Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 17 Aug 2011 09:34:21 -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/17/t1313588348tso1jolw6mbircm.htm/, Retrieved Wed, 15 May 2024 11:45:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123944, Retrieved Wed, 15 May 2024 11:45:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSimons Thomas
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdsreeks A - St...] [2011-08-17 13:34:21] [93a9440e82e53db41c1ce1bc7dd7ea5d] [Current]
Feedback Forum

Post a new message
Dataseries X:
161949
161634
161287
160652
167176
166856
161949
158687
159007
159007
159323
159990
159990
157043
155745
157043
161634
160967
154763
149510
148527
146563
147892
149510
148874
147545
144950
147545
149856
149190
141656
138394
135132
132505
132190
134150
131523
130541
129559
135132
135768
132505
123670
119745
113541
110910
112208
114172
114172
112559
112208
117465
121710
119745
113190
109932
103061
98817
102079
105341
105341
101097
100781
106319
109932
108630
102079
97835
88652
85075
86372
91946
92261
84092
87039
94226
97488
95523
86692
80484
73297
67724
70004
74910
73613
66426
68706
75893
79821
77541
68706
64782
58893
52684
53666
58573
59208
53319
54302
62502
64462
61173
49075
42871
34671
26502
29129
32706
32075
25835
29444
38280
42204
40244
32391
26186
19631
12093
13427
15707




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=123944&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=123944&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123944&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
alpha0.380162943418784
beta0.0252555708748419
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.380162943418784 \tabularnewline
beta & 0.0252555708748419 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123944&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]0.380162943418784[/C][/ROW]
[ROW][C]beta[/C][C]0.0252555708748419[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123944&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123944&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
alpha0.380162943418784
beta0.0252555708748419
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13159990162550.762372001-2560.76237200139
14157043158651.547560092-1608.54756009195
15155745156903.033399486-1158.03339948563
16157043158063.029557448-1020.02955744808
17161634162622.24725181-988.247251809982
18160967161819.817364787-852.817364787188
19154763154897.903296482-134.903296482138
20149510151302.622567946-1792.622567946
21148527150618.890428095-2091.89042809515
22146563149455.650012797-2892.65001279686
23147892148249.812137062-357.812137061759
24149510148413.8531547731096.14684522743
25148874147124.8543649951749.14563500453
26147545145485.5073389282059.492661072
27144950145363.332198204-413.332198204473
28147545146677.614497319867.385502680641
29149856151573.61287254-1717.61287254034
30149190150508.32156174-1318.32156173993
31141656144179.046420805-2523.04642080484
32138394138865.940641762-471.940641761961
33135132138399.694714824-3267.69471482374
34132505136224.960530891-3719.96053089137
35132190136020.961740508-3830.96174050783
36134150135475.175351774-1325.17535177374
37131523133584.869876047-2061.86987604664
38130541130662.692766616-121.692766615961
39129559128189.1483660511369.851633949
40135132130464.8300631064667.16993689425
41135768134674.0143215971093.98567840262
42132505134749.724709249-2244.72470924855
43123670127791.691925047-4121.69192504717
44119745123263.882841257-3518.88284125658
45113541119881.861713675-6340.86171367478
46110910116105.595312279-5195.59531227876
47112208114770.627842514-2562.6278425137
48114172115592.136996456-1420.13699645559
49114172113139.2033961061032.79660389424
50112559112430.07814195128.921858050075
51112208110889.4917218431318.50827815663
52117465114320.6439049923144.35609500756
53121710115383.6168935786326.3831064218
54119745115437.3658711714307.63412882861
55113190110454.7667861682735.23321383193
56109932109047.605058027884.394941972743
57103061105802.219523967-2741.21952396705
5898817104096.826161959-5279.82616195935
59102079104153.323973151-2074.32397315078
60105341105654.952594233-313.95259423292
61105341105170.961486502170.03851349774
62101097103693.62524757-2596.62524756957
63100781101879.386969109-1098.3869691093
64106319105035.6981371751283.30186282546
65109932106999.7189006172932.28109938311
66108630104740.7081394493889.29186055085
6710207999334.34925782952744.65074217053
689783597060.6105715456774.389428454393
698865292054.4597791024-3402.45977910244
708507588598.9119933468-3523.91199334679
718637290697.118495135-4325.11849513496
729194691830.8958840459115.104115954135
739226191648.5759905587612.424009441325
748409288865.6459259625-4773.64592596248
758703986936.5496454361102.450354563916
769422691131.8913036063094.108696394
779748894280.85998595443207.14001404557
789552392884.5922317422638.40776825804
798669287136.5474311243-444.547431124331
808048482896.2294623845-2412.22946238452
817329775115.2282884679-1818.22828846793
826772472303.8170163615-4579.81701636149
837000472711.5005488218-2707.50054882184
847491076011.6597416163-1101.65974161631
857361375376.4046960111-1763.40469601107
866642669211.6389023995-2785.63890239947
876870670206.3475403187-1500.34754031875
887589374068.77280261641824.22719738363
897982175979.58139577993841.41860422015
907754174705.12853916422835.8714608358
916870668581.8441159252124.155884074804
926478264117.5082197722664.491780227814
935889358908.4102523354-15.4102523354377
945268455535.8321405311-2851.83214053106
955366656854.7578932452-3188.75789324518
965857359590.3824455754-1017.38244557541
975920858410.6821658542797.31783414579
985331953561.9512933523-242.951293352256
995430255528.5945562925-1226.59455629254
1006250259997.6355041392504.36449586099
1016446262634.7515657591827.24843424097
1026117360366.4165351146806.583464885378
1034907553446.7882280464-4371.7882280464
1044287148299.9653125839-5428.96531258389
1053467141634.7092672294-6963.70926722935
1062650235088.5607652114-8586.56076521142
1072912932485.2492524932-3356.2492524932
1083270633528.3182824135-822.318282413529
1093207532605.9958874836-530.995887483583
1102583528468.0419484631-2633.0419484631
1112944427347.74116079342096.2588392066
1123828030924.48960495547355.51039504459
1134220433481.43865518518722.56134481492
1144024433973.07385569136270.92614430872
1153239129524.17005042892866.82994957114
1162618627476.1053042792-1290.10530427918
1171963122918.0790647287-3287.07906472869
1181209317925.9058338286-5832.90583382863
1191342717519.2833701927-4092.2833701927
1201570717470.09254933-1763.09254933003

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 159990 & 162550.762372001 & -2560.76237200139 \tabularnewline
14 & 157043 & 158651.547560092 & -1608.54756009195 \tabularnewline
15 & 155745 & 156903.033399486 & -1158.03339948563 \tabularnewline
16 & 157043 & 158063.029557448 & -1020.02955744808 \tabularnewline
17 & 161634 & 162622.24725181 & -988.247251809982 \tabularnewline
18 & 160967 & 161819.817364787 & -852.817364787188 \tabularnewline
19 & 154763 & 154897.903296482 & -134.903296482138 \tabularnewline
20 & 149510 & 151302.622567946 & -1792.622567946 \tabularnewline
21 & 148527 & 150618.890428095 & -2091.89042809515 \tabularnewline
22 & 146563 & 149455.650012797 & -2892.65001279686 \tabularnewline
23 & 147892 & 148249.812137062 & -357.812137061759 \tabularnewline
24 & 149510 & 148413.853154773 & 1096.14684522743 \tabularnewline
25 & 148874 & 147124.854364995 & 1749.14563500453 \tabularnewline
26 & 147545 & 145485.507338928 & 2059.492661072 \tabularnewline
27 & 144950 & 145363.332198204 & -413.332198204473 \tabularnewline
28 & 147545 & 146677.614497319 & 867.385502680641 \tabularnewline
29 & 149856 & 151573.61287254 & -1717.61287254034 \tabularnewline
30 & 149190 & 150508.32156174 & -1318.32156173993 \tabularnewline
31 & 141656 & 144179.046420805 & -2523.04642080484 \tabularnewline
32 & 138394 & 138865.940641762 & -471.940641761961 \tabularnewline
33 & 135132 & 138399.694714824 & -3267.69471482374 \tabularnewline
34 & 132505 & 136224.960530891 & -3719.96053089137 \tabularnewline
35 & 132190 & 136020.961740508 & -3830.96174050783 \tabularnewline
36 & 134150 & 135475.175351774 & -1325.17535177374 \tabularnewline
37 & 131523 & 133584.869876047 & -2061.86987604664 \tabularnewline
38 & 130541 & 130662.692766616 & -121.692766615961 \tabularnewline
39 & 129559 & 128189.148366051 & 1369.851633949 \tabularnewline
40 & 135132 & 130464.830063106 & 4667.16993689425 \tabularnewline
41 & 135768 & 134674.014321597 & 1093.98567840262 \tabularnewline
42 & 132505 & 134749.724709249 & -2244.72470924855 \tabularnewline
43 & 123670 & 127791.691925047 & -4121.69192504717 \tabularnewline
44 & 119745 & 123263.882841257 & -3518.88284125658 \tabularnewline
45 & 113541 & 119881.861713675 & -6340.86171367478 \tabularnewline
46 & 110910 & 116105.595312279 & -5195.59531227876 \tabularnewline
47 & 112208 & 114770.627842514 & -2562.6278425137 \tabularnewline
48 & 114172 & 115592.136996456 & -1420.13699645559 \tabularnewline
49 & 114172 & 113139.203396106 & 1032.79660389424 \tabularnewline
50 & 112559 & 112430.07814195 & 128.921858050075 \tabularnewline
51 & 112208 & 110889.491721843 & 1318.50827815663 \tabularnewline
52 & 117465 & 114320.643904992 & 3144.35609500756 \tabularnewline
53 & 121710 & 115383.616893578 & 6326.3831064218 \tabularnewline
54 & 119745 & 115437.365871171 & 4307.63412882861 \tabularnewline
55 & 113190 & 110454.766786168 & 2735.23321383193 \tabularnewline
56 & 109932 & 109047.605058027 & 884.394941972743 \tabularnewline
57 & 103061 & 105802.219523967 & -2741.21952396705 \tabularnewline
58 & 98817 & 104096.826161959 & -5279.82616195935 \tabularnewline
59 & 102079 & 104153.323973151 & -2074.32397315078 \tabularnewline
60 & 105341 & 105654.952594233 & -313.95259423292 \tabularnewline
61 & 105341 & 105170.961486502 & 170.03851349774 \tabularnewline
62 & 101097 & 103693.62524757 & -2596.62524756957 \tabularnewline
63 & 100781 & 101879.386969109 & -1098.3869691093 \tabularnewline
64 & 106319 & 105035.698137175 & 1283.30186282546 \tabularnewline
65 & 109932 & 106999.718900617 & 2932.28109938311 \tabularnewline
66 & 108630 & 104740.708139449 & 3889.29186055085 \tabularnewline
67 & 102079 & 99334.3492578295 & 2744.65074217053 \tabularnewline
68 & 97835 & 97060.6105715456 & 774.389428454393 \tabularnewline
69 & 88652 & 92054.4597791024 & -3402.45977910244 \tabularnewline
70 & 85075 & 88598.9119933468 & -3523.91199334679 \tabularnewline
71 & 86372 & 90697.118495135 & -4325.11849513496 \tabularnewline
72 & 91946 & 91830.8958840459 & 115.104115954135 \tabularnewline
73 & 92261 & 91648.5759905587 & 612.424009441325 \tabularnewline
74 & 84092 & 88865.6459259625 & -4773.64592596248 \tabularnewline
75 & 87039 & 86936.5496454361 & 102.450354563916 \tabularnewline
76 & 94226 & 91131.891303606 & 3094.108696394 \tabularnewline
77 & 97488 & 94280.8599859544 & 3207.14001404557 \tabularnewline
78 & 95523 & 92884.592231742 & 2638.40776825804 \tabularnewline
79 & 86692 & 87136.5474311243 & -444.547431124331 \tabularnewline
80 & 80484 & 82896.2294623845 & -2412.22946238452 \tabularnewline
81 & 73297 & 75115.2282884679 & -1818.22828846793 \tabularnewline
82 & 67724 & 72303.8170163615 & -4579.81701636149 \tabularnewline
83 & 70004 & 72711.5005488218 & -2707.50054882184 \tabularnewline
84 & 74910 & 76011.6597416163 & -1101.65974161631 \tabularnewline
85 & 73613 & 75376.4046960111 & -1763.40469601107 \tabularnewline
86 & 66426 & 69211.6389023995 & -2785.63890239947 \tabularnewline
87 & 68706 & 70206.3475403187 & -1500.34754031875 \tabularnewline
88 & 75893 & 74068.7728026164 & 1824.22719738363 \tabularnewline
89 & 79821 & 75979.5813957799 & 3841.41860422015 \tabularnewline
90 & 77541 & 74705.1285391642 & 2835.8714608358 \tabularnewline
91 & 68706 & 68581.8441159252 & 124.155884074804 \tabularnewline
92 & 64782 & 64117.5082197722 & 664.491780227814 \tabularnewline
93 & 58893 & 58908.4102523354 & -15.4102523354377 \tabularnewline
94 & 52684 & 55535.8321405311 & -2851.83214053106 \tabularnewline
95 & 53666 & 56854.7578932452 & -3188.75789324518 \tabularnewline
96 & 58573 & 59590.3824455754 & -1017.38244557541 \tabularnewline
97 & 59208 & 58410.6821658542 & 797.31783414579 \tabularnewline
98 & 53319 & 53561.9512933523 & -242.951293352256 \tabularnewline
99 & 54302 & 55528.5945562925 & -1226.59455629254 \tabularnewline
100 & 62502 & 59997.635504139 & 2504.36449586099 \tabularnewline
101 & 64462 & 62634.751565759 & 1827.24843424097 \tabularnewline
102 & 61173 & 60366.4165351146 & 806.583464885378 \tabularnewline
103 & 49075 & 53446.7882280464 & -4371.7882280464 \tabularnewline
104 & 42871 & 48299.9653125839 & -5428.96531258389 \tabularnewline
105 & 34671 & 41634.7092672294 & -6963.70926722935 \tabularnewline
106 & 26502 & 35088.5607652114 & -8586.56076521142 \tabularnewline
107 & 29129 & 32485.2492524932 & -3356.2492524932 \tabularnewline
108 & 32706 & 33528.3182824135 & -822.318282413529 \tabularnewline
109 & 32075 & 32605.9958874836 & -530.995887483583 \tabularnewline
110 & 25835 & 28468.0419484631 & -2633.0419484631 \tabularnewline
111 & 29444 & 27347.7411607934 & 2096.2588392066 \tabularnewline
112 & 38280 & 30924.4896049554 & 7355.51039504459 \tabularnewline
113 & 42204 & 33481.4386551851 & 8722.56134481492 \tabularnewline
114 & 40244 & 33973.0738556913 & 6270.92614430872 \tabularnewline
115 & 32391 & 29524.1700504289 & 2866.82994957114 \tabularnewline
116 & 26186 & 27476.1053042792 & -1290.10530427918 \tabularnewline
117 & 19631 & 22918.0790647287 & -3287.07906472869 \tabularnewline
118 & 12093 & 17925.9058338286 & -5832.90583382863 \tabularnewline
119 & 13427 & 17519.2833701927 & -4092.2833701927 \tabularnewline
120 & 15707 & 17470.09254933 & -1763.09254933003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123944&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]159990[/C][C]162550.762372001[/C][C]-2560.76237200139[/C][/ROW]
[ROW][C]14[/C][C]157043[/C][C]158651.547560092[/C][C]-1608.54756009195[/C][/ROW]
[ROW][C]15[/C][C]155745[/C][C]156903.033399486[/C][C]-1158.03339948563[/C][/ROW]
[ROW][C]16[/C][C]157043[/C][C]158063.029557448[/C][C]-1020.02955744808[/C][/ROW]
[ROW][C]17[/C][C]161634[/C][C]162622.24725181[/C][C]-988.247251809982[/C][/ROW]
[ROW][C]18[/C][C]160967[/C][C]161819.817364787[/C][C]-852.817364787188[/C][/ROW]
[ROW][C]19[/C][C]154763[/C][C]154897.903296482[/C][C]-134.903296482138[/C][/ROW]
[ROW][C]20[/C][C]149510[/C][C]151302.622567946[/C][C]-1792.622567946[/C][/ROW]
[ROW][C]21[/C][C]148527[/C][C]150618.890428095[/C][C]-2091.89042809515[/C][/ROW]
[ROW][C]22[/C][C]146563[/C][C]149455.650012797[/C][C]-2892.65001279686[/C][/ROW]
[ROW][C]23[/C][C]147892[/C][C]148249.812137062[/C][C]-357.812137061759[/C][/ROW]
[ROW][C]24[/C][C]149510[/C][C]148413.853154773[/C][C]1096.14684522743[/C][/ROW]
[ROW][C]25[/C][C]148874[/C][C]147124.854364995[/C][C]1749.14563500453[/C][/ROW]
[ROW][C]26[/C][C]147545[/C][C]145485.507338928[/C][C]2059.492661072[/C][/ROW]
[ROW][C]27[/C][C]144950[/C][C]145363.332198204[/C][C]-413.332198204473[/C][/ROW]
[ROW][C]28[/C][C]147545[/C][C]146677.614497319[/C][C]867.385502680641[/C][/ROW]
[ROW][C]29[/C][C]149856[/C][C]151573.61287254[/C][C]-1717.61287254034[/C][/ROW]
[ROW][C]30[/C][C]149190[/C][C]150508.32156174[/C][C]-1318.32156173993[/C][/ROW]
[ROW][C]31[/C][C]141656[/C][C]144179.046420805[/C][C]-2523.04642080484[/C][/ROW]
[ROW][C]32[/C][C]138394[/C][C]138865.940641762[/C][C]-471.940641761961[/C][/ROW]
[ROW][C]33[/C][C]135132[/C][C]138399.694714824[/C][C]-3267.69471482374[/C][/ROW]
[ROW][C]34[/C][C]132505[/C][C]136224.960530891[/C][C]-3719.96053089137[/C][/ROW]
[ROW][C]35[/C][C]132190[/C][C]136020.961740508[/C][C]-3830.96174050783[/C][/ROW]
[ROW][C]36[/C][C]134150[/C][C]135475.175351774[/C][C]-1325.17535177374[/C][/ROW]
[ROW][C]37[/C][C]131523[/C][C]133584.869876047[/C][C]-2061.86987604664[/C][/ROW]
[ROW][C]38[/C][C]130541[/C][C]130662.692766616[/C][C]-121.692766615961[/C][/ROW]
[ROW][C]39[/C][C]129559[/C][C]128189.148366051[/C][C]1369.851633949[/C][/ROW]
[ROW][C]40[/C][C]135132[/C][C]130464.830063106[/C][C]4667.16993689425[/C][/ROW]
[ROW][C]41[/C][C]135768[/C][C]134674.014321597[/C][C]1093.98567840262[/C][/ROW]
[ROW][C]42[/C][C]132505[/C][C]134749.724709249[/C][C]-2244.72470924855[/C][/ROW]
[ROW][C]43[/C][C]123670[/C][C]127791.691925047[/C][C]-4121.69192504717[/C][/ROW]
[ROW][C]44[/C][C]119745[/C][C]123263.882841257[/C][C]-3518.88284125658[/C][/ROW]
[ROW][C]45[/C][C]113541[/C][C]119881.861713675[/C][C]-6340.86171367478[/C][/ROW]
[ROW][C]46[/C][C]110910[/C][C]116105.595312279[/C][C]-5195.59531227876[/C][/ROW]
[ROW][C]47[/C][C]112208[/C][C]114770.627842514[/C][C]-2562.6278425137[/C][/ROW]
[ROW][C]48[/C][C]114172[/C][C]115592.136996456[/C][C]-1420.13699645559[/C][/ROW]
[ROW][C]49[/C][C]114172[/C][C]113139.203396106[/C][C]1032.79660389424[/C][/ROW]
[ROW][C]50[/C][C]112559[/C][C]112430.07814195[/C][C]128.921858050075[/C][/ROW]
[ROW][C]51[/C][C]112208[/C][C]110889.491721843[/C][C]1318.50827815663[/C][/ROW]
[ROW][C]52[/C][C]117465[/C][C]114320.643904992[/C][C]3144.35609500756[/C][/ROW]
[ROW][C]53[/C][C]121710[/C][C]115383.616893578[/C][C]6326.3831064218[/C][/ROW]
[ROW][C]54[/C][C]119745[/C][C]115437.365871171[/C][C]4307.63412882861[/C][/ROW]
[ROW][C]55[/C][C]113190[/C][C]110454.766786168[/C][C]2735.23321383193[/C][/ROW]
[ROW][C]56[/C][C]109932[/C][C]109047.605058027[/C][C]884.394941972743[/C][/ROW]
[ROW][C]57[/C][C]103061[/C][C]105802.219523967[/C][C]-2741.21952396705[/C][/ROW]
[ROW][C]58[/C][C]98817[/C][C]104096.826161959[/C][C]-5279.82616195935[/C][/ROW]
[ROW][C]59[/C][C]102079[/C][C]104153.323973151[/C][C]-2074.32397315078[/C][/ROW]
[ROW][C]60[/C][C]105341[/C][C]105654.952594233[/C][C]-313.95259423292[/C][/ROW]
[ROW][C]61[/C][C]105341[/C][C]105170.961486502[/C][C]170.03851349774[/C][/ROW]
[ROW][C]62[/C][C]101097[/C][C]103693.62524757[/C][C]-2596.62524756957[/C][/ROW]
[ROW][C]63[/C][C]100781[/C][C]101879.386969109[/C][C]-1098.3869691093[/C][/ROW]
[ROW][C]64[/C][C]106319[/C][C]105035.698137175[/C][C]1283.30186282546[/C][/ROW]
[ROW][C]65[/C][C]109932[/C][C]106999.718900617[/C][C]2932.28109938311[/C][/ROW]
[ROW][C]66[/C][C]108630[/C][C]104740.708139449[/C][C]3889.29186055085[/C][/ROW]
[ROW][C]67[/C][C]102079[/C][C]99334.3492578295[/C][C]2744.65074217053[/C][/ROW]
[ROW][C]68[/C][C]97835[/C][C]97060.6105715456[/C][C]774.389428454393[/C][/ROW]
[ROW][C]69[/C][C]88652[/C][C]92054.4597791024[/C][C]-3402.45977910244[/C][/ROW]
[ROW][C]70[/C][C]85075[/C][C]88598.9119933468[/C][C]-3523.91199334679[/C][/ROW]
[ROW][C]71[/C][C]86372[/C][C]90697.118495135[/C][C]-4325.11849513496[/C][/ROW]
[ROW][C]72[/C][C]91946[/C][C]91830.8958840459[/C][C]115.104115954135[/C][/ROW]
[ROW][C]73[/C][C]92261[/C][C]91648.5759905587[/C][C]612.424009441325[/C][/ROW]
[ROW][C]74[/C][C]84092[/C][C]88865.6459259625[/C][C]-4773.64592596248[/C][/ROW]
[ROW][C]75[/C][C]87039[/C][C]86936.5496454361[/C][C]102.450354563916[/C][/ROW]
[ROW][C]76[/C][C]94226[/C][C]91131.891303606[/C][C]3094.108696394[/C][/ROW]
[ROW][C]77[/C][C]97488[/C][C]94280.8599859544[/C][C]3207.14001404557[/C][/ROW]
[ROW][C]78[/C][C]95523[/C][C]92884.592231742[/C][C]2638.40776825804[/C][/ROW]
[ROW][C]79[/C][C]86692[/C][C]87136.5474311243[/C][C]-444.547431124331[/C][/ROW]
[ROW][C]80[/C][C]80484[/C][C]82896.2294623845[/C][C]-2412.22946238452[/C][/ROW]
[ROW][C]81[/C][C]73297[/C][C]75115.2282884679[/C][C]-1818.22828846793[/C][/ROW]
[ROW][C]82[/C][C]67724[/C][C]72303.8170163615[/C][C]-4579.81701636149[/C][/ROW]
[ROW][C]83[/C][C]70004[/C][C]72711.5005488218[/C][C]-2707.50054882184[/C][/ROW]
[ROW][C]84[/C][C]74910[/C][C]76011.6597416163[/C][C]-1101.65974161631[/C][/ROW]
[ROW][C]85[/C][C]73613[/C][C]75376.4046960111[/C][C]-1763.40469601107[/C][/ROW]
[ROW][C]86[/C][C]66426[/C][C]69211.6389023995[/C][C]-2785.63890239947[/C][/ROW]
[ROW][C]87[/C][C]68706[/C][C]70206.3475403187[/C][C]-1500.34754031875[/C][/ROW]
[ROW][C]88[/C][C]75893[/C][C]74068.7728026164[/C][C]1824.22719738363[/C][/ROW]
[ROW][C]89[/C][C]79821[/C][C]75979.5813957799[/C][C]3841.41860422015[/C][/ROW]
[ROW][C]90[/C][C]77541[/C][C]74705.1285391642[/C][C]2835.8714608358[/C][/ROW]
[ROW][C]91[/C][C]68706[/C][C]68581.8441159252[/C][C]124.155884074804[/C][/ROW]
[ROW][C]92[/C][C]64782[/C][C]64117.5082197722[/C][C]664.491780227814[/C][/ROW]
[ROW][C]93[/C][C]58893[/C][C]58908.4102523354[/C][C]-15.4102523354377[/C][/ROW]
[ROW][C]94[/C][C]52684[/C][C]55535.8321405311[/C][C]-2851.83214053106[/C][/ROW]
[ROW][C]95[/C][C]53666[/C][C]56854.7578932452[/C][C]-3188.75789324518[/C][/ROW]
[ROW][C]96[/C][C]58573[/C][C]59590.3824455754[/C][C]-1017.38244557541[/C][/ROW]
[ROW][C]97[/C][C]59208[/C][C]58410.6821658542[/C][C]797.31783414579[/C][/ROW]
[ROW][C]98[/C][C]53319[/C][C]53561.9512933523[/C][C]-242.951293352256[/C][/ROW]
[ROW][C]99[/C][C]54302[/C][C]55528.5945562925[/C][C]-1226.59455629254[/C][/ROW]
[ROW][C]100[/C][C]62502[/C][C]59997.635504139[/C][C]2504.36449586099[/C][/ROW]
[ROW][C]101[/C][C]64462[/C][C]62634.751565759[/C][C]1827.24843424097[/C][/ROW]
[ROW][C]102[/C][C]61173[/C][C]60366.4165351146[/C][C]806.583464885378[/C][/ROW]
[ROW][C]103[/C][C]49075[/C][C]53446.7882280464[/C][C]-4371.7882280464[/C][/ROW]
[ROW][C]104[/C][C]42871[/C][C]48299.9653125839[/C][C]-5428.96531258389[/C][/ROW]
[ROW][C]105[/C][C]34671[/C][C]41634.7092672294[/C][C]-6963.70926722935[/C][/ROW]
[ROW][C]106[/C][C]26502[/C][C]35088.5607652114[/C][C]-8586.56076521142[/C][/ROW]
[ROW][C]107[/C][C]29129[/C][C]32485.2492524932[/C][C]-3356.2492524932[/C][/ROW]
[ROW][C]108[/C][C]32706[/C][C]33528.3182824135[/C][C]-822.318282413529[/C][/ROW]
[ROW][C]109[/C][C]32075[/C][C]32605.9958874836[/C][C]-530.995887483583[/C][/ROW]
[ROW][C]110[/C][C]25835[/C][C]28468.0419484631[/C][C]-2633.0419484631[/C][/ROW]
[ROW][C]111[/C][C]29444[/C][C]27347.7411607934[/C][C]2096.2588392066[/C][/ROW]
[ROW][C]112[/C][C]38280[/C][C]30924.4896049554[/C][C]7355.51039504459[/C][/ROW]
[ROW][C]113[/C][C]42204[/C][C]33481.4386551851[/C][C]8722.56134481492[/C][/ROW]
[ROW][C]114[/C][C]40244[/C][C]33973.0738556913[/C][C]6270.92614430872[/C][/ROW]
[ROW][C]115[/C][C]32391[/C][C]29524.1700504289[/C][C]2866.82994957114[/C][/ROW]
[ROW][C]116[/C][C]26186[/C][C]27476.1053042792[/C][C]-1290.10530427918[/C][/ROW]
[ROW][C]117[/C][C]19631[/C][C]22918.0790647287[/C][C]-3287.07906472869[/C][/ROW]
[ROW][C]118[/C][C]12093[/C][C]17925.9058338286[/C][C]-5832.90583382863[/C][/ROW]
[ROW][C]119[/C][C]13427[/C][C]17519.2833701927[/C][C]-4092.2833701927[/C][/ROW]
[ROW][C]120[/C][C]15707[/C][C]17470.09254933[/C][C]-1763.09254933003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123944&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123944&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
13159990162550.762372001-2560.76237200139
14157043158651.547560092-1608.54756009195
15155745156903.033399486-1158.03339948563
16157043158063.029557448-1020.02955744808
17161634162622.24725181-988.247251809982
18160967161819.817364787-852.817364787188
19154763154897.903296482-134.903296482138
20149510151302.622567946-1792.622567946
21148527150618.890428095-2091.89042809515
22146563149455.650012797-2892.65001279686
23147892148249.812137062-357.812137061759
24149510148413.8531547731096.14684522743
25148874147124.8543649951749.14563500453
26147545145485.5073389282059.492661072
27144950145363.332198204-413.332198204473
28147545146677.614497319867.385502680641
29149856151573.61287254-1717.61287254034
30149190150508.32156174-1318.32156173993
31141656144179.046420805-2523.04642080484
32138394138865.940641762-471.940641761961
33135132138399.694714824-3267.69471482374
34132505136224.960530891-3719.96053089137
35132190136020.961740508-3830.96174050783
36134150135475.175351774-1325.17535177374
37131523133584.869876047-2061.86987604664
38130541130662.692766616-121.692766615961
39129559128189.1483660511369.851633949
40135132130464.8300631064667.16993689425
41135768134674.0143215971093.98567840262
42132505134749.724709249-2244.72470924855
43123670127791.691925047-4121.69192504717
44119745123263.882841257-3518.88284125658
45113541119881.861713675-6340.86171367478
46110910116105.595312279-5195.59531227876
47112208114770.627842514-2562.6278425137
48114172115592.136996456-1420.13699645559
49114172113139.2033961061032.79660389424
50112559112430.07814195128.921858050075
51112208110889.4917218431318.50827815663
52117465114320.6439049923144.35609500756
53121710115383.6168935786326.3831064218
54119745115437.3658711714307.63412882861
55113190110454.7667861682735.23321383193
56109932109047.605058027884.394941972743
57103061105802.219523967-2741.21952396705
5898817104096.826161959-5279.82616195935
59102079104153.323973151-2074.32397315078
60105341105654.952594233-313.95259423292
61105341105170.961486502170.03851349774
62101097103693.62524757-2596.62524756957
63100781101879.386969109-1098.3869691093
64106319105035.6981371751283.30186282546
65109932106999.7189006172932.28109938311
66108630104740.7081394493889.29186055085
6710207999334.34925782952744.65074217053
689783597060.6105715456774.389428454393
698865292054.4597791024-3402.45977910244
708507588598.9119933468-3523.91199334679
718637290697.118495135-4325.11849513496
729194691830.8958840459115.104115954135
739226191648.5759905587612.424009441325
748409288865.6459259625-4773.64592596248
758703986936.5496454361102.450354563916
769422691131.8913036063094.108696394
779748894280.85998595443207.14001404557
789552392884.5922317422638.40776825804
798669287136.5474311243-444.547431124331
808048482896.2294623845-2412.22946238452
817329775115.2282884679-1818.22828846793
826772472303.8170163615-4579.81701636149
837000472711.5005488218-2707.50054882184
847491076011.6597416163-1101.65974161631
857361375376.4046960111-1763.40469601107
866642669211.6389023995-2785.63890239947
876870670206.3475403187-1500.34754031875
887589374068.77280261641824.22719738363
897982175979.58139577993841.41860422015
907754174705.12853916422835.8714608358
916870668581.8441159252124.155884074804
926478264117.5082197722664.491780227814
935889358908.4102523354-15.4102523354377
945268455535.8321405311-2851.83214053106
955366656854.7578932452-3188.75789324518
965857359590.3824455754-1017.38244557541
975920858410.6821658542797.31783414579
985331953561.9512933523-242.951293352256
995430255528.5945562925-1226.59455629254
1006250259997.6355041392504.36449586099
1016446262634.7515657591827.24843424097
1026117360366.4165351146806.583464885378
1034907553446.7882280464-4371.7882280464
1044287148299.9653125839-5428.96531258389
1053467141634.7092672294-6963.70926722935
1062650235088.5607652114-8586.56076521142
1072912932485.2492524932-3356.2492524932
1083270633528.3182824135-822.318282413529
1093207532605.9958874836-530.995887483583
1102583528468.0419484631-2633.0419484631
1112944427347.74116079342096.2588392066
1123828030924.48960495547355.51039504459
1134220433481.43865518518722.56134481492
1144024433973.07385569136270.92614430872
1153239129524.17005042892866.82994957114
1162618627476.1053042792-1290.10530427918
1171963122918.0790647287-3287.07906472869
1181209317925.9058338286-5832.90583382863
1191342717519.2833701927-4092.2833701927
1201570717470.09254933-1763.09254933003







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12115873.17341449019925.648755530521820.6980734497
12212612.47422525586328.7965912666718896.1518592448
12313226.13334576136258.0760798583920194.1906116641
12414751.79084284576647.372038577422856.2096471139
12513568.04045753964818.6001544146422317.4807606645
12610802.80202259492004.4346440023219601.1694011874
1277258.36929446117-967.47728825982515484.2158771822
1284953.9301535843-3053.8380741695612961.6983813382
1293053.50893233595-4670.6170090694810777.6348737414
1301481.40188386271-5740.183815216728702.98758294213
131918.94625740231-7681.634859880889519.52737468551
132-111.168675140414-8994.264405400858771.92705512002

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 15873.1734144901 & 9925.6487555305 & 21820.6980734497 \tabularnewline
122 & 12612.4742252558 & 6328.79659126667 & 18896.1518592448 \tabularnewline
123 & 13226.1333457613 & 6258.07607985839 & 20194.1906116641 \tabularnewline
124 & 14751.7908428457 & 6647.3720385774 & 22856.2096471139 \tabularnewline
125 & 13568.0404575396 & 4818.60015441464 & 22317.4807606645 \tabularnewline
126 & 10802.8020225949 & 2004.43464400232 & 19601.1694011874 \tabularnewline
127 & 7258.36929446117 & -967.477288259825 & 15484.2158771822 \tabularnewline
128 & 4953.9301535843 & -3053.83807416956 & 12961.6983813382 \tabularnewline
129 & 3053.50893233595 & -4670.61700906948 & 10777.6348737414 \tabularnewline
130 & 1481.40188386271 & -5740.18381521672 & 8702.98758294213 \tabularnewline
131 & 918.94625740231 & -7681.63485988088 & 9519.52737468551 \tabularnewline
132 & -111.168675140414 & -8994.26440540085 & 8771.92705512002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123944&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]15873.1734144901[/C][C]9925.6487555305[/C][C]21820.6980734497[/C][/ROW]
[ROW][C]122[/C][C]12612.4742252558[/C][C]6328.79659126667[/C][C]18896.1518592448[/C][/ROW]
[ROW][C]123[/C][C]13226.1333457613[/C][C]6258.07607985839[/C][C]20194.1906116641[/C][/ROW]
[ROW][C]124[/C][C]14751.7908428457[/C][C]6647.3720385774[/C][C]22856.2096471139[/C][/ROW]
[ROW][C]125[/C][C]13568.0404575396[/C][C]4818.60015441464[/C][C]22317.4807606645[/C][/ROW]
[ROW][C]126[/C][C]10802.8020225949[/C][C]2004.43464400232[/C][C]19601.1694011874[/C][/ROW]
[ROW][C]127[/C][C]7258.36929446117[/C][C]-967.477288259825[/C][C]15484.2158771822[/C][/ROW]
[ROW][C]128[/C][C]4953.9301535843[/C][C]-3053.83807416956[/C][C]12961.6983813382[/C][/ROW]
[ROW][C]129[/C][C]3053.50893233595[/C][C]-4670.61700906948[/C][C]10777.6348737414[/C][/ROW]
[ROW][C]130[/C][C]1481.40188386271[/C][C]-5740.18381521672[/C][C]8702.98758294213[/C][/ROW]
[ROW][C]131[/C][C]918.94625740231[/C][C]-7681.63485988088[/C][C]9519.52737468551[/C][/ROW]
[ROW][C]132[/C][C]-111.168675140414[/C][C]-8994.26440540085[/C][C]8771.92705512002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123944&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123944&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
12115873.17341449019925.648755530521820.6980734497
12212612.47422525586328.7965912666718896.1518592448
12313226.13334576136258.0760798583920194.1906116641
12414751.79084284576647.372038577422856.2096471139
12513568.04045753964818.6001544146422317.4807606645
12610802.80202259492004.4346440023219601.1694011874
1277258.36929446117-967.47728825982515484.2158771822
1284953.9301535843-3053.8380741695612961.6983813382
1293053.50893233595-4670.6170090694810777.6348737414
1301481.40188386271-5740.183815216728702.98758294213
131918.94625740231-7681.634859880889519.52737468551
132-111.168675140414-8994.264405400858771.92705512002



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')