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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 21 Dec 2010 20:32:31 +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/2010/Dec/21/t1292963451xfpovn40kgg4d7t.htm/, Retrieved Sun, 19 May 2024 19:49:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113953, Retrieved Sun, 19 May 2024 19:49:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Double exponentia...] [2010-12-21 20:32:31] [be034431ba35f7eb1ce695fc7ca4deb9] [Current]
-   P     [Exponential Smoothing] [Triple exponentia...] [2010-12-21 20:38:51] [b11c112f8986de933f8b95cd30e75cc2]
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Dataseries X:
27951
29781
32914
33488
35652
36488
35387
35676
34844
32447
31068
29010
29812
30951
32974
32936
34012
32946
31948
30599
27691
25073
23406
22248
22896
25317
26558
26471
27543
26198
24725
25005
23462
20780
19815
19761
21454
23899
24939
23580
24562
24696
23785
23812
21917
19713
19282
18788
21453
24482
27474
27264
27349
30632
29429
30084
26290
24379
23335
21346
21106
24514
28353
30805
31348
34556
33855
34787
32529
29998
29257
28155
30466
35704
39327
39351
42234
43630
43722
43121
37985
37135
34646
33026
35087
38846
42013
43908
42868
44423
44167
43636
44382
42142
43452
36912
42413
45344
44873
47510
49554
47369
45998
48140
48441
44928
40454
38661
37246
36843
36424
37594
38144
38737
34560
36080
33508
35462
33374
32110
35533
35532
37903
36763
40399
44164
44496
43110
43880
43930
44327




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=113953&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=113953&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113953&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
alpha1
beta-6.64073830647371e-18
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & -6.64073830647371e-18 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113953&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]-6.64073830647371e-18[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113953&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113953&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
beta-6.64073830647371e-18
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
332914297813133
43348832914574
535652334882164
63648835652836
73538736488-1101
83567635387289
93484435676-832
103244734844-2397
113106832447-1379
122901031068-2058
132981229010802
1430951298121139
1532974309512023
163293632974-38
1734012329361076
183294634012-1066
193194832946-998
203059931948-1349
212769130599-2908
222507327691-2618
232340625073-1667
242224823406-1158
252289622248648
2625317228962421
2726558253171241
282647126558-87
2927543264711072
302619827543-1345
312472526198-1473
322500524725280
332346225005-1543
342078023462-2682
351981520780-965
361976119815-54
3721454197611693
3823899214542445
3924939238991040
402358024939-1359
412456223580982
422469624562134
432378524696-911
44238122378527
452191723812-1895
461971321917-2204
471928219713-431
481878819282-494
4921453187882665
5024482214533029
5127474244822992
522726427474-210
53273492726485
5430632273493283
552942930632-1203
563008429429655
572629030084-3794
582437926290-1911
592333524379-1044
602134623335-1989
612110621346-240
6224514211063408
6328353245143839
6430805283532452
653134830805543
6634556313483208
673385534556-701
683478733855932
693252934787-2258
702999832529-2531
712925729998-741
722815529257-1102
7330466281552311
7435704304665238
7539327357043623
76393513932724
7742234393512883
7843630422341396
79437224363092
804312143722-601
813798543121-5136
823713537985-850
833464637135-2489
843302634646-1620
8535087330262061
8638846350873759
8742013388463167
8843908420131895
894286843908-1040
9044423428681555
914416744423-256
924363644167-531
934438243636746
944214244382-2240
9543452421421310
963691243452-6540
9742413369125501
9845344424132931
994487345344-471
10047510448732637
10149554475102044
1024736949554-2185
1034599847369-1371
10448140459982142
1054844148140301
1064492848441-3513
1074045444928-4474
1083866140454-1793
1093724638661-1415
1103684337246-403
1113642436843-419
11237594364241170
1133814437594550
1143873738144593
1153456038737-4177
11636080345601520
1173350836080-2572
11835462335081954
1193337435462-2088
1203211033374-1264
12135533321103423
1223553235533-1
12337903355322371
1243676337903-1140
12540399367633636
12644164403993765
1274449644164332
1284311044496-1386
1294388043110770
130439304388050
1314432743930397

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 32914 & 29781 & 3133 \tabularnewline
4 & 33488 & 32914 & 574 \tabularnewline
5 & 35652 & 33488 & 2164 \tabularnewline
6 & 36488 & 35652 & 836 \tabularnewline
7 & 35387 & 36488 & -1101 \tabularnewline
8 & 35676 & 35387 & 289 \tabularnewline
9 & 34844 & 35676 & -832 \tabularnewline
10 & 32447 & 34844 & -2397 \tabularnewline
11 & 31068 & 32447 & -1379 \tabularnewline
12 & 29010 & 31068 & -2058 \tabularnewline
13 & 29812 & 29010 & 802 \tabularnewline
14 & 30951 & 29812 & 1139 \tabularnewline
15 & 32974 & 30951 & 2023 \tabularnewline
16 & 32936 & 32974 & -38 \tabularnewline
17 & 34012 & 32936 & 1076 \tabularnewline
18 & 32946 & 34012 & -1066 \tabularnewline
19 & 31948 & 32946 & -998 \tabularnewline
20 & 30599 & 31948 & -1349 \tabularnewline
21 & 27691 & 30599 & -2908 \tabularnewline
22 & 25073 & 27691 & -2618 \tabularnewline
23 & 23406 & 25073 & -1667 \tabularnewline
24 & 22248 & 23406 & -1158 \tabularnewline
25 & 22896 & 22248 & 648 \tabularnewline
26 & 25317 & 22896 & 2421 \tabularnewline
27 & 26558 & 25317 & 1241 \tabularnewline
28 & 26471 & 26558 & -87 \tabularnewline
29 & 27543 & 26471 & 1072 \tabularnewline
30 & 26198 & 27543 & -1345 \tabularnewline
31 & 24725 & 26198 & -1473 \tabularnewline
32 & 25005 & 24725 & 280 \tabularnewline
33 & 23462 & 25005 & -1543 \tabularnewline
34 & 20780 & 23462 & -2682 \tabularnewline
35 & 19815 & 20780 & -965 \tabularnewline
36 & 19761 & 19815 & -54 \tabularnewline
37 & 21454 & 19761 & 1693 \tabularnewline
38 & 23899 & 21454 & 2445 \tabularnewline
39 & 24939 & 23899 & 1040 \tabularnewline
40 & 23580 & 24939 & -1359 \tabularnewline
41 & 24562 & 23580 & 982 \tabularnewline
42 & 24696 & 24562 & 134 \tabularnewline
43 & 23785 & 24696 & -911 \tabularnewline
44 & 23812 & 23785 & 27 \tabularnewline
45 & 21917 & 23812 & -1895 \tabularnewline
46 & 19713 & 21917 & -2204 \tabularnewline
47 & 19282 & 19713 & -431 \tabularnewline
48 & 18788 & 19282 & -494 \tabularnewline
49 & 21453 & 18788 & 2665 \tabularnewline
50 & 24482 & 21453 & 3029 \tabularnewline
51 & 27474 & 24482 & 2992 \tabularnewline
52 & 27264 & 27474 & -210 \tabularnewline
53 & 27349 & 27264 & 85 \tabularnewline
54 & 30632 & 27349 & 3283 \tabularnewline
55 & 29429 & 30632 & -1203 \tabularnewline
56 & 30084 & 29429 & 655 \tabularnewline
57 & 26290 & 30084 & -3794 \tabularnewline
58 & 24379 & 26290 & -1911 \tabularnewline
59 & 23335 & 24379 & -1044 \tabularnewline
60 & 21346 & 23335 & -1989 \tabularnewline
61 & 21106 & 21346 & -240 \tabularnewline
62 & 24514 & 21106 & 3408 \tabularnewline
63 & 28353 & 24514 & 3839 \tabularnewline
64 & 30805 & 28353 & 2452 \tabularnewline
65 & 31348 & 30805 & 543 \tabularnewline
66 & 34556 & 31348 & 3208 \tabularnewline
67 & 33855 & 34556 & -701 \tabularnewline
68 & 34787 & 33855 & 932 \tabularnewline
69 & 32529 & 34787 & -2258 \tabularnewline
70 & 29998 & 32529 & -2531 \tabularnewline
71 & 29257 & 29998 & -741 \tabularnewline
72 & 28155 & 29257 & -1102 \tabularnewline
73 & 30466 & 28155 & 2311 \tabularnewline
74 & 35704 & 30466 & 5238 \tabularnewline
75 & 39327 & 35704 & 3623 \tabularnewline
76 & 39351 & 39327 & 24 \tabularnewline
77 & 42234 & 39351 & 2883 \tabularnewline
78 & 43630 & 42234 & 1396 \tabularnewline
79 & 43722 & 43630 & 92 \tabularnewline
80 & 43121 & 43722 & -601 \tabularnewline
81 & 37985 & 43121 & -5136 \tabularnewline
82 & 37135 & 37985 & -850 \tabularnewline
83 & 34646 & 37135 & -2489 \tabularnewline
84 & 33026 & 34646 & -1620 \tabularnewline
85 & 35087 & 33026 & 2061 \tabularnewline
86 & 38846 & 35087 & 3759 \tabularnewline
87 & 42013 & 38846 & 3167 \tabularnewline
88 & 43908 & 42013 & 1895 \tabularnewline
89 & 42868 & 43908 & -1040 \tabularnewline
90 & 44423 & 42868 & 1555 \tabularnewline
91 & 44167 & 44423 & -256 \tabularnewline
92 & 43636 & 44167 & -531 \tabularnewline
93 & 44382 & 43636 & 746 \tabularnewline
94 & 42142 & 44382 & -2240 \tabularnewline
95 & 43452 & 42142 & 1310 \tabularnewline
96 & 36912 & 43452 & -6540 \tabularnewline
97 & 42413 & 36912 & 5501 \tabularnewline
98 & 45344 & 42413 & 2931 \tabularnewline
99 & 44873 & 45344 & -471 \tabularnewline
100 & 47510 & 44873 & 2637 \tabularnewline
101 & 49554 & 47510 & 2044 \tabularnewline
102 & 47369 & 49554 & -2185 \tabularnewline
103 & 45998 & 47369 & -1371 \tabularnewline
104 & 48140 & 45998 & 2142 \tabularnewline
105 & 48441 & 48140 & 301 \tabularnewline
106 & 44928 & 48441 & -3513 \tabularnewline
107 & 40454 & 44928 & -4474 \tabularnewline
108 & 38661 & 40454 & -1793 \tabularnewline
109 & 37246 & 38661 & -1415 \tabularnewline
110 & 36843 & 37246 & -403 \tabularnewline
111 & 36424 & 36843 & -419 \tabularnewline
112 & 37594 & 36424 & 1170 \tabularnewline
113 & 38144 & 37594 & 550 \tabularnewline
114 & 38737 & 38144 & 593 \tabularnewline
115 & 34560 & 38737 & -4177 \tabularnewline
116 & 36080 & 34560 & 1520 \tabularnewline
117 & 33508 & 36080 & -2572 \tabularnewline
118 & 35462 & 33508 & 1954 \tabularnewline
119 & 33374 & 35462 & -2088 \tabularnewline
120 & 32110 & 33374 & -1264 \tabularnewline
121 & 35533 & 32110 & 3423 \tabularnewline
122 & 35532 & 35533 & -1 \tabularnewline
123 & 37903 & 35532 & 2371 \tabularnewline
124 & 36763 & 37903 & -1140 \tabularnewline
125 & 40399 & 36763 & 3636 \tabularnewline
126 & 44164 & 40399 & 3765 \tabularnewline
127 & 44496 & 44164 & 332 \tabularnewline
128 & 43110 & 44496 & -1386 \tabularnewline
129 & 43880 & 43110 & 770 \tabularnewline
130 & 43930 & 43880 & 50 \tabularnewline
131 & 44327 & 43930 & 397 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113953&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]32914[/C][C]29781[/C][C]3133[/C][/ROW]
[ROW][C]4[/C][C]33488[/C][C]32914[/C][C]574[/C][/ROW]
[ROW][C]5[/C][C]35652[/C][C]33488[/C][C]2164[/C][/ROW]
[ROW][C]6[/C][C]36488[/C][C]35652[/C][C]836[/C][/ROW]
[ROW][C]7[/C][C]35387[/C][C]36488[/C][C]-1101[/C][/ROW]
[ROW][C]8[/C][C]35676[/C][C]35387[/C][C]289[/C][/ROW]
[ROW][C]9[/C][C]34844[/C][C]35676[/C][C]-832[/C][/ROW]
[ROW][C]10[/C][C]32447[/C][C]34844[/C][C]-2397[/C][/ROW]
[ROW][C]11[/C][C]31068[/C][C]32447[/C][C]-1379[/C][/ROW]
[ROW][C]12[/C][C]29010[/C][C]31068[/C][C]-2058[/C][/ROW]
[ROW][C]13[/C][C]29812[/C][C]29010[/C][C]802[/C][/ROW]
[ROW][C]14[/C][C]30951[/C][C]29812[/C][C]1139[/C][/ROW]
[ROW][C]15[/C][C]32974[/C][C]30951[/C][C]2023[/C][/ROW]
[ROW][C]16[/C][C]32936[/C][C]32974[/C][C]-38[/C][/ROW]
[ROW][C]17[/C][C]34012[/C][C]32936[/C][C]1076[/C][/ROW]
[ROW][C]18[/C][C]32946[/C][C]34012[/C][C]-1066[/C][/ROW]
[ROW][C]19[/C][C]31948[/C][C]32946[/C][C]-998[/C][/ROW]
[ROW][C]20[/C][C]30599[/C][C]31948[/C][C]-1349[/C][/ROW]
[ROW][C]21[/C][C]27691[/C][C]30599[/C][C]-2908[/C][/ROW]
[ROW][C]22[/C][C]25073[/C][C]27691[/C][C]-2618[/C][/ROW]
[ROW][C]23[/C][C]23406[/C][C]25073[/C][C]-1667[/C][/ROW]
[ROW][C]24[/C][C]22248[/C][C]23406[/C][C]-1158[/C][/ROW]
[ROW][C]25[/C][C]22896[/C][C]22248[/C][C]648[/C][/ROW]
[ROW][C]26[/C][C]25317[/C][C]22896[/C][C]2421[/C][/ROW]
[ROW][C]27[/C][C]26558[/C][C]25317[/C][C]1241[/C][/ROW]
[ROW][C]28[/C][C]26471[/C][C]26558[/C][C]-87[/C][/ROW]
[ROW][C]29[/C][C]27543[/C][C]26471[/C][C]1072[/C][/ROW]
[ROW][C]30[/C][C]26198[/C][C]27543[/C][C]-1345[/C][/ROW]
[ROW][C]31[/C][C]24725[/C][C]26198[/C][C]-1473[/C][/ROW]
[ROW][C]32[/C][C]25005[/C][C]24725[/C][C]280[/C][/ROW]
[ROW][C]33[/C][C]23462[/C][C]25005[/C][C]-1543[/C][/ROW]
[ROW][C]34[/C][C]20780[/C][C]23462[/C][C]-2682[/C][/ROW]
[ROW][C]35[/C][C]19815[/C][C]20780[/C][C]-965[/C][/ROW]
[ROW][C]36[/C][C]19761[/C][C]19815[/C][C]-54[/C][/ROW]
[ROW][C]37[/C][C]21454[/C][C]19761[/C][C]1693[/C][/ROW]
[ROW][C]38[/C][C]23899[/C][C]21454[/C][C]2445[/C][/ROW]
[ROW][C]39[/C][C]24939[/C][C]23899[/C][C]1040[/C][/ROW]
[ROW][C]40[/C][C]23580[/C][C]24939[/C][C]-1359[/C][/ROW]
[ROW][C]41[/C][C]24562[/C][C]23580[/C][C]982[/C][/ROW]
[ROW][C]42[/C][C]24696[/C][C]24562[/C][C]134[/C][/ROW]
[ROW][C]43[/C][C]23785[/C][C]24696[/C][C]-911[/C][/ROW]
[ROW][C]44[/C][C]23812[/C][C]23785[/C][C]27[/C][/ROW]
[ROW][C]45[/C][C]21917[/C][C]23812[/C][C]-1895[/C][/ROW]
[ROW][C]46[/C][C]19713[/C][C]21917[/C][C]-2204[/C][/ROW]
[ROW][C]47[/C][C]19282[/C][C]19713[/C][C]-431[/C][/ROW]
[ROW][C]48[/C][C]18788[/C][C]19282[/C][C]-494[/C][/ROW]
[ROW][C]49[/C][C]21453[/C][C]18788[/C][C]2665[/C][/ROW]
[ROW][C]50[/C][C]24482[/C][C]21453[/C][C]3029[/C][/ROW]
[ROW][C]51[/C][C]27474[/C][C]24482[/C][C]2992[/C][/ROW]
[ROW][C]52[/C][C]27264[/C][C]27474[/C][C]-210[/C][/ROW]
[ROW][C]53[/C][C]27349[/C][C]27264[/C][C]85[/C][/ROW]
[ROW][C]54[/C][C]30632[/C][C]27349[/C][C]3283[/C][/ROW]
[ROW][C]55[/C][C]29429[/C][C]30632[/C][C]-1203[/C][/ROW]
[ROW][C]56[/C][C]30084[/C][C]29429[/C][C]655[/C][/ROW]
[ROW][C]57[/C][C]26290[/C][C]30084[/C][C]-3794[/C][/ROW]
[ROW][C]58[/C][C]24379[/C][C]26290[/C][C]-1911[/C][/ROW]
[ROW][C]59[/C][C]23335[/C][C]24379[/C][C]-1044[/C][/ROW]
[ROW][C]60[/C][C]21346[/C][C]23335[/C][C]-1989[/C][/ROW]
[ROW][C]61[/C][C]21106[/C][C]21346[/C][C]-240[/C][/ROW]
[ROW][C]62[/C][C]24514[/C][C]21106[/C][C]3408[/C][/ROW]
[ROW][C]63[/C][C]28353[/C][C]24514[/C][C]3839[/C][/ROW]
[ROW][C]64[/C][C]30805[/C][C]28353[/C][C]2452[/C][/ROW]
[ROW][C]65[/C][C]31348[/C][C]30805[/C][C]543[/C][/ROW]
[ROW][C]66[/C][C]34556[/C][C]31348[/C][C]3208[/C][/ROW]
[ROW][C]67[/C][C]33855[/C][C]34556[/C][C]-701[/C][/ROW]
[ROW][C]68[/C][C]34787[/C][C]33855[/C][C]932[/C][/ROW]
[ROW][C]69[/C][C]32529[/C][C]34787[/C][C]-2258[/C][/ROW]
[ROW][C]70[/C][C]29998[/C][C]32529[/C][C]-2531[/C][/ROW]
[ROW][C]71[/C][C]29257[/C][C]29998[/C][C]-741[/C][/ROW]
[ROW][C]72[/C][C]28155[/C][C]29257[/C][C]-1102[/C][/ROW]
[ROW][C]73[/C][C]30466[/C][C]28155[/C][C]2311[/C][/ROW]
[ROW][C]74[/C][C]35704[/C][C]30466[/C][C]5238[/C][/ROW]
[ROW][C]75[/C][C]39327[/C][C]35704[/C][C]3623[/C][/ROW]
[ROW][C]76[/C][C]39351[/C][C]39327[/C][C]24[/C][/ROW]
[ROW][C]77[/C][C]42234[/C][C]39351[/C][C]2883[/C][/ROW]
[ROW][C]78[/C][C]43630[/C][C]42234[/C][C]1396[/C][/ROW]
[ROW][C]79[/C][C]43722[/C][C]43630[/C][C]92[/C][/ROW]
[ROW][C]80[/C][C]43121[/C][C]43722[/C][C]-601[/C][/ROW]
[ROW][C]81[/C][C]37985[/C][C]43121[/C][C]-5136[/C][/ROW]
[ROW][C]82[/C][C]37135[/C][C]37985[/C][C]-850[/C][/ROW]
[ROW][C]83[/C][C]34646[/C][C]37135[/C][C]-2489[/C][/ROW]
[ROW][C]84[/C][C]33026[/C][C]34646[/C][C]-1620[/C][/ROW]
[ROW][C]85[/C][C]35087[/C][C]33026[/C][C]2061[/C][/ROW]
[ROW][C]86[/C][C]38846[/C][C]35087[/C][C]3759[/C][/ROW]
[ROW][C]87[/C][C]42013[/C][C]38846[/C][C]3167[/C][/ROW]
[ROW][C]88[/C][C]43908[/C][C]42013[/C][C]1895[/C][/ROW]
[ROW][C]89[/C][C]42868[/C][C]43908[/C][C]-1040[/C][/ROW]
[ROW][C]90[/C][C]44423[/C][C]42868[/C][C]1555[/C][/ROW]
[ROW][C]91[/C][C]44167[/C][C]44423[/C][C]-256[/C][/ROW]
[ROW][C]92[/C][C]43636[/C][C]44167[/C][C]-531[/C][/ROW]
[ROW][C]93[/C][C]44382[/C][C]43636[/C][C]746[/C][/ROW]
[ROW][C]94[/C][C]42142[/C][C]44382[/C][C]-2240[/C][/ROW]
[ROW][C]95[/C][C]43452[/C][C]42142[/C][C]1310[/C][/ROW]
[ROW][C]96[/C][C]36912[/C][C]43452[/C][C]-6540[/C][/ROW]
[ROW][C]97[/C][C]42413[/C][C]36912[/C][C]5501[/C][/ROW]
[ROW][C]98[/C][C]45344[/C][C]42413[/C][C]2931[/C][/ROW]
[ROW][C]99[/C][C]44873[/C][C]45344[/C][C]-471[/C][/ROW]
[ROW][C]100[/C][C]47510[/C][C]44873[/C][C]2637[/C][/ROW]
[ROW][C]101[/C][C]49554[/C][C]47510[/C][C]2044[/C][/ROW]
[ROW][C]102[/C][C]47369[/C][C]49554[/C][C]-2185[/C][/ROW]
[ROW][C]103[/C][C]45998[/C][C]47369[/C][C]-1371[/C][/ROW]
[ROW][C]104[/C][C]48140[/C][C]45998[/C][C]2142[/C][/ROW]
[ROW][C]105[/C][C]48441[/C][C]48140[/C][C]301[/C][/ROW]
[ROW][C]106[/C][C]44928[/C][C]48441[/C][C]-3513[/C][/ROW]
[ROW][C]107[/C][C]40454[/C][C]44928[/C][C]-4474[/C][/ROW]
[ROW][C]108[/C][C]38661[/C][C]40454[/C][C]-1793[/C][/ROW]
[ROW][C]109[/C][C]37246[/C][C]38661[/C][C]-1415[/C][/ROW]
[ROW][C]110[/C][C]36843[/C][C]37246[/C][C]-403[/C][/ROW]
[ROW][C]111[/C][C]36424[/C][C]36843[/C][C]-419[/C][/ROW]
[ROW][C]112[/C][C]37594[/C][C]36424[/C][C]1170[/C][/ROW]
[ROW][C]113[/C][C]38144[/C][C]37594[/C][C]550[/C][/ROW]
[ROW][C]114[/C][C]38737[/C][C]38144[/C][C]593[/C][/ROW]
[ROW][C]115[/C][C]34560[/C][C]38737[/C][C]-4177[/C][/ROW]
[ROW][C]116[/C][C]36080[/C][C]34560[/C][C]1520[/C][/ROW]
[ROW][C]117[/C][C]33508[/C][C]36080[/C][C]-2572[/C][/ROW]
[ROW][C]118[/C][C]35462[/C][C]33508[/C][C]1954[/C][/ROW]
[ROW][C]119[/C][C]33374[/C][C]35462[/C][C]-2088[/C][/ROW]
[ROW][C]120[/C][C]32110[/C][C]33374[/C][C]-1264[/C][/ROW]
[ROW][C]121[/C][C]35533[/C][C]32110[/C][C]3423[/C][/ROW]
[ROW][C]122[/C][C]35532[/C][C]35533[/C][C]-1[/C][/ROW]
[ROW][C]123[/C][C]37903[/C][C]35532[/C][C]2371[/C][/ROW]
[ROW][C]124[/C][C]36763[/C][C]37903[/C][C]-1140[/C][/ROW]
[ROW][C]125[/C][C]40399[/C][C]36763[/C][C]3636[/C][/ROW]
[ROW][C]126[/C][C]44164[/C][C]40399[/C][C]3765[/C][/ROW]
[ROW][C]127[/C][C]44496[/C][C]44164[/C][C]332[/C][/ROW]
[ROW][C]128[/C][C]43110[/C][C]44496[/C][C]-1386[/C][/ROW]
[ROW][C]129[/C][C]43880[/C][C]43110[/C][C]770[/C][/ROW]
[ROW][C]130[/C][C]43930[/C][C]43880[/C][C]50[/C][/ROW]
[ROW][C]131[/C][C]44327[/C][C]43930[/C][C]397[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113953&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113953&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
332914297813133
43348832914574
535652334882164
63648835652836
73538736488-1101
83567635387289
93484435676-832
103244734844-2397
113106832447-1379
122901031068-2058
132981229010802
1430951298121139
1532974309512023
163293632974-38
1734012329361076
183294634012-1066
193194832946-998
203059931948-1349
212769130599-2908
222507327691-2618
232340625073-1667
242224823406-1158
252289622248648
2625317228962421
2726558253171241
282647126558-87
2927543264711072
302619827543-1345
312472526198-1473
322500524725280
332346225005-1543
342078023462-2682
351981520780-965
361976119815-54
3721454197611693
3823899214542445
3924939238991040
402358024939-1359
412456223580982
422469624562134
432378524696-911
44238122378527
452191723812-1895
461971321917-2204
471928219713-431
481878819282-494
4921453187882665
5024482214533029
5127474244822992
522726427474-210
53273492726485
5430632273493283
552942930632-1203
563008429429655
572629030084-3794
582437926290-1911
592333524379-1044
602134623335-1989
612110621346-240
6224514211063408
6328353245143839
6430805283532452
653134830805543
6634556313483208
673385534556-701
683478733855932
693252934787-2258
702999832529-2531
712925729998-741
722815529257-1102
7330466281552311
7435704304665238
7539327357043623
76393513932724
7742234393512883
7843630422341396
79437224363092
804312143722-601
813798543121-5136
823713537985-850
833464637135-2489
843302634646-1620
8535087330262061
8638846350873759
8742013388463167
8843908420131895
894286843908-1040
9044423428681555
914416744423-256
924363644167-531
934438243636746
944214244382-2240
9543452421421310
963691243452-6540
9742413369125501
9845344424132931
994487345344-471
10047510448732637
10149554475102044
1024736949554-2185
1034599847369-1371
10448140459982142
1054844148140301
1064492848441-3513
1074045444928-4474
1083866140454-1793
1093724638661-1415
1103684337246-403
1113642436843-419
11237594364241170
1133814437594550
1143873738144593
1153456038737-4177
11636080345601520
1173350836080-2572
11835462335081954
1193337435462-2088
1203211033374-1264
12135533321103423
1223553235533-1
12337903355322371
1243676337903-1140
12540399367633636
12644164403993765
1274449644164332
1284311044496-1386
1294388043110770
130439304388050
1314432743930397







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1324432740126.895802299648527.1041977004
1334432738387.155680231950266.8443197681
1344432737052.206132499651601.7938675004
1354432735926.791604599252727.2083954008
1364432734935.281501359753718.7184986403
1374432734038.887849112354615.1121508877
1384432733214.568812326355439.4311876737
1394432732447.311360463856206.6886395362
1404432731726.687406898856927.3125931012
1414432731045.104325232657608.8956747674
1424432730396.830295831058257.169704169
1434432729777.412264999158876.5877350009

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
132 & 44327 & 40126.8958022996 & 48527.1041977004 \tabularnewline
133 & 44327 & 38387.1556802319 & 50266.8443197681 \tabularnewline
134 & 44327 & 37052.2061324996 & 51601.7938675004 \tabularnewline
135 & 44327 & 35926.7916045992 & 52727.2083954008 \tabularnewline
136 & 44327 & 34935.2815013597 & 53718.7184986403 \tabularnewline
137 & 44327 & 34038.8878491123 & 54615.1121508877 \tabularnewline
138 & 44327 & 33214.5688123263 & 55439.4311876737 \tabularnewline
139 & 44327 & 32447.3113604638 & 56206.6886395362 \tabularnewline
140 & 44327 & 31726.6874068988 & 56927.3125931012 \tabularnewline
141 & 44327 & 31045.1043252326 & 57608.8956747674 \tabularnewline
142 & 44327 & 30396.8302958310 & 58257.169704169 \tabularnewline
143 & 44327 & 29777.4122649991 & 58876.5877350009 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113953&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]132[/C][C]44327[/C][C]40126.8958022996[/C][C]48527.1041977004[/C][/ROW]
[ROW][C]133[/C][C]44327[/C][C]38387.1556802319[/C][C]50266.8443197681[/C][/ROW]
[ROW][C]134[/C][C]44327[/C][C]37052.2061324996[/C][C]51601.7938675004[/C][/ROW]
[ROW][C]135[/C][C]44327[/C][C]35926.7916045992[/C][C]52727.2083954008[/C][/ROW]
[ROW][C]136[/C][C]44327[/C][C]34935.2815013597[/C][C]53718.7184986403[/C][/ROW]
[ROW][C]137[/C][C]44327[/C][C]34038.8878491123[/C][C]54615.1121508877[/C][/ROW]
[ROW][C]138[/C][C]44327[/C][C]33214.5688123263[/C][C]55439.4311876737[/C][/ROW]
[ROW][C]139[/C][C]44327[/C][C]32447.3113604638[/C][C]56206.6886395362[/C][/ROW]
[ROW][C]140[/C][C]44327[/C][C]31726.6874068988[/C][C]56927.3125931012[/C][/ROW]
[ROW][C]141[/C][C]44327[/C][C]31045.1043252326[/C][C]57608.8956747674[/C][/ROW]
[ROW][C]142[/C][C]44327[/C][C]30396.8302958310[/C][C]58257.169704169[/C][/ROW]
[ROW][C]143[/C][C]44327[/C][C]29777.4122649991[/C][C]58876.5877350009[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113953&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113953&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
1324432740126.895802299648527.1041977004
1334432738387.155680231950266.8443197681
1344432737052.206132499651601.7938675004
1354432735926.791604599252727.2083954008
1364432734935.281501359753718.7184986403
1374432734038.887849112354615.1121508877
1384432733214.568812326355439.4311876737
1394432732447.311360463856206.6886395362
1404432731726.687406898856927.3125931012
1414432731045.104325232657608.8956747674
1424432730396.830295831058257.169704169
1434432729777.412264999158876.5877350009



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')