Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 May 2017 09:45:01 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/May/02/t1493714834z6cpeoe0dy2jd8n.htm/, Retrieved Fri, 17 May 2024 08:08:51 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 08:08:51 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
86,88
90,65
90,68
89,64
102,62
101,84
92,51
94,29
94,68
96,94
94,03
89,65
84,9
89,07
89,8
93,22
92,23
98,41
96,63
89,8
90
92,13
93,27
90,81
85,42
88,28
88,73
90,18
92,74
96,13
94,85
94,25
96,94
101,22
98,71
95,51
93,91
98,17
97,59
99,64
107,88
108,49
100,25
99,27
101,73
101,25
97,09
94,74
94,53
93,48
96,05
106,22
98,33
99,86
93,78
88,96
83,77
89,46
86,78
88,4
87,19
92,23
95,99
104,75
105,63
108,71
96,4
93,31
93,77
98,7
95,04
95,61




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.976930510334217
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.976930510334217 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.976930510334217[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.976930510334217
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
290.6586.883.77000000000001
390.6890.563028023960.116971976040006
489.6490.6773015162076-1.03730151620756
5102.6289.663930016608412.9560699833916
6101.84102.321110077409-0.481110077408985
792.51101.851098963959-9.34109896395888
894.2992.72549438601611.56450561398388
994.6894.25390765390610.426092346093867
1096.9494.67017026702512.26982973297487
1194.0396.887636186432-2.85763618643205
1289.6594.0959242084715-4.44592420847147
1384.989.7525652025822-4.85256520258218
1489.0785.01194620279354.05805379720647
1589.888.97638276986210.823617230137856
1693.2289.78099957082083.43900042917923
1792.2393.1406640151384-0.910664015138423
1898.4192.25100855408626.15899144591376
1996.6398.2679152104868-1.63791521048684
2089.896.6677858680218-6.86778586802176
219089.95843631510910.0415636848908605
2292.1389.99904114700092.13095885299906
2393.2792.08083986676251.18916013323748
2490.8193.2425666825953-2.43256668259531
2585.4290.8661180719455-5.44611807194546
2688.2885.54563916457942.73436083542062
2788.7388.21691969096470.51308030903526
2890.1888.7181634991131.461836500887
2992.7490.14627617794972.59372382205026
3096.1392.68016411509133.44983588490868
3194.8596.0504140467044-1.20041404670445
3294.2594.8776929394451-0.627692939445112
3396.9494.26448055577982.67551944422019
34101.2296.8782771318314.34172286816904
3598.71101.119838669161-2.40983866916109
3695.5198.7655937482744-3.25559374827441
3793.9195.5851048863318-1.67510488633181
3898.1793.94864381486434.22135618513566
3997.5998.0726154671114-0.482615467111415
4099.6497.60113369253112.03886630746892
41107.8899.59296439478998.28703560521006
42108.49107.6888223177460.801177682254362
43100.25108.471517239739-8.22151723973877
4499.27100.439666206999-1.16966620699922
45101.7399.29698360247482.43301639752524
46101.25101.673871553361-0.423871553360627
4797.09101.25977850042-4.16977850041987
4894.7497.1861946620241-2.44619466202406
4994.5394.796432462476-0.266432462476047
5093.4894.5361464609397-1.05614646093971
5196.0593.50436475986622.54563524013379
52106.2295.991273494134910.2287265058651
5398.33105.984028499579-7.65402849957881
5499.8698.50657453137261.35342546862736
5593.7899.8287771651381-6.04877716513809
5688.9693.9195422023018-4.95954220230179
5783.7789.074414107583-5.30441410758303
5889.4683.89237012643795.56762987356207
5986.7889.331557620169-2.55155762016895
6088.486.83886313215011.56113686784987
6187.1988.3639853691603-1.17398536916028
6292.2387.21708324334165.01291675665838
6395.9992.11435456868683.87564543131316
64104.7595.90059083777418.84940916222592
65105.63104.5458486467841.08415135321626
66108.71105.6049891815613.10501081843917
6796.4108.638368985012-12.2383689850119
6893.3196.6823329268258-3.37233292682578
6993.7793.3877979996050.382202000395012
7098.793.76118279490164.93881720509836
7195.0498.5860640075258-3.54606400752579
7295.6195.12180588697580.488194113024164

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 90.65 & 86.88 & 3.77000000000001 \tabularnewline
3 & 90.68 & 90.56302802396 & 0.116971976040006 \tabularnewline
4 & 89.64 & 90.6773015162076 & -1.03730151620756 \tabularnewline
5 & 102.62 & 89.6639300166084 & 12.9560699833916 \tabularnewline
6 & 101.84 & 102.321110077409 & -0.481110077408985 \tabularnewline
7 & 92.51 & 101.851098963959 & -9.34109896395888 \tabularnewline
8 & 94.29 & 92.7254943860161 & 1.56450561398388 \tabularnewline
9 & 94.68 & 94.2539076539061 & 0.426092346093867 \tabularnewline
10 & 96.94 & 94.6701702670251 & 2.26982973297487 \tabularnewline
11 & 94.03 & 96.887636186432 & -2.85763618643205 \tabularnewline
12 & 89.65 & 94.0959242084715 & -4.44592420847147 \tabularnewline
13 & 84.9 & 89.7525652025822 & -4.85256520258218 \tabularnewline
14 & 89.07 & 85.0119462027935 & 4.05805379720647 \tabularnewline
15 & 89.8 & 88.9763827698621 & 0.823617230137856 \tabularnewline
16 & 93.22 & 89.7809995708208 & 3.43900042917923 \tabularnewline
17 & 92.23 & 93.1406640151384 & -0.910664015138423 \tabularnewline
18 & 98.41 & 92.2510085540862 & 6.15899144591376 \tabularnewline
19 & 96.63 & 98.2679152104868 & -1.63791521048684 \tabularnewline
20 & 89.8 & 96.6677858680218 & -6.86778586802176 \tabularnewline
21 & 90 & 89.9584363151091 & 0.0415636848908605 \tabularnewline
22 & 92.13 & 89.9990411470009 & 2.13095885299906 \tabularnewline
23 & 93.27 & 92.0808398667625 & 1.18916013323748 \tabularnewline
24 & 90.81 & 93.2425666825953 & -2.43256668259531 \tabularnewline
25 & 85.42 & 90.8661180719455 & -5.44611807194546 \tabularnewline
26 & 88.28 & 85.5456391645794 & 2.73436083542062 \tabularnewline
27 & 88.73 & 88.2169196909647 & 0.51308030903526 \tabularnewline
28 & 90.18 & 88.718163499113 & 1.461836500887 \tabularnewline
29 & 92.74 & 90.1462761779497 & 2.59372382205026 \tabularnewline
30 & 96.13 & 92.6801641150913 & 3.44983588490868 \tabularnewline
31 & 94.85 & 96.0504140467044 & -1.20041404670445 \tabularnewline
32 & 94.25 & 94.8776929394451 & -0.627692939445112 \tabularnewline
33 & 96.94 & 94.2644805557798 & 2.67551944422019 \tabularnewline
34 & 101.22 & 96.878277131831 & 4.34172286816904 \tabularnewline
35 & 98.71 & 101.119838669161 & -2.40983866916109 \tabularnewline
36 & 95.51 & 98.7655937482744 & -3.25559374827441 \tabularnewline
37 & 93.91 & 95.5851048863318 & -1.67510488633181 \tabularnewline
38 & 98.17 & 93.9486438148643 & 4.22135618513566 \tabularnewline
39 & 97.59 & 98.0726154671114 & -0.482615467111415 \tabularnewline
40 & 99.64 & 97.6011336925311 & 2.03886630746892 \tabularnewline
41 & 107.88 & 99.5929643947899 & 8.28703560521006 \tabularnewline
42 & 108.49 & 107.688822317746 & 0.801177682254362 \tabularnewline
43 & 100.25 & 108.471517239739 & -8.22151723973877 \tabularnewline
44 & 99.27 & 100.439666206999 & -1.16966620699922 \tabularnewline
45 & 101.73 & 99.2969836024748 & 2.43301639752524 \tabularnewline
46 & 101.25 & 101.673871553361 & -0.423871553360627 \tabularnewline
47 & 97.09 & 101.25977850042 & -4.16977850041987 \tabularnewline
48 & 94.74 & 97.1861946620241 & -2.44619466202406 \tabularnewline
49 & 94.53 & 94.796432462476 & -0.266432462476047 \tabularnewline
50 & 93.48 & 94.5361464609397 & -1.05614646093971 \tabularnewline
51 & 96.05 & 93.5043647598662 & 2.54563524013379 \tabularnewline
52 & 106.22 & 95.9912734941349 & 10.2287265058651 \tabularnewline
53 & 98.33 & 105.984028499579 & -7.65402849957881 \tabularnewline
54 & 99.86 & 98.5065745313726 & 1.35342546862736 \tabularnewline
55 & 93.78 & 99.8287771651381 & -6.04877716513809 \tabularnewline
56 & 88.96 & 93.9195422023018 & -4.95954220230179 \tabularnewline
57 & 83.77 & 89.074414107583 & -5.30441410758303 \tabularnewline
58 & 89.46 & 83.8923701264379 & 5.56762987356207 \tabularnewline
59 & 86.78 & 89.331557620169 & -2.55155762016895 \tabularnewline
60 & 88.4 & 86.8388631321501 & 1.56113686784987 \tabularnewline
61 & 87.19 & 88.3639853691603 & -1.17398536916028 \tabularnewline
62 & 92.23 & 87.2170832433416 & 5.01291675665838 \tabularnewline
63 & 95.99 & 92.1143545686868 & 3.87564543131316 \tabularnewline
64 & 104.75 & 95.9005908377741 & 8.84940916222592 \tabularnewline
65 & 105.63 & 104.545848646784 & 1.08415135321626 \tabularnewline
66 & 108.71 & 105.604989181561 & 3.10501081843917 \tabularnewline
67 & 96.4 & 108.638368985012 & -12.2383689850119 \tabularnewline
68 & 93.31 & 96.6823329268258 & -3.37233292682578 \tabularnewline
69 & 93.77 & 93.387797999605 & 0.382202000395012 \tabularnewline
70 & 98.7 & 93.7611827949016 & 4.93881720509836 \tabularnewline
71 & 95.04 & 98.5860640075258 & -3.54606400752579 \tabularnewline
72 & 95.61 & 95.1218058869758 & 0.488194113024164 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]2[/C][C]90.65[/C][C]86.88[/C][C]3.77000000000001[/C][/ROW]
[ROW][C]3[/C][C]90.68[/C][C]90.56302802396[/C][C]0.116971976040006[/C][/ROW]
[ROW][C]4[/C][C]89.64[/C][C]90.6773015162076[/C][C]-1.03730151620756[/C][/ROW]
[ROW][C]5[/C][C]102.62[/C][C]89.6639300166084[/C][C]12.9560699833916[/C][/ROW]
[ROW][C]6[/C][C]101.84[/C][C]102.321110077409[/C][C]-0.481110077408985[/C][/ROW]
[ROW][C]7[/C][C]92.51[/C][C]101.851098963959[/C][C]-9.34109896395888[/C][/ROW]
[ROW][C]8[/C][C]94.29[/C][C]92.7254943860161[/C][C]1.56450561398388[/C][/ROW]
[ROW][C]9[/C][C]94.68[/C][C]94.2539076539061[/C][C]0.426092346093867[/C][/ROW]
[ROW][C]10[/C][C]96.94[/C][C]94.6701702670251[/C][C]2.26982973297487[/C][/ROW]
[ROW][C]11[/C][C]94.03[/C][C]96.887636186432[/C][C]-2.85763618643205[/C][/ROW]
[ROW][C]12[/C][C]89.65[/C][C]94.0959242084715[/C][C]-4.44592420847147[/C][/ROW]
[ROW][C]13[/C][C]84.9[/C][C]89.7525652025822[/C][C]-4.85256520258218[/C][/ROW]
[ROW][C]14[/C][C]89.07[/C][C]85.0119462027935[/C][C]4.05805379720647[/C][/ROW]
[ROW][C]15[/C][C]89.8[/C][C]88.9763827698621[/C][C]0.823617230137856[/C][/ROW]
[ROW][C]16[/C][C]93.22[/C][C]89.7809995708208[/C][C]3.43900042917923[/C][/ROW]
[ROW][C]17[/C][C]92.23[/C][C]93.1406640151384[/C][C]-0.910664015138423[/C][/ROW]
[ROW][C]18[/C][C]98.41[/C][C]92.2510085540862[/C][C]6.15899144591376[/C][/ROW]
[ROW][C]19[/C][C]96.63[/C][C]98.2679152104868[/C][C]-1.63791521048684[/C][/ROW]
[ROW][C]20[/C][C]89.8[/C][C]96.6677858680218[/C][C]-6.86778586802176[/C][/ROW]
[ROW][C]21[/C][C]90[/C][C]89.9584363151091[/C][C]0.0415636848908605[/C][/ROW]
[ROW][C]22[/C][C]92.13[/C][C]89.9990411470009[/C][C]2.13095885299906[/C][/ROW]
[ROW][C]23[/C][C]93.27[/C][C]92.0808398667625[/C][C]1.18916013323748[/C][/ROW]
[ROW][C]24[/C][C]90.81[/C][C]93.2425666825953[/C][C]-2.43256668259531[/C][/ROW]
[ROW][C]25[/C][C]85.42[/C][C]90.8661180719455[/C][C]-5.44611807194546[/C][/ROW]
[ROW][C]26[/C][C]88.28[/C][C]85.5456391645794[/C][C]2.73436083542062[/C][/ROW]
[ROW][C]27[/C][C]88.73[/C][C]88.2169196909647[/C][C]0.51308030903526[/C][/ROW]
[ROW][C]28[/C][C]90.18[/C][C]88.718163499113[/C][C]1.461836500887[/C][/ROW]
[ROW][C]29[/C][C]92.74[/C][C]90.1462761779497[/C][C]2.59372382205026[/C][/ROW]
[ROW][C]30[/C][C]96.13[/C][C]92.6801641150913[/C][C]3.44983588490868[/C][/ROW]
[ROW][C]31[/C][C]94.85[/C][C]96.0504140467044[/C][C]-1.20041404670445[/C][/ROW]
[ROW][C]32[/C][C]94.25[/C][C]94.8776929394451[/C][C]-0.627692939445112[/C][/ROW]
[ROW][C]33[/C][C]96.94[/C][C]94.2644805557798[/C][C]2.67551944422019[/C][/ROW]
[ROW][C]34[/C][C]101.22[/C][C]96.878277131831[/C][C]4.34172286816904[/C][/ROW]
[ROW][C]35[/C][C]98.71[/C][C]101.119838669161[/C][C]-2.40983866916109[/C][/ROW]
[ROW][C]36[/C][C]95.51[/C][C]98.7655937482744[/C][C]-3.25559374827441[/C][/ROW]
[ROW][C]37[/C][C]93.91[/C][C]95.5851048863318[/C][C]-1.67510488633181[/C][/ROW]
[ROW][C]38[/C][C]98.17[/C][C]93.9486438148643[/C][C]4.22135618513566[/C][/ROW]
[ROW][C]39[/C][C]97.59[/C][C]98.0726154671114[/C][C]-0.482615467111415[/C][/ROW]
[ROW][C]40[/C][C]99.64[/C][C]97.6011336925311[/C][C]2.03886630746892[/C][/ROW]
[ROW][C]41[/C][C]107.88[/C][C]99.5929643947899[/C][C]8.28703560521006[/C][/ROW]
[ROW][C]42[/C][C]108.49[/C][C]107.688822317746[/C][C]0.801177682254362[/C][/ROW]
[ROW][C]43[/C][C]100.25[/C][C]108.471517239739[/C][C]-8.22151723973877[/C][/ROW]
[ROW][C]44[/C][C]99.27[/C][C]100.439666206999[/C][C]-1.16966620699922[/C][/ROW]
[ROW][C]45[/C][C]101.73[/C][C]99.2969836024748[/C][C]2.43301639752524[/C][/ROW]
[ROW][C]46[/C][C]101.25[/C][C]101.673871553361[/C][C]-0.423871553360627[/C][/ROW]
[ROW][C]47[/C][C]97.09[/C][C]101.25977850042[/C][C]-4.16977850041987[/C][/ROW]
[ROW][C]48[/C][C]94.74[/C][C]97.1861946620241[/C][C]-2.44619466202406[/C][/ROW]
[ROW][C]49[/C][C]94.53[/C][C]94.796432462476[/C][C]-0.266432462476047[/C][/ROW]
[ROW][C]50[/C][C]93.48[/C][C]94.5361464609397[/C][C]-1.05614646093971[/C][/ROW]
[ROW][C]51[/C][C]96.05[/C][C]93.5043647598662[/C][C]2.54563524013379[/C][/ROW]
[ROW][C]52[/C][C]106.22[/C][C]95.9912734941349[/C][C]10.2287265058651[/C][/ROW]
[ROW][C]53[/C][C]98.33[/C][C]105.984028499579[/C][C]-7.65402849957881[/C][/ROW]
[ROW][C]54[/C][C]99.86[/C][C]98.5065745313726[/C][C]1.35342546862736[/C][/ROW]
[ROW][C]55[/C][C]93.78[/C][C]99.8287771651381[/C][C]-6.04877716513809[/C][/ROW]
[ROW][C]56[/C][C]88.96[/C][C]93.9195422023018[/C][C]-4.95954220230179[/C][/ROW]
[ROW][C]57[/C][C]83.77[/C][C]89.074414107583[/C][C]-5.30441410758303[/C][/ROW]
[ROW][C]58[/C][C]89.46[/C][C]83.8923701264379[/C][C]5.56762987356207[/C][/ROW]
[ROW][C]59[/C][C]86.78[/C][C]89.331557620169[/C][C]-2.55155762016895[/C][/ROW]
[ROW][C]60[/C][C]88.4[/C][C]86.8388631321501[/C][C]1.56113686784987[/C][/ROW]
[ROW][C]61[/C][C]87.19[/C][C]88.3639853691603[/C][C]-1.17398536916028[/C][/ROW]
[ROW][C]62[/C][C]92.23[/C][C]87.2170832433416[/C][C]5.01291675665838[/C][/ROW]
[ROW][C]63[/C][C]95.99[/C][C]92.1143545686868[/C][C]3.87564543131316[/C][/ROW]
[ROW][C]64[/C][C]104.75[/C][C]95.9005908377741[/C][C]8.84940916222592[/C][/ROW]
[ROW][C]65[/C][C]105.63[/C][C]104.545848646784[/C][C]1.08415135321626[/C][/ROW]
[ROW][C]66[/C][C]108.71[/C][C]105.604989181561[/C][C]3.10501081843917[/C][/ROW]
[ROW][C]67[/C][C]96.4[/C][C]108.638368985012[/C][C]-12.2383689850119[/C][/ROW]
[ROW][C]68[/C][C]93.31[/C][C]96.6823329268258[/C][C]-3.37233292682578[/C][/ROW]
[ROW][C]69[/C][C]93.77[/C][C]93.387797999605[/C][C]0.382202000395012[/C][/ROW]
[ROW][C]70[/C][C]98.7[/C][C]93.7611827949016[/C][C]4.93881720509836[/C][/ROW]
[ROW][C]71[/C][C]95.04[/C][C]98.5860640075258[/C][C]-3.54606400752579[/C][/ROW]
[ROW][C]72[/C][C]95.61[/C][C]95.1218058869758[/C][C]0.488194113024164[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
290.6586.883.77000000000001
390.6890.563028023960.116971976040006
489.6490.6773015162076-1.03730151620756
5102.6289.663930016608412.9560699833916
6101.84102.321110077409-0.481110077408985
792.51101.851098963959-9.34109896395888
894.2992.72549438601611.56450561398388
994.6894.25390765390610.426092346093867
1096.9494.67017026702512.26982973297487
1194.0396.887636186432-2.85763618643205
1289.6594.0959242084715-4.44592420847147
1384.989.7525652025822-4.85256520258218
1489.0785.01194620279354.05805379720647
1589.888.97638276986210.823617230137856
1693.2289.78099957082083.43900042917923
1792.2393.1406640151384-0.910664015138423
1898.4192.25100855408626.15899144591376
1996.6398.2679152104868-1.63791521048684
2089.896.6677858680218-6.86778586802176
219089.95843631510910.0415636848908605
2292.1389.99904114700092.13095885299906
2393.2792.08083986676251.18916013323748
2490.8193.2425666825953-2.43256668259531
2585.4290.8661180719455-5.44611807194546
2688.2885.54563916457942.73436083542062
2788.7388.21691969096470.51308030903526
2890.1888.7181634991131.461836500887
2992.7490.14627617794972.59372382205026
3096.1392.68016411509133.44983588490868
3194.8596.0504140467044-1.20041404670445
3294.2594.8776929394451-0.627692939445112
3396.9494.26448055577982.67551944422019
34101.2296.8782771318314.34172286816904
3598.71101.119838669161-2.40983866916109
3695.5198.7655937482744-3.25559374827441
3793.9195.5851048863318-1.67510488633181
3898.1793.94864381486434.22135618513566
3997.5998.0726154671114-0.482615467111415
4099.6497.60113369253112.03886630746892
41107.8899.59296439478998.28703560521006
42108.49107.6888223177460.801177682254362
43100.25108.471517239739-8.22151723973877
4499.27100.439666206999-1.16966620699922
45101.7399.29698360247482.43301639752524
46101.25101.673871553361-0.423871553360627
4797.09101.25977850042-4.16977850041987
4894.7497.1861946620241-2.44619466202406
4994.5394.796432462476-0.266432462476047
5093.4894.5361464609397-1.05614646093971
5196.0593.50436475986622.54563524013379
52106.2295.991273494134910.2287265058651
5398.33105.984028499579-7.65402849957881
5499.8698.50657453137261.35342546862736
5593.7899.8287771651381-6.04877716513809
5688.9693.9195422023018-4.95954220230179
5783.7789.074414107583-5.30441410758303
5889.4683.89237012643795.56762987356207
5986.7889.331557620169-2.55155762016895
6088.486.83886313215011.56113686784987
6187.1988.3639853691603-1.17398536916028
6292.2387.21708324334165.01291675665838
6395.9992.11435456868683.87564543131316
64104.7595.90059083777418.84940916222592
65105.63104.5458486467841.08415135321626
66108.71105.6049891815613.10501081843917
6796.4108.638368985012-12.2383689850119
6893.3196.6823329268258-3.37233292682578
6993.7793.3877979996050.382202000395012
7098.793.76118279490164.93881720509836
7195.0498.5860640075258-3.54606400752579
7295.6195.12180588697580.488194113024164







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7395.598737610954786.8819697897595104.31550543215
7495.598737610954783.4127297982338107.784745423676
7595.598737610954780.7321464894242110.465328732485
7695.598737610954778.4659539276813112.731521294228
7795.598737610954776.4663299762394114.73114524567
7895.598737610954774.6567757385802116.540699483329
7995.598737610954772.9916035106965118.205871711213
8095.598737610954771.4409385102475119.756536711662
8195.598737610954769.9839761919369121.213499029972
8295.598737610954768.6055394359278122.591935785982
8395.598737610954767.294153302413123.903321919496
8495.598737610954766.0408919850905125.156583236819

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 95.5987376109547 & 86.8819697897595 & 104.31550543215 \tabularnewline
74 & 95.5987376109547 & 83.4127297982338 & 107.784745423676 \tabularnewline
75 & 95.5987376109547 & 80.7321464894242 & 110.465328732485 \tabularnewline
76 & 95.5987376109547 & 78.4659539276813 & 112.731521294228 \tabularnewline
77 & 95.5987376109547 & 76.4663299762394 & 114.73114524567 \tabularnewline
78 & 95.5987376109547 & 74.6567757385802 & 116.540699483329 \tabularnewline
79 & 95.5987376109547 & 72.9916035106965 & 118.205871711213 \tabularnewline
80 & 95.5987376109547 & 71.4409385102475 & 119.756536711662 \tabularnewline
81 & 95.5987376109547 & 69.9839761919369 & 121.213499029972 \tabularnewline
82 & 95.5987376109547 & 68.6055394359278 & 122.591935785982 \tabularnewline
83 & 95.5987376109547 & 67.294153302413 & 123.903321919496 \tabularnewline
84 & 95.5987376109547 & 66.0408919850905 & 125.156583236819 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]73[/C][C]95.5987376109547[/C][C]86.8819697897595[/C][C]104.31550543215[/C][/ROW]
[ROW][C]74[/C][C]95.5987376109547[/C][C]83.4127297982338[/C][C]107.784745423676[/C][/ROW]
[ROW][C]75[/C][C]95.5987376109547[/C][C]80.7321464894242[/C][C]110.465328732485[/C][/ROW]
[ROW][C]76[/C][C]95.5987376109547[/C][C]78.4659539276813[/C][C]112.731521294228[/C][/ROW]
[ROW][C]77[/C][C]95.5987376109547[/C][C]76.4663299762394[/C][C]114.73114524567[/C][/ROW]
[ROW][C]78[/C][C]95.5987376109547[/C][C]74.6567757385802[/C][C]116.540699483329[/C][/ROW]
[ROW][C]79[/C][C]95.5987376109547[/C][C]72.9916035106965[/C][C]118.205871711213[/C][/ROW]
[ROW][C]80[/C][C]95.5987376109547[/C][C]71.4409385102475[/C][C]119.756536711662[/C][/ROW]
[ROW][C]81[/C][C]95.5987376109547[/C][C]69.9839761919369[/C][C]121.213499029972[/C][/ROW]
[ROW][C]82[/C][C]95.5987376109547[/C][C]68.6055394359278[/C][C]122.591935785982[/C][/ROW]
[ROW][C]83[/C][C]95.5987376109547[/C][C]67.294153302413[/C][C]123.903321919496[/C][/ROW]
[ROW][C]84[/C][C]95.5987376109547[/C][C]66.0408919850905[/C][C]125.156583236819[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
7395.598737610954786.8819697897595104.31550543215
7495.598737610954783.4127297982338107.784745423676
7595.598737610954780.7321464894242110.465328732485
7695.598737610954778.4659539276813112.731521294228
7795.598737610954776.4663299762394114.73114524567
7895.598737610954774.6567757385802116.540699483329
7995.598737610954772.9916035106965118.205871711213
8095.598737610954771.4409385102475119.756536711662
8195.598737610954769.9839761919369121.213499029972
8295.598737610954768.6055394359278122.591935785982
8395.598737610954767.294153302413123.903321919496
8495.598737610954766.0408919850905125.156583236819



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