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 23:16:18 +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/t1282259766khl3831gt14h1lh.htm/, Retrieved Wed, 08 May 2024 08:49:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79425, Retrieved Wed, 08 May 2024 08:49:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsDieter Van Boxel
Estimated Impact185
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 23:16:18] [f91e4cd4d3d1892f3fcf702e4827e40c] [Current]
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Dataseries X:
93
92
91
89
87
86
87
89
90
90
91
93
93
87
89
92
98
92
92
87
92
98
101
102
102
90
87
92
105
90
88
83
98
109
118
118
115
107
101
111
128
115
111
105
120
132
135
142
139
127
113
130
143
139
137
134
139
157
152
153
147
132
117
123
139
134
134
128
118
144
140
151
144
135
122
124
146
146
147
148
132
161
159
173




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79425&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79425&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79425&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.373511042776394
beta0.00909734578251893
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.373511042776394 \tabularnewline
beta & 0.00909734578251893 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79425&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]0.373511042776394[/C][/ROW]
[ROW][C]beta[/C][C]0.00909734578251893[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79425&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79425&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
alpha0.373511042776394
beta0.00909734578251893
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139390.76263994763732.23736005236272
148785.8857878960591.11421210394097
158988.61143267321230.388567326787694
169291.66764617337250.332353826627482
179897.34123640567250.658763594327468
189291.1684011386450.831598861355047
199290.08781225565851.91218774434149
208793.4508464783774-6.45084647837741
219292.6931746271342-0.693174627134184
229892.7169365368195.28306346318102
2310195.46677333869685.5332266613032
2410299.26753750769982.73246249230019
25102101.6929797367290.307020263271014
269094.7887630758412-4.7887630758412
278794.9788281228176-7.97882812281763
289294.9499166765758-2.94991667657584
2910599.6871385563315.31286144366892
309095.1041093141956-5.10410931419564
318892.4343723119153-4.43437231191533
328388.0748444720858-5.07484447208577
339891.34586227391516.65413772608485
3410997.840597195454211.1594028045458
35118102.88799085930015.1120091406997
36118108.4942462615819.50575373841885
37115111.9340363145013.0659636854986
38107101.7134383925325.28656160746831
39101103.518259211184-2.51825921118447
40111109.8024193071911.19758069280938
41128123.4457615863534.55423841364714
42115109.5228410867855.47715891321491
43111111.163069326092-0.163069326092099
44105107.185085362127-2.18508536212738
45120122.379409751109-2.37940975110898
46132129.7004170361712.29958296382898
47135134.0582089513420.941791048657706
48142130.18145240279211.8185475972083
49139129.8756163341309.1243836658702
50127121.6871766587825.31282334121799
51113117.840334277878-4.84033427787783
52130127.0353027864182.96469721358189
53143145.798997223635-2.79899722363479
54139127.68821388811111.3117861118893
55137127.4236622406539.57633775934681
56134124.9148654199439.08513458005665
57139147.786908234961-8.78690823496126
58157157.979956774861-0.97995677486125
59152160.838013178872-8.83801317887244
60153160.315987937495-7.31598793749484
61147150.314188458132-3.31418845813235
62132134.002251470766-2.00225147076577
63117120.382999554911-3.38299955491098
64123135.825886484309-12.8258864843092
65139145.114987861629-6.11498786162855
66134134.322702108223-0.322702108222501
67134128.5759521895625.42404781043794
68128124.2775990556813.72240094431938
69118133.217807005481-15.2178070054806
70144144.256997137560-0.256997137560319
71140142.371677286859-2.37167728685895
72151144.7715787763556.22842122364494
73144142.4155768286811.5844231713194
74135129.0651247273715.93487527262945
75122117.5484785095844.45152149041594
76124129.869070846281-5.8690708462806
77146146.564514681817-0.564514681816547
78146141.199880532394.80011946761013
79147140.7692075036336.23079249636666
80148135.17234844685912.8276515531415
81132134.791961754875-2.79196175487539
82161163.374736171705-2.37473617170534
83159159.004491639959-0.00449163995881463
84173168.8329591853304.16704081466963

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 93 & 90.7626399476373 & 2.23736005236272 \tabularnewline
14 & 87 & 85.885787896059 & 1.11421210394097 \tabularnewline
15 & 89 & 88.6114326732123 & 0.388567326787694 \tabularnewline
16 & 92 & 91.6676461733725 & 0.332353826627482 \tabularnewline
17 & 98 & 97.3412364056725 & 0.658763594327468 \tabularnewline
18 & 92 & 91.168401138645 & 0.831598861355047 \tabularnewline
19 & 92 & 90.0878122556585 & 1.91218774434149 \tabularnewline
20 & 87 & 93.4508464783774 & -6.45084647837741 \tabularnewline
21 & 92 & 92.6931746271342 & -0.693174627134184 \tabularnewline
22 & 98 & 92.716936536819 & 5.28306346318102 \tabularnewline
23 & 101 & 95.4667733386968 & 5.5332266613032 \tabularnewline
24 & 102 & 99.2675375076998 & 2.73246249230019 \tabularnewline
25 & 102 & 101.692979736729 & 0.307020263271014 \tabularnewline
26 & 90 & 94.7887630758412 & -4.7887630758412 \tabularnewline
27 & 87 & 94.9788281228176 & -7.97882812281763 \tabularnewline
28 & 92 & 94.9499166765758 & -2.94991667657584 \tabularnewline
29 & 105 & 99.687138556331 & 5.31286144366892 \tabularnewline
30 & 90 & 95.1041093141956 & -5.10410931419564 \tabularnewline
31 & 88 & 92.4343723119153 & -4.43437231191533 \tabularnewline
32 & 83 & 88.0748444720858 & -5.07484447208577 \tabularnewline
33 & 98 & 91.3458622739151 & 6.65413772608485 \tabularnewline
34 & 109 & 97.8405971954542 & 11.1594028045458 \tabularnewline
35 & 118 & 102.887990859300 & 15.1120091406997 \tabularnewline
36 & 118 & 108.494246261581 & 9.50575373841885 \tabularnewline
37 & 115 & 111.934036314501 & 3.0659636854986 \tabularnewline
38 & 107 & 101.713438392532 & 5.28656160746831 \tabularnewline
39 & 101 & 103.518259211184 & -2.51825921118447 \tabularnewline
40 & 111 & 109.802419307191 & 1.19758069280938 \tabularnewline
41 & 128 & 123.445761586353 & 4.55423841364714 \tabularnewline
42 & 115 & 109.522841086785 & 5.47715891321491 \tabularnewline
43 & 111 & 111.163069326092 & -0.163069326092099 \tabularnewline
44 & 105 & 107.185085362127 & -2.18508536212738 \tabularnewline
45 & 120 & 122.379409751109 & -2.37940975110898 \tabularnewline
46 & 132 & 129.700417036171 & 2.29958296382898 \tabularnewline
47 & 135 & 134.058208951342 & 0.941791048657706 \tabularnewline
48 & 142 & 130.181452402792 & 11.8185475972083 \tabularnewline
49 & 139 & 129.875616334130 & 9.1243836658702 \tabularnewline
50 & 127 & 121.687176658782 & 5.31282334121799 \tabularnewline
51 & 113 & 117.840334277878 & -4.84033427787783 \tabularnewline
52 & 130 & 127.035302786418 & 2.96469721358189 \tabularnewline
53 & 143 & 145.798997223635 & -2.79899722363479 \tabularnewline
54 & 139 & 127.688213888111 & 11.3117861118893 \tabularnewline
55 & 137 & 127.423662240653 & 9.57633775934681 \tabularnewline
56 & 134 & 124.914865419943 & 9.08513458005665 \tabularnewline
57 & 139 & 147.786908234961 & -8.78690823496126 \tabularnewline
58 & 157 & 157.979956774861 & -0.97995677486125 \tabularnewline
59 & 152 & 160.838013178872 & -8.83801317887244 \tabularnewline
60 & 153 & 160.315987937495 & -7.31598793749484 \tabularnewline
61 & 147 & 150.314188458132 & -3.31418845813235 \tabularnewline
62 & 132 & 134.002251470766 & -2.00225147076577 \tabularnewline
63 & 117 & 120.382999554911 & -3.38299955491098 \tabularnewline
64 & 123 & 135.825886484309 & -12.8258864843092 \tabularnewline
65 & 139 & 145.114987861629 & -6.11498786162855 \tabularnewline
66 & 134 & 134.322702108223 & -0.322702108222501 \tabularnewline
67 & 134 & 128.575952189562 & 5.42404781043794 \tabularnewline
68 & 128 & 124.277599055681 & 3.72240094431938 \tabularnewline
69 & 118 & 133.217807005481 & -15.2178070054806 \tabularnewline
70 & 144 & 144.256997137560 & -0.256997137560319 \tabularnewline
71 & 140 & 142.371677286859 & -2.37167728685895 \tabularnewline
72 & 151 & 144.771578776355 & 6.22842122364494 \tabularnewline
73 & 144 & 142.415576828681 & 1.5844231713194 \tabularnewline
74 & 135 & 129.065124727371 & 5.93487527262945 \tabularnewline
75 & 122 & 117.548478509584 & 4.45152149041594 \tabularnewline
76 & 124 & 129.869070846281 & -5.8690708462806 \tabularnewline
77 & 146 & 146.564514681817 & -0.564514681816547 \tabularnewline
78 & 146 & 141.19988053239 & 4.80011946761013 \tabularnewline
79 & 147 & 140.769207503633 & 6.23079249636666 \tabularnewline
80 & 148 & 135.172348446859 & 12.8276515531415 \tabularnewline
81 & 132 & 134.791961754875 & -2.79196175487539 \tabularnewline
82 & 161 & 163.374736171705 & -2.37473617170534 \tabularnewline
83 & 159 & 159.004491639959 & -0.00449163995881463 \tabularnewline
84 & 173 & 168.832959185330 & 4.16704081466963 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79425&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]93[/C][C]90.7626399476373[/C][C]2.23736005236272[/C][/ROW]
[ROW][C]14[/C][C]87[/C][C]85.885787896059[/C][C]1.11421210394097[/C][/ROW]
[ROW][C]15[/C][C]89[/C][C]88.6114326732123[/C][C]0.388567326787694[/C][/ROW]
[ROW][C]16[/C][C]92[/C][C]91.6676461733725[/C][C]0.332353826627482[/C][/ROW]
[ROW][C]17[/C][C]98[/C][C]97.3412364056725[/C][C]0.658763594327468[/C][/ROW]
[ROW][C]18[/C][C]92[/C][C]91.168401138645[/C][C]0.831598861355047[/C][/ROW]
[ROW][C]19[/C][C]92[/C][C]90.0878122556585[/C][C]1.91218774434149[/C][/ROW]
[ROW][C]20[/C][C]87[/C][C]93.4508464783774[/C][C]-6.45084647837741[/C][/ROW]
[ROW][C]21[/C][C]92[/C][C]92.6931746271342[/C][C]-0.693174627134184[/C][/ROW]
[ROW][C]22[/C][C]98[/C][C]92.716936536819[/C][C]5.28306346318102[/C][/ROW]
[ROW][C]23[/C][C]101[/C][C]95.4667733386968[/C][C]5.5332266613032[/C][/ROW]
[ROW][C]24[/C][C]102[/C][C]99.2675375076998[/C][C]2.73246249230019[/C][/ROW]
[ROW][C]25[/C][C]102[/C][C]101.692979736729[/C][C]0.307020263271014[/C][/ROW]
[ROW][C]26[/C][C]90[/C][C]94.7887630758412[/C][C]-4.7887630758412[/C][/ROW]
[ROW][C]27[/C][C]87[/C][C]94.9788281228176[/C][C]-7.97882812281763[/C][/ROW]
[ROW][C]28[/C][C]92[/C][C]94.9499166765758[/C][C]-2.94991667657584[/C][/ROW]
[ROW][C]29[/C][C]105[/C][C]99.687138556331[/C][C]5.31286144366892[/C][/ROW]
[ROW][C]30[/C][C]90[/C][C]95.1041093141956[/C][C]-5.10410931419564[/C][/ROW]
[ROW][C]31[/C][C]88[/C][C]92.4343723119153[/C][C]-4.43437231191533[/C][/ROW]
[ROW][C]32[/C][C]83[/C][C]88.0748444720858[/C][C]-5.07484447208577[/C][/ROW]
[ROW][C]33[/C][C]98[/C][C]91.3458622739151[/C][C]6.65413772608485[/C][/ROW]
[ROW][C]34[/C][C]109[/C][C]97.8405971954542[/C][C]11.1594028045458[/C][/ROW]
[ROW][C]35[/C][C]118[/C][C]102.887990859300[/C][C]15.1120091406997[/C][/ROW]
[ROW][C]36[/C][C]118[/C][C]108.494246261581[/C][C]9.50575373841885[/C][/ROW]
[ROW][C]37[/C][C]115[/C][C]111.934036314501[/C][C]3.0659636854986[/C][/ROW]
[ROW][C]38[/C][C]107[/C][C]101.713438392532[/C][C]5.28656160746831[/C][/ROW]
[ROW][C]39[/C][C]101[/C][C]103.518259211184[/C][C]-2.51825921118447[/C][/ROW]
[ROW][C]40[/C][C]111[/C][C]109.802419307191[/C][C]1.19758069280938[/C][/ROW]
[ROW][C]41[/C][C]128[/C][C]123.445761586353[/C][C]4.55423841364714[/C][/ROW]
[ROW][C]42[/C][C]115[/C][C]109.522841086785[/C][C]5.47715891321491[/C][/ROW]
[ROW][C]43[/C][C]111[/C][C]111.163069326092[/C][C]-0.163069326092099[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]107.185085362127[/C][C]-2.18508536212738[/C][/ROW]
[ROW][C]45[/C][C]120[/C][C]122.379409751109[/C][C]-2.37940975110898[/C][/ROW]
[ROW][C]46[/C][C]132[/C][C]129.700417036171[/C][C]2.29958296382898[/C][/ROW]
[ROW][C]47[/C][C]135[/C][C]134.058208951342[/C][C]0.941791048657706[/C][/ROW]
[ROW][C]48[/C][C]142[/C][C]130.181452402792[/C][C]11.8185475972083[/C][/ROW]
[ROW][C]49[/C][C]139[/C][C]129.875616334130[/C][C]9.1243836658702[/C][/ROW]
[ROW][C]50[/C][C]127[/C][C]121.687176658782[/C][C]5.31282334121799[/C][/ROW]
[ROW][C]51[/C][C]113[/C][C]117.840334277878[/C][C]-4.84033427787783[/C][/ROW]
[ROW][C]52[/C][C]130[/C][C]127.035302786418[/C][C]2.96469721358189[/C][/ROW]
[ROW][C]53[/C][C]143[/C][C]145.798997223635[/C][C]-2.79899722363479[/C][/ROW]
[ROW][C]54[/C][C]139[/C][C]127.688213888111[/C][C]11.3117861118893[/C][/ROW]
[ROW][C]55[/C][C]137[/C][C]127.423662240653[/C][C]9.57633775934681[/C][/ROW]
[ROW][C]56[/C][C]134[/C][C]124.914865419943[/C][C]9.08513458005665[/C][/ROW]
[ROW][C]57[/C][C]139[/C][C]147.786908234961[/C][C]-8.78690823496126[/C][/ROW]
[ROW][C]58[/C][C]157[/C][C]157.979956774861[/C][C]-0.97995677486125[/C][/ROW]
[ROW][C]59[/C][C]152[/C][C]160.838013178872[/C][C]-8.83801317887244[/C][/ROW]
[ROW][C]60[/C][C]153[/C][C]160.315987937495[/C][C]-7.31598793749484[/C][/ROW]
[ROW][C]61[/C][C]147[/C][C]150.314188458132[/C][C]-3.31418845813235[/C][/ROW]
[ROW][C]62[/C][C]132[/C][C]134.002251470766[/C][C]-2.00225147076577[/C][/ROW]
[ROW][C]63[/C][C]117[/C][C]120.382999554911[/C][C]-3.38299955491098[/C][/ROW]
[ROW][C]64[/C][C]123[/C][C]135.825886484309[/C][C]-12.8258864843092[/C][/ROW]
[ROW][C]65[/C][C]139[/C][C]145.114987861629[/C][C]-6.11498786162855[/C][/ROW]
[ROW][C]66[/C][C]134[/C][C]134.322702108223[/C][C]-0.322702108222501[/C][/ROW]
[ROW][C]67[/C][C]134[/C][C]128.575952189562[/C][C]5.42404781043794[/C][/ROW]
[ROW][C]68[/C][C]128[/C][C]124.277599055681[/C][C]3.72240094431938[/C][/ROW]
[ROW][C]69[/C][C]118[/C][C]133.217807005481[/C][C]-15.2178070054806[/C][/ROW]
[ROW][C]70[/C][C]144[/C][C]144.256997137560[/C][C]-0.256997137560319[/C][/ROW]
[ROW][C]71[/C][C]140[/C][C]142.371677286859[/C][C]-2.37167728685895[/C][/ROW]
[ROW][C]72[/C][C]151[/C][C]144.771578776355[/C][C]6.22842122364494[/C][/ROW]
[ROW][C]73[/C][C]144[/C][C]142.415576828681[/C][C]1.5844231713194[/C][/ROW]
[ROW][C]74[/C][C]135[/C][C]129.065124727371[/C][C]5.93487527262945[/C][/ROW]
[ROW][C]75[/C][C]122[/C][C]117.548478509584[/C][C]4.45152149041594[/C][/ROW]
[ROW][C]76[/C][C]124[/C][C]129.869070846281[/C][C]-5.8690708462806[/C][/ROW]
[ROW][C]77[/C][C]146[/C][C]146.564514681817[/C][C]-0.564514681816547[/C][/ROW]
[ROW][C]78[/C][C]146[/C][C]141.19988053239[/C][C]4.80011946761013[/C][/ROW]
[ROW][C]79[/C][C]147[/C][C]140.769207503633[/C][C]6.23079249636666[/C][/ROW]
[ROW][C]80[/C][C]148[/C][C]135.172348446859[/C][C]12.8276515531415[/C][/ROW]
[ROW][C]81[/C][C]132[/C][C]134.791961754875[/C][C]-2.79196175487539[/C][/ROW]
[ROW][C]82[/C][C]161[/C][C]163.374736171705[/C][C]-2.37473617170534[/C][/ROW]
[ROW][C]83[/C][C]159[/C][C]159.004491639959[/C][C]-0.00449163995881463[/C][/ROW]
[ROW][C]84[/C][C]173[/C][C]168.832959185330[/C][C]4.16704081466963[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79425&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79425&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
139390.76263994763732.23736005236272
148785.8857878960591.11421210394097
158988.61143267321230.388567326787694
169291.66764617337250.332353826627482
179897.34123640567250.658763594327468
189291.1684011386450.831598861355047
199290.08781225565851.91218774434149
208793.4508464783774-6.45084647837741
219292.6931746271342-0.693174627134184
229892.7169365368195.28306346318102
2310195.46677333869685.5332266613032
2410299.26753750769982.73246249230019
25102101.6929797367290.307020263271014
269094.7887630758412-4.7887630758412
278794.9788281228176-7.97882812281763
289294.9499166765758-2.94991667657584
2910599.6871385563315.31286144366892
309095.1041093141956-5.10410931419564
318892.4343723119153-4.43437231191533
328388.0748444720858-5.07484447208577
339891.34586227391516.65413772608485
3410997.840597195454211.1594028045458
35118102.88799085930015.1120091406997
36118108.4942462615819.50575373841885
37115111.9340363145013.0659636854986
38107101.7134383925325.28656160746831
39101103.518259211184-2.51825921118447
40111109.8024193071911.19758069280938
41128123.4457615863534.55423841364714
42115109.5228410867855.47715891321491
43111111.163069326092-0.163069326092099
44105107.185085362127-2.18508536212738
45120122.379409751109-2.37940975110898
46132129.7004170361712.29958296382898
47135134.0582089513420.941791048657706
48142130.18145240279211.8185475972083
49139129.8756163341309.1243836658702
50127121.6871766587825.31282334121799
51113117.840334277878-4.84033427787783
52130127.0353027864182.96469721358189
53143145.798997223635-2.79899722363479
54139127.68821388811111.3117861118893
55137127.4236622406539.57633775934681
56134124.9148654199439.08513458005665
57139147.786908234961-8.78690823496126
58157157.979956774861-0.97995677486125
59152160.838013178872-8.83801317887244
60153160.315987937495-7.31598793749484
61147150.314188458132-3.31418845813235
62132134.002251470766-2.00225147076577
63117120.382999554911-3.38299955491098
64123135.825886484309-12.8258864843092
65139145.114987861629-6.11498786162855
66134134.322702108223-0.322702108222501
67134128.5759521895625.42404781043794
68128124.2775990556813.72240094431938
69118133.217807005481-15.2178070054806
70144144.256997137560-0.256997137560319
71140142.371677286859-2.37167728685895
72151144.7715787763556.22842122364494
73144142.4155768286811.5844231713194
74135129.0651247273715.93487527262945
75122117.5484785095844.45152149041594
76124129.869070846281-5.8690708462806
77146146.564514681817-0.564514681816547
78146141.199880532394.80011946761013
79147140.7692075036336.23079249636666
80148135.17234844685912.8276515531415
81132134.791961754875-2.79196175487539
82161163.374736171705-2.37473617170534
83159159.004491639959-0.00449163995881463
84173168.8329591853304.16704081466963







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85161.858561825761150.123013955486173.594109696037
86149.213768800595136.795030289055161.632507312136
87132.981614256612120.082387859530145.880840653694
88137.489660098904123.725832588980151.253487608828
89162.139783985959146.731885454870177.547682517048
90160.131188383047144.165785027919176.096591738174
91158.618845241228142.098391841271175.139298641184
92154.229969759351137.341785262358171.118154256344
93138.602498657158122.057751410036155.147245904281
94169.950555024538150.625180674227189.275929374849
95167.821139854713148.101900772924187.540378936501
96180.908500239743150.662431825259211.154568654228

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 161.858561825761 & 150.123013955486 & 173.594109696037 \tabularnewline
86 & 149.213768800595 & 136.795030289055 & 161.632507312136 \tabularnewline
87 & 132.981614256612 & 120.082387859530 & 145.880840653694 \tabularnewline
88 & 137.489660098904 & 123.725832588980 & 151.253487608828 \tabularnewline
89 & 162.139783985959 & 146.731885454870 & 177.547682517048 \tabularnewline
90 & 160.131188383047 & 144.165785027919 & 176.096591738174 \tabularnewline
91 & 158.618845241228 & 142.098391841271 & 175.139298641184 \tabularnewline
92 & 154.229969759351 & 137.341785262358 & 171.118154256344 \tabularnewline
93 & 138.602498657158 & 122.057751410036 & 155.147245904281 \tabularnewline
94 & 169.950555024538 & 150.625180674227 & 189.275929374849 \tabularnewline
95 & 167.821139854713 & 148.101900772924 & 187.540378936501 \tabularnewline
96 & 180.908500239743 & 150.662431825259 & 211.154568654228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79425&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]161.858561825761[/C][C]150.123013955486[/C][C]173.594109696037[/C][/ROW]
[ROW][C]86[/C][C]149.213768800595[/C][C]136.795030289055[/C][C]161.632507312136[/C][/ROW]
[ROW][C]87[/C][C]132.981614256612[/C][C]120.082387859530[/C][C]145.880840653694[/C][/ROW]
[ROW][C]88[/C][C]137.489660098904[/C][C]123.725832588980[/C][C]151.253487608828[/C][/ROW]
[ROW][C]89[/C][C]162.139783985959[/C][C]146.731885454870[/C][C]177.547682517048[/C][/ROW]
[ROW][C]90[/C][C]160.131188383047[/C][C]144.165785027919[/C][C]176.096591738174[/C][/ROW]
[ROW][C]91[/C][C]158.618845241228[/C][C]142.098391841271[/C][C]175.139298641184[/C][/ROW]
[ROW][C]92[/C][C]154.229969759351[/C][C]137.341785262358[/C][C]171.118154256344[/C][/ROW]
[ROW][C]93[/C][C]138.602498657158[/C][C]122.057751410036[/C][C]155.147245904281[/C][/ROW]
[ROW][C]94[/C][C]169.950555024538[/C][C]150.625180674227[/C][C]189.275929374849[/C][/ROW]
[ROW][C]95[/C][C]167.821139854713[/C][C]148.101900772924[/C][C]187.540378936501[/C][/ROW]
[ROW][C]96[/C][C]180.908500239743[/C][C]150.662431825259[/C][C]211.154568654228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79425&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79425&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
85161.858561825761150.123013955486173.594109696037
86149.213768800595136.795030289055161.632507312136
87132.981614256612120.082387859530145.880840653694
88137.489660098904123.725832588980151.253487608828
89162.139783985959146.731885454870177.547682517048
90160.131188383047144.165785027919176.096591738174
91158.618845241228142.098391841271175.139298641184
92154.229969759351137.341785262358171.118154256344
93138.602498657158122.057751410036155.147245904281
94169.950555024538150.625180674227189.275929374849
95167.821139854713148.101900772924187.540378936501
96180.908500239743150.662431825259211.154568654228



Parameters (Session):
par1 = multiplicative ; par2 = 12 ;
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')