Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 11 Jan 2016 19:46:13 +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/2016/Jan/11/t1452541607sd0pxxxnj9f4ndl.htm/, Retrieved Tue, 07 May 2024 12:50:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=289693, Retrieved Tue, 07 May 2024 12:50:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Spreidingsgrafiek] [2016-01-11 19:46:13] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
46626
46018
42408
42483
40113
41381
62348
63611
58389
46175
40555
37909
37866
34418
31736
29533
27604
30575
51345
52455
43367
37077
33016
33117
32279
30369
28983
27864
24591
29528
46549
47932
41584
37295
34666
36773
39591
39833
39280
37742
35602
40096
57284
59961
53802
47364
44964
48612
45570
45118
41921
40167
37315
39206
57075
58664
51705
45527
41057
40867
41484
39738
37254
35177
32846
34079
51287
52800
48443
42223
38796
38952
42343
42023
39340
37149
35431
36537
49626
58677
56009
50069
46470
45603
46729
46989
44666
42920
40125
40941
57748
61246
59809
52682
48394
47436
49750
48172
44960
41831
38672
39704
56207
59254
57374
51309
47083
45092




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289693&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289693&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289693&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289693&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]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289693&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289693&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
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
34240845410-3002
44248341800683
54011341875-1762
641381395051876
7623484077321575
863611617401871
95838963003-4614
104617557781-11606
114055545567-5012
123790939947-2038
133786637301565
143441837258-2840
153173633810-2074
162953331128-1595
172760428925-1321
1830575269963579
19513452996721378
2052455507371718
214336751847-8480
223707742759-5682
233301636469-3453
243311732408709
253227932509-230
263036931671-1302
272898329761-778
282786428375-511
292459127256-2665
3029528239835545
31465492892017629
3247932459411991
334158447324-5740
343729540976-3681
353466636687-2021
3636773340582715
3739591361653426
383983338983850
39392803922555
403774238672-930
413560237134-1532
4240096349945102
43572843948817796
4459961566763285
455380259353-5551
464736453194-5830
474496446756-1792
4848612443564256
494557048004-2434
504511844962156
514192144510-2589
524016741313-1146
533731539559-2244
5439206367072499
55570753859818477
5658664564672197
575170558056-6351
584552751097-5570
594105744919-3862
604086740449418
6141484402591225
623973840876-1138
633725439130-1876
643517736646-1469
653284634569-1723
6634079322381841
67512873347117816
6852800506792121
694844352192-3749
704222347835-5612
713879641615-2819
723895238188764
7342343383443999
744202341735288
753934041415-2075
763714938732-1583
773543136541-1110
7836537348231714
79496263592913697
8058677490189659
815600958069-2060
825006955401-5332
834647049461-2991
844560345862-259
8546729449951734
864698946121868
874466646381-1715
884292044058-1138
894012542312-2187
9040941395171424
91577484033317415
9261246571404106
935980960638-829
945268259201-6519
954839452074-3680
964743647786-350
9749750468282922
984817249142-970
994496047564-2604
1004183144352-2521
1013867241223-2551
10239704380641640
103562073909617111
10459254555993655
1055737458646-1272
1065130956766-5457
1074708350701-3618
1084509246475-1383

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 42408 & 45410 & -3002 \tabularnewline
4 & 42483 & 41800 & 683 \tabularnewline
5 & 40113 & 41875 & -1762 \tabularnewline
6 & 41381 & 39505 & 1876 \tabularnewline
7 & 62348 & 40773 & 21575 \tabularnewline
8 & 63611 & 61740 & 1871 \tabularnewline
9 & 58389 & 63003 & -4614 \tabularnewline
10 & 46175 & 57781 & -11606 \tabularnewline
11 & 40555 & 45567 & -5012 \tabularnewline
12 & 37909 & 39947 & -2038 \tabularnewline
13 & 37866 & 37301 & 565 \tabularnewline
14 & 34418 & 37258 & -2840 \tabularnewline
15 & 31736 & 33810 & -2074 \tabularnewline
16 & 29533 & 31128 & -1595 \tabularnewline
17 & 27604 & 28925 & -1321 \tabularnewline
18 & 30575 & 26996 & 3579 \tabularnewline
19 & 51345 & 29967 & 21378 \tabularnewline
20 & 52455 & 50737 & 1718 \tabularnewline
21 & 43367 & 51847 & -8480 \tabularnewline
22 & 37077 & 42759 & -5682 \tabularnewline
23 & 33016 & 36469 & -3453 \tabularnewline
24 & 33117 & 32408 & 709 \tabularnewline
25 & 32279 & 32509 & -230 \tabularnewline
26 & 30369 & 31671 & -1302 \tabularnewline
27 & 28983 & 29761 & -778 \tabularnewline
28 & 27864 & 28375 & -511 \tabularnewline
29 & 24591 & 27256 & -2665 \tabularnewline
30 & 29528 & 23983 & 5545 \tabularnewline
31 & 46549 & 28920 & 17629 \tabularnewline
32 & 47932 & 45941 & 1991 \tabularnewline
33 & 41584 & 47324 & -5740 \tabularnewline
34 & 37295 & 40976 & -3681 \tabularnewline
35 & 34666 & 36687 & -2021 \tabularnewline
36 & 36773 & 34058 & 2715 \tabularnewline
37 & 39591 & 36165 & 3426 \tabularnewline
38 & 39833 & 38983 & 850 \tabularnewline
39 & 39280 & 39225 & 55 \tabularnewline
40 & 37742 & 38672 & -930 \tabularnewline
41 & 35602 & 37134 & -1532 \tabularnewline
42 & 40096 & 34994 & 5102 \tabularnewline
43 & 57284 & 39488 & 17796 \tabularnewline
44 & 59961 & 56676 & 3285 \tabularnewline
45 & 53802 & 59353 & -5551 \tabularnewline
46 & 47364 & 53194 & -5830 \tabularnewline
47 & 44964 & 46756 & -1792 \tabularnewline
48 & 48612 & 44356 & 4256 \tabularnewline
49 & 45570 & 48004 & -2434 \tabularnewline
50 & 45118 & 44962 & 156 \tabularnewline
51 & 41921 & 44510 & -2589 \tabularnewline
52 & 40167 & 41313 & -1146 \tabularnewline
53 & 37315 & 39559 & -2244 \tabularnewline
54 & 39206 & 36707 & 2499 \tabularnewline
55 & 57075 & 38598 & 18477 \tabularnewline
56 & 58664 & 56467 & 2197 \tabularnewline
57 & 51705 & 58056 & -6351 \tabularnewline
58 & 45527 & 51097 & -5570 \tabularnewline
59 & 41057 & 44919 & -3862 \tabularnewline
60 & 40867 & 40449 & 418 \tabularnewline
61 & 41484 & 40259 & 1225 \tabularnewline
62 & 39738 & 40876 & -1138 \tabularnewline
63 & 37254 & 39130 & -1876 \tabularnewline
64 & 35177 & 36646 & -1469 \tabularnewline
65 & 32846 & 34569 & -1723 \tabularnewline
66 & 34079 & 32238 & 1841 \tabularnewline
67 & 51287 & 33471 & 17816 \tabularnewline
68 & 52800 & 50679 & 2121 \tabularnewline
69 & 48443 & 52192 & -3749 \tabularnewline
70 & 42223 & 47835 & -5612 \tabularnewline
71 & 38796 & 41615 & -2819 \tabularnewline
72 & 38952 & 38188 & 764 \tabularnewline
73 & 42343 & 38344 & 3999 \tabularnewline
74 & 42023 & 41735 & 288 \tabularnewline
75 & 39340 & 41415 & -2075 \tabularnewline
76 & 37149 & 38732 & -1583 \tabularnewline
77 & 35431 & 36541 & -1110 \tabularnewline
78 & 36537 & 34823 & 1714 \tabularnewline
79 & 49626 & 35929 & 13697 \tabularnewline
80 & 58677 & 49018 & 9659 \tabularnewline
81 & 56009 & 58069 & -2060 \tabularnewline
82 & 50069 & 55401 & -5332 \tabularnewline
83 & 46470 & 49461 & -2991 \tabularnewline
84 & 45603 & 45862 & -259 \tabularnewline
85 & 46729 & 44995 & 1734 \tabularnewline
86 & 46989 & 46121 & 868 \tabularnewline
87 & 44666 & 46381 & -1715 \tabularnewline
88 & 42920 & 44058 & -1138 \tabularnewline
89 & 40125 & 42312 & -2187 \tabularnewline
90 & 40941 & 39517 & 1424 \tabularnewline
91 & 57748 & 40333 & 17415 \tabularnewline
92 & 61246 & 57140 & 4106 \tabularnewline
93 & 59809 & 60638 & -829 \tabularnewline
94 & 52682 & 59201 & -6519 \tabularnewline
95 & 48394 & 52074 & -3680 \tabularnewline
96 & 47436 & 47786 & -350 \tabularnewline
97 & 49750 & 46828 & 2922 \tabularnewline
98 & 48172 & 49142 & -970 \tabularnewline
99 & 44960 & 47564 & -2604 \tabularnewline
100 & 41831 & 44352 & -2521 \tabularnewline
101 & 38672 & 41223 & -2551 \tabularnewline
102 & 39704 & 38064 & 1640 \tabularnewline
103 & 56207 & 39096 & 17111 \tabularnewline
104 & 59254 & 55599 & 3655 \tabularnewline
105 & 57374 & 58646 & -1272 \tabularnewline
106 & 51309 & 56766 & -5457 \tabularnewline
107 & 47083 & 50701 & -3618 \tabularnewline
108 & 45092 & 46475 & -1383 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289693&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]42408[/C][C]45410[/C][C]-3002[/C][/ROW]
[ROW][C]4[/C][C]42483[/C][C]41800[/C][C]683[/C][/ROW]
[ROW][C]5[/C][C]40113[/C][C]41875[/C][C]-1762[/C][/ROW]
[ROW][C]6[/C][C]41381[/C][C]39505[/C][C]1876[/C][/ROW]
[ROW][C]7[/C][C]62348[/C][C]40773[/C][C]21575[/C][/ROW]
[ROW][C]8[/C][C]63611[/C][C]61740[/C][C]1871[/C][/ROW]
[ROW][C]9[/C][C]58389[/C][C]63003[/C][C]-4614[/C][/ROW]
[ROW][C]10[/C][C]46175[/C][C]57781[/C][C]-11606[/C][/ROW]
[ROW][C]11[/C][C]40555[/C][C]45567[/C][C]-5012[/C][/ROW]
[ROW][C]12[/C][C]37909[/C][C]39947[/C][C]-2038[/C][/ROW]
[ROW][C]13[/C][C]37866[/C][C]37301[/C][C]565[/C][/ROW]
[ROW][C]14[/C][C]34418[/C][C]37258[/C][C]-2840[/C][/ROW]
[ROW][C]15[/C][C]31736[/C][C]33810[/C][C]-2074[/C][/ROW]
[ROW][C]16[/C][C]29533[/C][C]31128[/C][C]-1595[/C][/ROW]
[ROW][C]17[/C][C]27604[/C][C]28925[/C][C]-1321[/C][/ROW]
[ROW][C]18[/C][C]30575[/C][C]26996[/C][C]3579[/C][/ROW]
[ROW][C]19[/C][C]51345[/C][C]29967[/C][C]21378[/C][/ROW]
[ROW][C]20[/C][C]52455[/C][C]50737[/C][C]1718[/C][/ROW]
[ROW][C]21[/C][C]43367[/C][C]51847[/C][C]-8480[/C][/ROW]
[ROW][C]22[/C][C]37077[/C][C]42759[/C][C]-5682[/C][/ROW]
[ROW][C]23[/C][C]33016[/C][C]36469[/C][C]-3453[/C][/ROW]
[ROW][C]24[/C][C]33117[/C][C]32408[/C][C]709[/C][/ROW]
[ROW][C]25[/C][C]32279[/C][C]32509[/C][C]-230[/C][/ROW]
[ROW][C]26[/C][C]30369[/C][C]31671[/C][C]-1302[/C][/ROW]
[ROW][C]27[/C][C]28983[/C][C]29761[/C][C]-778[/C][/ROW]
[ROW][C]28[/C][C]27864[/C][C]28375[/C][C]-511[/C][/ROW]
[ROW][C]29[/C][C]24591[/C][C]27256[/C][C]-2665[/C][/ROW]
[ROW][C]30[/C][C]29528[/C][C]23983[/C][C]5545[/C][/ROW]
[ROW][C]31[/C][C]46549[/C][C]28920[/C][C]17629[/C][/ROW]
[ROW][C]32[/C][C]47932[/C][C]45941[/C][C]1991[/C][/ROW]
[ROW][C]33[/C][C]41584[/C][C]47324[/C][C]-5740[/C][/ROW]
[ROW][C]34[/C][C]37295[/C][C]40976[/C][C]-3681[/C][/ROW]
[ROW][C]35[/C][C]34666[/C][C]36687[/C][C]-2021[/C][/ROW]
[ROW][C]36[/C][C]36773[/C][C]34058[/C][C]2715[/C][/ROW]
[ROW][C]37[/C][C]39591[/C][C]36165[/C][C]3426[/C][/ROW]
[ROW][C]38[/C][C]39833[/C][C]38983[/C][C]850[/C][/ROW]
[ROW][C]39[/C][C]39280[/C][C]39225[/C][C]55[/C][/ROW]
[ROW][C]40[/C][C]37742[/C][C]38672[/C][C]-930[/C][/ROW]
[ROW][C]41[/C][C]35602[/C][C]37134[/C][C]-1532[/C][/ROW]
[ROW][C]42[/C][C]40096[/C][C]34994[/C][C]5102[/C][/ROW]
[ROW][C]43[/C][C]57284[/C][C]39488[/C][C]17796[/C][/ROW]
[ROW][C]44[/C][C]59961[/C][C]56676[/C][C]3285[/C][/ROW]
[ROW][C]45[/C][C]53802[/C][C]59353[/C][C]-5551[/C][/ROW]
[ROW][C]46[/C][C]47364[/C][C]53194[/C][C]-5830[/C][/ROW]
[ROW][C]47[/C][C]44964[/C][C]46756[/C][C]-1792[/C][/ROW]
[ROW][C]48[/C][C]48612[/C][C]44356[/C][C]4256[/C][/ROW]
[ROW][C]49[/C][C]45570[/C][C]48004[/C][C]-2434[/C][/ROW]
[ROW][C]50[/C][C]45118[/C][C]44962[/C][C]156[/C][/ROW]
[ROW][C]51[/C][C]41921[/C][C]44510[/C][C]-2589[/C][/ROW]
[ROW][C]52[/C][C]40167[/C][C]41313[/C][C]-1146[/C][/ROW]
[ROW][C]53[/C][C]37315[/C][C]39559[/C][C]-2244[/C][/ROW]
[ROW][C]54[/C][C]39206[/C][C]36707[/C][C]2499[/C][/ROW]
[ROW][C]55[/C][C]57075[/C][C]38598[/C][C]18477[/C][/ROW]
[ROW][C]56[/C][C]58664[/C][C]56467[/C][C]2197[/C][/ROW]
[ROW][C]57[/C][C]51705[/C][C]58056[/C][C]-6351[/C][/ROW]
[ROW][C]58[/C][C]45527[/C][C]51097[/C][C]-5570[/C][/ROW]
[ROW][C]59[/C][C]41057[/C][C]44919[/C][C]-3862[/C][/ROW]
[ROW][C]60[/C][C]40867[/C][C]40449[/C][C]418[/C][/ROW]
[ROW][C]61[/C][C]41484[/C][C]40259[/C][C]1225[/C][/ROW]
[ROW][C]62[/C][C]39738[/C][C]40876[/C][C]-1138[/C][/ROW]
[ROW][C]63[/C][C]37254[/C][C]39130[/C][C]-1876[/C][/ROW]
[ROW][C]64[/C][C]35177[/C][C]36646[/C][C]-1469[/C][/ROW]
[ROW][C]65[/C][C]32846[/C][C]34569[/C][C]-1723[/C][/ROW]
[ROW][C]66[/C][C]34079[/C][C]32238[/C][C]1841[/C][/ROW]
[ROW][C]67[/C][C]51287[/C][C]33471[/C][C]17816[/C][/ROW]
[ROW][C]68[/C][C]52800[/C][C]50679[/C][C]2121[/C][/ROW]
[ROW][C]69[/C][C]48443[/C][C]52192[/C][C]-3749[/C][/ROW]
[ROW][C]70[/C][C]42223[/C][C]47835[/C][C]-5612[/C][/ROW]
[ROW][C]71[/C][C]38796[/C][C]41615[/C][C]-2819[/C][/ROW]
[ROW][C]72[/C][C]38952[/C][C]38188[/C][C]764[/C][/ROW]
[ROW][C]73[/C][C]42343[/C][C]38344[/C][C]3999[/C][/ROW]
[ROW][C]74[/C][C]42023[/C][C]41735[/C][C]288[/C][/ROW]
[ROW][C]75[/C][C]39340[/C][C]41415[/C][C]-2075[/C][/ROW]
[ROW][C]76[/C][C]37149[/C][C]38732[/C][C]-1583[/C][/ROW]
[ROW][C]77[/C][C]35431[/C][C]36541[/C][C]-1110[/C][/ROW]
[ROW][C]78[/C][C]36537[/C][C]34823[/C][C]1714[/C][/ROW]
[ROW][C]79[/C][C]49626[/C][C]35929[/C][C]13697[/C][/ROW]
[ROW][C]80[/C][C]58677[/C][C]49018[/C][C]9659[/C][/ROW]
[ROW][C]81[/C][C]56009[/C][C]58069[/C][C]-2060[/C][/ROW]
[ROW][C]82[/C][C]50069[/C][C]55401[/C][C]-5332[/C][/ROW]
[ROW][C]83[/C][C]46470[/C][C]49461[/C][C]-2991[/C][/ROW]
[ROW][C]84[/C][C]45603[/C][C]45862[/C][C]-259[/C][/ROW]
[ROW][C]85[/C][C]46729[/C][C]44995[/C][C]1734[/C][/ROW]
[ROW][C]86[/C][C]46989[/C][C]46121[/C][C]868[/C][/ROW]
[ROW][C]87[/C][C]44666[/C][C]46381[/C][C]-1715[/C][/ROW]
[ROW][C]88[/C][C]42920[/C][C]44058[/C][C]-1138[/C][/ROW]
[ROW][C]89[/C][C]40125[/C][C]42312[/C][C]-2187[/C][/ROW]
[ROW][C]90[/C][C]40941[/C][C]39517[/C][C]1424[/C][/ROW]
[ROW][C]91[/C][C]57748[/C][C]40333[/C][C]17415[/C][/ROW]
[ROW][C]92[/C][C]61246[/C][C]57140[/C][C]4106[/C][/ROW]
[ROW][C]93[/C][C]59809[/C][C]60638[/C][C]-829[/C][/ROW]
[ROW][C]94[/C][C]52682[/C][C]59201[/C][C]-6519[/C][/ROW]
[ROW][C]95[/C][C]48394[/C][C]52074[/C][C]-3680[/C][/ROW]
[ROW][C]96[/C][C]47436[/C][C]47786[/C][C]-350[/C][/ROW]
[ROW][C]97[/C][C]49750[/C][C]46828[/C][C]2922[/C][/ROW]
[ROW][C]98[/C][C]48172[/C][C]49142[/C][C]-970[/C][/ROW]
[ROW][C]99[/C][C]44960[/C][C]47564[/C][C]-2604[/C][/ROW]
[ROW][C]100[/C][C]41831[/C][C]44352[/C][C]-2521[/C][/ROW]
[ROW][C]101[/C][C]38672[/C][C]41223[/C][C]-2551[/C][/ROW]
[ROW][C]102[/C][C]39704[/C][C]38064[/C][C]1640[/C][/ROW]
[ROW][C]103[/C][C]56207[/C][C]39096[/C][C]17111[/C][/ROW]
[ROW][C]104[/C][C]59254[/C][C]55599[/C][C]3655[/C][/ROW]
[ROW][C]105[/C][C]57374[/C][C]58646[/C][C]-1272[/C][/ROW]
[ROW][C]106[/C][C]51309[/C][C]56766[/C][C]-5457[/C][/ROW]
[ROW][C]107[/C][C]47083[/C][C]50701[/C][C]-3618[/C][/ROW]
[ROW][C]108[/C][C]45092[/C][C]46475[/C][C]-1383[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289693&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289693&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
34240845410-3002
44248341800683
54011341875-1762
641381395051876
7623484077321575
863611617401871
95838963003-4614
104617557781-11606
114055545567-5012
123790939947-2038
133786637301565
143441837258-2840
153173633810-2074
162953331128-1595
172760428925-1321
1830575269963579
19513452996721378
2052455507371718
214336751847-8480
223707742759-5682
233301636469-3453
243311732408709
253227932509-230
263036931671-1302
272898329761-778
282786428375-511
292459127256-2665
3029528239835545
31465492892017629
3247932459411991
334158447324-5740
343729540976-3681
353466636687-2021
3636773340582715
3739591361653426
383983338983850
39392803922555
403774238672-930
413560237134-1532
4240096349945102
43572843948817796
4459961566763285
455380259353-5551
464736453194-5830
474496446756-1792
4848612443564256
494557048004-2434
504511844962156
514192144510-2589
524016741313-1146
533731539559-2244
5439206367072499
55570753859818477
5658664564672197
575170558056-6351
584552751097-5570
594105744919-3862
604086740449418
6141484402591225
623973840876-1138
633725439130-1876
643517736646-1469
653284634569-1723
6634079322381841
67512873347117816
6852800506792121
694844352192-3749
704222347835-5612
713879641615-2819
723895238188764
7342343383443999
744202341735288
753934041415-2075
763714938732-1583
773543136541-1110
7836537348231714
79496263592913697
8058677490189659
815600958069-2060
825006955401-5332
834647049461-2991
844560345862-259
8546729449951734
864698946121868
874466646381-1715
884292044058-1138
894012542312-2187
9040941395171424
91577484033317415
9261246571404106
935980960638-829
945268259201-6519
954839452074-3680
964743647786-350
9749750468282922
984817249142-970
994496047564-2604
1004183144352-2521
1013867241223-2551
10239704380641640
103562073909617111
10459254555993655
1055737458646-1272
1065130956766-5457
1074708350701-3618
1084509246475-1383







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1094448432263.946490194556704.0535098055
1104387626594.234593508161157.7654064919
1114326822102.246449806564433.7535501935
1124266018219.89298038967100.107019611
1134205214727.1296633969376.87033661
1144144411511.104271469871376.8957285302
115408368504.7774051526173167.2225948474
116402285664.4691870161974791.5308129838
117396202959.8394705834576280.1605294165
11839012368.79777987981777655.2022201202
11938404-2125.3324100904978933.3324100905
12037796-4535.5071003870880127.5071003871

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 44484 & 32263.9464901945 & 56704.0535098055 \tabularnewline
110 & 43876 & 26594.2345935081 & 61157.7654064919 \tabularnewline
111 & 43268 & 22102.2464498065 & 64433.7535501935 \tabularnewline
112 & 42660 & 18219.892980389 & 67100.107019611 \tabularnewline
113 & 42052 & 14727.12966339 & 69376.87033661 \tabularnewline
114 & 41444 & 11511.1042714698 & 71376.8957285302 \tabularnewline
115 & 40836 & 8504.77740515261 & 73167.2225948474 \tabularnewline
116 & 40228 & 5664.46918701619 & 74791.5308129838 \tabularnewline
117 & 39620 & 2959.83947058345 & 76280.1605294165 \tabularnewline
118 & 39012 & 368.797779879817 & 77655.2022201202 \tabularnewline
119 & 38404 & -2125.33241009049 & 78933.3324100905 \tabularnewline
120 & 37796 & -4535.50710038708 & 80127.5071003871 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289693&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]109[/C][C]44484[/C][C]32263.9464901945[/C][C]56704.0535098055[/C][/ROW]
[ROW][C]110[/C][C]43876[/C][C]26594.2345935081[/C][C]61157.7654064919[/C][/ROW]
[ROW][C]111[/C][C]43268[/C][C]22102.2464498065[/C][C]64433.7535501935[/C][/ROW]
[ROW][C]112[/C][C]42660[/C][C]18219.892980389[/C][C]67100.107019611[/C][/ROW]
[ROW][C]113[/C][C]42052[/C][C]14727.12966339[/C][C]69376.87033661[/C][/ROW]
[ROW][C]114[/C][C]41444[/C][C]11511.1042714698[/C][C]71376.8957285302[/C][/ROW]
[ROW][C]115[/C][C]40836[/C][C]8504.77740515261[/C][C]73167.2225948474[/C][/ROW]
[ROW][C]116[/C][C]40228[/C][C]5664.46918701619[/C][C]74791.5308129838[/C][/ROW]
[ROW][C]117[/C][C]39620[/C][C]2959.83947058345[/C][C]76280.1605294165[/C][/ROW]
[ROW][C]118[/C][C]39012[/C][C]368.797779879817[/C][C]77655.2022201202[/C][/ROW]
[ROW][C]119[/C][C]38404[/C][C]-2125.33241009049[/C][C]78933.3324100905[/C][/ROW]
[ROW][C]120[/C][C]37796[/C][C]-4535.50710038708[/C][C]80127.5071003871[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289693&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289693&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
1094448432263.946490194556704.0535098055
1104387626594.234593508161157.7654064919
1114326822102.246449806564433.7535501935
1124266018219.89298038967100.107019611
1134205214727.1296633969376.87033661
1144144411511.104271469871376.8957285302
115408368504.7774051526173167.2225948474
116402285664.4691870161974791.5308129838
117396202959.8394705834576280.1605294165
11839012368.79777987981777655.2022201202
11938404-2125.3324100904978933.3324100905
12037796-4535.5071003870880127.5071003871



Parameters (Session):
par1 = 12 ;
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')