Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 23:17:54 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/20/t12822598713zvangy2u5tc43p.htm/, Retrieved Wed, 08 May 2024 15:31:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79426, Retrieved Wed, 08 May 2024 15:31:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMertens Jeroen
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS B - STA...] [2010-08-19 23:17:54] [2c551c5731a2f7145d4349f791500f25] [Current]
Feedback Forum

Post a new message
Dataseries X:
76
75
74
72
70
69
70
72
73
73
74
76
74
67
66
58
55
58
64
68
66
76
75
88
85
83
77
66
65
65
63
62
57
68
69
79
74
76
82
75
75
76
78
77
67
74
68
87
76
88
95
96
96
105
108
113
101
107
102
116
105
121
134
140
131
141
131
128
123
129
125
144
135
141
156
159
146
154
145
133
126
127
122
148




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79426&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79426&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79426&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.799413060083523
beta0.0296431814529341
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.799413060083523 \tabularnewline
beta & 0.0296431814529341 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79426&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]0.799413060083523[/C][/ROW]
[ROW][C]beta[/C][C]0.0296431814529341[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79426&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79426&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
alpha0.799413060083523
beta0.0296431814529341
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
374740
47273-1
57071.1768897935206-1.17688979352057
66969.1844826461764-0.18448264617642
77067.98104702106552.01895297893452
87268.58691003602983.41308996397022
97370.38814485691572.61185514308433
107371.61075561148221.38924438851775
117471.88891648910412.11108351089588
127672.7941516434463.20584835655403
137474.6505255709556-0.650525570955594
146773.4086482165592-6.40864821655921
156667.411785742717-1.41178574271699
165865.3760250964807-7.37602509648069
175558.3975828708504-3.39758287085043
185854.5190463004943.480953699506
196456.22179036815727.77820963184282
206861.54413832299566.4558616770044
216665.96236955203310.0376304479668903
227665.250674648176510.7493253518235
237573.35677688261241.64322311738765
248874.222281763158313.7777182368417
258585.1147531257755-0.114753125775479
268384.8986821226593-1.89868212265927
277783.2115216329525-6.21152163295253
286677.9294255751957-11.9294255751957
296567.7936690854322-2.79366908543224
306564.89495366202930.105046337970705
316364.3159985040094-1.31599850400944
326262.56985613114-0.569856131140043
335761.4066857516599-4.40668575165992
346857.071877786843110.9281222131569
356965.25488089489113.74511910510886
367967.784446143448911.2155538565511
377476.5517511184612-2.5517511184612
387674.25282347447571.74717652552428
398275.43191783135126.56808216864884
407580.6205519254615-5.62055192546151
417575.9322416983573-0.932241698357316
427674.9697364285211.03026357147898
437875.60049780855432.39950219144571
447777.3827077784677-0.38270777846769
456776.9317136802845-9.93171368028455
467468.61176628033055.38823371966953
476872.6664706749626-4.66647067496264
488768.572731022509918.4272689774901
497683.3771021450328-7.37710214503282
508877.378305715460410.6216942845396
519586.01968606190618.98031393809386
529693.56173333691092.4382666630891
539695.93176254266050.0682374573395066
5410596.40877648157088.59122351842925
55108103.9027642700624.09723572993789
56113107.9012923234885.09870767651155
57101112.821234952553-11.8212349525532
58107103.9350249328293.0649750671713
59102107.021676780885-5.02167678088469
60116103.52475411942712.4752458805734
61105114.310727672766-9.31072767276633
62121107.46007176421813.5399282357819
63134119.19738628203114.8026137179686
64140132.2948877693997.70511223060072
65131139.901143046328-8.90114304632846
66141134.021209285946.97879071406018
67131141.001279392085-10.0012793920845
68128134.170257912343-6.1702579123428
69123130.255587531918-7.25558753191788
70129125.3013537591773.69864624082298
71125129.191724889009-4.19172488900864
72144126.67509837040117.3249016295993
73135141.769694829919-6.76969482991862
74141137.4423337528163.55766624718447
75156141.45510653483414.5448934651658
76159154.5958847187694.4041152812309
77146159.73435734762-13.7343573476201
78154150.047232990283.95276700972005
79145154.593096138017-9.5930961380171
80133148.082890371777-15.0828903717765
81126136.826649936684-10.8266499366842
82127128.716342983733-1.71634298373343
83122127.84826195939-5.84826195939013
84148123.53848382288724.4615161771133

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 74 & 74 & 0 \tabularnewline
4 & 72 & 73 & -1 \tabularnewline
5 & 70 & 71.1768897935206 & -1.17688979352057 \tabularnewline
6 & 69 & 69.1844826461764 & -0.18448264617642 \tabularnewline
7 & 70 & 67.9810470210655 & 2.01895297893452 \tabularnewline
8 & 72 & 68.5869100360298 & 3.41308996397022 \tabularnewline
9 & 73 & 70.3881448569157 & 2.61185514308433 \tabularnewline
10 & 73 & 71.6107556114822 & 1.38924438851775 \tabularnewline
11 & 74 & 71.8889164891041 & 2.11108351089588 \tabularnewline
12 & 76 & 72.794151643446 & 3.20584835655403 \tabularnewline
13 & 74 & 74.6505255709556 & -0.650525570955594 \tabularnewline
14 & 67 & 73.4086482165592 & -6.40864821655921 \tabularnewline
15 & 66 & 67.411785742717 & -1.41178574271699 \tabularnewline
16 & 58 & 65.3760250964807 & -7.37602509648069 \tabularnewline
17 & 55 & 58.3975828708504 & -3.39758287085043 \tabularnewline
18 & 58 & 54.519046300494 & 3.480953699506 \tabularnewline
19 & 64 & 56.2217903681572 & 7.77820963184282 \tabularnewline
20 & 68 & 61.5441383229956 & 6.4558616770044 \tabularnewline
21 & 66 & 65.9623695520331 & 0.0376304479668903 \tabularnewline
22 & 76 & 65.2506746481765 & 10.7493253518235 \tabularnewline
23 & 75 & 73.3567768826124 & 1.64322311738765 \tabularnewline
24 & 88 & 74.2222817631583 & 13.7777182368417 \tabularnewline
25 & 85 & 85.1147531257755 & -0.114753125775479 \tabularnewline
26 & 83 & 84.8986821226593 & -1.89868212265927 \tabularnewline
27 & 77 & 83.2115216329525 & -6.21152163295253 \tabularnewline
28 & 66 & 77.9294255751957 & -11.9294255751957 \tabularnewline
29 & 65 & 67.7936690854322 & -2.79366908543224 \tabularnewline
30 & 65 & 64.8949536620293 & 0.105046337970705 \tabularnewline
31 & 63 & 64.3159985040094 & -1.31599850400944 \tabularnewline
32 & 62 & 62.56985613114 & -0.569856131140043 \tabularnewline
33 & 57 & 61.4066857516599 & -4.40668575165992 \tabularnewline
34 & 68 & 57.0718777868431 & 10.9281222131569 \tabularnewline
35 & 69 & 65.2548808948911 & 3.74511910510886 \tabularnewline
36 & 79 & 67.7844461434489 & 11.2155538565511 \tabularnewline
37 & 74 & 76.5517511184612 & -2.5517511184612 \tabularnewline
38 & 76 & 74.2528234744757 & 1.74717652552428 \tabularnewline
39 & 82 & 75.4319178313512 & 6.56808216864884 \tabularnewline
40 & 75 & 80.6205519254615 & -5.62055192546151 \tabularnewline
41 & 75 & 75.9322416983573 & -0.932241698357316 \tabularnewline
42 & 76 & 74.969736428521 & 1.03026357147898 \tabularnewline
43 & 78 & 75.6004978085543 & 2.39950219144571 \tabularnewline
44 & 77 & 77.3827077784677 & -0.38270777846769 \tabularnewline
45 & 67 & 76.9317136802845 & -9.93171368028455 \tabularnewline
46 & 74 & 68.6117662803305 & 5.38823371966953 \tabularnewline
47 & 68 & 72.6664706749626 & -4.66647067496264 \tabularnewline
48 & 87 & 68.5727310225099 & 18.4272689774901 \tabularnewline
49 & 76 & 83.3771021450328 & -7.37710214503282 \tabularnewline
50 & 88 & 77.3783057154604 & 10.6216942845396 \tabularnewline
51 & 95 & 86.0196860619061 & 8.98031393809386 \tabularnewline
52 & 96 & 93.5617333369109 & 2.4382666630891 \tabularnewline
53 & 96 & 95.9317625426605 & 0.0682374573395066 \tabularnewline
54 & 105 & 96.4087764815708 & 8.59122351842925 \tabularnewline
55 & 108 & 103.902764270062 & 4.09723572993789 \tabularnewline
56 & 113 & 107.901292323488 & 5.09870767651155 \tabularnewline
57 & 101 & 112.821234952553 & -11.8212349525532 \tabularnewline
58 & 107 & 103.935024932829 & 3.0649750671713 \tabularnewline
59 & 102 & 107.021676780885 & -5.02167678088469 \tabularnewline
60 & 116 & 103.524754119427 & 12.4752458805734 \tabularnewline
61 & 105 & 114.310727672766 & -9.31072767276633 \tabularnewline
62 & 121 & 107.460071764218 & 13.5399282357819 \tabularnewline
63 & 134 & 119.197386282031 & 14.8026137179686 \tabularnewline
64 & 140 & 132.294887769399 & 7.70511223060072 \tabularnewline
65 & 131 & 139.901143046328 & -8.90114304632846 \tabularnewline
66 & 141 & 134.02120928594 & 6.97879071406018 \tabularnewline
67 & 131 & 141.001279392085 & -10.0012793920845 \tabularnewline
68 & 128 & 134.170257912343 & -6.1702579123428 \tabularnewline
69 & 123 & 130.255587531918 & -7.25558753191788 \tabularnewline
70 & 129 & 125.301353759177 & 3.69864624082298 \tabularnewline
71 & 125 & 129.191724889009 & -4.19172488900864 \tabularnewline
72 & 144 & 126.675098370401 & 17.3249016295993 \tabularnewline
73 & 135 & 141.769694829919 & -6.76969482991862 \tabularnewline
74 & 141 & 137.442333752816 & 3.55766624718447 \tabularnewline
75 & 156 & 141.455106534834 & 14.5448934651658 \tabularnewline
76 & 159 & 154.595884718769 & 4.4041152812309 \tabularnewline
77 & 146 & 159.73435734762 & -13.7343573476201 \tabularnewline
78 & 154 & 150.04723299028 & 3.95276700972005 \tabularnewline
79 & 145 & 154.593096138017 & -9.5930961380171 \tabularnewline
80 & 133 & 148.082890371777 & -15.0828903717765 \tabularnewline
81 & 126 & 136.826649936684 & -10.8266499366842 \tabularnewline
82 & 127 & 128.716342983733 & -1.71634298373343 \tabularnewline
83 & 122 & 127.84826195939 & -5.84826195939013 \tabularnewline
84 & 148 & 123.538483822887 & 24.4615161771133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79426&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]3[/C][C]74[/C][C]74[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]72[/C][C]73[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]70[/C][C]71.1768897935206[/C][C]-1.17688979352057[/C][/ROW]
[ROW][C]6[/C][C]69[/C][C]69.1844826461764[/C][C]-0.18448264617642[/C][/ROW]
[ROW][C]7[/C][C]70[/C][C]67.9810470210655[/C][C]2.01895297893452[/C][/ROW]
[ROW][C]8[/C][C]72[/C][C]68.5869100360298[/C][C]3.41308996397022[/C][/ROW]
[ROW][C]9[/C][C]73[/C][C]70.3881448569157[/C][C]2.61185514308433[/C][/ROW]
[ROW][C]10[/C][C]73[/C][C]71.6107556114822[/C][C]1.38924438851775[/C][/ROW]
[ROW][C]11[/C][C]74[/C][C]71.8889164891041[/C][C]2.11108351089588[/C][/ROW]
[ROW][C]12[/C][C]76[/C][C]72.794151643446[/C][C]3.20584835655403[/C][/ROW]
[ROW][C]13[/C][C]74[/C][C]74.6505255709556[/C][C]-0.650525570955594[/C][/ROW]
[ROW][C]14[/C][C]67[/C][C]73.4086482165592[/C][C]-6.40864821655921[/C][/ROW]
[ROW][C]15[/C][C]66[/C][C]67.411785742717[/C][C]-1.41178574271699[/C][/ROW]
[ROW][C]16[/C][C]58[/C][C]65.3760250964807[/C][C]-7.37602509648069[/C][/ROW]
[ROW][C]17[/C][C]55[/C][C]58.3975828708504[/C][C]-3.39758287085043[/C][/ROW]
[ROW][C]18[/C][C]58[/C][C]54.519046300494[/C][C]3.480953699506[/C][/ROW]
[ROW][C]19[/C][C]64[/C][C]56.2217903681572[/C][C]7.77820963184282[/C][/ROW]
[ROW][C]20[/C][C]68[/C][C]61.5441383229956[/C][C]6.4558616770044[/C][/ROW]
[ROW][C]21[/C][C]66[/C][C]65.9623695520331[/C][C]0.0376304479668903[/C][/ROW]
[ROW][C]22[/C][C]76[/C][C]65.2506746481765[/C][C]10.7493253518235[/C][/ROW]
[ROW][C]23[/C][C]75[/C][C]73.3567768826124[/C][C]1.64322311738765[/C][/ROW]
[ROW][C]24[/C][C]88[/C][C]74.2222817631583[/C][C]13.7777182368417[/C][/ROW]
[ROW][C]25[/C][C]85[/C][C]85.1147531257755[/C][C]-0.114753125775479[/C][/ROW]
[ROW][C]26[/C][C]83[/C][C]84.8986821226593[/C][C]-1.89868212265927[/C][/ROW]
[ROW][C]27[/C][C]77[/C][C]83.2115216329525[/C][C]-6.21152163295253[/C][/ROW]
[ROW][C]28[/C][C]66[/C][C]77.9294255751957[/C][C]-11.9294255751957[/C][/ROW]
[ROW][C]29[/C][C]65[/C][C]67.7936690854322[/C][C]-2.79366908543224[/C][/ROW]
[ROW][C]30[/C][C]65[/C][C]64.8949536620293[/C][C]0.105046337970705[/C][/ROW]
[ROW][C]31[/C][C]63[/C][C]64.3159985040094[/C][C]-1.31599850400944[/C][/ROW]
[ROW][C]32[/C][C]62[/C][C]62.56985613114[/C][C]-0.569856131140043[/C][/ROW]
[ROW][C]33[/C][C]57[/C][C]61.4066857516599[/C][C]-4.40668575165992[/C][/ROW]
[ROW][C]34[/C][C]68[/C][C]57.0718777868431[/C][C]10.9281222131569[/C][/ROW]
[ROW][C]35[/C][C]69[/C][C]65.2548808948911[/C][C]3.74511910510886[/C][/ROW]
[ROW][C]36[/C][C]79[/C][C]67.7844461434489[/C][C]11.2155538565511[/C][/ROW]
[ROW][C]37[/C][C]74[/C][C]76.5517511184612[/C][C]-2.5517511184612[/C][/ROW]
[ROW][C]38[/C][C]76[/C][C]74.2528234744757[/C][C]1.74717652552428[/C][/ROW]
[ROW][C]39[/C][C]82[/C][C]75.4319178313512[/C][C]6.56808216864884[/C][/ROW]
[ROW][C]40[/C][C]75[/C][C]80.6205519254615[/C][C]-5.62055192546151[/C][/ROW]
[ROW][C]41[/C][C]75[/C][C]75.9322416983573[/C][C]-0.932241698357316[/C][/ROW]
[ROW][C]42[/C][C]76[/C][C]74.969736428521[/C][C]1.03026357147898[/C][/ROW]
[ROW][C]43[/C][C]78[/C][C]75.6004978085543[/C][C]2.39950219144571[/C][/ROW]
[ROW][C]44[/C][C]77[/C][C]77.3827077784677[/C][C]-0.38270777846769[/C][/ROW]
[ROW][C]45[/C][C]67[/C][C]76.9317136802845[/C][C]-9.93171368028455[/C][/ROW]
[ROW][C]46[/C][C]74[/C][C]68.6117662803305[/C][C]5.38823371966953[/C][/ROW]
[ROW][C]47[/C][C]68[/C][C]72.6664706749626[/C][C]-4.66647067496264[/C][/ROW]
[ROW][C]48[/C][C]87[/C][C]68.5727310225099[/C][C]18.4272689774901[/C][/ROW]
[ROW][C]49[/C][C]76[/C][C]83.3771021450328[/C][C]-7.37710214503282[/C][/ROW]
[ROW][C]50[/C][C]88[/C][C]77.3783057154604[/C][C]10.6216942845396[/C][/ROW]
[ROW][C]51[/C][C]95[/C][C]86.0196860619061[/C][C]8.98031393809386[/C][/ROW]
[ROW][C]52[/C][C]96[/C][C]93.5617333369109[/C][C]2.4382666630891[/C][/ROW]
[ROW][C]53[/C][C]96[/C][C]95.9317625426605[/C][C]0.0682374573395066[/C][/ROW]
[ROW][C]54[/C][C]105[/C][C]96.4087764815708[/C][C]8.59122351842925[/C][/ROW]
[ROW][C]55[/C][C]108[/C][C]103.902764270062[/C][C]4.09723572993789[/C][/ROW]
[ROW][C]56[/C][C]113[/C][C]107.901292323488[/C][C]5.09870767651155[/C][/ROW]
[ROW][C]57[/C][C]101[/C][C]112.821234952553[/C][C]-11.8212349525532[/C][/ROW]
[ROW][C]58[/C][C]107[/C][C]103.935024932829[/C][C]3.0649750671713[/C][/ROW]
[ROW][C]59[/C][C]102[/C][C]107.021676780885[/C][C]-5.02167678088469[/C][/ROW]
[ROW][C]60[/C][C]116[/C][C]103.524754119427[/C][C]12.4752458805734[/C][/ROW]
[ROW][C]61[/C][C]105[/C][C]114.310727672766[/C][C]-9.31072767276633[/C][/ROW]
[ROW][C]62[/C][C]121[/C][C]107.460071764218[/C][C]13.5399282357819[/C][/ROW]
[ROW][C]63[/C][C]134[/C][C]119.197386282031[/C][C]14.8026137179686[/C][/ROW]
[ROW][C]64[/C][C]140[/C][C]132.294887769399[/C][C]7.70511223060072[/C][/ROW]
[ROW][C]65[/C][C]131[/C][C]139.901143046328[/C][C]-8.90114304632846[/C][/ROW]
[ROW][C]66[/C][C]141[/C][C]134.02120928594[/C][C]6.97879071406018[/C][/ROW]
[ROW][C]67[/C][C]131[/C][C]141.001279392085[/C][C]-10.0012793920845[/C][/ROW]
[ROW][C]68[/C][C]128[/C][C]134.170257912343[/C][C]-6.1702579123428[/C][/ROW]
[ROW][C]69[/C][C]123[/C][C]130.255587531918[/C][C]-7.25558753191788[/C][/ROW]
[ROW][C]70[/C][C]129[/C][C]125.301353759177[/C][C]3.69864624082298[/C][/ROW]
[ROW][C]71[/C][C]125[/C][C]129.191724889009[/C][C]-4.19172488900864[/C][/ROW]
[ROW][C]72[/C][C]144[/C][C]126.675098370401[/C][C]17.3249016295993[/C][/ROW]
[ROW][C]73[/C][C]135[/C][C]141.769694829919[/C][C]-6.76969482991862[/C][/ROW]
[ROW][C]74[/C][C]141[/C][C]137.442333752816[/C][C]3.55766624718447[/C][/ROW]
[ROW][C]75[/C][C]156[/C][C]141.455106534834[/C][C]14.5448934651658[/C][/ROW]
[ROW][C]76[/C][C]159[/C][C]154.595884718769[/C][C]4.4041152812309[/C][/ROW]
[ROW][C]77[/C][C]146[/C][C]159.73435734762[/C][C]-13.7343573476201[/C][/ROW]
[ROW][C]78[/C][C]154[/C][C]150.04723299028[/C][C]3.95276700972005[/C][/ROW]
[ROW][C]79[/C][C]145[/C][C]154.593096138017[/C][C]-9.5930961380171[/C][/ROW]
[ROW][C]80[/C][C]133[/C][C]148.082890371777[/C][C]-15.0828903717765[/C][/ROW]
[ROW][C]81[/C][C]126[/C][C]136.826649936684[/C][C]-10.8266499366842[/C][/ROW]
[ROW][C]82[/C][C]127[/C][C]128.716342983733[/C][C]-1.71634298373343[/C][/ROW]
[ROW][C]83[/C][C]122[/C][C]127.84826195939[/C][C]-5.84826195939013[/C][/ROW]
[ROW][C]84[/C][C]148[/C][C]123.538483822887[/C][C]24.4615161771133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79426&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79426&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
374740
47273-1
57071.1768897935206-1.17688979352057
66969.1844826461764-0.18448264617642
77067.98104702106552.01895297893452
87268.58691003602983.41308996397022
97370.38814485691572.61185514308433
107371.61075561148221.38924438851775
117471.88891648910412.11108351089588
127672.7941516434463.20584835655403
137474.6505255709556-0.650525570955594
146773.4086482165592-6.40864821655921
156667.411785742717-1.41178574271699
165865.3760250964807-7.37602509648069
175558.3975828708504-3.39758287085043
185854.5190463004943.480953699506
196456.22179036815727.77820963184282
206861.54413832299566.4558616770044
216665.96236955203310.0376304479668903
227665.250674648176510.7493253518235
237573.35677688261241.64322311738765
248874.222281763158313.7777182368417
258585.1147531257755-0.114753125775479
268384.8986821226593-1.89868212265927
277783.2115216329525-6.21152163295253
286677.9294255751957-11.9294255751957
296567.7936690854322-2.79366908543224
306564.89495366202930.105046337970705
316364.3159985040094-1.31599850400944
326262.56985613114-0.569856131140043
335761.4066857516599-4.40668575165992
346857.071877786843110.9281222131569
356965.25488089489113.74511910510886
367967.784446143448911.2155538565511
377476.5517511184612-2.5517511184612
387674.25282347447571.74717652552428
398275.43191783135126.56808216864884
407580.6205519254615-5.62055192546151
417575.9322416983573-0.932241698357316
427674.9697364285211.03026357147898
437875.60049780855432.39950219144571
447777.3827077784677-0.38270777846769
456776.9317136802845-9.93171368028455
467468.61176628033055.38823371966953
476872.6664706749626-4.66647067496264
488768.572731022509918.4272689774901
497683.3771021450328-7.37710214503282
508877.378305715460410.6216942845396
519586.01968606190618.98031393809386
529693.56173333691092.4382666630891
539695.93176254266050.0682374573395066
5410596.40877648157088.59122351842925
55108103.9027642700624.09723572993789
56113107.9012923234885.09870767651155
57101112.821234952553-11.8212349525532
58107103.9350249328293.0649750671713
59102107.021676780885-5.02167678088469
60116103.52475411942712.4752458805734
61105114.310727672766-9.31072767276633
62121107.46007176421813.5399282357819
63134119.19738628203114.8026137179686
64140132.2948877693997.70511223060072
65131139.901143046328-8.90114304632846
66141134.021209285946.97879071406018
67131141.001279392085-10.0012793920845
68128134.170257912343-6.1702579123428
69123130.255587531918-7.25558753191788
70129125.3013537591773.69864624082298
71125129.191724889009-4.19172488900864
72144126.67509837040117.3249016295993
73135141.769694829919-6.76969482991862
74141137.4423337528163.55766624718447
75156141.45510653483414.5448934651658
76159154.5958847187694.4041152812309
77146159.73435734762-13.7343573476201
78154150.047232990283.95276700972005
79145154.593096138017-9.5930961380171
80133148.082890371777-15.0828903717765
81126136.826649936684-10.8266499366842
82127128.716342983733-1.71634298373343
83122127.84826195939-5.84826195939013
84148123.53848382288724.4615161771133







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85144.038406306853128.623463301162159.453349312544
86144.98347328939125.018233271885164.948713306895
87145.928540271928122.074728544236169.782351999619
88146.873607254465119.504502106086174.242712402844
89147.818674237003117.174450787734178.462897686272
90148.76374121954115.010626543989182.516855895091
91149.708808202077112.967173114577186.450443289578
92150.653875184615111.013487946108190.294262423122
93151.598942167152109.128042969563194.069841364741
94152.54400914969107.295080351259197.792937948121
95153.489076132227105.502702957299201.475449307155
96154.434143114765103.74170273467205.126583494859

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 144.038406306853 & 128.623463301162 & 159.453349312544 \tabularnewline
86 & 144.98347328939 & 125.018233271885 & 164.948713306895 \tabularnewline
87 & 145.928540271928 & 122.074728544236 & 169.782351999619 \tabularnewline
88 & 146.873607254465 & 119.504502106086 & 174.242712402844 \tabularnewline
89 & 147.818674237003 & 117.174450787734 & 178.462897686272 \tabularnewline
90 & 148.76374121954 & 115.010626543989 & 182.516855895091 \tabularnewline
91 & 149.708808202077 & 112.967173114577 & 186.450443289578 \tabularnewline
92 & 150.653875184615 & 111.013487946108 & 190.294262423122 \tabularnewline
93 & 151.598942167152 & 109.128042969563 & 194.069841364741 \tabularnewline
94 & 152.54400914969 & 107.295080351259 & 197.792937948121 \tabularnewline
95 & 153.489076132227 & 105.502702957299 & 201.475449307155 \tabularnewline
96 & 154.434143114765 & 103.74170273467 & 205.126583494859 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79426&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]85[/C][C]144.038406306853[/C][C]128.623463301162[/C][C]159.453349312544[/C][/ROW]
[ROW][C]86[/C][C]144.98347328939[/C][C]125.018233271885[/C][C]164.948713306895[/C][/ROW]
[ROW][C]87[/C][C]145.928540271928[/C][C]122.074728544236[/C][C]169.782351999619[/C][/ROW]
[ROW][C]88[/C][C]146.873607254465[/C][C]119.504502106086[/C][C]174.242712402844[/C][/ROW]
[ROW][C]89[/C][C]147.818674237003[/C][C]117.174450787734[/C][C]178.462897686272[/C][/ROW]
[ROW][C]90[/C][C]148.76374121954[/C][C]115.010626543989[/C][C]182.516855895091[/C][/ROW]
[ROW][C]91[/C][C]149.708808202077[/C][C]112.967173114577[/C][C]186.450443289578[/C][/ROW]
[ROW][C]92[/C][C]150.653875184615[/C][C]111.013487946108[/C][C]190.294262423122[/C][/ROW]
[ROW][C]93[/C][C]151.598942167152[/C][C]109.128042969563[/C][C]194.069841364741[/C][/ROW]
[ROW][C]94[/C][C]152.54400914969[/C][C]107.295080351259[/C][C]197.792937948121[/C][/ROW]
[ROW][C]95[/C][C]153.489076132227[/C][C]105.502702957299[/C][C]201.475449307155[/C][/ROW]
[ROW][C]96[/C][C]154.434143114765[/C][C]103.74170273467[/C][C]205.126583494859[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79426&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79426&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
85144.038406306853128.623463301162159.453349312544
86144.98347328939125.018233271885164.948713306895
87145.928540271928122.074728544236169.782351999619
88146.873607254465119.504502106086174.242712402844
89147.818674237003117.174450787734178.462897686272
90148.76374121954115.010626543989182.516855895091
91149.708808202077112.967173114577186.450443289578
92150.653875184615111.013487946108190.294262423122
93151.598942167152109.128042969563194.069841364741
94152.54400914969107.295080351259197.792937948121
95153.489076132227105.502702957299201.475449307155
96154.434143114765103.74170273467205.126583494859



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