Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 24 Jul 2011 15:00:51 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Jul/24/t13115353465qqqi1d7vlei9js.htm/, Retrieved Wed, 15 May 2024 13:51:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123119, Retrieved Wed, 15 May 2024 13:51:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsThomas Schroeven
Estimated Impact212
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks - Stap 32] [2011-07-24 19:00:51] [1757923712b2aedbf315e1364d6f70a4] [Current]
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Dataseries X:
588264
577918
567562
546859
756344
745987
588264
483527
493873
493873
504229
526055
462824
399492
347630
347630
546859
567562
409838
231412
325803
325803
399492
442021
431664
325803
378790
357986
536412
493873
325803
200263
315447
347630
378790
420195
336150
263595
294755
305101
577918
577918
420195
399492
462824
431664
515709
620447
641250
493873
452367
409838
694135
714939
661953
714939
704481
620447
714939
819676
862205
735641
651596
714939
987746
1071790
1051088
1092483
1082137
977399
1155825
1198354
1260562
1071790
998102
1082137
1282389
1460814
1418286
1418286
1439089
1366423
1555307
1555307
1523124
1344597
1376780
1397583
1534503
1712929
1586355
1649698
1596712
1565653
1807421
1754435
1680746
1576009
1680746
1733732
1796963
1880998
1796963
1848826
1785585
1775239
2037699
2059525
1975491
1828123
1953664
2006549
2069882
2164273
2069882
2143570
2111388
1996193
2237951
2237951




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123119&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123119&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123119&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.147613880927442
beta0.099258308999054
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.147613880927442 \tabularnewline
beta & 0.099258308999054 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123119&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]0.147613880927442[/C][/ROW]
[ROW][C]beta[/C][C]0.099258308999054[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123119&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123119&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
alpha0.147613880927442
beta0.099258308999054
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13462824552690.548749618-89866.548749618
14399492469138.674039863-69646.674039863
15347630400922.917506421-53292.9175064208
16347630390427.696103243-42797.6961032425
17546859594633.868312176-47774.8683121755
18567562593143.670402356-25581.670402356
19409838413555.983259999-3717.98325999855
20231412329227.423953497-97815.423953497
21325803310985.66951379714817.3304862027
22325803302760.60876661223042.3912333883
23399492301429.93956515898062.060434842
24442021318643.00959176123377.99040824
25431664246664.344527797184999.655472203
26325803237681.32244458888121.677555412
27378790220863.403376531157926.596623469
28357986250413.772301776107572.227698224
29536412432468.377689933103943.622310067
30493873480752.52057688613120.4794231136
31325803359946.522857001-34143.5228570013
32200263216318.061290409-16055.0612904089
33315447311396.2002535114050.79974648857
34347630322093.1814216225536.8185783799
35378790399478.18189504-20688.1818950398
36420195432694.898031684-12499.898031684
37336150392635.57854808-56485.5785480799
38263595280343.561691637-16748.5616916367
39294755295614.515886537-859.515886536683
40305101262145.6620135742955.3379864302
41577918385953.60826743191964.39173257
42577918379073.364931566198844.635068434
43420195274932.242546384145262.757453616
44399492187212.428512761212279.571487239
45462824355134.512161316107689.487838684
46431664419422.60614212712241.3938578726
47515709479663.04447969636045.9555203044
48620447561586.54187571558860.4581242847
49641250485555.74532497155694.25467503
50493873422036.02240340471836.9775965963
51452367509555.35830362-57188.3583036196
52409838532850.936835209-123012.936835209
53694135950536.842315573-256401.842315573
54714939876103.673462543-161164.673462543
55661953588082.98317550473870.016824496
56714939495795.953105806219143.046894194
57704481589475.965316681115005.034683319
58620447565921.9582876254525.0417123799
59714939681895.55172142533043.4482785751
60819676817657.584666652018.41533335007
61862205809994.21979972152210.7802002786
62735641614569.474068684121071.525931316
63651596589432.87620014762163.1237998527
64714939563212.870668008151726.129331992
659877461041983.39842389-54237.3984238855
6610717901107037.73065192-35247.7306519174
6710510881014601.6030875336486.3969124722
6810924831045883.9814732946599.018526713
6910821371014454.7777135367682.2222864737
70977399893409.87081085683989.1291891442
7111558251040526.8515095115298.148490497
7211983541217506.00390586-19152.0039058591
7312605621270881.82721563-10319.8272156338
7410717901055706.7232900516083.2767099468
75998102923696.3009124574405.6990875495
761082137986922.96965550395214.0303444966
7712823891391884.81990801-109495.819908008
7814608141497559.35219056-36745.3521905555
7914182861453592.03187711-35306.031877113
8014182861492611.20411868-74325.2041186846
8114390891448971.94467041-9882.94467041385
8213664231284783.10005781639.8999430032
8315553071503130.9165074752176.0834925307
8415553071563063.85300927-7756.8530092747
8515231241638123.06696551-114999.066965506
8613445971368776.44037556-24179.4403755583
8713767801250216.33658276126563.663417239
8813975831350392.4634980247190.5365019792
8915345031619444.86957244-84941.8695724404
9017129291828938.66907435-116009.66907435
9115863551756957.53481248-170602.534812484
9216496981734966.53966679-85268.5396667935
9315967121740012.54505546-143300.54505546
9415656531606955.16502372-41302.1650237169
9518074211800136.530056327284.46994367754
9617544351789638.86582762-35203.8658276196
9716807461753229.65592649-72483.6559264944
9815760091532094.3445502343914.6554497737
9916807461543106.70846274137639.291537261
10017337321569807.74378432163924.25621568
10117969631755535.114652941427.885347103
10218809981977846.34611971-96848.34611971
10317969631838655.11431502-41692.1143150195
10418488261915016.54145979-66190.5414597897
10517855851862722.24559458-77137.2455945804
10617752391819327.7726794-44088.7726794048
10720376992088269.82430142-50570.8243014195
10820595252021880.4591072237644.5408927759
10919754911951578.6577531823912.3422468209
11018281231824408.565529933714.43447007122
11119536641919113.5196957334550.480304271
11220065491951165.0023170555383.9976829486
11320698822018231.2041005351650.7958994694
11421642732130422.383606733850.6163933002
11520698822043298.4237908926583.5762091121
11621435702114464.5751138529105.4248861535
11721113882057630.4068426653757.5931573387
11819961932061544.81655843-65351.8165584297
11922379512364128.56298381-126177.562983809
12022379512363637.09294939-125686.092949392

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 462824 & 552690.548749618 & -89866.548749618 \tabularnewline
14 & 399492 & 469138.674039863 & -69646.674039863 \tabularnewline
15 & 347630 & 400922.917506421 & -53292.9175064208 \tabularnewline
16 & 347630 & 390427.696103243 & -42797.6961032425 \tabularnewline
17 & 546859 & 594633.868312176 & -47774.8683121755 \tabularnewline
18 & 567562 & 593143.670402356 & -25581.670402356 \tabularnewline
19 & 409838 & 413555.983259999 & -3717.98325999855 \tabularnewline
20 & 231412 & 329227.423953497 & -97815.423953497 \tabularnewline
21 & 325803 & 310985.669513797 & 14817.3304862027 \tabularnewline
22 & 325803 & 302760.608766612 & 23042.3912333883 \tabularnewline
23 & 399492 & 301429.939565158 & 98062.060434842 \tabularnewline
24 & 442021 & 318643.00959176 & 123377.99040824 \tabularnewline
25 & 431664 & 246664.344527797 & 184999.655472203 \tabularnewline
26 & 325803 & 237681.322444588 & 88121.677555412 \tabularnewline
27 & 378790 & 220863.403376531 & 157926.596623469 \tabularnewline
28 & 357986 & 250413.772301776 & 107572.227698224 \tabularnewline
29 & 536412 & 432468.377689933 & 103943.622310067 \tabularnewline
30 & 493873 & 480752.520576886 & 13120.4794231136 \tabularnewline
31 & 325803 & 359946.522857001 & -34143.5228570013 \tabularnewline
32 & 200263 & 216318.061290409 & -16055.0612904089 \tabularnewline
33 & 315447 & 311396.200253511 & 4050.79974648857 \tabularnewline
34 & 347630 & 322093.18142162 & 25536.8185783799 \tabularnewline
35 & 378790 & 399478.18189504 & -20688.1818950398 \tabularnewline
36 & 420195 & 432694.898031684 & -12499.898031684 \tabularnewline
37 & 336150 & 392635.57854808 & -56485.5785480799 \tabularnewline
38 & 263595 & 280343.561691637 & -16748.5616916367 \tabularnewline
39 & 294755 & 295614.515886537 & -859.515886536683 \tabularnewline
40 & 305101 & 262145.66201357 & 42955.3379864302 \tabularnewline
41 & 577918 & 385953.60826743 & 191964.39173257 \tabularnewline
42 & 577918 & 379073.364931566 & 198844.635068434 \tabularnewline
43 & 420195 & 274932.242546384 & 145262.757453616 \tabularnewline
44 & 399492 & 187212.428512761 & 212279.571487239 \tabularnewline
45 & 462824 & 355134.512161316 & 107689.487838684 \tabularnewline
46 & 431664 & 419422.606142127 & 12241.3938578726 \tabularnewline
47 & 515709 & 479663.044479696 & 36045.9555203044 \tabularnewline
48 & 620447 & 561586.541875715 & 58860.4581242847 \tabularnewline
49 & 641250 & 485555.74532497 & 155694.25467503 \tabularnewline
50 & 493873 & 422036.022403404 & 71836.9775965963 \tabularnewline
51 & 452367 & 509555.35830362 & -57188.3583036196 \tabularnewline
52 & 409838 & 532850.936835209 & -123012.936835209 \tabularnewline
53 & 694135 & 950536.842315573 & -256401.842315573 \tabularnewline
54 & 714939 & 876103.673462543 & -161164.673462543 \tabularnewline
55 & 661953 & 588082.983175504 & 73870.016824496 \tabularnewline
56 & 714939 & 495795.953105806 & 219143.046894194 \tabularnewline
57 & 704481 & 589475.965316681 & 115005.034683319 \tabularnewline
58 & 620447 & 565921.95828762 & 54525.0417123799 \tabularnewline
59 & 714939 & 681895.551721425 & 33043.4482785751 \tabularnewline
60 & 819676 & 817657.58466665 & 2018.41533335007 \tabularnewline
61 & 862205 & 809994.219799721 & 52210.7802002786 \tabularnewline
62 & 735641 & 614569.474068684 & 121071.525931316 \tabularnewline
63 & 651596 & 589432.876200147 & 62163.1237998527 \tabularnewline
64 & 714939 & 563212.870668008 & 151726.129331992 \tabularnewline
65 & 987746 & 1041983.39842389 & -54237.3984238855 \tabularnewline
66 & 1071790 & 1107037.73065192 & -35247.7306519174 \tabularnewline
67 & 1051088 & 1014601.60308753 & 36486.3969124722 \tabularnewline
68 & 1092483 & 1045883.98147329 & 46599.018526713 \tabularnewline
69 & 1082137 & 1014454.77771353 & 67682.2222864737 \tabularnewline
70 & 977399 & 893409.870810856 & 83989.1291891442 \tabularnewline
71 & 1155825 & 1040526.8515095 & 115298.148490497 \tabularnewline
72 & 1198354 & 1217506.00390586 & -19152.0039058591 \tabularnewline
73 & 1260562 & 1270881.82721563 & -10319.8272156338 \tabularnewline
74 & 1071790 & 1055706.72329005 & 16083.2767099468 \tabularnewline
75 & 998102 & 923696.30091245 & 74405.6990875495 \tabularnewline
76 & 1082137 & 986922.969655503 & 95214.0303444966 \tabularnewline
77 & 1282389 & 1391884.81990801 & -109495.819908008 \tabularnewline
78 & 1460814 & 1497559.35219056 & -36745.3521905555 \tabularnewline
79 & 1418286 & 1453592.03187711 & -35306.031877113 \tabularnewline
80 & 1418286 & 1492611.20411868 & -74325.2041186846 \tabularnewline
81 & 1439089 & 1448971.94467041 & -9882.94467041385 \tabularnewline
82 & 1366423 & 1284783.100057 & 81639.8999430032 \tabularnewline
83 & 1555307 & 1503130.91650747 & 52176.0834925307 \tabularnewline
84 & 1555307 & 1563063.85300927 & -7756.8530092747 \tabularnewline
85 & 1523124 & 1638123.06696551 & -114999.066965506 \tabularnewline
86 & 1344597 & 1368776.44037556 & -24179.4403755583 \tabularnewline
87 & 1376780 & 1250216.33658276 & 126563.663417239 \tabularnewline
88 & 1397583 & 1350392.46349802 & 47190.5365019792 \tabularnewline
89 & 1534503 & 1619444.86957244 & -84941.8695724404 \tabularnewline
90 & 1712929 & 1828938.66907435 & -116009.66907435 \tabularnewline
91 & 1586355 & 1756957.53481248 & -170602.534812484 \tabularnewline
92 & 1649698 & 1734966.53966679 & -85268.5396667935 \tabularnewline
93 & 1596712 & 1740012.54505546 & -143300.54505546 \tabularnewline
94 & 1565653 & 1606955.16502372 & -41302.1650237169 \tabularnewline
95 & 1807421 & 1800136.53005632 & 7284.46994367754 \tabularnewline
96 & 1754435 & 1789638.86582762 & -35203.8658276196 \tabularnewline
97 & 1680746 & 1753229.65592649 & -72483.6559264944 \tabularnewline
98 & 1576009 & 1532094.34455023 & 43914.6554497737 \tabularnewline
99 & 1680746 & 1543106.70846274 & 137639.291537261 \tabularnewline
100 & 1733732 & 1569807.74378432 & 163924.25621568 \tabularnewline
101 & 1796963 & 1755535.1146529 & 41427.885347103 \tabularnewline
102 & 1880998 & 1977846.34611971 & -96848.34611971 \tabularnewline
103 & 1796963 & 1838655.11431502 & -41692.1143150195 \tabularnewline
104 & 1848826 & 1915016.54145979 & -66190.5414597897 \tabularnewline
105 & 1785585 & 1862722.24559458 & -77137.2455945804 \tabularnewline
106 & 1775239 & 1819327.7726794 & -44088.7726794048 \tabularnewline
107 & 2037699 & 2088269.82430142 & -50570.8243014195 \tabularnewline
108 & 2059525 & 2021880.45910722 & 37644.5408927759 \tabularnewline
109 & 1975491 & 1951578.65775318 & 23912.3422468209 \tabularnewline
110 & 1828123 & 1824408.56552993 & 3714.43447007122 \tabularnewline
111 & 1953664 & 1919113.51969573 & 34550.480304271 \tabularnewline
112 & 2006549 & 1951165.00231705 & 55383.9976829486 \tabularnewline
113 & 2069882 & 2018231.20410053 & 51650.7958994694 \tabularnewline
114 & 2164273 & 2130422.3836067 & 33850.6163933002 \tabularnewline
115 & 2069882 & 2043298.42379089 & 26583.5762091121 \tabularnewline
116 & 2143570 & 2114464.57511385 & 29105.4248861535 \tabularnewline
117 & 2111388 & 2057630.40684266 & 53757.5931573387 \tabularnewline
118 & 1996193 & 2061544.81655843 & -65351.8165584297 \tabularnewline
119 & 2237951 & 2364128.56298381 & -126177.562983809 \tabularnewline
120 & 2237951 & 2363637.09294939 & -125686.092949392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123119&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]462824[/C][C]552690.548749618[/C][C]-89866.548749618[/C][/ROW]
[ROW][C]14[/C][C]399492[/C][C]469138.674039863[/C][C]-69646.674039863[/C][/ROW]
[ROW][C]15[/C][C]347630[/C][C]400922.917506421[/C][C]-53292.9175064208[/C][/ROW]
[ROW][C]16[/C][C]347630[/C][C]390427.696103243[/C][C]-42797.6961032425[/C][/ROW]
[ROW][C]17[/C][C]546859[/C][C]594633.868312176[/C][C]-47774.8683121755[/C][/ROW]
[ROW][C]18[/C][C]567562[/C][C]593143.670402356[/C][C]-25581.670402356[/C][/ROW]
[ROW][C]19[/C][C]409838[/C][C]413555.983259999[/C][C]-3717.98325999855[/C][/ROW]
[ROW][C]20[/C][C]231412[/C][C]329227.423953497[/C][C]-97815.423953497[/C][/ROW]
[ROW][C]21[/C][C]325803[/C][C]310985.669513797[/C][C]14817.3304862027[/C][/ROW]
[ROW][C]22[/C][C]325803[/C][C]302760.608766612[/C][C]23042.3912333883[/C][/ROW]
[ROW][C]23[/C][C]399492[/C][C]301429.939565158[/C][C]98062.060434842[/C][/ROW]
[ROW][C]24[/C][C]442021[/C][C]318643.00959176[/C][C]123377.99040824[/C][/ROW]
[ROW][C]25[/C][C]431664[/C][C]246664.344527797[/C][C]184999.655472203[/C][/ROW]
[ROW][C]26[/C][C]325803[/C][C]237681.322444588[/C][C]88121.677555412[/C][/ROW]
[ROW][C]27[/C][C]378790[/C][C]220863.403376531[/C][C]157926.596623469[/C][/ROW]
[ROW][C]28[/C][C]357986[/C][C]250413.772301776[/C][C]107572.227698224[/C][/ROW]
[ROW][C]29[/C][C]536412[/C][C]432468.377689933[/C][C]103943.622310067[/C][/ROW]
[ROW][C]30[/C][C]493873[/C][C]480752.520576886[/C][C]13120.4794231136[/C][/ROW]
[ROW][C]31[/C][C]325803[/C][C]359946.522857001[/C][C]-34143.5228570013[/C][/ROW]
[ROW][C]32[/C][C]200263[/C][C]216318.061290409[/C][C]-16055.0612904089[/C][/ROW]
[ROW][C]33[/C][C]315447[/C][C]311396.200253511[/C][C]4050.79974648857[/C][/ROW]
[ROW][C]34[/C][C]347630[/C][C]322093.18142162[/C][C]25536.8185783799[/C][/ROW]
[ROW][C]35[/C][C]378790[/C][C]399478.18189504[/C][C]-20688.1818950398[/C][/ROW]
[ROW][C]36[/C][C]420195[/C][C]432694.898031684[/C][C]-12499.898031684[/C][/ROW]
[ROW][C]37[/C][C]336150[/C][C]392635.57854808[/C][C]-56485.5785480799[/C][/ROW]
[ROW][C]38[/C][C]263595[/C][C]280343.561691637[/C][C]-16748.5616916367[/C][/ROW]
[ROW][C]39[/C][C]294755[/C][C]295614.515886537[/C][C]-859.515886536683[/C][/ROW]
[ROW][C]40[/C][C]305101[/C][C]262145.66201357[/C][C]42955.3379864302[/C][/ROW]
[ROW][C]41[/C][C]577918[/C][C]385953.60826743[/C][C]191964.39173257[/C][/ROW]
[ROW][C]42[/C][C]577918[/C][C]379073.364931566[/C][C]198844.635068434[/C][/ROW]
[ROW][C]43[/C][C]420195[/C][C]274932.242546384[/C][C]145262.757453616[/C][/ROW]
[ROW][C]44[/C][C]399492[/C][C]187212.428512761[/C][C]212279.571487239[/C][/ROW]
[ROW][C]45[/C][C]462824[/C][C]355134.512161316[/C][C]107689.487838684[/C][/ROW]
[ROW][C]46[/C][C]431664[/C][C]419422.606142127[/C][C]12241.3938578726[/C][/ROW]
[ROW][C]47[/C][C]515709[/C][C]479663.044479696[/C][C]36045.9555203044[/C][/ROW]
[ROW][C]48[/C][C]620447[/C][C]561586.541875715[/C][C]58860.4581242847[/C][/ROW]
[ROW][C]49[/C][C]641250[/C][C]485555.74532497[/C][C]155694.25467503[/C][/ROW]
[ROW][C]50[/C][C]493873[/C][C]422036.022403404[/C][C]71836.9775965963[/C][/ROW]
[ROW][C]51[/C][C]452367[/C][C]509555.35830362[/C][C]-57188.3583036196[/C][/ROW]
[ROW][C]52[/C][C]409838[/C][C]532850.936835209[/C][C]-123012.936835209[/C][/ROW]
[ROW][C]53[/C][C]694135[/C][C]950536.842315573[/C][C]-256401.842315573[/C][/ROW]
[ROW][C]54[/C][C]714939[/C][C]876103.673462543[/C][C]-161164.673462543[/C][/ROW]
[ROW][C]55[/C][C]661953[/C][C]588082.983175504[/C][C]73870.016824496[/C][/ROW]
[ROW][C]56[/C][C]714939[/C][C]495795.953105806[/C][C]219143.046894194[/C][/ROW]
[ROW][C]57[/C][C]704481[/C][C]589475.965316681[/C][C]115005.034683319[/C][/ROW]
[ROW][C]58[/C][C]620447[/C][C]565921.95828762[/C][C]54525.0417123799[/C][/ROW]
[ROW][C]59[/C][C]714939[/C][C]681895.551721425[/C][C]33043.4482785751[/C][/ROW]
[ROW][C]60[/C][C]819676[/C][C]817657.58466665[/C][C]2018.41533335007[/C][/ROW]
[ROW][C]61[/C][C]862205[/C][C]809994.219799721[/C][C]52210.7802002786[/C][/ROW]
[ROW][C]62[/C][C]735641[/C][C]614569.474068684[/C][C]121071.525931316[/C][/ROW]
[ROW][C]63[/C][C]651596[/C][C]589432.876200147[/C][C]62163.1237998527[/C][/ROW]
[ROW][C]64[/C][C]714939[/C][C]563212.870668008[/C][C]151726.129331992[/C][/ROW]
[ROW][C]65[/C][C]987746[/C][C]1041983.39842389[/C][C]-54237.3984238855[/C][/ROW]
[ROW][C]66[/C][C]1071790[/C][C]1107037.73065192[/C][C]-35247.7306519174[/C][/ROW]
[ROW][C]67[/C][C]1051088[/C][C]1014601.60308753[/C][C]36486.3969124722[/C][/ROW]
[ROW][C]68[/C][C]1092483[/C][C]1045883.98147329[/C][C]46599.018526713[/C][/ROW]
[ROW][C]69[/C][C]1082137[/C][C]1014454.77771353[/C][C]67682.2222864737[/C][/ROW]
[ROW][C]70[/C][C]977399[/C][C]893409.870810856[/C][C]83989.1291891442[/C][/ROW]
[ROW][C]71[/C][C]1155825[/C][C]1040526.8515095[/C][C]115298.148490497[/C][/ROW]
[ROW][C]72[/C][C]1198354[/C][C]1217506.00390586[/C][C]-19152.0039058591[/C][/ROW]
[ROW][C]73[/C][C]1260562[/C][C]1270881.82721563[/C][C]-10319.8272156338[/C][/ROW]
[ROW][C]74[/C][C]1071790[/C][C]1055706.72329005[/C][C]16083.2767099468[/C][/ROW]
[ROW][C]75[/C][C]998102[/C][C]923696.30091245[/C][C]74405.6990875495[/C][/ROW]
[ROW][C]76[/C][C]1082137[/C][C]986922.969655503[/C][C]95214.0303444966[/C][/ROW]
[ROW][C]77[/C][C]1282389[/C][C]1391884.81990801[/C][C]-109495.819908008[/C][/ROW]
[ROW][C]78[/C][C]1460814[/C][C]1497559.35219056[/C][C]-36745.3521905555[/C][/ROW]
[ROW][C]79[/C][C]1418286[/C][C]1453592.03187711[/C][C]-35306.031877113[/C][/ROW]
[ROW][C]80[/C][C]1418286[/C][C]1492611.20411868[/C][C]-74325.2041186846[/C][/ROW]
[ROW][C]81[/C][C]1439089[/C][C]1448971.94467041[/C][C]-9882.94467041385[/C][/ROW]
[ROW][C]82[/C][C]1366423[/C][C]1284783.100057[/C][C]81639.8999430032[/C][/ROW]
[ROW][C]83[/C][C]1555307[/C][C]1503130.91650747[/C][C]52176.0834925307[/C][/ROW]
[ROW][C]84[/C][C]1555307[/C][C]1563063.85300927[/C][C]-7756.8530092747[/C][/ROW]
[ROW][C]85[/C][C]1523124[/C][C]1638123.06696551[/C][C]-114999.066965506[/C][/ROW]
[ROW][C]86[/C][C]1344597[/C][C]1368776.44037556[/C][C]-24179.4403755583[/C][/ROW]
[ROW][C]87[/C][C]1376780[/C][C]1250216.33658276[/C][C]126563.663417239[/C][/ROW]
[ROW][C]88[/C][C]1397583[/C][C]1350392.46349802[/C][C]47190.5365019792[/C][/ROW]
[ROW][C]89[/C][C]1534503[/C][C]1619444.86957244[/C][C]-84941.8695724404[/C][/ROW]
[ROW][C]90[/C][C]1712929[/C][C]1828938.66907435[/C][C]-116009.66907435[/C][/ROW]
[ROW][C]91[/C][C]1586355[/C][C]1756957.53481248[/C][C]-170602.534812484[/C][/ROW]
[ROW][C]92[/C][C]1649698[/C][C]1734966.53966679[/C][C]-85268.5396667935[/C][/ROW]
[ROW][C]93[/C][C]1596712[/C][C]1740012.54505546[/C][C]-143300.54505546[/C][/ROW]
[ROW][C]94[/C][C]1565653[/C][C]1606955.16502372[/C][C]-41302.1650237169[/C][/ROW]
[ROW][C]95[/C][C]1807421[/C][C]1800136.53005632[/C][C]7284.46994367754[/C][/ROW]
[ROW][C]96[/C][C]1754435[/C][C]1789638.86582762[/C][C]-35203.8658276196[/C][/ROW]
[ROW][C]97[/C][C]1680746[/C][C]1753229.65592649[/C][C]-72483.6559264944[/C][/ROW]
[ROW][C]98[/C][C]1576009[/C][C]1532094.34455023[/C][C]43914.6554497737[/C][/ROW]
[ROW][C]99[/C][C]1680746[/C][C]1543106.70846274[/C][C]137639.291537261[/C][/ROW]
[ROW][C]100[/C][C]1733732[/C][C]1569807.74378432[/C][C]163924.25621568[/C][/ROW]
[ROW][C]101[/C][C]1796963[/C][C]1755535.1146529[/C][C]41427.885347103[/C][/ROW]
[ROW][C]102[/C][C]1880998[/C][C]1977846.34611971[/C][C]-96848.34611971[/C][/ROW]
[ROW][C]103[/C][C]1796963[/C][C]1838655.11431502[/C][C]-41692.1143150195[/C][/ROW]
[ROW][C]104[/C][C]1848826[/C][C]1915016.54145979[/C][C]-66190.5414597897[/C][/ROW]
[ROW][C]105[/C][C]1785585[/C][C]1862722.24559458[/C][C]-77137.2455945804[/C][/ROW]
[ROW][C]106[/C][C]1775239[/C][C]1819327.7726794[/C][C]-44088.7726794048[/C][/ROW]
[ROW][C]107[/C][C]2037699[/C][C]2088269.82430142[/C][C]-50570.8243014195[/C][/ROW]
[ROW][C]108[/C][C]2059525[/C][C]2021880.45910722[/C][C]37644.5408927759[/C][/ROW]
[ROW][C]109[/C][C]1975491[/C][C]1951578.65775318[/C][C]23912.3422468209[/C][/ROW]
[ROW][C]110[/C][C]1828123[/C][C]1824408.56552993[/C][C]3714.43447007122[/C][/ROW]
[ROW][C]111[/C][C]1953664[/C][C]1919113.51969573[/C][C]34550.480304271[/C][/ROW]
[ROW][C]112[/C][C]2006549[/C][C]1951165.00231705[/C][C]55383.9976829486[/C][/ROW]
[ROW][C]113[/C][C]2069882[/C][C]2018231.20410053[/C][C]51650.7958994694[/C][/ROW]
[ROW][C]114[/C][C]2164273[/C][C]2130422.3836067[/C][C]33850.6163933002[/C][/ROW]
[ROW][C]115[/C][C]2069882[/C][C]2043298.42379089[/C][C]26583.5762091121[/C][/ROW]
[ROW][C]116[/C][C]2143570[/C][C]2114464.57511385[/C][C]29105.4248861535[/C][/ROW]
[ROW][C]117[/C][C]2111388[/C][C]2057630.40684266[/C][C]53757.5931573387[/C][/ROW]
[ROW][C]118[/C][C]1996193[/C][C]2061544.81655843[/C][C]-65351.8165584297[/C][/ROW]
[ROW][C]119[/C][C]2237951[/C][C]2364128.56298381[/C][C]-126177.562983809[/C][/ROW]
[ROW][C]120[/C][C]2237951[/C][C]2363637.09294939[/C][C]-125686.092949392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123119&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123119&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
13462824552690.548749618-89866.548749618
14399492469138.674039863-69646.674039863
15347630400922.917506421-53292.9175064208
16347630390427.696103243-42797.6961032425
17546859594633.868312176-47774.8683121755
18567562593143.670402356-25581.670402356
19409838413555.983259999-3717.98325999855
20231412329227.423953497-97815.423953497
21325803310985.66951379714817.3304862027
22325803302760.60876661223042.3912333883
23399492301429.93956515898062.060434842
24442021318643.00959176123377.99040824
25431664246664.344527797184999.655472203
26325803237681.32244458888121.677555412
27378790220863.403376531157926.596623469
28357986250413.772301776107572.227698224
29536412432468.377689933103943.622310067
30493873480752.52057688613120.4794231136
31325803359946.522857001-34143.5228570013
32200263216318.061290409-16055.0612904089
33315447311396.2002535114050.79974648857
34347630322093.1814216225536.8185783799
35378790399478.18189504-20688.1818950398
36420195432694.898031684-12499.898031684
37336150392635.57854808-56485.5785480799
38263595280343.561691637-16748.5616916367
39294755295614.515886537-859.515886536683
40305101262145.6620135742955.3379864302
41577918385953.60826743191964.39173257
42577918379073.364931566198844.635068434
43420195274932.242546384145262.757453616
44399492187212.428512761212279.571487239
45462824355134.512161316107689.487838684
46431664419422.60614212712241.3938578726
47515709479663.04447969636045.9555203044
48620447561586.54187571558860.4581242847
49641250485555.74532497155694.25467503
50493873422036.02240340471836.9775965963
51452367509555.35830362-57188.3583036196
52409838532850.936835209-123012.936835209
53694135950536.842315573-256401.842315573
54714939876103.673462543-161164.673462543
55661953588082.98317550473870.016824496
56714939495795.953105806219143.046894194
57704481589475.965316681115005.034683319
58620447565921.9582876254525.0417123799
59714939681895.55172142533043.4482785751
60819676817657.584666652018.41533335007
61862205809994.21979972152210.7802002786
62735641614569.474068684121071.525931316
63651596589432.87620014762163.1237998527
64714939563212.870668008151726.129331992
659877461041983.39842389-54237.3984238855
6610717901107037.73065192-35247.7306519174
6710510881014601.6030875336486.3969124722
6810924831045883.9814732946599.018526713
6910821371014454.7777135367682.2222864737
70977399893409.87081085683989.1291891442
7111558251040526.8515095115298.148490497
7211983541217506.00390586-19152.0039058591
7312605621270881.82721563-10319.8272156338
7410717901055706.7232900516083.2767099468
75998102923696.3009124574405.6990875495
761082137986922.96965550395214.0303444966
7712823891391884.81990801-109495.819908008
7814608141497559.35219056-36745.3521905555
7914182861453592.03187711-35306.031877113
8014182861492611.20411868-74325.2041186846
8114390891448971.94467041-9882.94467041385
8213664231284783.10005781639.8999430032
8315553071503130.9165074752176.0834925307
8415553071563063.85300927-7756.8530092747
8515231241638123.06696551-114999.066965506
8613445971368776.44037556-24179.4403755583
8713767801250216.33658276126563.663417239
8813975831350392.4634980247190.5365019792
8915345031619444.86957244-84941.8695724404
9017129291828938.66907435-116009.66907435
9115863551756957.53481248-170602.534812484
9216496981734966.53966679-85268.5396667935
9315967121740012.54505546-143300.54505546
9415656531606955.16502372-41302.1650237169
9518074211800136.530056327284.46994367754
9617544351789638.86582762-35203.8658276196
9716807461753229.65592649-72483.6559264944
9815760091532094.3445502343914.6554497737
9916807461543106.70846274137639.291537261
10017337321569807.74378432163924.25621568
10117969631755535.114652941427.885347103
10218809981977846.34611971-96848.34611971
10317969631838655.11431502-41692.1143150195
10418488261915016.54145979-66190.5414597897
10517855851862722.24559458-77137.2455945804
10617752391819327.7726794-44088.7726794048
10720376992088269.82430142-50570.8243014195
10820595252021880.4591072237644.5408927759
10919754911951578.6577531823912.3422468209
11018281231824408.565529933714.43447007122
11119536641919113.5196957334550.480304271
11220065491951165.0023170555383.9976829486
11320698822018231.2041005351650.7958994694
11421642732130422.383606733850.6163933002
11520698822043298.4237908926583.5762091121
11621435702114464.5751138529105.4248861535
11721113882057630.4068426653757.5931573387
11819961932061544.81655843-65351.8165584297
11922379512364128.56298381-126177.562983809
12022379512363637.09294939-125686.092949392







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1212242764.925609822066270.964688532419258.88653112
1222072173.637304781893742.278761892250604.99584767
1232205767.055259822024182.992529642387351.11799
1242252653.369877512067733.425214562437573.31454046
1252310766.99762362121853.071668292499680.92357892
1262405362.50021442211328.146363512599396.85406529
1272290788.868644532094362.40082382487215.33646526
1282361817.093060612159487.37596472564146.81015652
1292311526.654683662105457.425858292517595.88350903
1302189474.796742591981549.796882472397399.79660272
1312468279.622780232246282.138116722690277.10744374
1322483760.789919032338175.767402182629345.81243588

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 2242764.92560982 & 2066270.96468853 & 2419258.88653112 \tabularnewline
122 & 2072173.63730478 & 1893742.27876189 & 2250604.99584767 \tabularnewline
123 & 2205767.05525982 & 2024182.99252964 & 2387351.11799 \tabularnewline
124 & 2252653.36987751 & 2067733.42521456 & 2437573.31454046 \tabularnewline
125 & 2310766.9976236 & 2121853.07166829 & 2499680.92357892 \tabularnewline
126 & 2405362.5002144 & 2211328.14636351 & 2599396.85406529 \tabularnewline
127 & 2290788.86864453 & 2094362.4008238 & 2487215.33646526 \tabularnewline
128 & 2361817.09306061 & 2159487.3759647 & 2564146.81015652 \tabularnewline
129 & 2311526.65468366 & 2105457.42585829 & 2517595.88350903 \tabularnewline
130 & 2189474.79674259 & 1981549.79688247 & 2397399.79660272 \tabularnewline
131 & 2468279.62278023 & 2246282.13811672 & 2690277.10744374 \tabularnewline
132 & 2483760.78991903 & 2338175.76740218 & 2629345.81243588 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123119&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]121[/C][C]2242764.92560982[/C][C]2066270.96468853[/C][C]2419258.88653112[/C][/ROW]
[ROW][C]122[/C][C]2072173.63730478[/C][C]1893742.27876189[/C][C]2250604.99584767[/C][/ROW]
[ROW][C]123[/C][C]2205767.05525982[/C][C]2024182.99252964[/C][C]2387351.11799[/C][/ROW]
[ROW][C]124[/C][C]2252653.36987751[/C][C]2067733.42521456[/C][C]2437573.31454046[/C][/ROW]
[ROW][C]125[/C][C]2310766.9976236[/C][C]2121853.07166829[/C][C]2499680.92357892[/C][/ROW]
[ROW][C]126[/C][C]2405362.5002144[/C][C]2211328.14636351[/C][C]2599396.85406529[/C][/ROW]
[ROW][C]127[/C][C]2290788.86864453[/C][C]2094362.4008238[/C][C]2487215.33646526[/C][/ROW]
[ROW][C]128[/C][C]2361817.09306061[/C][C]2159487.3759647[/C][C]2564146.81015652[/C][/ROW]
[ROW][C]129[/C][C]2311526.65468366[/C][C]2105457.42585829[/C][C]2517595.88350903[/C][/ROW]
[ROW][C]130[/C][C]2189474.79674259[/C][C]1981549.79688247[/C][C]2397399.79660272[/C][/ROW]
[ROW][C]131[/C][C]2468279.62278023[/C][C]2246282.13811672[/C][C]2690277.10744374[/C][/ROW]
[ROW][C]132[/C][C]2483760.78991903[/C][C]2338175.76740218[/C][C]2629345.81243588[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123119&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123119&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
1212242764.925609822066270.964688532419258.88653112
1222072173.637304781893742.278761892250604.99584767
1232205767.055259822024182.992529642387351.11799
1242252653.369877512067733.425214562437573.31454046
1252310766.99762362121853.071668292499680.92357892
1262405362.50021442211328.146363512599396.85406529
1272290788.868644532094362.40082382487215.33646526
1282361817.093060612159487.37596472564146.81015652
1292311526.654683662105457.425858292517595.88350903
1302189474.796742591981549.796882472397399.79660272
1312468279.622780232246282.138116722690277.10744374
1322483760.789919032338175.767402182629345.81243588



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')