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 14:11:02 -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/t13136910781n5j3g9pk5jmu85.htm/, Retrieved Wed, 15 May 2024 13:33:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124139, Retrieved Wed, 15 May 2024 13:33:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGregory Goris
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A - Sta...] [2011-08-18 18:11:02] [4069dbe0e58b4004934f5f5b0dc60f40] [Current]
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Dataseries X:
34671
34355
34035
33373
39924
39577
34671
31409
31724
31724
32075
32706
34671
34035
35017
36631
45813
45813
43853
41888
43502
45466
45813
46795
49742
47777
47777
50724
58893
59555
57911
53982
56928
56928
57244
58893
60191
60853
60853
62817
70355
72315
72630
67724
70355
69373
67408
71653
72630
70986
71333
73613
82133
86372
86372
84412
87355
84412
82764
89004
89981
87670
93559
95870
102741
107301
106670
106319
108950
108630
104706
110594
112559
110594
118763
122692
131839
135448
134470
132505
134150
136114
129559
134785
138079
136750
145265
148207
160652
162932
159990
161634
162616
163598
157358
163247
166509
163247
172749
175692
188451
190416
191047
194340
194340
195638
189749
192696
194656
191047
201527
203491
216567
218878
222140
225087
225402
225749
219860
225749




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124139&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124139&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124139&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.214228687951557
beta0.107872744024592
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.214228687951557 \tabularnewline
beta & 0.107872744024592 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124139&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]0.214228687951557[/C][/ROW]
[ROW][C]beta[/C][C]0.107872744024592[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124139&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124139&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
alpha0.214228687951557
beta0.107872744024592
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133467132695.67875888821975.32124111182
143403532432.74107969651602.25892030347
153501733577.16905635541439.83094364458
163663135205.73470251111425.26529748895
174581344065.59035963241747.40964036756
184581344125.79079526811687.20920473185
194385341288.66897612332564.33102387669
204188838777.48763389293110.5123661071
214350240748.75976661252753.24023338754
224546642126.06670944513339.93329055486
234581343917.71906358141895.2809364186
244679545674.77479746161120.22520253844
254974251298.8969557804-1556.89695578041
264777749681.0200199166-1904.02001991656
274777750322.9826094446-2545.98260944457
285072451624.6998925508-900.699892550794
295889363715.361079862-4822.36107986203
305955561978.2557378779-2423.25573787791
315791157799.6814299492111.318570050767
325398254009.7346393416-27.7346393416374
335692854922.45266836892005.54733163109
345692856499.5227668783428.47723312171
355724456064.51600531141179.48399468863
365889356780.11206046382112.88793953615
376019160796.9996095738-605.999609573759
386085358369.715906452483.28409354998
396085359262.262367591590.73763240995
406281763315.1408716331-498.14087163315
417035574382.1915154703-4027.1915154703
427231574793.2432594624-2478.24325946244
437263072021.4363273919608.563672608056
446772467127.2744277507596.725572249314
457035570249.2657017956105.734298204377
466937369989.8632938816-616.863293881557
476740869745.8082752139-2337.80827521386
487165370420.25605146371232.74394853627
497263072116.6111866833513.388813316662
507098672113.8588804404-1127.85888044043
517133371144.4328004761188.567199523881
527361373256.4470045753356.552995424718
538213382733.878876542-600.878876541989
548637285227.97026717931144.02973282068
558637285490.6012199638881.39878003615
568441279562.71465094534849.2853490547
578735583611.28337241893743.71662758109
588441283371.95498911821040.04501088183
598276481829.095423432934.90457656802
608900486962.0481612622041.95183873799
618998188558.01252199771422.98747800234
628767087255.902488557414.097511443004
639355987867.49316193095691.50683806908
649587092097.50932414623772.49067585375
65102741104176.636779695-1435.6367796952
66107301109266.703368822-1965.7033688224
67106670108877.345109858-2207.3451098579
68106319104769.9010128961549.09898710351
69108950107824.8963492771125.10365072294
70108630104162.9801928234467.01980717687
71104706102892.2622783261813.73772167422
72110594110604.447821446-10.4478214457049
73112559111471.8556123551087.14438764521
74110594108748.8435614411845.15643855912
75118763114932.9662694543830.03373054622
76122692117560.5200516555131.47994834537
77131839127526.0376121434312.96238785658
78135448134778.43281613669.567183870298
79134470134878.676914925-408.676914924901
80132505134128.04308795-1623.04308794989
81134150136915.926396732-2765.92639673199
82136114134729.6837304921384.31626950848
83129559129617.941315725-58.9413157246599
84134785136805.909392368-2020.90939236825
85138079138377.81704437-298.817044370255
86136750135253.1639528121496.83604718803
87145265144380.27320841884.726791590336
88148207147716.556563698490.443436301663
89160652157316.3307875243335.66921247618
90162932161764.7404403191167.25955968135
91159990160553.204377797-563.204377796501
92161634158118.7073150573515.29268494324
93162616161275.8050925011340.19490749887
94163598163396.721818525201.278181474801
95157358155398.1094817521959.89051824767
96163247162471.045555437775.954444563045
97166509166607.229142097-98.2291420973488
98163247164519.097352684-1272.09735268407
99172749174104.234719612-1355.23471961179
100175692177019.630581484-1327.6305814845
101188451190470.727284626-2019.72728462607
102190416192081.169854188-1665.16985418825
103191047188004.2241497023042.77585029774
104194340189374.0543982434965.94560175698
105194340190959.6989850823380.30101491848
106195638192538.0174065023099.98259349752
107189749185151.156216534597.84378347037
108192696192768.77827421-72.7782742098789
109194656196474.553239328-1818.5532393285
110191047192381.095124959-1334.09512495936
111201527203432.021760548-1905.02176054826
112203491206625.849748342-3134.84974834218
113216567221181.445994528-4614.44599452772
114218878222626.829272265-3748.82927226502
115222140221483.523177848656.476822151657
116225087223822.3534036871264.64659631328
117225402222801.8989348272600.10106517302
118225749223615.6146096912133.38539030924
119219860215714.5778928144145.4221071857
120225749219501.6768377096247.323162291

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 34671 & 32695.6787588882 & 1975.32124111182 \tabularnewline
14 & 34035 & 32432.7410796965 & 1602.25892030347 \tabularnewline
15 & 35017 & 33577.1690563554 & 1439.83094364458 \tabularnewline
16 & 36631 & 35205.7347025111 & 1425.26529748895 \tabularnewline
17 & 45813 & 44065.5903596324 & 1747.40964036756 \tabularnewline
18 & 45813 & 44125.7907952681 & 1687.20920473185 \tabularnewline
19 & 43853 & 41288.6689761233 & 2564.33102387669 \tabularnewline
20 & 41888 & 38777.4876338929 & 3110.5123661071 \tabularnewline
21 & 43502 & 40748.7597666125 & 2753.24023338754 \tabularnewline
22 & 45466 & 42126.0667094451 & 3339.93329055486 \tabularnewline
23 & 45813 & 43917.7190635814 & 1895.2809364186 \tabularnewline
24 & 46795 & 45674.7747974616 & 1120.22520253844 \tabularnewline
25 & 49742 & 51298.8969557804 & -1556.89695578041 \tabularnewline
26 & 47777 & 49681.0200199166 & -1904.02001991656 \tabularnewline
27 & 47777 & 50322.9826094446 & -2545.98260944457 \tabularnewline
28 & 50724 & 51624.6998925508 & -900.699892550794 \tabularnewline
29 & 58893 & 63715.361079862 & -4822.36107986203 \tabularnewline
30 & 59555 & 61978.2557378779 & -2423.25573787791 \tabularnewline
31 & 57911 & 57799.6814299492 & 111.318570050767 \tabularnewline
32 & 53982 & 54009.7346393416 & -27.7346393416374 \tabularnewline
33 & 56928 & 54922.4526683689 & 2005.54733163109 \tabularnewline
34 & 56928 & 56499.5227668783 & 428.47723312171 \tabularnewline
35 & 57244 & 56064.5160053114 & 1179.48399468863 \tabularnewline
36 & 58893 & 56780.1120604638 & 2112.88793953615 \tabularnewline
37 & 60191 & 60796.9996095738 & -605.999609573759 \tabularnewline
38 & 60853 & 58369.71590645 & 2483.28409354998 \tabularnewline
39 & 60853 & 59262.26236759 & 1590.73763240995 \tabularnewline
40 & 62817 & 63315.1408716331 & -498.14087163315 \tabularnewline
41 & 70355 & 74382.1915154703 & -4027.1915154703 \tabularnewline
42 & 72315 & 74793.2432594624 & -2478.24325946244 \tabularnewline
43 & 72630 & 72021.4363273919 & 608.563672608056 \tabularnewline
44 & 67724 & 67127.2744277507 & 596.725572249314 \tabularnewline
45 & 70355 & 70249.2657017956 & 105.734298204377 \tabularnewline
46 & 69373 & 69989.8632938816 & -616.863293881557 \tabularnewline
47 & 67408 & 69745.8082752139 & -2337.80827521386 \tabularnewline
48 & 71653 & 70420.2560514637 & 1232.74394853627 \tabularnewline
49 & 72630 & 72116.6111866833 & 513.388813316662 \tabularnewline
50 & 70986 & 72113.8588804404 & -1127.85888044043 \tabularnewline
51 & 71333 & 71144.4328004761 & 188.567199523881 \tabularnewline
52 & 73613 & 73256.4470045753 & 356.552995424718 \tabularnewline
53 & 82133 & 82733.878876542 & -600.878876541989 \tabularnewline
54 & 86372 & 85227.9702671793 & 1144.02973282068 \tabularnewline
55 & 86372 & 85490.6012199638 & 881.39878003615 \tabularnewline
56 & 84412 & 79562.7146509453 & 4849.2853490547 \tabularnewline
57 & 87355 & 83611.2833724189 & 3743.71662758109 \tabularnewline
58 & 84412 & 83371.9549891182 & 1040.04501088183 \tabularnewline
59 & 82764 & 81829.095423432 & 934.90457656802 \tabularnewline
60 & 89004 & 86962.048161262 & 2041.95183873799 \tabularnewline
61 & 89981 & 88558.0125219977 & 1422.98747800234 \tabularnewline
62 & 87670 & 87255.902488557 & 414.097511443004 \tabularnewline
63 & 93559 & 87867.4931619309 & 5691.50683806908 \tabularnewline
64 & 95870 & 92097.5093241462 & 3772.49067585375 \tabularnewline
65 & 102741 & 104176.636779695 & -1435.6367796952 \tabularnewline
66 & 107301 & 109266.703368822 & -1965.7033688224 \tabularnewline
67 & 106670 & 108877.345109858 & -2207.3451098579 \tabularnewline
68 & 106319 & 104769.901012896 & 1549.09898710351 \tabularnewline
69 & 108950 & 107824.896349277 & 1125.10365072294 \tabularnewline
70 & 108630 & 104162.980192823 & 4467.01980717687 \tabularnewline
71 & 104706 & 102892.262278326 & 1813.73772167422 \tabularnewline
72 & 110594 & 110604.447821446 & -10.4478214457049 \tabularnewline
73 & 112559 & 111471.855612355 & 1087.14438764521 \tabularnewline
74 & 110594 & 108748.843561441 & 1845.15643855912 \tabularnewline
75 & 118763 & 114932.966269454 & 3830.03373054622 \tabularnewline
76 & 122692 & 117560.520051655 & 5131.47994834537 \tabularnewline
77 & 131839 & 127526.037612143 & 4312.96238785658 \tabularnewline
78 & 135448 & 134778.43281613 & 669.567183870298 \tabularnewline
79 & 134470 & 134878.676914925 & -408.676914924901 \tabularnewline
80 & 132505 & 134128.04308795 & -1623.04308794989 \tabularnewline
81 & 134150 & 136915.926396732 & -2765.92639673199 \tabularnewline
82 & 136114 & 134729.683730492 & 1384.31626950848 \tabularnewline
83 & 129559 & 129617.941315725 & -58.9413157246599 \tabularnewline
84 & 134785 & 136805.909392368 & -2020.90939236825 \tabularnewline
85 & 138079 & 138377.81704437 & -298.817044370255 \tabularnewline
86 & 136750 & 135253.163952812 & 1496.83604718803 \tabularnewline
87 & 145265 & 144380.27320841 & 884.726791590336 \tabularnewline
88 & 148207 & 147716.556563698 & 490.443436301663 \tabularnewline
89 & 160652 & 157316.330787524 & 3335.66921247618 \tabularnewline
90 & 162932 & 161764.740440319 & 1167.25955968135 \tabularnewline
91 & 159990 & 160553.204377797 & -563.204377796501 \tabularnewline
92 & 161634 & 158118.707315057 & 3515.29268494324 \tabularnewline
93 & 162616 & 161275.805092501 & 1340.19490749887 \tabularnewline
94 & 163598 & 163396.721818525 & 201.278181474801 \tabularnewline
95 & 157358 & 155398.109481752 & 1959.89051824767 \tabularnewline
96 & 163247 & 162471.045555437 & 775.954444563045 \tabularnewline
97 & 166509 & 166607.229142097 & -98.2291420973488 \tabularnewline
98 & 163247 & 164519.097352684 & -1272.09735268407 \tabularnewline
99 & 172749 & 174104.234719612 & -1355.23471961179 \tabularnewline
100 & 175692 & 177019.630581484 & -1327.6305814845 \tabularnewline
101 & 188451 & 190470.727284626 & -2019.72728462607 \tabularnewline
102 & 190416 & 192081.169854188 & -1665.16985418825 \tabularnewline
103 & 191047 & 188004.224149702 & 3042.77585029774 \tabularnewline
104 & 194340 & 189374.054398243 & 4965.94560175698 \tabularnewline
105 & 194340 & 190959.698985082 & 3380.30101491848 \tabularnewline
106 & 195638 & 192538.017406502 & 3099.98259349752 \tabularnewline
107 & 189749 & 185151.15621653 & 4597.84378347037 \tabularnewline
108 & 192696 & 192768.77827421 & -72.7782742098789 \tabularnewline
109 & 194656 & 196474.553239328 & -1818.5532393285 \tabularnewline
110 & 191047 & 192381.095124959 & -1334.09512495936 \tabularnewline
111 & 201527 & 203432.021760548 & -1905.02176054826 \tabularnewline
112 & 203491 & 206625.849748342 & -3134.84974834218 \tabularnewline
113 & 216567 & 221181.445994528 & -4614.44599452772 \tabularnewline
114 & 218878 & 222626.829272265 & -3748.82927226502 \tabularnewline
115 & 222140 & 221483.523177848 & 656.476822151657 \tabularnewline
116 & 225087 & 223822.353403687 & 1264.64659631328 \tabularnewline
117 & 225402 & 222801.898934827 & 2600.10106517302 \tabularnewline
118 & 225749 & 223615.614609691 & 2133.38539030924 \tabularnewline
119 & 219860 & 215714.577892814 & 4145.4221071857 \tabularnewline
120 & 225749 & 219501.676837709 & 6247.323162291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124139&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]34671[/C][C]32695.6787588882[/C][C]1975.32124111182[/C][/ROW]
[ROW][C]14[/C][C]34035[/C][C]32432.7410796965[/C][C]1602.25892030347[/C][/ROW]
[ROW][C]15[/C][C]35017[/C][C]33577.1690563554[/C][C]1439.83094364458[/C][/ROW]
[ROW][C]16[/C][C]36631[/C][C]35205.7347025111[/C][C]1425.26529748895[/C][/ROW]
[ROW][C]17[/C][C]45813[/C][C]44065.5903596324[/C][C]1747.40964036756[/C][/ROW]
[ROW][C]18[/C][C]45813[/C][C]44125.7907952681[/C][C]1687.20920473185[/C][/ROW]
[ROW][C]19[/C][C]43853[/C][C]41288.6689761233[/C][C]2564.33102387669[/C][/ROW]
[ROW][C]20[/C][C]41888[/C][C]38777.4876338929[/C][C]3110.5123661071[/C][/ROW]
[ROW][C]21[/C][C]43502[/C][C]40748.7597666125[/C][C]2753.24023338754[/C][/ROW]
[ROW][C]22[/C][C]45466[/C][C]42126.0667094451[/C][C]3339.93329055486[/C][/ROW]
[ROW][C]23[/C][C]45813[/C][C]43917.7190635814[/C][C]1895.2809364186[/C][/ROW]
[ROW][C]24[/C][C]46795[/C][C]45674.7747974616[/C][C]1120.22520253844[/C][/ROW]
[ROW][C]25[/C][C]49742[/C][C]51298.8969557804[/C][C]-1556.89695578041[/C][/ROW]
[ROW][C]26[/C][C]47777[/C][C]49681.0200199166[/C][C]-1904.02001991656[/C][/ROW]
[ROW][C]27[/C][C]47777[/C][C]50322.9826094446[/C][C]-2545.98260944457[/C][/ROW]
[ROW][C]28[/C][C]50724[/C][C]51624.6998925508[/C][C]-900.699892550794[/C][/ROW]
[ROW][C]29[/C][C]58893[/C][C]63715.361079862[/C][C]-4822.36107986203[/C][/ROW]
[ROW][C]30[/C][C]59555[/C][C]61978.2557378779[/C][C]-2423.25573787791[/C][/ROW]
[ROW][C]31[/C][C]57911[/C][C]57799.6814299492[/C][C]111.318570050767[/C][/ROW]
[ROW][C]32[/C][C]53982[/C][C]54009.7346393416[/C][C]-27.7346393416374[/C][/ROW]
[ROW][C]33[/C][C]56928[/C][C]54922.4526683689[/C][C]2005.54733163109[/C][/ROW]
[ROW][C]34[/C][C]56928[/C][C]56499.5227668783[/C][C]428.47723312171[/C][/ROW]
[ROW][C]35[/C][C]57244[/C][C]56064.5160053114[/C][C]1179.48399468863[/C][/ROW]
[ROW][C]36[/C][C]58893[/C][C]56780.1120604638[/C][C]2112.88793953615[/C][/ROW]
[ROW][C]37[/C][C]60191[/C][C]60796.9996095738[/C][C]-605.999609573759[/C][/ROW]
[ROW][C]38[/C][C]60853[/C][C]58369.71590645[/C][C]2483.28409354998[/C][/ROW]
[ROW][C]39[/C][C]60853[/C][C]59262.26236759[/C][C]1590.73763240995[/C][/ROW]
[ROW][C]40[/C][C]62817[/C][C]63315.1408716331[/C][C]-498.14087163315[/C][/ROW]
[ROW][C]41[/C][C]70355[/C][C]74382.1915154703[/C][C]-4027.1915154703[/C][/ROW]
[ROW][C]42[/C][C]72315[/C][C]74793.2432594624[/C][C]-2478.24325946244[/C][/ROW]
[ROW][C]43[/C][C]72630[/C][C]72021.4363273919[/C][C]608.563672608056[/C][/ROW]
[ROW][C]44[/C][C]67724[/C][C]67127.2744277507[/C][C]596.725572249314[/C][/ROW]
[ROW][C]45[/C][C]70355[/C][C]70249.2657017956[/C][C]105.734298204377[/C][/ROW]
[ROW][C]46[/C][C]69373[/C][C]69989.8632938816[/C][C]-616.863293881557[/C][/ROW]
[ROW][C]47[/C][C]67408[/C][C]69745.8082752139[/C][C]-2337.80827521386[/C][/ROW]
[ROW][C]48[/C][C]71653[/C][C]70420.2560514637[/C][C]1232.74394853627[/C][/ROW]
[ROW][C]49[/C][C]72630[/C][C]72116.6111866833[/C][C]513.388813316662[/C][/ROW]
[ROW][C]50[/C][C]70986[/C][C]72113.8588804404[/C][C]-1127.85888044043[/C][/ROW]
[ROW][C]51[/C][C]71333[/C][C]71144.4328004761[/C][C]188.567199523881[/C][/ROW]
[ROW][C]52[/C][C]73613[/C][C]73256.4470045753[/C][C]356.552995424718[/C][/ROW]
[ROW][C]53[/C][C]82133[/C][C]82733.878876542[/C][C]-600.878876541989[/C][/ROW]
[ROW][C]54[/C][C]86372[/C][C]85227.9702671793[/C][C]1144.02973282068[/C][/ROW]
[ROW][C]55[/C][C]86372[/C][C]85490.6012199638[/C][C]881.39878003615[/C][/ROW]
[ROW][C]56[/C][C]84412[/C][C]79562.7146509453[/C][C]4849.2853490547[/C][/ROW]
[ROW][C]57[/C][C]87355[/C][C]83611.2833724189[/C][C]3743.71662758109[/C][/ROW]
[ROW][C]58[/C][C]84412[/C][C]83371.9549891182[/C][C]1040.04501088183[/C][/ROW]
[ROW][C]59[/C][C]82764[/C][C]81829.095423432[/C][C]934.90457656802[/C][/ROW]
[ROW][C]60[/C][C]89004[/C][C]86962.048161262[/C][C]2041.95183873799[/C][/ROW]
[ROW][C]61[/C][C]89981[/C][C]88558.0125219977[/C][C]1422.98747800234[/C][/ROW]
[ROW][C]62[/C][C]87670[/C][C]87255.902488557[/C][C]414.097511443004[/C][/ROW]
[ROW][C]63[/C][C]93559[/C][C]87867.4931619309[/C][C]5691.50683806908[/C][/ROW]
[ROW][C]64[/C][C]95870[/C][C]92097.5093241462[/C][C]3772.49067585375[/C][/ROW]
[ROW][C]65[/C][C]102741[/C][C]104176.636779695[/C][C]-1435.6367796952[/C][/ROW]
[ROW][C]66[/C][C]107301[/C][C]109266.703368822[/C][C]-1965.7033688224[/C][/ROW]
[ROW][C]67[/C][C]106670[/C][C]108877.345109858[/C][C]-2207.3451098579[/C][/ROW]
[ROW][C]68[/C][C]106319[/C][C]104769.901012896[/C][C]1549.09898710351[/C][/ROW]
[ROW][C]69[/C][C]108950[/C][C]107824.896349277[/C][C]1125.10365072294[/C][/ROW]
[ROW][C]70[/C][C]108630[/C][C]104162.980192823[/C][C]4467.01980717687[/C][/ROW]
[ROW][C]71[/C][C]104706[/C][C]102892.262278326[/C][C]1813.73772167422[/C][/ROW]
[ROW][C]72[/C][C]110594[/C][C]110604.447821446[/C][C]-10.4478214457049[/C][/ROW]
[ROW][C]73[/C][C]112559[/C][C]111471.855612355[/C][C]1087.14438764521[/C][/ROW]
[ROW][C]74[/C][C]110594[/C][C]108748.843561441[/C][C]1845.15643855912[/C][/ROW]
[ROW][C]75[/C][C]118763[/C][C]114932.966269454[/C][C]3830.03373054622[/C][/ROW]
[ROW][C]76[/C][C]122692[/C][C]117560.520051655[/C][C]5131.47994834537[/C][/ROW]
[ROW][C]77[/C][C]131839[/C][C]127526.037612143[/C][C]4312.96238785658[/C][/ROW]
[ROW][C]78[/C][C]135448[/C][C]134778.43281613[/C][C]669.567183870298[/C][/ROW]
[ROW][C]79[/C][C]134470[/C][C]134878.676914925[/C][C]-408.676914924901[/C][/ROW]
[ROW][C]80[/C][C]132505[/C][C]134128.04308795[/C][C]-1623.04308794989[/C][/ROW]
[ROW][C]81[/C][C]134150[/C][C]136915.926396732[/C][C]-2765.92639673199[/C][/ROW]
[ROW][C]82[/C][C]136114[/C][C]134729.683730492[/C][C]1384.31626950848[/C][/ROW]
[ROW][C]83[/C][C]129559[/C][C]129617.941315725[/C][C]-58.9413157246599[/C][/ROW]
[ROW][C]84[/C][C]134785[/C][C]136805.909392368[/C][C]-2020.90939236825[/C][/ROW]
[ROW][C]85[/C][C]138079[/C][C]138377.81704437[/C][C]-298.817044370255[/C][/ROW]
[ROW][C]86[/C][C]136750[/C][C]135253.163952812[/C][C]1496.83604718803[/C][/ROW]
[ROW][C]87[/C][C]145265[/C][C]144380.27320841[/C][C]884.726791590336[/C][/ROW]
[ROW][C]88[/C][C]148207[/C][C]147716.556563698[/C][C]490.443436301663[/C][/ROW]
[ROW][C]89[/C][C]160652[/C][C]157316.330787524[/C][C]3335.66921247618[/C][/ROW]
[ROW][C]90[/C][C]162932[/C][C]161764.740440319[/C][C]1167.25955968135[/C][/ROW]
[ROW][C]91[/C][C]159990[/C][C]160553.204377797[/C][C]-563.204377796501[/C][/ROW]
[ROW][C]92[/C][C]161634[/C][C]158118.707315057[/C][C]3515.29268494324[/C][/ROW]
[ROW][C]93[/C][C]162616[/C][C]161275.805092501[/C][C]1340.19490749887[/C][/ROW]
[ROW][C]94[/C][C]163598[/C][C]163396.721818525[/C][C]201.278181474801[/C][/ROW]
[ROW][C]95[/C][C]157358[/C][C]155398.109481752[/C][C]1959.89051824767[/C][/ROW]
[ROW][C]96[/C][C]163247[/C][C]162471.045555437[/C][C]775.954444563045[/C][/ROW]
[ROW][C]97[/C][C]166509[/C][C]166607.229142097[/C][C]-98.2291420973488[/C][/ROW]
[ROW][C]98[/C][C]163247[/C][C]164519.097352684[/C][C]-1272.09735268407[/C][/ROW]
[ROW][C]99[/C][C]172749[/C][C]174104.234719612[/C][C]-1355.23471961179[/C][/ROW]
[ROW][C]100[/C][C]175692[/C][C]177019.630581484[/C][C]-1327.6305814845[/C][/ROW]
[ROW][C]101[/C][C]188451[/C][C]190470.727284626[/C][C]-2019.72728462607[/C][/ROW]
[ROW][C]102[/C][C]190416[/C][C]192081.169854188[/C][C]-1665.16985418825[/C][/ROW]
[ROW][C]103[/C][C]191047[/C][C]188004.224149702[/C][C]3042.77585029774[/C][/ROW]
[ROW][C]104[/C][C]194340[/C][C]189374.054398243[/C][C]4965.94560175698[/C][/ROW]
[ROW][C]105[/C][C]194340[/C][C]190959.698985082[/C][C]3380.30101491848[/C][/ROW]
[ROW][C]106[/C][C]195638[/C][C]192538.017406502[/C][C]3099.98259349752[/C][/ROW]
[ROW][C]107[/C][C]189749[/C][C]185151.15621653[/C][C]4597.84378347037[/C][/ROW]
[ROW][C]108[/C][C]192696[/C][C]192768.77827421[/C][C]-72.7782742098789[/C][/ROW]
[ROW][C]109[/C][C]194656[/C][C]196474.553239328[/C][C]-1818.5532393285[/C][/ROW]
[ROW][C]110[/C][C]191047[/C][C]192381.095124959[/C][C]-1334.09512495936[/C][/ROW]
[ROW][C]111[/C][C]201527[/C][C]203432.021760548[/C][C]-1905.02176054826[/C][/ROW]
[ROW][C]112[/C][C]203491[/C][C]206625.849748342[/C][C]-3134.84974834218[/C][/ROW]
[ROW][C]113[/C][C]216567[/C][C]221181.445994528[/C][C]-4614.44599452772[/C][/ROW]
[ROW][C]114[/C][C]218878[/C][C]222626.829272265[/C][C]-3748.82927226502[/C][/ROW]
[ROW][C]115[/C][C]222140[/C][C]221483.523177848[/C][C]656.476822151657[/C][/ROW]
[ROW][C]116[/C][C]225087[/C][C]223822.353403687[/C][C]1264.64659631328[/C][/ROW]
[ROW][C]117[/C][C]225402[/C][C]222801.898934827[/C][C]2600.10106517302[/C][/ROW]
[ROW][C]118[/C][C]225749[/C][C]223615.614609691[/C][C]2133.38539030924[/C][/ROW]
[ROW][C]119[/C][C]219860[/C][C]215714.577892814[/C][C]4145.4221071857[/C][/ROW]
[ROW][C]120[/C][C]225749[/C][C]219501.676837709[/C][C]6247.323162291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124139&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124139&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
133467132695.67875888821975.32124111182
143403532432.74107969651602.25892030347
153501733577.16905635541439.83094364458
163663135205.73470251111425.26529748895
174581344065.59035963241747.40964036756
184581344125.79079526811687.20920473185
194385341288.66897612332564.33102387669
204188838777.48763389293110.5123661071
214350240748.75976661252753.24023338754
224546642126.06670944513339.93329055486
234581343917.71906358141895.2809364186
244679545674.77479746161120.22520253844
254974251298.8969557804-1556.89695578041
264777749681.0200199166-1904.02001991656
274777750322.9826094446-2545.98260944457
285072451624.6998925508-900.699892550794
295889363715.361079862-4822.36107986203
305955561978.2557378779-2423.25573787791
315791157799.6814299492111.318570050767
325398254009.7346393416-27.7346393416374
335692854922.45266836892005.54733163109
345692856499.5227668783428.47723312171
355724456064.51600531141179.48399468863
365889356780.11206046382112.88793953615
376019160796.9996095738-605.999609573759
386085358369.715906452483.28409354998
396085359262.262367591590.73763240995
406281763315.1408716331-498.14087163315
417035574382.1915154703-4027.1915154703
427231574793.2432594624-2478.24325946244
437263072021.4363273919608.563672608056
446772467127.2744277507596.725572249314
457035570249.2657017956105.734298204377
466937369989.8632938816-616.863293881557
476740869745.8082752139-2337.80827521386
487165370420.25605146371232.74394853627
497263072116.6111866833513.388813316662
507098672113.8588804404-1127.85888044043
517133371144.4328004761188.567199523881
527361373256.4470045753356.552995424718
538213382733.878876542-600.878876541989
548637285227.97026717931144.02973282068
558637285490.6012199638881.39878003615
568441279562.71465094534849.2853490547
578735583611.28337241893743.71662758109
588441283371.95498911821040.04501088183
598276481829.095423432934.90457656802
608900486962.0481612622041.95183873799
618998188558.01252199771422.98747800234
628767087255.902488557414.097511443004
639355987867.49316193095691.50683806908
649587092097.50932414623772.49067585375
65102741104176.636779695-1435.6367796952
66107301109266.703368822-1965.7033688224
67106670108877.345109858-2207.3451098579
68106319104769.9010128961549.09898710351
69108950107824.8963492771125.10365072294
70108630104162.9801928234467.01980717687
71104706102892.2622783261813.73772167422
72110594110604.447821446-10.4478214457049
73112559111471.8556123551087.14438764521
74110594108748.8435614411845.15643855912
75118763114932.9662694543830.03373054622
76122692117560.5200516555131.47994834537
77131839127526.0376121434312.96238785658
78135448134778.43281613669.567183870298
79134470134878.676914925-408.676914924901
80132505134128.04308795-1623.04308794989
81134150136915.926396732-2765.92639673199
82136114134729.6837304921384.31626950848
83129559129617.941315725-58.9413157246599
84134785136805.909392368-2020.90939236825
85138079138377.81704437-298.817044370255
86136750135253.1639528121496.83604718803
87145265144380.27320841884.726791590336
88148207147716.556563698490.443436301663
89160652157316.3307875243335.66921247618
90162932161764.7404403191167.25955968135
91159990160553.204377797-563.204377796501
92161634158118.7073150573515.29268494324
93162616161275.8050925011340.19490749887
94163598163396.721818525201.278181474801
95157358155398.1094817521959.89051824767
96163247162471.045555437775.954444563045
97166509166607.229142097-98.2291420973488
98163247164519.097352684-1272.09735268407
99172749174104.234719612-1355.23471961179
100175692177019.630581484-1327.6305814845
101188451190470.727284626-2019.72728462607
102190416192081.169854188-1665.16985418825
103191047188004.2241497023042.77585029774
104194340189374.0543982434965.94560175698
105194340190959.6989850823380.30101491848
106195638192538.0174065023099.98259349752
107189749185151.156216534597.84378347037
108192696192768.77827421-72.7782742098789
109194656196474.553239328-1818.5532393285
110191047192381.095124959-1334.09512495936
111201527203432.021760548-1905.02176054826
112203491206625.849748342-3134.84974834218
113216567221181.445994528-4614.44599452772
114218878222626.829272265-3748.82927226502
115222140221483.523177848656.476822151657
116225087223822.3534036871264.64659631328
117225402222801.8989348272600.10106517302
118225749223615.6146096912133.38539030924
119219860215714.5778928144145.4221071857
120225749219501.6768377096247.323162291







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121223181.869663087218724.056267944227639.68305823
122219077.683980778214503.1327205223652.235241056
123231291.073555692226550.184936854236031.962174529
124234085.433505686229175.35307372238995.513937652
125250092.188267394244922.569926011255261.806608778
126253632.234893972248237.380063161259027.089724783
127257294.6663469251651.339256487262937.993437313
128260422.341137772254513.890569818266330.791705726
129260134.959827236253980.075497412266289.844157061
130259940.080504546253526.784989341266353.376019751
131252010.995918223245438.812407408258583.179429038
132256981.556220405251683.470115602262279.642325208

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 223181.869663087 & 218724.056267944 & 227639.68305823 \tabularnewline
122 & 219077.683980778 & 214503.1327205 & 223652.235241056 \tabularnewline
123 & 231291.073555692 & 226550.184936854 & 236031.962174529 \tabularnewline
124 & 234085.433505686 & 229175.35307372 & 238995.513937652 \tabularnewline
125 & 250092.188267394 & 244922.569926011 & 255261.806608778 \tabularnewline
126 & 253632.234893972 & 248237.380063161 & 259027.089724783 \tabularnewline
127 & 257294.6663469 & 251651.339256487 & 262937.993437313 \tabularnewline
128 & 260422.341137772 & 254513.890569818 & 266330.791705726 \tabularnewline
129 & 260134.959827236 & 253980.075497412 & 266289.844157061 \tabularnewline
130 & 259940.080504546 & 253526.784989341 & 266353.376019751 \tabularnewline
131 & 252010.995918223 & 245438.812407408 & 258583.179429038 \tabularnewline
132 & 256981.556220405 & 251683.470115602 & 262279.642325208 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124139&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]223181.869663087[/C][C]218724.056267944[/C][C]227639.68305823[/C][/ROW]
[ROW][C]122[/C][C]219077.683980778[/C][C]214503.1327205[/C][C]223652.235241056[/C][/ROW]
[ROW][C]123[/C][C]231291.073555692[/C][C]226550.184936854[/C][C]236031.962174529[/C][/ROW]
[ROW][C]124[/C][C]234085.433505686[/C][C]229175.35307372[/C][C]238995.513937652[/C][/ROW]
[ROW][C]125[/C][C]250092.188267394[/C][C]244922.569926011[/C][C]255261.806608778[/C][/ROW]
[ROW][C]126[/C][C]253632.234893972[/C][C]248237.380063161[/C][C]259027.089724783[/C][/ROW]
[ROW][C]127[/C][C]257294.6663469[/C][C]251651.339256487[/C][C]262937.993437313[/C][/ROW]
[ROW][C]128[/C][C]260422.341137772[/C][C]254513.890569818[/C][C]266330.791705726[/C][/ROW]
[ROW][C]129[/C][C]260134.959827236[/C][C]253980.075497412[/C][C]266289.844157061[/C][/ROW]
[ROW][C]130[/C][C]259940.080504546[/C][C]253526.784989341[/C][C]266353.376019751[/C][/ROW]
[ROW][C]131[/C][C]252010.995918223[/C][C]245438.812407408[/C][C]258583.179429038[/C][/ROW]
[ROW][C]132[/C][C]256981.556220405[/C][C]251683.470115602[/C][C]262279.642325208[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124139&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124139&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
121223181.869663087218724.056267944227639.68305823
122219077.683980778214503.1327205223652.235241056
123231291.073555692226550.184936854236031.962174529
124234085.433505686229175.35307372238995.513937652
125250092.188267394244922.569926011255261.806608778
126253632.234893972248237.380063161259027.089724783
127257294.6663469251651.339256487262937.993437313
128260422.341137772254513.890569818266330.791705726
129260134.959827236253980.075497412266289.844157061
130259940.080504546253526.784989341266353.376019751
131252010.995918223245438.812407408258583.179429038
132256981.556220405251683.470115602262279.642325208



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')