Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 18 Aug 2011 11:57:48 -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/Aug/18/t13136833350428bhxdoic0kqy.htm/, Retrieved Wed, 15 May 2024 05:39:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124103, Retrieved Wed, 15 May 2024 05:39:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSébastien Delforge
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Reeks 1 - stap 33] [2011-08-18 15:57:48] [923770d86edf74ed976a539eae527e37] [Current]
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Dataseries X:
58109
57087
56064
54019
74712
73689
58109
47763
48785
48785
49808
51964
45718
39462
34339
34339
54019
56064
40484
22859
32183
32183
39462
43663
42640
32183
37417
35362
52987
48785
32183
19782
31160
34339
37417
41507
33205
26038
29116
30138
57087
57087
41507
39462
45718
42640
50942
61288
63343
48785
44685
40484
68567
70622
65388
70622
69589
61288
70622
80968
85169
72667
64365
70622
97570
105872
103827
107916
106894
96548
114173
118374
124519
105872
98593
106894
126675
144300
140099
140099
142154
134976
153634
153634
150455
132820
135999
138054
151579
169204
156701
162958
157724
154656
178538
173304
166025
155679
166025
171259
177505
185806
177505
182628
176381
175359
201285
203441
195140
180583
192984
198208
204464
213788
204464
211743
208564
197185
221066
221066




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124103&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124103&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124103&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.653616535247791
beta0.0529317881414159
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.653616535247791 \tabularnewline
beta & 0.0529317881414159 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124103&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]0.653616535247791[/C][/ROW]
[ROW][C]beta[/C][C]0.0529317881414159[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124103&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124103&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
alpha0.653616535247791
beta0.0529317881414159
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134571855185.9009081197-9467.90090811966
143946242642.520902755-3180.52090275503
153433935189.0146580996-850.014658099644
163433934006.4411284809332.558871519082
175401953027.6561151639991.343884836118
185606454532.88649528131531.11350471867
194048439519.1829655835964.817034416468
202285929176.1352293838-6317.13522938383
213218325611.84524283136571.15475716868
223218329762.52254803742420.47745196261
233946232263.99001509867198.0099849014
244366339184.53695681764478.4630431824
254264032673.12719301499966.87280698509
263218335844.518075824-3661.51807582399
273741729701.26880837017715.73119162989
283536235640.7780716049-278.778071604895
295298755583.2006308747-2596.20063087474
304878555898.9965299153-7113.99652991533
313218335707.931396356-3524.93139635596
321978220422.0107492981-640.010749298082
333116025743.13449151545416.86550848464
343433928372.14897563355966.85102436648
353741735639.66303850831777.33696149168
364150738680.84276159782826.15723840219
373320533539.0684104527-334.068410452659
382603825449.0773392543588.922660745673
392911626364.06313630752751.93686369253
403013826457.44137914323680.55862085675
415708748489.46939703468597.53060296539
425708755248.48825724851838.51174275153
434150743153.559063066-1646.55906306599
443946231161.08434626488300.91565373522
454571845799.8991673456-81.8991673455603
464264046210.8467149124-3570.8467149124
475094246648.71951506274293.28048493731
486128852640.23394230548647.7660576946
496334351352.898617337211990.1013826628
504878553208.2671368694-4423.26713686943
514468552993.3975525015-8308.39755250146
524048447193.5245443988-6709.5245443988
536856764792.42051845843774.57948154159
547062266545.84664670594076.15335329408
556538855271.702241915910116.2977580841
567062255385.622775785315236.3772242147
576958972866.2050912836-3277.2050912836
586128871081.889393482-9793.88939348199
597062271062.7383277797-440.738327779749
608096876191.01439819024776.98560180984
618516974120.157723170611048.8422768294
627266770231.17451327822435.82548672182
636436573947.2712505813-9582.27125058128
647062268618.01907682832003.98092317168
659757096594.6111068163975.38889318367
6610587297576.94085457858295.05914542149
6710382792252.551725210211574.4482747898
6810791696243.504722995111672.4952770049
69106894106009.026439244884.973560755927
7096548105859.057479933-9311.05747993261
71114173110583.1244254333589.87557456722
72118374121480.511418614-3106.51141861387
73124519117483.893845687035.10615432006
74105872108903.751807185-3031.75180718477
7598593105609.809422281-7016.8094222806
76106894106785.959002737108.040997263088
77126675133916.739379413-7241.73937941319
78144300132529.03551945811770.9644805418
79140099131198.1425382298900.85746177143
80140099133968.7165424746130.28345752606
81142154136676.5557214695477.44427853095
82134976136456.869032099-1480.86903209903
83153634151498.7522907892135.24770921149
84153634159806.732616107-6172.73261610724
85150455157893.668349687-7438.66834968678
86132820136440.281869208-3620.28186920774
87135999131434.9940527964564.00594720445
88138054143102.834571456-5048.83457145593
89151579164593.088662729-13014.0886627292
90169204166094.3968508253109.60314917465
91156701157884.708107258-1183.70810725828
92162958152531.8364743610426.1635256401
93157724157397.700352883326.299647116801
94154656150798.9802093533857.01979064665
95178538170165.1188679838372.88113201654
96173304179470.936462561-6166.93646256137
97166025176921.925915922-10896.9259159224
98155679154209.9098543381469.09014566193
99166025155221.21799137610803.7820086238
100171259167708.8247014513550.17529854857
101177505192429.076642462-14924.0766424623
102185806198569.4604312-12763.4604311998
103177505178251.076089586-746.07608958552
104182628176974.1895878765653.81041212424
105176381174825.7032225681555.29677743168
106175359169899.1432352915459.85676470856
107201285191578.4800731649706.51992683631
108203441196467.1113967726973.88860322841
109195140201070.883354153-5930.88335415346
110180583186262.061034831-5679.06103483107
111192984185961.2197504847022.78024951572
112198208193460.7775779724747.22242202752
113204464212601.484076903-8137.48407690297
114213788224198.115241462-10410.1152414621
115204464209933.974882204-5469.9748822042
116211743207976.2871459933766.71285400706
117208564203299.419438895264.58056111011
118197185202402.828294417-5217.82829441677
119221066218457.6552783382608.34472166246
120221066217398.3151507353667.68484926483

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 45718 & 55185.9009081197 & -9467.90090811966 \tabularnewline
14 & 39462 & 42642.520902755 & -3180.52090275503 \tabularnewline
15 & 34339 & 35189.0146580996 & -850.014658099644 \tabularnewline
16 & 34339 & 34006.4411284809 & 332.558871519082 \tabularnewline
17 & 54019 & 53027.6561151639 & 991.343884836118 \tabularnewline
18 & 56064 & 54532.8864952813 & 1531.11350471867 \tabularnewline
19 & 40484 & 39519.1829655835 & 964.817034416468 \tabularnewline
20 & 22859 & 29176.1352293838 & -6317.13522938383 \tabularnewline
21 & 32183 & 25611.8452428313 & 6571.15475716868 \tabularnewline
22 & 32183 & 29762.5225480374 & 2420.47745196261 \tabularnewline
23 & 39462 & 32263.9900150986 & 7198.0099849014 \tabularnewline
24 & 43663 & 39184.5369568176 & 4478.4630431824 \tabularnewline
25 & 42640 & 32673.1271930149 & 9966.87280698509 \tabularnewline
26 & 32183 & 35844.518075824 & -3661.51807582399 \tabularnewline
27 & 37417 & 29701.2688083701 & 7715.73119162989 \tabularnewline
28 & 35362 & 35640.7780716049 & -278.778071604895 \tabularnewline
29 & 52987 & 55583.2006308747 & -2596.20063087474 \tabularnewline
30 & 48785 & 55898.9965299153 & -7113.99652991533 \tabularnewline
31 & 32183 & 35707.931396356 & -3524.93139635596 \tabularnewline
32 & 19782 & 20422.0107492981 & -640.010749298082 \tabularnewline
33 & 31160 & 25743.1344915154 & 5416.86550848464 \tabularnewline
34 & 34339 & 28372.1489756335 & 5966.85102436648 \tabularnewline
35 & 37417 & 35639.6630385083 & 1777.33696149168 \tabularnewline
36 & 41507 & 38680.8427615978 & 2826.15723840219 \tabularnewline
37 & 33205 & 33539.0684104527 & -334.068410452659 \tabularnewline
38 & 26038 & 25449.0773392543 & 588.922660745673 \tabularnewline
39 & 29116 & 26364.0631363075 & 2751.93686369253 \tabularnewline
40 & 30138 & 26457.4413791432 & 3680.55862085675 \tabularnewline
41 & 57087 & 48489.4693970346 & 8597.53060296539 \tabularnewline
42 & 57087 & 55248.4882572485 & 1838.51174275153 \tabularnewline
43 & 41507 & 43153.559063066 & -1646.55906306599 \tabularnewline
44 & 39462 & 31161.0843462648 & 8300.91565373522 \tabularnewline
45 & 45718 & 45799.8991673456 & -81.8991673455603 \tabularnewline
46 & 42640 & 46210.8467149124 & -3570.8467149124 \tabularnewline
47 & 50942 & 46648.7195150627 & 4293.28048493731 \tabularnewline
48 & 61288 & 52640.2339423054 & 8647.7660576946 \tabularnewline
49 & 63343 & 51352.8986173372 & 11990.1013826628 \tabularnewline
50 & 48785 & 53208.2671368694 & -4423.26713686943 \tabularnewline
51 & 44685 & 52993.3975525015 & -8308.39755250146 \tabularnewline
52 & 40484 & 47193.5245443988 & -6709.5245443988 \tabularnewline
53 & 68567 & 64792.4205184584 & 3774.57948154159 \tabularnewline
54 & 70622 & 66545.8466467059 & 4076.15335329408 \tabularnewline
55 & 65388 & 55271.7022419159 & 10116.2977580841 \tabularnewline
56 & 70622 & 55385.6227757853 & 15236.3772242147 \tabularnewline
57 & 69589 & 72866.2050912836 & -3277.2050912836 \tabularnewline
58 & 61288 & 71081.889393482 & -9793.88939348199 \tabularnewline
59 & 70622 & 71062.7383277797 & -440.738327779749 \tabularnewline
60 & 80968 & 76191.0143981902 & 4776.98560180984 \tabularnewline
61 & 85169 & 74120.1577231706 & 11048.8422768294 \tabularnewline
62 & 72667 & 70231.1745132782 & 2435.82548672182 \tabularnewline
63 & 64365 & 73947.2712505813 & -9582.27125058128 \tabularnewline
64 & 70622 & 68618.0190768283 & 2003.98092317168 \tabularnewline
65 & 97570 & 96594.6111068163 & 975.38889318367 \tabularnewline
66 & 105872 & 97576.9408545785 & 8295.05914542149 \tabularnewline
67 & 103827 & 92252.5517252102 & 11574.4482747898 \tabularnewline
68 & 107916 & 96243.5047229951 & 11672.4952770049 \tabularnewline
69 & 106894 & 106009.026439244 & 884.973560755927 \tabularnewline
70 & 96548 & 105859.057479933 & -9311.05747993261 \tabularnewline
71 & 114173 & 110583.124425433 & 3589.87557456722 \tabularnewline
72 & 118374 & 121480.511418614 & -3106.51141861387 \tabularnewline
73 & 124519 & 117483.89384568 & 7035.10615432006 \tabularnewline
74 & 105872 & 108903.751807185 & -3031.75180718477 \tabularnewline
75 & 98593 & 105609.809422281 & -7016.8094222806 \tabularnewline
76 & 106894 & 106785.959002737 & 108.040997263088 \tabularnewline
77 & 126675 & 133916.739379413 & -7241.73937941319 \tabularnewline
78 & 144300 & 132529.035519458 & 11770.9644805418 \tabularnewline
79 & 140099 & 131198.142538229 & 8900.85746177143 \tabularnewline
80 & 140099 & 133968.716542474 & 6130.28345752606 \tabularnewline
81 & 142154 & 136676.555721469 & 5477.44427853095 \tabularnewline
82 & 134976 & 136456.869032099 & -1480.86903209903 \tabularnewline
83 & 153634 & 151498.752290789 & 2135.24770921149 \tabularnewline
84 & 153634 & 159806.732616107 & -6172.73261610724 \tabularnewline
85 & 150455 & 157893.668349687 & -7438.66834968678 \tabularnewline
86 & 132820 & 136440.281869208 & -3620.28186920774 \tabularnewline
87 & 135999 & 131434.994052796 & 4564.00594720445 \tabularnewline
88 & 138054 & 143102.834571456 & -5048.83457145593 \tabularnewline
89 & 151579 & 164593.088662729 & -13014.0886627292 \tabularnewline
90 & 169204 & 166094.396850825 & 3109.60314917465 \tabularnewline
91 & 156701 & 157884.708107258 & -1183.70810725828 \tabularnewline
92 & 162958 & 152531.83647436 & 10426.1635256401 \tabularnewline
93 & 157724 & 157397.700352883 & 326.299647116801 \tabularnewline
94 & 154656 & 150798.980209353 & 3857.01979064665 \tabularnewline
95 & 178538 & 170165.118867983 & 8372.88113201654 \tabularnewline
96 & 173304 & 179470.936462561 & -6166.93646256137 \tabularnewline
97 & 166025 & 176921.925915922 & -10896.9259159224 \tabularnewline
98 & 155679 & 154209.909854338 & 1469.09014566193 \tabularnewline
99 & 166025 & 155221.217991376 & 10803.7820086238 \tabularnewline
100 & 171259 & 167708.824701451 & 3550.17529854857 \tabularnewline
101 & 177505 & 192429.076642462 & -14924.0766424623 \tabularnewline
102 & 185806 & 198569.4604312 & -12763.4604311998 \tabularnewline
103 & 177505 & 178251.076089586 & -746.07608958552 \tabularnewline
104 & 182628 & 176974.189587876 & 5653.81041212424 \tabularnewline
105 & 176381 & 174825.703222568 & 1555.29677743168 \tabularnewline
106 & 175359 & 169899.143235291 & 5459.85676470856 \tabularnewline
107 & 201285 & 191578.480073164 & 9706.51992683631 \tabularnewline
108 & 203441 & 196467.111396772 & 6973.88860322841 \tabularnewline
109 & 195140 & 201070.883354153 & -5930.88335415346 \tabularnewline
110 & 180583 & 186262.061034831 & -5679.06103483107 \tabularnewline
111 & 192984 & 185961.219750484 & 7022.78024951572 \tabularnewline
112 & 198208 & 193460.777577972 & 4747.22242202752 \tabularnewline
113 & 204464 & 212601.484076903 & -8137.48407690297 \tabularnewline
114 & 213788 & 224198.115241462 & -10410.1152414621 \tabularnewline
115 & 204464 & 209933.974882204 & -5469.9748822042 \tabularnewline
116 & 211743 & 207976.287145993 & 3766.71285400706 \tabularnewline
117 & 208564 & 203299.41943889 & 5264.58056111011 \tabularnewline
118 & 197185 & 202402.828294417 & -5217.82829441677 \tabularnewline
119 & 221066 & 218457.655278338 & 2608.34472166246 \tabularnewline
120 & 221066 & 217398.315150735 & 3667.68484926483 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124103&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]45718[/C][C]55185.9009081197[/C][C]-9467.90090811966[/C][/ROW]
[ROW][C]14[/C][C]39462[/C][C]42642.520902755[/C][C]-3180.52090275503[/C][/ROW]
[ROW][C]15[/C][C]34339[/C][C]35189.0146580996[/C][C]-850.014658099644[/C][/ROW]
[ROW][C]16[/C][C]34339[/C][C]34006.4411284809[/C][C]332.558871519082[/C][/ROW]
[ROW][C]17[/C][C]54019[/C][C]53027.6561151639[/C][C]991.343884836118[/C][/ROW]
[ROW][C]18[/C][C]56064[/C][C]54532.8864952813[/C][C]1531.11350471867[/C][/ROW]
[ROW][C]19[/C][C]40484[/C][C]39519.1829655835[/C][C]964.817034416468[/C][/ROW]
[ROW][C]20[/C][C]22859[/C][C]29176.1352293838[/C][C]-6317.13522938383[/C][/ROW]
[ROW][C]21[/C][C]32183[/C][C]25611.8452428313[/C][C]6571.15475716868[/C][/ROW]
[ROW][C]22[/C][C]32183[/C][C]29762.5225480374[/C][C]2420.47745196261[/C][/ROW]
[ROW][C]23[/C][C]39462[/C][C]32263.9900150986[/C][C]7198.0099849014[/C][/ROW]
[ROW][C]24[/C][C]43663[/C][C]39184.5369568176[/C][C]4478.4630431824[/C][/ROW]
[ROW][C]25[/C][C]42640[/C][C]32673.1271930149[/C][C]9966.87280698509[/C][/ROW]
[ROW][C]26[/C][C]32183[/C][C]35844.518075824[/C][C]-3661.51807582399[/C][/ROW]
[ROW][C]27[/C][C]37417[/C][C]29701.2688083701[/C][C]7715.73119162989[/C][/ROW]
[ROW][C]28[/C][C]35362[/C][C]35640.7780716049[/C][C]-278.778071604895[/C][/ROW]
[ROW][C]29[/C][C]52987[/C][C]55583.2006308747[/C][C]-2596.20063087474[/C][/ROW]
[ROW][C]30[/C][C]48785[/C][C]55898.9965299153[/C][C]-7113.99652991533[/C][/ROW]
[ROW][C]31[/C][C]32183[/C][C]35707.931396356[/C][C]-3524.93139635596[/C][/ROW]
[ROW][C]32[/C][C]19782[/C][C]20422.0107492981[/C][C]-640.010749298082[/C][/ROW]
[ROW][C]33[/C][C]31160[/C][C]25743.1344915154[/C][C]5416.86550848464[/C][/ROW]
[ROW][C]34[/C][C]34339[/C][C]28372.1489756335[/C][C]5966.85102436648[/C][/ROW]
[ROW][C]35[/C][C]37417[/C][C]35639.6630385083[/C][C]1777.33696149168[/C][/ROW]
[ROW][C]36[/C][C]41507[/C][C]38680.8427615978[/C][C]2826.15723840219[/C][/ROW]
[ROW][C]37[/C][C]33205[/C][C]33539.0684104527[/C][C]-334.068410452659[/C][/ROW]
[ROW][C]38[/C][C]26038[/C][C]25449.0773392543[/C][C]588.922660745673[/C][/ROW]
[ROW][C]39[/C][C]29116[/C][C]26364.0631363075[/C][C]2751.93686369253[/C][/ROW]
[ROW][C]40[/C][C]30138[/C][C]26457.4413791432[/C][C]3680.55862085675[/C][/ROW]
[ROW][C]41[/C][C]57087[/C][C]48489.4693970346[/C][C]8597.53060296539[/C][/ROW]
[ROW][C]42[/C][C]57087[/C][C]55248.4882572485[/C][C]1838.51174275153[/C][/ROW]
[ROW][C]43[/C][C]41507[/C][C]43153.559063066[/C][C]-1646.55906306599[/C][/ROW]
[ROW][C]44[/C][C]39462[/C][C]31161.0843462648[/C][C]8300.91565373522[/C][/ROW]
[ROW][C]45[/C][C]45718[/C][C]45799.8991673456[/C][C]-81.8991673455603[/C][/ROW]
[ROW][C]46[/C][C]42640[/C][C]46210.8467149124[/C][C]-3570.8467149124[/C][/ROW]
[ROW][C]47[/C][C]50942[/C][C]46648.7195150627[/C][C]4293.28048493731[/C][/ROW]
[ROW][C]48[/C][C]61288[/C][C]52640.2339423054[/C][C]8647.7660576946[/C][/ROW]
[ROW][C]49[/C][C]63343[/C][C]51352.8986173372[/C][C]11990.1013826628[/C][/ROW]
[ROW][C]50[/C][C]48785[/C][C]53208.2671368694[/C][C]-4423.26713686943[/C][/ROW]
[ROW][C]51[/C][C]44685[/C][C]52993.3975525015[/C][C]-8308.39755250146[/C][/ROW]
[ROW][C]52[/C][C]40484[/C][C]47193.5245443988[/C][C]-6709.5245443988[/C][/ROW]
[ROW][C]53[/C][C]68567[/C][C]64792.4205184584[/C][C]3774.57948154159[/C][/ROW]
[ROW][C]54[/C][C]70622[/C][C]66545.8466467059[/C][C]4076.15335329408[/C][/ROW]
[ROW][C]55[/C][C]65388[/C][C]55271.7022419159[/C][C]10116.2977580841[/C][/ROW]
[ROW][C]56[/C][C]70622[/C][C]55385.6227757853[/C][C]15236.3772242147[/C][/ROW]
[ROW][C]57[/C][C]69589[/C][C]72866.2050912836[/C][C]-3277.2050912836[/C][/ROW]
[ROW][C]58[/C][C]61288[/C][C]71081.889393482[/C][C]-9793.88939348199[/C][/ROW]
[ROW][C]59[/C][C]70622[/C][C]71062.7383277797[/C][C]-440.738327779749[/C][/ROW]
[ROW][C]60[/C][C]80968[/C][C]76191.0143981902[/C][C]4776.98560180984[/C][/ROW]
[ROW][C]61[/C][C]85169[/C][C]74120.1577231706[/C][C]11048.8422768294[/C][/ROW]
[ROW][C]62[/C][C]72667[/C][C]70231.1745132782[/C][C]2435.82548672182[/C][/ROW]
[ROW][C]63[/C][C]64365[/C][C]73947.2712505813[/C][C]-9582.27125058128[/C][/ROW]
[ROW][C]64[/C][C]70622[/C][C]68618.0190768283[/C][C]2003.98092317168[/C][/ROW]
[ROW][C]65[/C][C]97570[/C][C]96594.6111068163[/C][C]975.38889318367[/C][/ROW]
[ROW][C]66[/C][C]105872[/C][C]97576.9408545785[/C][C]8295.05914542149[/C][/ROW]
[ROW][C]67[/C][C]103827[/C][C]92252.5517252102[/C][C]11574.4482747898[/C][/ROW]
[ROW][C]68[/C][C]107916[/C][C]96243.5047229951[/C][C]11672.4952770049[/C][/ROW]
[ROW][C]69[/C][C]106894[/C][C]106009.026439244[/C][C]884.973560755927[/C][/ROW]
[ROW][C]70[/C][C]96548[/C][C]105859.057479933[/C][C]-9311.05747993261[/C][/ROW]
[ROW][C]71[/C][C]114173[/C][C]110583.124425433[/C][C]3589.87557456722[/C][/ROW]
[ROW][C]72[/C][C]118374[/C][C]121480.511418614[/C][C]-3106.51141861387[/C][/ROW]
[ROW][C]73[/C][C]124519[/C][C]117483.89384568[/C][C]7035.10615432006[/C][/ROW]
[ROW][C]74[/C][C]105872[/C][C]108903.751807185[/C][C]-3031.75180718477[/C][/ROW]
[ROW][C]75[/C][C]98593[/C][C]105609.809422281[/C][C]-7016.8094222806[/C][/ROW]
[ROW][C]76[/C][C]106894[/C][C]106785.959002737[/C][C]108.040997263088[/C][/ROW]
[ROW][C]77[/C][C]126675[/C][C]133916.739379413[/C][C]-7241.73937941319[/C][/ROW]
[ROW][C]78[/C][C]144300[/C][C]132529.035519458[/C][C]11770.9644805418[/C][/ROW]
[ROW][C]79[/C][C]140099[/C][C]131198.142538229[/C][C]8900.85746177143[/C][/ROW]
[ROW][C]80[/C][C]140099[/C][C]133968.716542474[/C][C]6130.28345752606[/C][/ROW]
[ROW][C]81[/C][C]142154[/C][C]136676.555721469[/C][C]5477.44427853095[/C][/ROW]
[ROW][C]82[/C][C]134976[/C][C]136456.869032099[/C][C]-1480.86903209903[/C][/ROW]
[ROW][C]83[/C][C]153634[/C][C]151498.752290789[/C][C]2135.24770921149[/C][/ROW]
[ROW][C]84[/C][C]153634[/C][C]159806.732616107[/C][C]-6172.73261610724[/C][/ROW]
[ROW][C]85[/C][C]150455[/C][C]157893.668349687[/C][C]-7438.66834968678[/C][/ROW]
[ROW][C]86[/C][C]132820[/C][C]136440.281869208[/C][C]-3620.28186920774[/C][/ROW]
[ROW][C]87[/C][C]135999[/C][C]131434.994052796[/C][C]4564.00594720445[/C][/ROW]
[ROW][C]88[/C][C]138054[/C][C]143102.834571456[/C][C]-5048.83457145593[/C][/ROW]
[ROW][C]89[/C][C]151579[/C][C]164593.088662729[/C][C]-13014.0886627292[/C][/ROW]
[ROW][C]90[/C][C]169204[/C][C]166094.396850825[/C][C]3109.60314917465[/C][/ROW]
[ROW][C]91[/C][C]156701[/C][C]157884.708107258[/C][C]-1183.70810725828[/C][/ROW]
[ROW][C]92[/C][C]162958[/C][C]152531.83647436[/C][C]10426.1635256401[/C][/ROW]
[ROW][C]93[/C][C]157724[/C][C]157397.700352883[/C][C]326.299647116801[/C][/ROW]
[ROW][C]94[/C][C]154656[/C][C]150798.980209353[/C][C]3857.01979064665[/C][/ROW]
[ROW][C]95[/C][C]178538[/C][C]170165.118867983[/C][C]8372.88113201654[/C][/ROW]
[ROW][C]96[/C][C]173304[/C][C]179470.936462561[/C][C]-6166.93646256137[/C][/ROW]
[ROW][C]97[/C][C]166025[/C][C]176921.925915922[/C][C]-10896.9259159224[/C][/ROW]
[ROW][C]98[/C][C]155679[/C][C]154209.909854338[/C][C]1469.09014566193[/C][/ROW]
[ROW][C]99[/C][C]166025[/C][C]155221.217991376[/C][C]10803.7820086238[/C][/ROW]
[ROW][C]100[/C][C]171259[/C][C]167708.824701451[/C][C]3550.17529854857[/C][/ROW]
[ROW][C]101[/C][C]177505[/C][C]192429.076642462[/C][C]-14924.0766424623[/C][/ROW]
[ROW][C]102[/C][C]185806[/C][C]198569.4604312[/C][C]-12763.4604311998[/C][/ROW]
[ROW][C]103[/C][C]177505[/C][C]178251.076089586[/C][C]-746.07608958552[/C][/ROW]
[ROW][C]104[/C][C]182628[/C][C]176974.189587876[/C][C]5653.81041212424[/C][/ROW]
[ROW][C]105[/C][C]176381[/C][C]174825.703222568[/C][C]1555.29677743168[/C][/ROW]
[ROW][C]106[/C][C]175359[/C][C]169899.143235291[/C][C]5459.85676470856[/C][/ROW]
[ROW][C]107[/C][C]201285[/C][C]191578.480073164[/C][C]9706.51992683631[/C][/ROW]
[ROW][C]108[/C][C]203441[/C][C]196467.111396772[/C][C]6973.88860322841[/C][/ROW]
[ROW][C]109[/C][C]195140[/C][C]201070.883354153[/C][C]-5930.88335415346[/C][/ROW]
[ROW][C]110[/C][C]180583[/C][C]186262.061034831[/C][C]-5679.06103483107[/C][/ROW]
[ROW][C]111[/C][C]192984[/C][C]185961.219750484[/C][C]7022.78024951572[/C][/ROW]
[ROW][C]112[/C][C]198208[/C][C]193460.777577972[/C][C]4747.22242202752[/C][/ROW]
[ROW][C]113[/C][C]204464[/C][C]212601.484076903[/C][C]-8137.48407690297[/C][/ROW]
[ROW][C]114[/C][C]213788[/C][C]224198.115241462[/C][C]-10410.1152414621[/C][/ROW]
[ROW][C]115[/C][C]204464[/C][C]209933.974882204[/C][C]-5469.9748822042[/C][/ROW]
[ROW][C]116[/C][C]211743[/C][C]207976.287145993[/C][C]3766.71285400706[/C][/ROW]
[ROW][C]117[/C][C]208564[/C][C]203299.41943889[/C][C]5264.58056111011[/C][/ROW]
[ROW][C]118[/C][C]197185[/C][C]202402.828294417[/C][C]-5217.82829441677[/C][/ROW]
[ROW][C]119[/C][C]221066[/C][C]218457.655278338[/C][C]2608.34472166246[/C][/ROW]
[ROW][C]120[/C][C]221066[/C][C]217398.315150735[/C][C]3667.68484926483[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124103&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124103&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
134571855185.9009081197-9467.90090811966
143946242642.520902755-3180.52090275503
153433935189.0146580996-850.014658099644
163433934006.4411284809332.558871519082
175401953027.6561151639991.343884836118
185606454532.88649528131531.11350471867
194048439519.1829655835964.817034416468
202285929176.1352293838-6317.13522938383
213218325611.84524283136571.15475716868
223218329762.52254803742420.47745196261
233946232263.99001509867198.0099849014
244366339184.53695681764478.4630431824
254264032673.12719301499966.87280698509
263218335844.518075824-3661.51807582399
273741729701.26880837017715.73119162989
283536235640.7780716049-278.778071604895
295298755583.2006308747-2596.20063087474
304878555898.9965299153-7113.99652991533
313218335707.931396356-3524.93139635596
321978220422.0107492981-640.010749298082
333116025743.13449151545416.86550848464
343433928372.14897563355966.85102436648
353741735639.66303850831777.33696149168
364150738680.84276159782826.15723840219
373320533539.0684104527-334.068410452659
382603825449.0773392543588.922660745673
392911626364.06313630752751.93686369253
403013826457.44137914323680.55862085675
415708748489.46939703468597.53060296539
425708755248.48825724851838.51174275153
434150743153.559063066-1646.55906306599
443946231161.08434626488300.91565373522
454571845799.8991673456-81.8991673455603
464264046210.8467149124-3570.8467149124
475094246648.71951506274293.28048493731
486128852640.23394230548647.7660576946
496334351352.898617337211990.1013826628
504878553208.2671368694-4423.26713686943
514468552993.3975525015-8308.39755250146
524048447193.5245443988-6709.5245443988
536856764792.42051845843774.57948154159
547062266545.84664670594076.15335329408
556538855271.702241915910116.2977580841
567062255385.622775785315236.3772242147
576958972866.2050912836-3277.2050912836
586128871081.889393482-9793.88939348199
597062271062.7383277797-440.738327779749
608096876191.01439819024776.98560180984
618516974120.157723170611048.8422768294
627266770231.17451327822435.82548672182
636436573947.2712505813-9582.27125058128
647062268618.01907682832003.98092317168
659757096594.6111068163975.38889318367
6610587297576.94085457858295.05914542149
6710382792252.551725210211574.4482747898
6810791696243.504722995111672.4952770049
69106894106009.026439244884.973560755927
7096548105859.057479933-9311.05747993261
71114173110583.1244254333589.87557456722
72118374121480.511418614-3106.51141861387
73124519117483.893845687035.10615432006
74105872108903.751807185-3031.75180718477
7598593105609.809422281-7016.8094222806
76106894106785.959002737108.040997263088
77126675133916.739379413-7241.73937941319
78144300132529.03551945811770.9644805418
79140099131198.1425382298900.85746177143
80140099133968.7165424746130.28345752606
81142154136676.5557214695477.44427853095
82134976136456.869032099-1480.86903209903
83153634151498.7522907892135.24770921149
84153634159806.732616107-6172.73261610724
85150455157893.668349687-7438.66834968678
86132820136440.281869208-3620.28186920774
87135999131434.9940527964564.00594720445
88138054143102.834571456-5048.83457145593
89151579164593.088662729-13014.0886627292
90169204166094.3968508253109.60314917465
91156701157884.708107258-1183.70810725828
92162958152531.8364743610426.1635256401
93157724157397.700352883326.299647116801
94154656150798.9802093533857.01979064665
95178538170165.1188679838372.88113201654
96173304179470.936462561-6166.93646256137
97166025176921.925915922-10896.9259159224
98155679154209.9098543381469.09014566193
99166025155221.21799137610803.7820086238
100171259167708.8247014513550.17529854857
101177505192429.076642462-14924.0766424623
102185806198569.4604312-12763.4604311998
103177505178251.076089586-746.07608958552
104182628176974.1895878765653.81041212424
105176381174825.7032225681555.29677743168
106175359169899.1432352915459.85676470856
107201285191578.4800731649706.51992683631
108203441196467.1113967726973.88860322841
109195140201070.883354153-5930.88335415346
110180583186262.061034831-5679.06103483107
111192984185961.2197504847022.78024951572
112198208193460.7775779724747.22242202752
113204464212601.484076903-8137.48407690297
114213788224198.115241462-10410.1152414621
115204464209933.974882204-5469.9748822042
116211743207976.2871459933766.71285400706
117208564203299.419438895264.58056111011
118197185202402.828294417-5217.82829441677
119221066218457.6552783382608.34472166246
120221066217398.3151507353667.68484926483







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121214894.764546586202182.612412768227606.916680404
122203778.550563891188346.825145257219210.275982524
123211514.682086575193554.550936897229474.813236252
124213318.188058044192940.009762207233696.366353881
125224411.111158295201681.471415062247140.750901527
126240338.996851229215297.984855998265380.008846461
127234750.084833329207420.53522942262079.634437239
128239916.166204192210309.082989024269523.249419359
129233514.899163045201632.860005419265396.93832067
130225582.968701245191422.373437124259743.563965367
131247976.243833809211528.860188433284423.627479184
132245705.875600296206959.936555518284451.814645075

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 214894.764546586 & 202182.612412768 & 227606.916680404 \tabularnewline
122 & 203778.550563891 & 188346.825145257 & 219210.275982524 \tabularnewline
123 & 211514.682086575 & 193554.550936897 & 229474.813236252 \tabularnewline
124 & 213318.188058044 & 192940.009762207 & 233696.366353881 \tabularnewline
125 & 224411.111158295 & 201681.471415062 & 247140.750901527 \tabularnewline
126 & 240338.996851229 & 215297.984855998 & 265380.008846461 \tabularnewline
127 & 234750.084833329 & 207420.53522942 & 262079.634437239 \tabularnewline
128 & 239916.166204192 & 210309.082989024 & 269523.249419359 \tabularnewline
129 & 233514.899163045 & 201632.860005419 & 265396.93832067 \tabularnewline
130 & 225582.968701245 & 191422.373437124 & 259743.563965367 \tabularnewline
131 & 247976.243833809 & 211528.860188433 & 284423.627479184 \tabularnewline
132 & 245705.875600296 & 206959.936555518 & 284451.814645075 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124103&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]214894.764546586[/C][C]202182.612412768[/C][C]227606.916680404[/C][/ROW]
[ROW][C]122[/C][C]203778.550563891[/C][C]188346.825145257[/C][C]219210.275982524[/C][/ROW]
[ROW][C]123[/C][C]211514.682086575[/C][C]193554.550936897[/C][C]229474.813236252[/C][/ROW]
[ROW][C]124[/C][C]213318.188058044[/C][C]192940.009762207[/C][C]233696.366353881[/C][/ROW]
[ROW][C]125[/C][C]224411.111158295[/C][C]201681.471415062[/C][C]247140.750901527[/C][/ROW]
[ROW][C]126[/C][C]240338.996851229[/C][C]215297.984855998[/C][C]265380.008846461[/C][/ROW]
[ROW][C]127[/C][C]234750.084833329[/C][C]207420.53522942[/C][C]262079.634437239[/C][/ROW]
[ROW][C]128[/C][C]239916.166204192[/C][C]210309.082989024[/C][C]269523.249419359[/C][/ROW]
[ROW][C]129[/C][C]233514.899163045[/C][C]201632.860005419[/C][C]265396.93832067[/C][/ROW]
[ROW][C]130[/C][C]225582.968701245[/C][C]191422.373437124[/C][C]259743.563965367[/C][/ROW]
[ROW][C]131[/C][C]247976.243833809[/C][C]211528.860188433[/C][C]284423.627479184[/C][/ROW]
[ROW][C]132[/C][C]245705.875600296[/C][C]206959.936555518[/C][C]284451.814645075[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124103&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124103&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
121214894.764546586202182.612412768227606.916680404
122203778.550563891188346.825145257219210.275982524
123211514.682086575193554.550936897229474.813236252
124213318.188058044192940.009762207233696.366353881
125224411.111158295201681.471415062247140.750901527
126240338.996851229215297.984855998265380.008846461
127234750.084833329207420.53522942262079.634437239
128239916.166204192210309.082989024269523.249419359
129233514.899163045201632.860005419265396.93832067
130225582.968701245191422.373437124259743.563965367
131247976.243833809211528.860188433284423.627479184
132245705.875600296206959.936555518284451.814645075



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')