
593220432770.4481006758-566.4481006758
603491431983.9019976132930.09800238696
613488835115.7201189936-227.720118993588
623324235056.9374363952-1814.9374363952
633231633149.6582917318-833.658291731845
643529532103.64449894913191.35550105091
653780035542.07335798872257.92664201133
663454038372.1254120744-3832.12541207438
673261434560.4510513878-1946.45105138778
683585932354.23915226813504.76084773189
693986636103.78597475463762.21402524539
703460940652.3958632525-6043.39586325246
713237534525.3860930265-2150.38609302653
723439531981.81562089072413.18437910935
733534834349.2186430802998.781356919797
743322135446.0036206825-2225.00362068253
753389232998.6911783763893.308821623723
763676233798.29228613552963.70771386452







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7737094.948875493631044.536394007943145.3613569792
7837427.897750987228234.763508153846621.0319938205
7937760.846626480725709.455448954649812.2378040069
8038093.795501974323251.565925560952936.0250783877

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
77 & 37094.9488754936 & 31044.5363940079 & 43145.3613569792 \tabularnewline
78 & 37427.8977509872 & 28234.7635081538 & 46621.0319938205 \tabularnewline
79 & 37760.8466264807 & 25709.4554489546 & 49812.2378040069 \tabularnewline
80 & 38093.7955019743 & 23251.5659255609 & 52936.0250783877 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294895&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]77[/C][C]37094.9488754936[/C][C]31044.5363940079[/C][C]43145.3613569792[/C][/ROW]
[ROW][C]78[/C][C]37427.8977509872[/C][C]28234.7635081538[/C][C]46621.0319938205[/C][/ROW]
[ROW][C]79[/C][C]37760.8466264807[/C][C]25709.4554489546[/C][C]49812.2378040069[/C][/ROW]
[ROW][C]80[/C][C]38093.7955019743[/C][C]23251.5659255609[/C][C]52936.0250783877[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294895&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294895&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
7737094.948875493631044.536394007943145.3613569792
7837427.897750987228234.763508153846621.0319938205
7937760.846626480725709.455448954649812.2378040069
8038093.795501974323251.565925560952936.0250783877



Parameters (Session):
par1 = 4 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 4 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '4'
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')