Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 31 Jul 2012 12:59:22 -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/2012/Jul/31/t1343754345fg7ha2tv4tykd38.htm/, Retrieved Mon, 29 Apr 2024 10:38:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168958, Retrieved Mon, 29 Apr 2024 10:38:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsyasmien naciri
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-07-31 16:59:22] [d06e8713ea83045a022ab0926c74dd0b] [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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168958&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168958&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168958&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.653615272491929
beta0.0529317928553807
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.653615272491929 \tabularnewline
beta & 0.0529317928553807 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168958&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]0.653615272491929[/C][/ROW]
[ROW][C]beta[/C][C]0.0529317928553807[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168958&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168958&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
alpha0.653615272491929
beta0.0529317928553807
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13462824558671.733707265-95847.733707265
14399492431689.970570098-32197.9705700981
15347630356235.210613738-8605.21061373776
16347630344263.4491707283366.55082927167
17546859536823.21149951310035.7885004871
18567562552061.7978839515500.2021160501
19409838400070.8110592789767.18894072168
20231412295363.638310469-63951.6383104689
21325803259280.34423200966522.6557679914
22325803301299.31929575324503.680704247
23399492326622.513389372869.4866107003
24442021396682.57124031845338.4287596825
25431664330765.16798842100898.83201158
26325803362870.606234644-37067.6062346441
27378790300680.01020164778109.9897983534
28357986360808.412101891-2822.41210189089
29536412562693.924757772-26281.9247577717
30493873565891.832512064-72018.8325120637
31325803361487.68530039-35684.6853003898
32200263206741.343205462-6478.34320546151
33315447260610.12629222554836.8737077754
34347630287224.42209415560405.5779058452
35378790360796.97755139517993.0224486051
36420195391584.19631693928610.803683061
37336150339531.504829378-3381.50482937793
38263595257633.3332693575961.66673064331
39294755266896.85048906927858.1495109314
40305101267841.33285322637259.6671467735
41577918490881.00731238287036.9926876178
42577918559305.74117725518612.2588227447
43420195436863.036865004-16668.0368650044
44399492315458.80074873284033.1992512684
45462824463653.298693989-829.298693989054
46431664467813.6976716-36149.6976715997
47515709472246.11284615843462.8871538417
48620447532900.76699809587546.2330019053
49641250519868.621415624121381.378584376
50493873538651.22910481-44778.2291048102
51452367536477.054370399-84110.0543703993
52409838477762.255327648-67924.2553276478
53694135655923.47040627138211.5295937294
54714939673673.89061364341265.1093863568
55661953559540.638598795102412.361401205
56714939560694.126385505154244.873614495
57704481737657.675763943-33176.6757639428
58620447719594.467159778-99147.4671597781
59714939719401.204828258-4462.20482825767
60819676771317.06216838348358.9378316172
61862205750351.693205281111853.306794719
62735641710982.02780211924658.972197881
63651596748602.016132604-97006.0161326036
64714939694651.46255801320287.5374419868
65987746977871.6628650589874.33713494195
661071790987816.38738075983973.6126192407
671051088933914.33953695117173.66046305
681092483974316.525497155118166.474502845
6910821371073177.01155258959.988447499
709773991071659.79062202-94260.7906220192
7111558251119483.2229994336341.7770005683
7211983541229802.4791591-31448.4791590972
7312605621189342.999838171219.0001619034
7410717901102481.27550392-30691.2755039206
759981021069135.57898985-71033.5789898504
7610821371081043.24794921093.75205080328
7712823891355700.62086235-73311.6208623494
7814608141341652.10061132119161.899388679
7914182861328178.5645785290107.4354214796
8014182861356226.2577922262059.7422077821
8114390891383638.4513042155450.5486957948
8213664231381413.88786069-14990.8878606949
8315553071533690.395904921616.6040951016
8415553071617796.41930872-62489.4193087157
8515231241598429.50455274-75305.5045527376
8613445971381246.60092359-36649.6009235887
8713767801330575.991611746204.0083882969
8813975831448695.31371276-51112.3137127643
8915345031666250.51478733-131747.514787332
9017129291681448.9762821131480.0237178891
9115863551598339.35889205-11984.3588920489
9216496981544149.0851734105548.914826602
9315967121593407.820133473304.17986652721
9415656531526606.3241478839046.6758521234
9518074211722658.9927017284762.0072982791
9617544351816865.5247771-62430.5247770955
9716807461791060.59651607-110314.59651607
9815760091561136.6081310814872.391868921
9916807461571374.87068257109371.129317428
10017337321697791.7803143835940.2196856181
10117969631948046.28381445-151083.283814455
10218809982010208.39690715-129210.396907149
10317969631804516.53620369-7553.53620368824
10418488261791590.2082284957235.7917715057
10517855851769839.4043328915745.5956671124
10617752391719965.5693650355273.4306349694
10720376991939435.8896934698263.1103065431
10820595251988925.3062176370599.6937823654
10919754912035530.70203437-60039.7020343684
11018281231885615.42797314-57492.4279731382
11119536641882569.6654004771094.3345995336
11220065491958490.4753472448058.5246527561
11320698822152260.40363999-82378.4036399946
11421642732269659.29524517-105386.295245171
11520698822125257.33846745-55375.3384674527
11621435702105439.5203305138130.4796694946
11721113882058092.1718054753295.82819453
11819961932049015.2565196-52822.2565195966
11922379512211545.4396461626405.5603538356
12022379512200821.3077340537129.6922659529

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 462824 & 558671.733707265 & -95847.733707265 \tabularnewline
14 & 399492 & 431689.970570098 & -32197.9705700981 \tabularnewline
15 & 347630 & 356235.210613738 & -8605.21061373776 \tabularnewline
16 & 347630 & 344263.449170728 & 3366.55082927167 \tabularnewline
17 & 546859 & 536823.211499513 & 10035.7885004871 \tabularnewline
18 & 567562 & 552061.79788395 & 15500.2021160501 \tabularnewline
19 & 409838 & 400070.811059278 & 9767.18894072168 \tabularnewline
20 & 231412 & 295363.638310469 & -63951.6383104689 \tabularnewline
21 & 325803 & 259280.344232009 & 66522.6557679914 \tabularnewline
22 & 325803 & 301299.319295753 & 24503.680704247 \tabularnewline
23 & 399492 & 326622.5133893 & 72869.4866107003 \tabularnewline
24 & 442021 & 396682.571240318 & 45338.4287596825 \tabularnewline
25 & 431664 & 330765.16798842 & 100898.83201158 \tabularnewline
26 & 325803 & 362870.606234644 & -37067.6062346441 \tabularnewline
27 & 378790 & 300680.010201647 & 78109.9897983534 \tabularnewline
28 & 357986 & 360808.412101891 & -2822.41210189089 \tabularnewline
29 & 536412 & 562693.924757772 & -26281.9247577717 \tabularnewline
30 & 493873 & 565891.832512064 & -72018.8325120637 \tabularnewline
31 & 325803 & 361487.68530039 & -35684.6853003898 \tabularnewline
32 & 200263 & 206741.343205462 & -6478.34320546151 \tabularnewline
33 & 315447 & 260610.126292225 & 54836.8737077754 \tabularnewline
34 & 347630 & 287224.422094155 & 60405.5779058452 \tabularnewline
35 & 378790 & 360796.977551395 & 17993.0224486051 \tabularnewline
36 & 420195 & 391584.196316939 & 28610.803683061 \tabularnewline
37 & 336150 & 339531.504829378 & -3381.50482937793 \tabularnewline
38 & 263595 & 257633.333269357 & 5961.66673064331 \tabularnewline
39 & 294755 & 266896.850489069 & 27858.1495109314 \tabularnewline
40 & 305101 & 267841.332853226 & 37259.6671467735 \tabularnewline
41 & 577918 & 490881.007312382 & 87036.9926876178 \tabularnewline
42 & 577918 & 559305.741177255 & 18612.2588227447 \tabularnewline
43 & 420195 & 436863.036865004 & -16668.0368650044 \tabularnewline
44 & 399492 & 315458.800748732 & 84033.1992512684 \tabularnewline
45 & 462824 & 463653.298693989 & -829.298693989054 \tabularnewline
46 & 431664 & 467813.6976716 & -36149.6976715997 \tabularnewline
47 & 515709 & 472246.112846158 & 43462.8871538417 \tabularnewline
48 & 620447 & 532900.766998095 & 87546.2330019053 \tabularnewline
49 & 641250 & 519868.621415624 & 121381.378584376 \tabularnewline
50 & 493873 & 538651.22910481 & -44778.2291048102 \tabularnewline
51 & 452367 & 536477.054370399 & -84110.0543703993 \tabularnewline
52 & 409838 & 477762.255327648 & -67924.2553276478 \tabularnewline
53 & 694135 & 655923.470406271 & 38211.5295937294 \tabularnewline
54 & 714939 & 673673.890613643 & 41265.1093863568 \tabularnewline
55 & 661953 & 559540.638598795 & 102412.361401205 \tabularnewline
56 & 714939 & 560694.126385505 & 154244.873614495 \tabularnewline
57 & 704481 & 737657.675763943 & -33176.6757639428 \tabularnewline
58 & 620447 & 719594.467159778 & -99147.4671597781 \tabularnewline
59 & 714939 & 719401.204828258 & -4462.20482825767 \tabularnewline
60 & 819676 & 771317.062168383 & 48358.9378316172 \tabularnewline
61 & 862205 & 750351.693205281 & 111853.306794719 \tabularnewline
62 & 735641 & 710982.027802119 & 24658.972197881 \tabularnewline
63 & 651596 & 748602.016132604 & -97006.0161326036 \tabularnewline
64 & 714939 & 694651.462558013 & 20287.5374419868 \tabularnewline
65 & 987746 & 977871.662865058 & 9874.33713494195 \tabularnewline
66 & 1071790 & 987816.387380759 & 83973.6126192407 \tabularnewline
67 & 1051088 & 933914.33953695 & 117173.66046305 \tabularnewline
68 & 1092483 & 974316.525497155 & 118166.474502845 \tabularnewline
69 & 1082137 & 1073177.0115525 & 8959.988447499 \tabularnewline
70 & 977399 & 1071659.79062202 & -94260.7906220192 \tabularnewline
71 & 1155825 & 1119483.22299943 & 36341.7770005683 \tabularnewline
72 & 1198354 & 1229802.4791591 & -31448.4791590972 \tabularnewline
73 & 1260562 & 1189342.9998381 & 71219.0001619034 \tabularnewline
74 & 1071790 & 1102481.27550392 & -30691.2755039206 \tabularnewline
75 & 998102 & 1069135.57898985 & -71033.5789898504 \tabularnewline
76 & 1082137 & 1081043.2479492 & 1093.75205080328 \tabularnewline
77 & 1282389 & 1355700.62086235 & -73311.6208623494 \tabularnewline
78 & 1460814 & 1341652.10061132 & 119161.899388679 \tabularnewline
79 & 1418286 & 1328178.56457852 & 90107.4354214796 \tabularnewline
80 & 1418286 & 1356226.25779222 & 62059.7422077821 \tabularnewline
81 & 1439089 & 1383638.45130421 & 55450.5486957948 \tabularnewline
82 & 1366423 & 1381413.88786069 & -14990.8878606949 \tabularnewline
83 & 1555307 & 1533690.3959049 & 21616.6040951016 \tabularnewline
84 & 1555307 & 1617796.41930872 & -62489.4193087157 \tabularnewline
85 & 1523124 & 1598429.50455274 & -75305.5045527376 \tabularnewline
86 & 1344597 & 1381246.60092359 & -36649.6009235887 \tabularnewline
87 & 1376780 & 1330575.9916117 & 46204.0083882969 \tabularnewline
88 & 1397583 & 1448695.31371276 & -51112.3137127643 \tabularnewline
89 & 1534503 & 1666250.51478733 & -131747.514787332 \tabularnewline
90 & 1712929 & 1681448.97628211 & 31480.0237178891 \tabularnewline
91 & 1586355 & 1598339.35889205 & -11984.3588920489 \tabularnewline
92 & 1649698 & 1544149.0851734 & 105548.914826602 \tabularnewline
93 & 1596712 & 1593407.82013347 & 3304.17986652721 \tabularnewline
94 & 1565653 & 1526606.32414788 & 39046.6758521234 \tabularnewline
95 & 1807421 & 1722658.99270172 & 84762.0072982791 \tabularnewline
96 & 1754435 & 1816865.5247771 & -62430.5247770955 \tabularnewline
97 & 1680746 & 1791060.59651607 & -110314.59651607 \tabularnewline
98 & 1576009 & 1561136.60813108 & 14872.391868921 \tabularnewline
99 & 1680746 & 1571374.87068257 & 109371.129317428 \tabularnewline
100 & 1733732 & 1697791.78031438 & 35940.2196856181 \tabularnewline
101 & 1796963 & 1948046.28381445 & -151083.283814455 \tabularnewline
102 & 1880998 & 2010208.39690715 & -129210.396907149 \tabularnewline
103 & 1796963 & 1804516.53620369 & -7553.53620368824 \tabularnewline
104 & 1848826 & 1791590.20822849 & 57235.7917715057 \tabularnewline
105 & 1785585 & 1769839.40433289 & 15745.5956671124 \tabularnewline
106 & 1775239 & 1719965.56936503 & 55273.4306349694 \tabularnewline
107 & 2037699 & 1939435.88969346 & 98263.1103065431 \tabularnewline
108 & 2059525 & 1988925.30621763 & 70599.6937823654 \tabularnewline
109 & 1975491 & 2035530.70203437 & -60039.7020343684 \tabularnewline
110 & 1828123 & 1885615.42797314 & -57492.4279731382 \tabularnewline
111 & 1953664 & 1882569.66540047 & 71094.3345995336 \tabularnewline
112 & 2006549 & 1958490.47534724 & 48058.5246527561 \tabularnewline
113 & 2069882 & 2152260.40363999 & -82378.4036399946 \tabularnewline
114 & 2164273 & 2269659.29524517 & -105386.295245171 \tabularnewline
115 & 2069882 & 2125257.33846745 & -55375.3384674527 \tabularnewline
116 & 2143570 & 2105439.52033051 & 38130.4796694946 \tabularnewline
117 & 2111388 & 2058092.17180547 & 53295.82819453 \tabularnewline
118 & 1996193 & 2049015.2565196 & -52822.2565195966 \tabularnewline
119 & 2237951 & 2211545.43964616 & 26405.5603538356 \tabularnewline
120 & 2237951 & 2200821.30773405 & 37129.6922659529 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168958&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]558671.733707265[/C][C]-95847.733707265[/C][/ROW]
[ROW][C]14[/C][C]399492[/C][C]431689.970570098[/C][C]-32197.9705700981[/C][/ROW]
[ROW][C]15[/C][C]347630[/C][C]356235.210613738[/C][C]-8605.21061373776[/C][/ROW]
[ROW][C]16[/C][C]347630[/C][C]344263.449170728[/C][C]3366.55082927167[/C][/ROW]
[ROW][C]17[/C][C]546859[/C][C]536823.211499513[/C][C]10035.7885004871[/C][/ROW]
[ROW][C]18[/C][C]567562[/C][C]552061.79788395[/C][C]15500.2021160501[/C][/ROW]
[ROW][C]19[/C][C]409838[/C][C]400070.811059278[/C][C]9767.18894072168[/C][/ROW]
[ROW][C]20[/C][C]231412[/C][C]295363.638310469[/C][C]-63951.6383104689[/C][/ROW]
[ROW][C]21[/C][C]325803[/C][C]259280.344232009[/C][C]66522.6557679914[/C][/ROW]
[ROW][C]22[/C][C]325803[/C][C]301299.319295753[/C][C]24503.680704247[/C][/ROW]
[ROW][C]23[/C][C]399492[/C][C]326622.5133893[/C][C]72869.4866107003[/C][/ROW]
[ROW][C]24[/C][C]442021[/C][C]396682.571240318[/C][C]45338.4287596825[/C][/ROW]
[ROW][C]25[/C][C]431664[/C][C]330765.16798842[/C][C]100898.83201158[/C][/ROW]
[ROW][C]26[/C][C]325803[/C][C]362870.606234644[/C][C]-37067.6062346441[/C][/ROW]
[ROW][C]27[/C][C]378790[/C][C]300680.010201647[/C][C]78109.9897983534[/C][/ROW]
[ROW][C]28[/C][C]357986[/C][C]360808.412101891[/C][C]-2822.41210189089[/C][/ROW]
[ROW][C]29[/C][C]536412[/C][C]562693.924757772[/C][C]-26281.9247577717[/C][/ROW]
[ROW][C]30[/C][C]493873[/C][C]565891.832512064[/C][C]-72018.8325120637[/C][/ROW]
[ROW][C]31[/C][C]325803[/C][C]361487.68530039[/C][C]-35684.6853003898[/C][/ROW]
[ROW][C]32[/C][C]200263[/C][C]206741.343205462[/C][C]-6478.34320546151[/C][/ROW]
[ROW][C]33[/C][C]315447[/C][C]260610.126292225[/C][C]54836.8737077754[/C][/ROW]
[ROW][C]34[/C][C]347630[/C][C]287224.422094155[/C][C]60405.5779058452[/C][/ROW]
[ROW][C]35[/C][C]378790[/C][C]360796.977551395[/C][C]17993.0224486051[/C][/ROW]
[ROW][C]36[/C][C]420195[/C][C]391584.196316939[/C][C]28610.803683061[/C][/ROW]
[ROW][C]37[/C][C]336150[/C][C]339531.504829378[/C][C]-3381.50482937793[/C][/ROW]
[ROW][C]38[/C][C]263595[/C][C]257633.333269357[/C][C]5961.66673064331[/C][/ROW]
[ROW][C]39[/C][C]294755[/C][C]266896.850489069[/C][C]27858.1495109314[/C][/ROW]
[ROW][C]40[/C][C]305101[/C][C]267841.332853226[/C][C]37259.6671467735[/C][/ROW]
[ROW][C]41[/C][C]577918[/C][C]490881.007312382[/C][C]87036.9926876178[/C][/ROW]
[ROW][C]42[/C][C]577918[/C][C]559305.741177255[/C][C]18612.2588227447[/C][/ROW]
[ROW][C]43[/C][C]420195[/C][C]436863.036865004[/C][C]-16668.0368650044[/C][/ROW]
[ROW][C]44[/C][C]399492[/C][C]315458.800748732[/C][C]84033.1992512684[/C][/ROW]
[ROW][C]45[/C][C]462824[/C][C]463653.298693989[/C][C]-829.298693989054[/C][/ROW]
[ROW][C]46[/C][C]431664[/C][C]467813.6976716[/C][C]-36149.6976715997[/C][/ROW]
[ROW][C]47[/C][C]515709[/C][C]472246.112846158[/C][C]43462.8871538417[/C][/ROW]
[ROW][C]48[/C][C]620447[/C][C]532900.766998095[/C][C]87546.2330019053[/C][/ROW]
[ROW][C]49[/C][C]641250[/C][C]519868.621415624[/C][C]121381.378584376[/C][/ROW]
[ROW][C]50[/C][C]493873[/C][C]538651.22910481[/C][C]-44778.2291048102[/C][/ROW]
[ROW][C]51[/C][C]452367[/C][C]536477.054370399[/C][C]-84110.0543703993[/C][/ROW]
[ROW][C]52[/C][C]409838[/C][C]477762.255327648[/C][C]-67924.2553276478[/C][/ROW]
[ROW][C]53[/C][C]694135[/C][C]655923.470406271[/C][C]38211.5295937294[/C][/ROW]
[ROW][C]54[/C][C]714939[/C][C]673673.890613643[/C][C]41265.1093863568[/C][/ROW]
[ROW][C]55[/C][C]661953[/C][C]559540.638598795[/C][C]102412.361401205[/C][/ROW]
[ROW][C]56[/C][C]714939[/C][C]560694.126385505[/C][C]154244.873614495[/C][/ROW]
[ROW][C]57[/C][C]704481[/C][C]737657.675763943[/C][C]-33176.6757639428[/C][/ROW]
[ROW][C]58[/C][C]620447[/C][C]719594.467159778[/C][C]-99147.4671597781[/C][/ROW]
[ROW][C]59[/C][C]714939[/C][C]719401.204828258[/C][C]-4462.20482825767[/C][/ROW]
[ROW][C]60[/C][C]819676[/C][C]771317.062168383[/C][C]48358.9378316172[/C][/ROW]
[ROW][C]61[/C][C]862205[/C][C]750351.693205281[/C][C]111853.306794719[/C][/ROW]
[ROW][C]62[/C][C]735641[/C][C]710982.027802119[/C][C]24658.972197881[/C][/ROW]
[ROW][C]63[/C][C]651596[/C][C]748602.016132604[/C][C]-97006.0161326036[/C][/ROW]
[ROW][C]64[/C][C]714939[/C][C]694651.462558013[/C][C]20287.5374419868[/C][/ROW]
[ROW][C]65[/C][C]987746[/C][C]977871.662865058[/C][C]9874.33713494195[/C][/ROW]
[ROW][C]66[/C][C]1071790[/C][C]987816.387380759[/C][C]83973.6126192407[/C][/ROW]
[ROW][C]67[/C][C]1051088[/C][C]933914.33953695[/C][C]117173.66046305[/C][/ROW]
[ROW][C]68[/C][C]1092483[/C][C]974316.525497155[/C][C]118166.474502845[/C][/ROW]
[ROW][C]69[/C][C]1082137[/C][C]1073177.0115525[/C][C]8959.988447499[/C][/ROW]
[ROW][C]70[/C][C]977399[/C][C]1071659.79062202[/C][C]-94260.7906220192[/C][/ROW]
[ROW][C]71[/C][C]1155825[/C][C]1119483.22299943[/C][C]36341.7770005683[/C][/ROW]
[ROW][C]72[/C][C]1198354[/C][C]1229802.4791591[/C][C]-31448.4791590972[/C][/ROW]
[ROW][C]73[/C][C]1260562[/C][C]1189342.9998381[/C][C]71219.0001619034[/C][/ROW]
[ROW][C]74[/C][C]1071790[/C][C]1102481.27550392[/C][C]-30691.2755039206[/C][/ROW]
[ROW][C]75[/C][C]998102[/C][C]1069135.57898985[/C][C]-71033.5789898504[/C][/ROW]
[ROW][C]76[/C][C]1082137[/C][C]1081043.2479492[/C][C]1093.75205080328[/C][/ROW]
[ROW][C]77[/C][C]1282389[/C][C]1355700.62086235[/C][C]-73311.6208623494[/C][/ROW]
[ROW][C]78[/C][C]1460814[/C][C]1341652.10061132[/C][C]119161.899388679[/C][/ROW]
[ROW][C]79[/C][C]1418286[/C][C]1328178.56457852[/C][C]90107.4354214796[/C][/ROW]
[ROW][C]80[/C][C]1418286[/C][C]1356226.25779222[/C][C]62059.7422077821[/C][/ROW]
[ROW][C]81[/C][C]1439089[/C][C]1383638.45130421[/C][C]55450.5486957948[/C][/ROW]
[ROW][C]82[/C][C]1366423[/C][C]1381413.88786069[/C][C]-14990.8878606949[/C][/ROW]
[ROW][C]83[/C][C]1555307[/C][C]1533690.3959049[/C][C]21616.6040951016[/C][/ROW]
[ROW][C]84[/C][C]1555307[/C][C]1617796.41930872[/C][C]-62489.4193087157[/C][/ROW]
[ROW][C]85[/C][C]1523124[/C][C]1598429.50455274[/C][C]-75305.5045527376[/C][/ROW]
[ROW][C]86[/C][C]1344597[/C][C]1381246.60092359[/C][C]-36649.6009235887[/C][/ROW]
[ROW][C]87[/C][C]1376780[/C][C]1330575.9916117[/C][C]46204.0083882969[/C][/ROW]
[ROW][C]88[/C][C]1397583[/C][C]1448695.31371276[/C][C]-51112.3137127643[/C][/ROW]
[ROW][C]89[/C][C]1534503[/C][C]1666250.51478733[/C][C]-131747.514787332[/C][/ROW]
[ROW][C]90[/C][C]1712929[/C][C]1681448.97628211[/C][C]31480.0237178891[/C][/ROW]
[ROW][C]91[/C][C]1586355[/C][C]1598339.35889205[/C][C]-11984.3588920489[/C][/ROW]
[ROW][C]92[/C][C]1649698[/C][C]1544149.0851734[/C][C]105548.914826602[/C][/ROW]
[ROW][C]93[/C][C]1596712[/C][C]1593407.82013347[/C][C]3304.17986652721[/C][/ROW]
[ROW][C]94[/C][C]1565653[/C][C]1526606.32414788[/C][C]39046.6758521234[/C][/ROW]
[ROW][C]95[/C][C]1807421[/C][C]1722658.99270172[/C][C]84762.0072982791[/C][/ROW]
[ROW][C]96[/C][C]1754435[/C][C]1816865.5247771[/C][C]-62430.5247770955[/C][/ROW]
[ROW][C]97[/C][C]1680746[/C][C]1791060.59651607[/C][C]-110314.59651607[/C][/ROW]
[ROW][C]98[/C][C]1576009[/C][C]1561136.60813108[/C][C]14872.391868921[/C][/ROW]
[ROW][C]99[/C][C]1680746[/C][C]1571374.87068257[/C][C]109371.129317428[/C][/ROW]
[ROW][C]100[/C][C]1733732[/C][C]1697791.78031438[/C][C]35940.2196856181[/C][/ROW]
[ROW][C]101[/C][C]1796963[/C][C]1948046.28381445[/C][C]-151083.283814455[/C][/ROW]
[ROW][C]102[/C][C]1880998[/C][C]2010208.39690715[/C][C]-129210.396907149[/C][/ROW]
[ROW][C]103[/C][C]1796963[/C][C]1804516.53620369[/C][C]-7553.53620368824[/C][/ROW]
[ROW][C]104[/C][C]1848826[/C][C]1791590.20822849[/C][C]57235.7917715057[/C][/ROW]
[ROW][C]105[/C][C]1785585[/C][C]1769839.40433289[/C][C]15745.5956671124[/C][/ROW]
[ROW][C]106[/C][C]1775239[/C][C]1719965.56936503[/C][C]55273.4306349694[/C][/ROW]
[ROW][C]107[/C][C]2037699[/C][C]1939435.88969346[/C][C]98263.1103065431[/C][/ROW]
[ROW][C]108[/C][C]2059525[/C][C]1988925.30621763[/C][C]70599.6937823654[/C][/ROW]
[ROW][C]109[/C][C]1975491[/C][C]2035530.70203437[/C][C]-60039.7020343684[/C][/ROW]
[ROW][C]110[/C][C]1828123[/C][C]1885615.42797314[/C][C]-57492.4279731382[/C][/ROW]
[ROW][C]111[/C][C]1953664[/C][C]1882569.66540047[/C][C]71094.3345995336[/C][/ROW]
[ROW][C]112[/C][C]2006549[/C][C]1958490.47534724[/C][C]48058.5246527561[/C][/ROW]
[ROW][C]113[/C][C]2069882[/C][C]2152260.40363999[/C][C]-82378.4036399946[/C][/ROW]
[ROW][C]114[/C][C]2164273[/C][C]2269659.29524517[/C][C]-105386.295245171[/C][/ROW]
[ROW][C]115[/C][C]2069882[/C][C]2125257.33846745[/C][C]-55375.3384674527[/C][/ROW]
[ROW][C]116[/C][C]2143570[/C][C]2105439.52033051[/C][C]38130.4796694946[/C][/ROW]
[ROW][C]117[/C][C]2111388[/C][C]2058092.17180547[/C][C]53295.82819453[/C][/ROW]
[ROW][C]118[/C][C]1996193[/C][C]2049015.2565196[/C][C]-52822.2565195966[/C][/ROW]
[ROW][C]119[/C][C]2237951[/C][C]2211545.43964616[/C][C]26405.5603538356[/C][/ROW]
[ROW][C]120[/C][C]2237951[/C][C]2200821.30773405[/C][C]37129.6922659529[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168958&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168958&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
13462824558671.733707265-95847.733707265
14399492431689.970570098-32197.9705700981
15347630356235.210613738-8605.21061373776
16347630344263.4491707283366.55082927167
17546859536823.21149951310035.7885004871
18567562552061.7978839515500.2021160501
19409838400070.8110592789767.18894072168
20231412295363.638310469-63951.6383104689
21325803259280.34423200966522.6557679914
22325803301299.31929575324503.680704247
23399492326622.513389372869.4866107003
24442021396682.57124031845338.4287596825
25431664330765.16798842100898.83201158
26325803362870.606234644-37067.6062346441
27378790300680.01020164778109.9897983534
28357986360808.412101891-2822.41210189089
29536412562693.924757772-26281.9247577717
30493873565891.832512064-72018.8325120637
31325803361487.68530039-35684.6853003898
32200263206741.343205462-6478.34320546151
33315447260610.12629222554836.8737077754
34347630287224.42209415560405.5779058452
35378790360796.97755139517993.0224486051
36420195391584.19631693928610.803683061
37336150339531.504829378-3381.50482937793
38263595257633.3332693575961.66673064331
39294755266896.85048906927858.1495109314
40305101267841.33285322637259.6671467735
41577918490881.00731238287036.9926876178
42577918559305.74117725518612.2588227447
43420195436863.036865004-16668.0368650044
44399492315458.80074873284033.1992512684
45462824463653.298693989-829.298693989054
46431664467813.6976716-36149.6976715997
47515709472246.11284615843462.8871538417
48620447532900.76699809587546.2330019053
49641250519868.621415624121381.378584376
50493873538651.22910481-44778.2291048102
51452367536477.054370399-84110.0543703993
52409838477762.255327648-67924.2553276478
53694135655923.47040627138211.5295937294
54714939673673.89061364341265.1093863568
55661953559540.638598795102412.361401205
56714939560694.126385505154244.873614495
57704481737657.675763943-33176.6757639428
58620447719594.467159778-99147.4671597781
59714939719401.204828258-4462.20482825767
60819676771317.06216838348358.9378316172
61862205750351.693205281111853.306794719
62735641710982.02780211924658.972197881
63651596748602.016132604-97006.0161326036
64714939694651.46255801320287.5374419868
65987746977871.6628650589874.33713494195
661071790987816.38738075983973.6126192407
671051088933914.33953695117173.66046305
681092483974316.525497155118166.474502845
6910821371073177.01155258959.988447499
709773991071659.79062202-94260.7906220192
7111558251119483.2229994336341.7770005683
7211983541229802.4791591-31448.4791590972
7312605621189342.999838171219.0001619034
7410717901102481.27550392-30691.2755039206
759981021069135.57898985-71033.5789898504
7610821371081043.24794921093.75205080328
7712823891355700.62086235-73311.6208623494
7814608141341652.10061132119161.899388679
7914182861328178.5645785290107.4354214796
8014182861356226.2577922262059.7422077821
8114390891383638.4513042155450.5486957948
8213664231381413.88786069-14990.8878606949
8315553071533690.395904921616.6040951016
8415553071617796.41930872-62489.4193087157
8515231241598429.50455274-75305.5045527376
8613445971381246.60092359-36649.6009235887
8713767801330575.991611746204.0083882969
8813975831448695.31371276-51112.3137127643
8915345031666250.51478733-131747.514787332
9017129291681448.9762821131480.0237178891
9115863551598339.35889205-11984.3588920489
9216496981544149.0851734105548.914826602
9315967121593407.820133473304.17986652721
9415656531526606.3241478839046.6758521234
9518074211722658.9927017284762.0072982791
9617544351816865.5247771-62430.5247770955
9716807461791060.59651607-110314.59651607
9815760091561136.6081310814872.391868921
9916807461571374.87068257109371.129317428
10017337321697791.7803143835940.2196856181
10117969631948046.28381445-151083.283814455
10218809982010208.39690715-129210.396907149
10317969631804516.53620369-7553.53620368824
10418488261791590.2082284957235.7917715057
10517855851769839.4043328915745.5956671124
10617752391719965.5693650355273.4306349694
10720376991939435.8896934698263.1103065431
10820595251988925.3062176370599.6937823654
10919754912035530.70203437-60039.7020343684
11018281231885615.42797314-57492.4279731382
11119536641882569.6654004771094.3345995336
11220065491958490.4753472448058.5246527561
11320698822152260.40363999-82378.4036399946
11421642732269659.29524517-105386.295245171
11520698822125257.33846745-55375.3384674527
11621435702105439.5203305138130.4796694946
11721113882058092.1718054753295.82819453
11819961932049015.2565196-52822.2565195966
11922379512211545.4396461626405.5603538356
12022379512200821.3077340537129.6922659529







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1212175476.573932172046785.663038492304167.48482585
1222062941.564237741906719.270042992219163.85843249
1232141258.3498381959439.929761762323076.76991425
1242159516.039933941953218.694011072365813.38585681
1252271814.616325792041712.415700962501916.81695062
1262433059.550013292179558.331804682686560.76822191
1272376480.611188562099811.53810862653149.68426853
1282428779.663709812129054.13227992728505.19513971
1292363977.211541612041221.315281282686733.10780194
1302283678.282958611937855.574768332629500.99114888
1312510375.336359892141402.476463382879348.1962564
1322487391.379442722095149.244463842879633.51442159

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 2175476.57393217 & 2046785.66303849 & 2304167.48482585 \tabularnewline
122 & 2062941.56423774 & 1906719.27004299 & 2219163.85843249 \tabularnewline
123 & 2141258.349838 & 1959439.92976176 & 2323076.76991425 \tabularnewline
124 & 2159516.03993394 & 1953218.69401107 & 2365813.38585681 \tabularnewline
125 & 2271814.61632579 & 2041712.41570096 & 2501916.81695062 \tabularnewline
126 & 2433059.55001329 & 2179558.33180468 & 2686560.76822191 \tabularnewline
127 & 2376480.61118856 & 2099811.5381086 & 2653149.68426853 \tabularnewline
128 & 2428779.66370981 & 2129054.1322799 & 2728505.19513971 \tabularnewline
129 & 2363977.21154161 & 2041221.31528128 & 2686733.10780194 \tabularnewline
130 & 2283678.28295861 & 1937855.57476833 & 2629500.99114888 \tabularnewline
131 & 2510375.33635989 & 2141402.47646338 & 2879348.1962564 \tabularnewline
132 & 2487391.37944272 & 2095149.24446384 & 2879633.51442159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168958&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]2175476.57393217[/C][C]2046785.66303849[/C][C]2304167.48482585[/C][/ROW]
[ROW][C]122[/C][C]2062941.56423774[/C][C]1906719.27004299[/C][C]2219163.85843249[/C][/ROW]
[ROW][C]123[/C][C]2141258.349838[/C][C]1959439.92976176[/C][C]2323076.76991425[/C][/ROW]
[ROW][C]124[/C][C]2159516.03993394[/C][C]1953218.69401107[/C][C]2365813.38585681[/C][/ROW]
[ROW][C]125[/C][C]2271814.61632579[/C][C]2041712.41570096[/C][C]2501916.81695062[/C][/ROW]
[ROW][C]126[/C][C]2433059.55001329[/C][C]2179558.33180468[/C][C]2686560.76822191[/C][/ROW]
[ROW][C]127[/C][C]2376480.61118856[/C][C]2099811.5381086[/C][C]2653149.68426853[/C][/ROW]
[ROW][C]128[/C][C]2428779.66370981[/C][C]2129054.1322799[/C][C]2728505.19513971[/C][/ROW]
[ROW][C]129[/C][C]2363977.21154161[/C][C]2041221.31528128[/C][C]2686733.10780194[/C][/ROW]
[ROW][C]130[/C][C]2283678.28295861[/C][C]1937855.57476833[/C][C]2629500.99114888[/C][/ROW]
[ROW][C]131[/C][C]2510375.33635989[/C][C]2141402.47646338[/C][C]2879348.1962564[/C][/ROW]
[ROW][C]132[/C][C]2487391.37944272[/C][C]2095149.24446384[/C][C]2879633.51442159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168958&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168958&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
1212175476.573932172046785.663038492304167.48482585
1222062941.564237741906719.270042992219163.85843249
1232141258.3498381959439.929761762323076.76991425
1242159516.039933941953218.694011072365813.38585681
1252271814.616325792041712.415700962501916.81695062
1262433059.550013292179558.331804682686560.76822191
1272376480.611188562099811.53810862653149.68426853
1282428779.663709812129054.13227992728505.19513971
1292363977.211541612041221.315281282686733.10780194
1302283678.282958611937855.574768332629500.99114888
1312510375.336359892141402.476463382879348.1962564
1322487391.379442722095149.244463842879633.51442159



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')