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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 18 Aug 2010 12:07:22 +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/18/t1282133203yisx0d6e8e9dwel.htm/, Retrieved Thu, 16 May 2024 06:50:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79193, Retrieved Thu, 16 May 2024 06:50:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMagali De Reu
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks 2 stap 27] [2010-08-18 12:07:22] [07915b1f88a41fb8d82e27c5eaa7bbed] [Current]
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Dataseries X:
120
119
118
116
114
113
114
116
117
117
118
120
123
125
120
116
111
108
113
112
126
124
124
118
119
122
114
108
104
101
107
104
123
125
134
131
127
124
123
117
112
118
123
124
144
148
152
154
146
132
136
128
120
124
126
121
140
142
142
139
131
117
122
112
98
103
108
102
126
129
126
126
112
99
106
104
90
98
99
91
118
115
119
123




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=79193&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=79193&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79193&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
alpha0.989880786698701
beta0.00360535147989007
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.989880786698701 \tabularnewline
beta & 0.00360535147989007 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79193&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]0.989880786698701[/C][/ROW]
[ROW][C]beta[/C][C]0.00360535147989007[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79193&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79193&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
alpha0.989880786698701
beta0.00360535147989007
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31181180
4116117-1
5114115.006550345142-1.00655034514206
6113113.003024384004-0.0030243840043056
7114111.9928586971222.00714130287761
8116112.9796806244533.02031937554719
9117114.9802071810732.01979281892662
10117115.9975400969931.00245990300682
11118116.0114123529971.98858764700346
12120117.0085305231482.99146947685203
13123119.0090583081613.990941691839
14125122.0131875803582.98681241964178
15120124.034008118388-4.03400811838775
16116119.090656455834-3.09065645583438
17111115.070080333726-4.07008033372648
18108110.065465752751-2.06546575275068
19113107.037809255265.9621907447401
20112111.977853959560.0221460404395657
21126111.03804157524114.9619584247589
22124124.940259684065-0.940259684064742
23124123.0978219582240.902178041776153
24118123.082397692369-5.08239769236896
25119117.1248184834441.87518151655634
26122118.0611055309753.93889446902489
27114121.05427977447-7.05427977446952
28108113.140346255024-5.14034625502431
29104107.10263353542-3.10263353541953
30101103.070940595729-2.07094059572874
31107100.0531097608596.94689023914121
32104105.986648942506-1.98664894250591
33123103.06995924286619.930040757134
34125121.9193072728073.08069272719256
35134124.1008040056939.89919599430729
36131133.067135042123-2.06713504212334
37127130.180847565882-3.18084756588223
38124126.180765434869-2.18076543486922
39123123.162862526143-0.1628625261434
40117122.141861701305-5.1418617013048
41112116.17389462948-4.17389462948026
42118111.1492034845696.85079651543133
43123117.0620918728425.93790812715828
44124122.092521196411.90747880358957
45144123.14011351079820.859886489202
46148143.0227762395514.97722376044925
47152147.2012593468964.79874065310435
48154151.2201915282512.77980847174913
49146153.250542303578-7.25054230357847
50132145.326165332996-13.3261653329964
51136131.3400865312284.65991346877232
52128135.174712180182-7.17471218018213
53120127.268863679613-7.26886367961336
54124119.2438748025794.75612519742128
55126123.1391653589652.86083464103531
56121125.168554150032-4.16855415003194
57140120.2248090144119.7751909855896
58142139.0530921996022.94690780039755
59142141.2338983120650.766101687934878
60139141.258700470207-2.25870047020669
61131138.28124808425-7.2812480842498
62117130.306086500425-13.3060865004248
63122116.3195654570295.68043454297148
64112121.147709522712-9.14770952271184
6598111.265111706129-13.2651117061293
6610397.25943514227385.74056485772621
67108102.0875999663255.91240003367457
68102107.106961705752-5.1069617057522
69126101.20024290461624.7997570953845
70129124.9861175013794.01388249862056
71126128.210779217522-2.21077921752237
72126125.26587791760.734122082400063
73112125.23869781812-13.2386978181196
7499111.332844596001-12.3328445960008
7510698.2796637776357.72033622236505
76104105.104294225687-1.10429422568701
7790103.189651462995-13.1896514629955
789889.26487364356458.73512635643553
799997.07418665454651.92581334545352
809198.1499645192691-7.14996451926913
8111890.21628697064527.783713029355
82115116.961942044908-1.96194204490753
83119114.2559427608974.74405723910347
84123118.205014238574.7949857614305

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 118 & 118 & 0 \tabularnewline
4 & 116 & 117 & -1 \tabularnewline
5 & 114 & 115.006550345142 & -1.00655034514206 \tabularnewline
6 & 113 & 113.003024384004 & -0.0030243840043056 \tabularnewline
7 & 114 & 111.992858697122 & 2.00714130287761 \tabularnewline
8 & 116 & 112.979680624453 & 3.02031937554719 \tabularnewline
9 & 117 & 114.980207181073 & 2.01979281892662 \tabularnewline
10 & 117 & 115.997540096993 & 1.00245990300682 \tabularnewline
11 & 118 & 116.011412352997 & 1.98858764700346 \tabularnewline
12 & 120 & 117.008530523148 & 2.99146947685203 \tabularnewline
13 & 123 & 119.009058308161 & 3.990941691839 \tabularnewline
14 & 125 & 122.013187580358 & 2.98681241964178 \tabularnewline
15 & 120 & 124.034008118388 & -4.03400811838775 \tabularnewline
16 & 116 & 119.090656455834 & -3.09065645583438 \tabularnewline
17 & 111 & 115.070080333726 & -4.07008033372648 \tabularnewline
18 & 108 & 110.065465752751 & -2.06546575275068 \tabularnewline
19 & 113 & 107.03780925526 & 5.9621907447401 \tabularnewline
20 & 112 & 111.97785395956 & 0.0221460404395657 \tabularnewline
21 & 126 & 111.038041575241 & 14.9619584247589 \tabularnewline
22 & 124 & 124.940259684065 & -0.940259684064742 \tabularnewline
23 & 124 & 123.097821958224 & 0.902178041776153 \tabularnewline
24 & 118 & 123.082397692369 & -5.08239769236896 \tabularnewline
25 & 119 & 117.124818483444 & 1.87518151655634 \tabularnewline
26 & 122 & 118.061105530975 & 3.93889446902489 \tabularnewline
27 & 114 & 121.05427977447 & -7.05427977446952 \tabularnewline
28 & 108 & 113.140346255024 & -5.14034625502431 \tabularnewline
29 & 104 & 107.10263353542 & -3.10263353541953 \tabularnewline
30 & 101 & 103.070940595729 & -2.07094059572874 \tabularnewline
31 & 107 & 100.053109760859 & 6.94689023914121 \tabularnewline
32 & 104 & 105.986648942506 & -1.98664894250591 \tabularnewline
33 & 123 & 103.069959242866 & 19.930040757134 \tabularnewline
34 & 125 & 121.919307272807 & 3.08069272719256 \tabularnewline
35 & 134 & 124.100804005693 & 9.89919599430729 \tabularnewline
36 & 131 & 133.067135042123 & -2.06713504212334 \tabularnewline
37 & 127 & 130.180847565882 & -3.18084756588223 \tabularnewline
38 & 124 & 126.180765434869 & -2.18076543486922 \tabularnewline
39 & 123 & 123.162862526143 & -0.1628625261434 \tabularnewline
40 & 117 & 122.141861701305 & -5.1418617013048 \tabularnewline
41 & 112 & 116.17389462948 & -4.17389462948026 \tabularnewline
42 & 118 & 111.149203484569 & 6.85079651543133 \tabularnewline
43 & 123 & 117.062091872842 & 5.93790812715828 \tabularnewline
44 & 124 & 122.09252119641 & 1.90747880358957 \tabularnewline
45 & 144 & 123.140113510798 & 20.859886489202 \tabularnewline
46 & 148 & 143.022776239551 & 4.97722376044925 \tabularnewline
47 & 152 & 147.201259346896 & 4.79874065310435 \tabularnewline
48 & 154 & 151.220191528251 & 2.77980847174913 \tabularnewline
49 & 146 & 153.250542303578 & -7.25054230357847 \tabularnewline
50 & 132 & 145.326165332996 & -13.3261653329964 \tabularnewline
51 & 136 & 131.340086531228 & 4.65991346877232 \tabularnewline
52 & 128 & 135.174712180182 & -7.17471218018213 \tabularnewline
53 & 120 & 127.268863679613 & -7.26886367961336 \tabularnewline
54 & 124 & 119.243874802579 & 4.75612519742128 \tabularnewline
55 & 126 & 123.139165358965 & 2.86083464103531 \tabularnewline
56 & 121 & 125.168554150032 & -4.16855415003194 \tabularnewline
57 & 140 & 120.22480901441 & 19.7751909855896 \tabularnewline
58 & 142 & 139.053092199602 & 2.94690780039755 \tabularnewline
59 & 142 & 141.233898312065 & 0.766101687934878 \tabularnewline
60 & 139 & 141.258700470207 & -2.25870047020669 \tabularnewline
61 & 131 & 138.28124808425 & -7.2812480842498 \tabularnewline
62 & 117 & 130.306086500425 & -13.3060865004248 \tabularnewline
63 & 122 & 116.319565457029 & 5.68043454297148 \tabularnewline
64 & 112 & 121.147709522712 & -9.14770952271184 \tabularnewline
65 & 98 & 111.265111706129 & -13.2651117061293 \tabularnewline
66 & 103 & 97.2594351422738 & 5.74056485772621 \tabularnewline
67 & 108 & 102.087599966325 & 5.91240003367457 \tabularnewline
68 & 102 & 107.106961705752 & -5.1069617057522 \tabularnewline
69 & 126 & 101.200242904616 & 24.7997570953845 \tabularnewline
70 & 129 & 124.986117501379 & 4.01388249862056 \tabularnewline
71 & 126 & 128.210779217522 & -2.21077921752237 \tabularnewline
72 & 126 & 125.2658779176 & 0.734122082400063 \tabularnewline
73 & 112 & 125.23869781812 & -13.2386978181196 \tabularnewline
74 & 99 & 111.332844596001 & -12.3328445960008 \tabularnewline
75 & 106 & 98.279663777635 & 7.72033622236505 \tabularnewline
76 & 104 & 105.104294225687 & -1.10429422568701 \tabularnewline
77 & 90 & 103.189651462995 & -13.1896514629955 \tabularnewline
78 & 98 & 89.2648736435645 & 8.73512635643553 \tabularnewline
79 & 99 & 97.0741866545465 & 1.92581334545352 \tabularnewline
80 & 91 & 98.1499645192691 & -7.14996451926913 \tabularnewline
81 & 118 & 90.216286970645 & 27.783713029355 \tabularnewline
82 & 115 & 116.961942044908 & -1.96194204490753 \tabularnewline
83 & 119 & 114.255942760897 & 4.74405723910347 \tabularnewline
84 & 123 & 118.20501423857 & 4.7949857614305 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79193&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]118[/C][C]118[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]116[/C][C]117[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]114[/C][C]115.006550345142[/C][C]-1.00655034514206[/C][/ROW]
[ROW][C]6[/C][C]113[/C][C]113.003024384004[/C][C]-0.0030243840043056[/C][/ROW]
[ROW][C]7[/C][C]114[/C][C]111.992858697122[/C][C]2.00714130287761[/C][/ROW]
[ROW][C]8[/C][C]116[/C][C]112.979680624453[/C][C]3.02031937554719[/C][/ROW]
[ROW][C]9[/C][C]117[/C][C]114.980207181073[/C][C]2.01979281892662[/C][/ROW]
[ROW][C]10[/C][C]117[/C][C]115.997540096993[/C][C]1.00245990300682[/C][/ROW]
[ROW][C]11[/C][C]118[/C][C]116.011412352997[/C][C]1.98858764700346[/C][/ROW]
[ROW][C]12[/C][C]120[/C][C]117.008530523148[/C][C]2.99146947685203[/C][/ROW]
[ROW][C]13[/C][C]123[/C][C]119.009058308161[/C][C]3.990941691839[/C][/ROW]
[ROW][C]14[/C][C]125[/C][C]122.013187580358[/C][C]2.98681241964178[/C][/ROW]
[ROW][C]15[/C][C]120[/C][C]124.034008118388[/C][C]-4.03400811838775[/C][/ROW]
[ROW][C]16[/C][C]116[/C][C]119.090656455834[/C][C]-3.09065645583438[/C][/ROW]
[ROW][C]17[/C][C]111[/C][C]115.070080333726[/C][C]-4.07008033372648[/C][/ROW]
[ROW][C]18[/C][C]108[/C][C]110.065465752751[/C][C]-2.06546575275068[/C][/ROW]
[ROW][C]19[/C][C]113[/C][C]107.03780925526[/C][C]5.9621907447401[/C][/ROW]
[ROW][C]20[/C][C]112[/C][C]111.97785395956[/C][C]0.0221460404395657[/C][/ROW]
[ROW][C]21[/C][C]126[/C][C]111.038041575241[/C][C]14.9619584247589[/C][/ROW]
[ROW][C]22[/C][C]124[/C][C]124.940259684065[/C][C]-0.940259684064742[/C][/ROW]
[ROW][C]23[/C][C]124[/C][C]123.097821958224[/C][C]0.902178041776153[/C][/ROW]
[ROW][C]24[/C][C]118[/C][C]123.082397692369[/C][C]-5.08239769236896[/C][/ROW]
[ROW][C]25[/C][C]119[/C][C]117.124818483444[/C][C]1.87518151655634[/C][/ROW]
[ROW][C]26[/C][C]122[/C][C]118.061105530975[/C][C]3.93889446902489[/C][/ROW]
[ROW][C]27[/C][C]114[/C][C]121.05427977447[/C][C]-7.05427977446952[/C][/ROW]
[ROW][C]28[/C][C]108[/C][C]113.140346255024[/C][C]-5.14034625502431[/C][/ROW]
[ROW][C]29[/C][C]104[/C][C]107.10263353542[/C][C]-3.10263353541953[/C][/ROW]
[ROW][C]30[/C][C]101[/C][C]103.070940595729[/C][C]-2.07094059572874[/C][/ROW]
[ROW][C]31[/C][C]107[/C][C]100.053109760859[/C][C]6.94689023914121[/C][/ROW]
[ROW][C]32[/C][C]104[/C][C]105.986648942506[/C][C]-1.98664894250591[/C][/ROW]
[ROW][C]33[/C][C]123[/C][C]103.069959242866[/C][C]19.930040757134[/C][/ROW]
[ROW][C]34[/C][C]125[/C][C]121.919307272807[/C][C]3.08069272719256[/C][/ROW]
[ROW][C]35[/C][C]134[/C][C]124.100804005693[/C][C]9.89919599430729[/C][/ROW]
[ROW][C]36[/C][C]131[/C][C]133.067135042123[/C][C]-2.06713504212334[/C][/ROW]
[ROW][C]37[/C][C]127[/C][C]130.180847565882[/C][C]-3.18084756588223[/C][/ROW]
[ROW][C]38[/C][C]124[/C][C]126.180765434869[/C][C]-2.18076543486922[/C][/ROW]
[ROW][C]39[/C][C]123[/C][C]123.162862526143[/C][C]-0.1628625261434[/C][/ROW]
[ROW][C]40[/C][C]117[/C][C]122.141861701305[/C][C]-5.1418617013048[/C][/ROW]
[ROW][C]41[/C][C]112[/C][C]116.17389462948[/C][C]-4.17389462948026[/C][/ROW]
[ROW][C]42[/C][C]118[/C][C]111.149203484569[/C][C]6.85079651543133[/C][/ROW]
[ROW][C]43[/C][C]123[/C][C]117.062091872842[/C][C]5.93790812715828[/C][/ROW]
[ROW][C]44[/C][C]124[/C][C]122.09252119641[/C][C]1.90747880358957[/C][/ROW]
[ROW][C]45[/C][C]144[/C][C]123.140113510798[/C][C]20.859886489202[/C][/ROW]
[ROW][C]46[/C][C]148[/C][C]143.022776239551[/C][C]4.97722376044925[/C][/ROW]
[ROW][C]47[/C][C]152[/C][C]147.201259346896[/C][C]4.79874065310435[/C][/ROW]
[ROW][C]48[/C][C]154[/C][C]151.220191528251[/C][C]2.77980847174913[/C][/ROW]
[ROW][C]49[/C][C]146[/C][C]153.250542303578[/C][C]-7.25054230357847[/C][/ROW]
[ROW][C]50[/C][C]132[/C][C]145.326165332996[/C][C]-13.3261653329964[/C][/ROW]
[ROW][C]51[/C][C]136[/C][C]131.340086531228[/C][C]4.65991346877232[/C][/ROW]
[ROW][C]52[/C][C]128[/C][C]135.174712180182[/C][C]-7.17471218018213[/C][/ROW]
[ROW][C]53[/C][C]120[/C][C]127.268863679613[/C][C]-7.26886367961336[/C][/ROW]
[ROW][C]54[/C][C]124[/C][C]119.243874802579[/C][C]4.75612519742128[/C][/ROW]
[ROW][C]55[/C][C]126[/C][C]123.139165358965[/C][C]2.86083464103531[/C][/ROW]
[ROW][C]56[/C][C]121[/C][C]125.168554150032[/C][C]-4.16855415003194[/C][/ROW]
[ROW][C]57[/C][C]140[/C][C]120.22480901441[/C][C]19.7751909855896[/C][/ROW]
[ROW][C]58[/C][C]142[/C][C]139.053092199602[/C][C]2.94690780039755[/C][/ROW]
[ROW][C]59[/C][C]142[/C][C]141.233898312065[/C][C]0.766101687934878[/C][/ROW]
[ROW][C]60[/C][C]139[/C][C]141.258700470207[/C][C]-2.25870047020669[/C][/ROW]
[ROW][C]61[/C][C]131[/C][C]138.28124808425[/C][C]-7.2812480842498[/C][/ROW]
[ROW][C]62[/C][C]117[/C][C]130.306086500425[/C][C]-13.3060865004248[/C][/ROW]
[ROW][C]63[/C][C]122[/C][C]116.319565457029[/C][C]5.68043454297148[/C][/ROW]
[ROW][C]64[/C][C]112[/C][C]121.147709522712[/C][C]-9.14770952271184[/C][/ROW]
[ROW][C]65[/C][C]98[/C][C]111.265111706129[/C][C]-13.2651117061293[/C][/ROW]
[ROW][C]66[/C][C]103[/C][C]97.2594351422738[/C][C]5.74056485772621[/C][/ROW]
[ROW][C]67[/C][C]108[/C][C]102.087599966325[/C][C]5.91240003367457[/C][/ROW]
[ROW][C]68[/C][C]102[/C][C]107.106961705752[/C][C]-5.1069617057522[/C][/ROW]
[ROW][C]69[/C][C]126[/C][C]101.200242904616[/C][C]24.7997570953845[/C][/ROW]
[ROW][C]70[/C][C]129[/C][C]124.986117501379[/C][C]4.01388249862056[/C][/ROW]
[ROW][C]71[/C][C]126[/C][C]128.210779217522[/C][C]-2.21077921752237[/C][/ROW]
[ROW][C]72[/C][C]126[/C][C]125.2658779176[/C][C]0.734122082400063[/C][/ROW]
[ROW][C]73[/C][C]112[/C][C]125.23869781812[/C][C]-13.2386978181196[/C][/ROW]
[ROW][C]74[/C][C]99[/C][C]111.332844596001[/C][C]-12.3328445960008[/C][/ROW]
[ROW][C]75[/C][C]106[/C][C]98.279663777635[/C][C]7.72033622236505[/C][/ROW]
[ROW][C]76[/C][C]104[/C][C]105.104294225687[/C][C]-1.10429422568701[/C][/ROW]
[ROW][C]77[/C][C]90[/C][C]103.189651462995[/C][C]-13.1896514629955[/C][/ROW]
[ROW][C]78[/C][C]98[/C][C]89.2648736435645[/C][C]8.73512635643553[/C][/ROW]
[ROW][C]79[/C][C]99[/C][C]97.0741866545465[/C][C]1.92581334545352[/C][/ROW]
[ROW][C]80[/C][C]91[/C][C]98.1499645192691[/C][C]-7.14996451926913[/C][/ROW]
[ROW][C]81[/C][C]118[/C][C]90.216286970645[/C][C]27.783713029355[/C][/ROW]
[ROW][C]82[/C][C]115[/C][C]116.961942044908[/C][C]-1.96194204490753[/C][/ROW]
[ROW][C]83[/C][C]119[/C][C]114.255942760897[/C][C]4.74405723910347[/C][/ROW]
[ROW][C]84[/C][C]123[/C][C]118.20501423857[/C][C]4.7949857614305[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79193&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79193&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
31181180
4116117-1
5114115.006550345142-1.00655034514206
6113113.003024384004-0.0030243840043056
7114111.9928586971222.00714130287761
8116112.9796806244533.02031937554719
9117114.9802071810732.01979281892662
10117115.9975400969931.00245990300682
11118116.0114123529971.98858764700346
12120117.0085305231482.99146947685203
13123119.0090583081613.990941691839
14125122.0131875803582.98681241964178
15120124.034008118388-4.03400811838775
16116119.090656455834-3.09065645583438
17111115.070080333726-4.07008033372648
18108110.065465752751-2.06546575275068
19113107.037809255265.9621907447401
20112111.977853959560.0221460404395657
21126111.03804157524114.9619584247589
22124124.940259684065-0.940259684064742
23124123.0978219582240.902178041776153
24118123.082397692369-5.08239769236896
25119117.1248184834441.87518151655634
26122118.0611055309753.93889446902489
27114121.05427977447-7.05427977446952
28108113.140346255024-5.14034625502431
29104107.10263353542-3.10263353541953
30101103.070940595729-2.07094059572874
31107100.0531097608596.94689023914121
32104105.986648942506-1.98664894250591
33123103.06995924286619.930040757134
34125121.9193072728073.08069272719256
35134124.1008040056939.89919599430729
36131133.067135042123-2.06713504212334
37127130.180847565882-3.18084756588223
38124126.180765434869-2.18076543486922
39123123.162862526143-0.1628625261434
40117122.141861701305-5.1418617013048
41112116.17389462948-4.17389462948026
42118111.1492034845696.85079651543133
43123117.0620918728425.93790812715828
44124122.092521196411.90747880358957
45144123.14011351079820.859886489202
46148143.0227762395514.97722376044925
47152147.2012593468964.79874065310435
48154151.2201915282512.77980847174913
49146153.250542303578-7.25054230357847
50132145.326165332996-13.3261653329964
51136131.3400865312284.65991346877232
52128135.174712180182-7.17471218018213
53120127.268863679613-7.26886367961336
54124119.2438748025794.75612519742128
55126123.1391653589652.86083464103531
56121125.168554150032-4.16855415003194
57140120.2248090144119.7751909855896
58142139.0530921996022.94690780039755
59142141.2338983120650.766101687934878
60139141.258700470207-2.25870047020669
61131138.28124808425-7.2812480842498
62117130.306086500425-13.3060865004248
63122116.3195654570295.68043454297148
64112121.147709522712-9.14770952271184
6598111.265111706129-13.2651117061293
6610397.25943514227385.74056485772621
67108102.0875999663255.91240003367457
68102107.106961705752-5.1069617057522
69126101.20024290461624.7997570953845
70129124.9861175013794.01388249862056
71126128.210779217522-2.21077921752237
72126125.26587791760.734122082400063
73112125.23869781812-13.2386978181196
7499111.332844596001-12.3328445960008
7510698.2796637776357.72033622236505
76104105.104294225687-1.10429422568701
7790103.189651462995-13.1896514629955
789889.26487364356458.73512635643553
799997.07418665454651.92581334545352
809198.1499645192691-7.14996451926913
8111890.21628697064527.783713029355
82115116.961942044908-1.96194204490753
83119114.2559427608974.74405723910347
84123118.205014238574.7949857614305







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85122.221611553997106.5114034321137.931819675894
86121.4917445916999.3468020848194143.636687098562
87120.76187762938493.6373575168301147.886397741938
88120.03201066707888.6817273428426151.382293991312
89119.30214370477184.2064632680227154.397824141519
90118.57227674246580.0710372698533157.073516215076
91117.84240978015876.1919293687375159.492890191579
92117.11254281785272.5147367596157161.710348876088
93116.38267585554569.0016977291876163.763653981903
94115.65280889323965.6253448892086165.680272897269
95114.92294193093262.3649664013723167.480917460492
96114.19307496862659.2044917294697169.181658207782

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 122.221611553997 & 106.5114034321 & 137.931819675894 \tabularnewline
86 & 121.49174459169 & 99.3468020848194 & 143.636687098562 \tabularnewline
87 & 120.761877629384 & 93.6373575168301 & 147.886397741938 \tabularnewline
88 & 120.032010667078 & 88.6817273428426 & 151.382293991312 \tabularnewline
89 & 119.302143704771 & 84.2064632680227 & 154.397824141519 \tabularnewline
90 & 118.572276742465 & 80.0710372698533 & 157.073516215076 \tabularnewline
91 & 117.842409780158 & 76.1919293687375 & 159.492890191579 \tabularnewline
92 & 117.112542817852 & 72.5147367596157 & 161.710348876088 \tabularnewline
93 & 116.382675855545 & 69.0016977291876 & 163.763653981903 \tabularnewline
94 & 115.652808893239 & 65.6253448892086 & 165.680272897269 \tabularnewline
95 & 114.922941930932 & 62.3649664013723 & 167.480917460492 \tabularnewline
96 & 114.193074968626 & 59.2044917294697 & 169.181658207782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79193&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]122.221611553997[/C][C]106.5114034321[/C][C]137.931819675894[/C][/ROW]
[ROW][C]86[/C][C]121.49174459169[/C][C]99.3468020848194[/C][C]143.636687098562[/C][/ROW]
[ROW][C]87[/C][C]120.761877629384[/C][C]93.6373575168301[/C][C]147.886397741938[/C][/ROW]
[ROW][C]88[/C][C]120.032010667078[/C][C]88.6817273428426[/C][C]151.382293991312[/C][/ROW]
[ROW][C]89[/C][C]119.302143704771[/C][C]84.2064632680227[/C][C]154.397824141519[/C][/ROW]
[ROW][C]90[/C][C]118.572276742465[/C][C]80.0710372698533[/C][C]157.073516215076[/C][/ROW]
[ROW][C]91[/C][C]117.842409780158[/C][C]76.1919293687375[/C][C]159.492890191579[/C][/ROW]
[ROW][C]92[/C][C]117.112542817852[/C][C]72.5147367596157[/C][C]161.710348876088[/C][/ROW]
[ROW][C]93[/C][C]116.382675855545[/C][C]69.0016977291876[/C][C]163.763653981903[/C][/ROW]
[ROW][C]94[/C][C]115.652808893239[/C][C]65.6253448892086[/C][C]165.680272897269[/C][/ROW]
[ROW][C]95[/C][C]114.922941930932[/C][C]62.3649664013723[/C][C]167.480917460492[/C][/ROW]
[ROW][C]96[/C][C]114.193074968626[/C][C]59.2044917294697[/C][C]169.181658207782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79193&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79193&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
85122.221611553997106.5114034321137.931819675894
86121.4917445916999.3468020848194143.636687098562
87120.76187762938493.6373575168301147.886397741938
88120.03201066707888.6817273428426151.382293991312
89119.30214370477184.2064632680227154.397824141519
90118.57227674246580.0710372698533157.073516215076
91117.84240978015876.1919293687375159.492890191579
92117.11254281785272.5147367596157161.710348876088
93116.38267585554569.0016977291876163.763653981903
94115.65280889323965.6253448892086165.680272897269
95114.92294193093262.3649664013723167.480917460492
96114.19307496862659.2044917294697169.181658207782



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