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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 11 Jan 2014 04:14:02 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Jan/11/t1389431686au2irswi4s5mkrs.htm/, Retrieved Sun, 19 May 2024 09:25:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232891, Retrieved Sun, 19 May 2024 09:25:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-01-11 09:14:02] [fea6726c28a9f2dda0f0277c639abb27] [Current]
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Dataseries X:
110,12
112,28
113,77
114,38
119,06
119,94
120,98
122,33
121,7
123,73
121,73
119,75
117,4
120,99
125,18
126,41
129,38
131,93
129,34
128,58
125,37
123,25
122,78
120,37
116,83
116,39
120,69
123,51
127,43
125,99
120,62
113,71
110,79
108,15
111,22
112,65
112,47
117,48
122,46
123,46
122,33
129,2
129,22
131,17
120,22
120,38
115,32
112,25
109,83
107,05
112,87
113,68
115,08
120,61
119,14
118,63
115,78
117,26
117,61
113,92
113,65
115,89
116,55
117,78
117,36
121,09
124,26
121,88
119,52
122,49
120,86
120,31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232891&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]4 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=232891&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232891&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232891&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]0.999933893038648[/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=232891&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232891&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2112.28110.122.16
3113.77112.2798572089631.49014279103652
4114.38113.7699014911880.610098508811902
5119.06114.3799596682414.68004033175855
6119.94119.0596906167550.880309383245333
7120.98119.9399418054221.04005819457838
8122.33120.9799312449131.35006875508687
9121.7122.329910751057-0.629910751056983
10123.73121.7000416414862.02995835851432
11121.73123.729865805621-1.99986580562125
12119.75121.730132205052-1.98013220505152
13117.4119.750130900523-2.35013090052314
14120.99117.4001553600133.58984463998738
15125.18120.9897626862794.19023731372089
16126.41125.1797229961441.23027700385614
17129.38126.4099186701262.97008132987435
18131.93129.3798036569482.55019634305171
19129.34131.929831414269-2.5898314142689
20128.58129.340171205885-0.7601712058852
21125.37128.580050252609-3.21005025260854
22123.25125.370212206668-2.12021220666799
23122.78123.250140160786-0.4701401607864
24120.37122.780031079537-2.41003107953743
25116.83120.370159319831-3.54015931983143
26116.39116.830234029175-0.440234029175329
27120.69116.3900291025344.29997089746604
28123.51120.689715741992.82028425800993
29127.43123.5098135595783.92018644042244
30125.99127.429740848387-1.43974084838651
31120.62125.990095176893-5.3700951768926
32113.71120.620355000674-6.91035500067433
33110.79113.710456822571-2.92045682257094
34108.15110.790193062526-2.64019306252629
35111.22108.1501745351413.06982546485925
36112.65111.2197970631671.43020293683337
37112.47112.64990545363-0.179905453629743
38117.48112.4700118930035.00998810699714
39122.46117.479668804914.98033119509016
40123.46122.4596707654381.00032923456183
41122.33123.459933871274-1.12993387127395
42129.2122.3300746964956.86992530350523
43129.22129.1995458501130.0204541498865467
44131.17129.2199986478381.95000135216168
45120.22131.169871091336-10.949871091336
46120.38120.2207238627050.159276137294952
47115.32120.379989470739-5.05998947073854
48112.25115.320334500528-3.07033450052838
49109.83112.250202970484-2.42020297048417
50107.05109.830159992264-2.78015999226423
51112.87107.0501837879295.81981621207085
52113.68112.8696152696350.810384730365413
53115.08113.6799464279281.40005357207204
54120.61115.0799074467135.53009255328737
55119.14120.609634422385-1.46963442238531
56118.63119.140097153066-0.510097153065971
57115.78118.630033720973-2.85003372097277
58117.26115.7801884070691.47981159293096
59117.61117.2599021741520.350097825847783
60113.92117.609976856097-3.68997685609655
61113.65113.920243933157-0.270243933157417
62115.89113.6500178650052.23998213499475
63116.55115.8898519215880.660148078412419
64117.78116.5499563596161.23004364038351
65117.36117.779918685553-0.419918685552602
66121.09117.3600277595483.72997224045169
67124.26121.0897534228693.17024657713074
68121.88124.259790424632-2.37979042463206
69119.52121.880157320714-2.36015732071363
70122.49119.5201560228292.96984397717121
71120.86122.489803672639-1.62980367263897
72120.31120.860107741368-0.550107741368393

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 112.28 & 110.12 & 2.16 \tabularnewline
3 & 113.77 & 112.279857208963 & 1.49014279103652 \tabularnewline
4 & 114.38 & 113.769901491188 & 0.610098508811902 \tabularnewline
5 & 119.06 & 114.379959668241 & 4.68004033175855 \tabularnewline
6 & 119.94 & 119.059690616755 & 0.880309383245333 \tabularnewline
7 & 120.98 & 119.939941805422 & 1.04005819457838 \tabularnewline
8 & 122.33 & 120.979931244913 & 1.35006875508687 \tabularnewline
9 & 121.7 & 122.329910751057 & -0.629910751056983 \tabularnewline
10 & 123.73 & 121.700041641486 & 2.02995835851432 \tabularnewline
11 & 121.73 & 123.729865805621 & -1.99986580562125 \tabularnewline
12 & 119.75 & 121.730132205052 & -1.98013220505152 \tabularnewline
13 & 117.4 & 119.750130900523 & -2.35013090052314 \tabularnewline
14 & 120.99 & 117.400155360013 & 3.58984463998738 \tabularnewline
15 & 125.18 & 120.989762686279 & 4.19023731372089 \tabularnewline
16 & 126.41 & 125.179722996144 & 1.23027700385614 \tabularnewline
17 & 129.38 & 126.409918670126 & 2.97008132987435 \tabularnewline
18 & 131.93 & 129.379803656948 & 2.55019634305171 \tabularnewline
19 & 129.34 & 131.929831414269 & -2.5898314142689 \tabularnewline
20 & 128.58 & 129.340171205885 & -0.7601712058852 \tabularnewline
21 & 125.37 & 128.580050252609 & -3.21005025260854 \tabularnewline
22 & 123.25 & 125.370212206668 & -2.12021220666799 \tabularnewline
23 & 122.78 & 123.250140160786 & -0.4701401607864 \tabularnewline
24 & 120.37 & 122.780031079537 & -2.41003107953743 \tabularnewline
25 & 116.83 & 120.370159319831 & -3.54015931983143 \tabularnewline
26 & 116.39 & 116.830234029175 & -0.440234029175329 \tabularnewline
27 & 120.69 & 116.390029102534 & 4.29997089746604 \tabularnewline
28 & 123.51 & 120.68971574199 & 2.82028425800993 \tabularnewline
29 & 127.43 & 123.509813559578 & 3.92018644042244 \tabularnewline
30 & 125.99 & 127.429740848387 & -1.43974084838651 \tabularnewline
31 & 120.62 & 125.990095176893 & -5.3700951768926 \tabularnewline
32 & 113.71 & 120.620355000674 & -6.91035500067433 \tabularnewline
33 & 110.79 & 113.710456822571 & -2.92045682257094 \tabularnewline
34 & 108.15 & 110.790193062526 & -2.64019306252629 \tabularnewline
35 & 111.22 & 108.150174535141 & 3.06982546485925 \tabularnewline
36 & 112.65 & 111.219797063167 & 1.43020293683337 \tabularnewline
37 & 112.47 & 112.64990545363 & -0.179905453629743 \tabularnewline
38 & 117.48 & 112.470011893003 & 5.00998810699714 \tabularnewline
39 & 122.46 & 117.47966880491 & 4.98033119509016 \tabularnewline
40 & 123.46 & 122.459670765438 & 1.00032923456183 \tabularnewline
41 & 122.33 & 123.459933871274 & -1.12993387127395 \tabularnewline
42 & 129.2 & 122.330074696495 & 6.86992530350523 \tabularnewline
43 & 129.22 & 129.199545850113 & 0.0204541498865467 \tabularnewline
44 & 131.17 & 129.219998647838 & 1.95000135216168 \tabularnewline
45 & 120.22 & 131.169871091336 & -10.949871091336 \tabularnewline
46 & 120.38 & 120.220723862705 & 0.159276137294952 \tabularnewline
47 & 115.32 & 120.379989470739 & -5.05998947073854 \tabularnewline
48 & 112.25 & 115.320334500528 & -3.07033450052838 \tabularnewline
49 & 109.83 & 112.250202970484 & -2.42020297048417 \tabularnewline
50 & 107.05 & 109.830159992264 & -2.78015999226423 \tabularnewline
51 & 112.87 & 107.050183787929 & 5.81981621207085 \tabularnewline
52 & 113.68 & 112.869615269635 & 0.810384730365413 \tabularnewline
53 & 115.08 & 113.679946427928 & 1.40005357207204 \tabularnewline
54 & 120.61 & 115.079907446713 & 5.53009255328737 \tabularnewline
55 & 119.14 & 120.609634422385 & -1.46963442238531 \tabularnewline
56 & 118.63 & 119.140097153066 & -0.510097153065971 \tabularnewline
57 & 115.78 & 118.630033720973 & -2.85003372097277 \tabularnewline
58 & 117.26 & 115.780188407069 & 1.47981159293096 \tabularnewline
59 & 117.61 & 117.259902174152 & 0.350097825847783 \tabularnewline
60 & 113.92 & 117.609976856097 & -3.68997685609655 \tabularnewline
61 & 113.65 & 113.920243933157 & -0.270243933157417 \tabularnewline
62 & 115.89 & 113.650017865005 & 2.23998213499475 \tabularnewline
63 & 116.55 & 115.889851921588 & 0.660148078412419 \tabularnewline
64 & 117.78 & 116.549956359616 & 1.23004364038351 \tabularnewline
65 & 117.36 & 117.779918685553 & -0.419918685552602 \tabularnewline
66 & 121.09 & 117.360027759548 & 3.72997224045169 \tabularnewline
67 & 124.26 & 121.089753422869 & 3.17024657713074 \tabularnewline
68 & 121.88 & 124.259790424632 & -2.37979042463206 \tabularnewline
69 & 119.52 & 121.880157320714 & -2.36015732071363 \tabularnewline
70 & 122.49 & 119.520156022829 & 2.96984397717121 \tabularnewline
71 & 120.86 & 122.489803672639 & -1.62980367263897 \tabularnewline
72 & 120.31 & 120.860107741368 & -0.550107741368393 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232891&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]112.28[/C][C]110.12[/C][C]2.16[/C][/ROW]
[ROW][C]3[/C][C]113.77[/C][C]112.279857208963[/C][C]1.49014279103652[/C][/ROW]
[ROW][C]4[/C][C]114.38[/C][C]113.769901491188[/C][C]0.610098508811902[/C][/ROW]
[ROW][C]5[/C][C]119.06[/C][C]114.379959668241[/C][C]4.68004033175855[/C][/ROW]
[ROW][C]6[/C][C]119.94[/C][C]119.059690616755[/C][C]0.880309383245333[/C][/ROW]
[ROW][C]7[/C][C]120.98[/C][C]119.939941805422[/C][C]1.04005819457838[/C][/ROW]
[ROW][C]8[/C][C]122.33[/C][C]120.979931244913[/C][C]1.35006875508687[/C][/ROW]
[ROW][C]9[/C][C]121.7[/C][C]122.329910751057[/C][C]-0.629910751056983[/C][/ROW]
[ROW][C]10[/C][C]123.73[/C][C]121.700041641486[/C][C]2.02995835851432[/C][/ROW]
[ROW][C]11[/C][C]121.73[/C][C]123.729865805621[/C][C]-1.99986580562125[/C][/ROW]
[ROW][C]12[/C][C]119.75[/C][C]121.730132205052[/C][C]-1.98013220505152[/C][/ROW]
[ROW][C]13[/C][C]117.4[/C][C]119.750130900523[/C][C]-2.35013090052314[/C][/ROW]
[ROW][C]14[/C][C]120.99[/C][C]117.400155360013[/C][C]3.58984463998738[/C][/ROW]
[ROW][C]15[/C][C]125.18[/C][C]120.989762686279[/C][C]4.19023731372089[/C][/ROW]
[ROW][C]16[/C][C]126.41[/C][C]125.179722996144[/C][C]1.23027700385614[/C][/ROW]
[ROW][C]17[/C][C]129.38[/C][C]126.409918670126[/C][C]2.97008132987435[/C][/ROW]
[ROW][C]18[/C][C]131.93[/C][C]129.379803656948[/C][C]2.55019634305171[/C][/ROW]
[ROW][C]19[/C][C]129.34[/C][C]131.929831414269[/C][C]-2.5898314142689[/C][/ROW]
[ROW][C]20[/C][C]128.58[/C][C]129.340171205885[/C][C]-0.7601712058852[/C][/ROW]
[ROW][C]21[/C][C]125.37[/C][C]128.580050252609[/C][C]-3.21005025260854[/C][/ROW]
[ROW][C]22[/C][C]123.25[/C][C]125.370212206668[/C][C]-2.12021220666799[/C][/ROW]
[ROW][C]23[/C][C]122.78[/C][C]123.250140160786[/C][C]-0.4701401607864[/C][/ROW]
[ROW][C]24[/C][C]120.37[/C][C]122.780031079537[/C][C]-2.41003107953743[/C][/ROW]
[ROW][C]25[/C][C]116.83[/C][C]120.370159319831[/C][C]-3.54015931983143[/C][/ROW]
[ROW][C]26[/C][C]116.39[/C][C]116.830234029175[/C][C]-0.440234029175329[/C][/ROW]
[ROW][C]27[/C][C]120.69[/C][C]116.390029102534[/C][C]4.29997089746604[/C][/ROW]
[ROW][C]28[/C][C]123.51[/C][C]120.68971574199[/C][C]2.82028425800993[/C][/ROW]
[ROW][C]29[/C][C]127.43[/C][C]123.509813559578[/C][C]3.92018644042244[/C][/ROW]
[ROW][C]30[/C][C]125.99[/C][C]127.429740848387[/C][C]-1.43974084838651[/C][/ROW]
[ROW][C]31[/C][C]120.62[/C][C]125.990095176893[/C][C]-5.3700951768926[/C][/ROW]
[ROW][C]32[/C][C]113.71[/C][C]120.620355000674[/C][C]-6.91035500067433[/C][/ROW]
[ROW][C]33[/C][C]110.79[/C][C]113.710456822571[/C][C]-2.92045682257094[/C][/ROW]
[ROW][C]34[/C][C]108.15[/C][C]110.790193062526[/C][C]-2.64019306252629[/C][/ROW]
[ROW][C]35[/C][C]111.22[/C][C]108.150174535141[/C][C]3.06982546485925[/C][/ROW]
[ROW][C]36[/C][C]112.65[/C][C]111.219797063167[/C][C]1.43020293683337[/C][/ROW]
[ROW][C]37[/C][C]112.47[/C][C]112.64990545363[/C][C]-0.179905453629743[/C][/ROW]
[ROW][C]38[/C][C]117.48[/C][C]112.470011893003[/C][C]5.00998810699714[/C][/ROW]
[ROW][C]39[/C][C]122.46[/C][C]117.47966880491[/C][C]4.98033119509016[/C][/ROW]
[ROW][C]40[/C][C]123.46[/C][C]122.459670765438[/C][C]1.00032923456183[/C][/ROW]
[ROW][C]41[/C][C]122.33[/C][C]123.459933871274[/C][C]-1.12993387127395[/C][/ROW]
[ROW][C]42[/C][C]129.2[/C][C]122.330074696495[/C][C]6.86992530350523[/C][/ROW]
[ROW][C]43[/C][C]129.22[/C][C]129.199545850113[/C][C]0.0204541498865467[/C][/ROW]
[ROW][C]44[/C][C]131.17[/C][C]129.219998647838[/C][C]1.95000135216168[/C][/ROW]
[ROW][C]45[/C][C]120.22[/C][C]131.169871091336[/C][C]-10.949871091336[/C][/ROW]
[ROW][C]46[/C][C]120.38[/C][C]120.220723862705[/C][C]0.159276137294952[/C][/ROW]
[ROW][C]47[/C][C]115.32[/C][C]120.379989470739[/C][C]-5.05998947073854[/C][/ROW]
[ROW][C]48[/C][C]112.25[/C][C]115.320334500528[/C][C]-3.07033450052838[/C][/ROW]
[ROW][C]49[/C][C]109.83[/C][C]112.250202970484[/C][C]-2.42020297048417[/C][/ROW]
[ROW][C]50[/C][C]107.05[/C][C]109.830159992264[/C][C]-2.78015999226423[/C][/ROW]
[ROW][C]51[/C][C]112.87[/C][C]107.050183787929[/C][C]5.81981621207085[/C][/ROW]
[ROW][C]52[/C][C]113.68[/C][C]112.869615269635[/C][C]0.810384730365413[/C][/ROW]
[ROW][C]53[/C][C]115.08[/C][C]113.679946427928[/C][C]1.40005357207204[/C][/ROW]
[ROW][C]54[/C][C]120.61[/C][C]115.079907446713[/C][C]5.53009255328737[/C][/ROW]
[ROW][C]55[/C][C]119.14[/C][C]120.609634422385[/C][C]-1.46963442238531[/C][/ROW]
[ROW][C]56[/C][C]118.63[/C][C]119.140097153066[/C][C]-0.510097153065971[/C][/ROW]
[ROW][C]57[/C][C]115.78[/C][C]118.630033720973[/C][C]-2.85003372097277[/C][/ROW]
[ROW][C]58[/C][C]117.26[/C][C]115.780188407069[/C][C]1.47981159293096[/C][/ROW]
[ROW][C]59[/C][C]117.61[/C][C]117.259902174152[/C][C]0.350097825847783[/C][/ROW]
[ROW][C]60[/C][C]113.92[/C][C]117.609976856097[/C][C]-3.68997685609655[/C][/ROW]
[ROW][C]61[/C][C]113.65[/C][C]113.920243933157[/C][C]-0.270243933157417[/C][/ROW]
[ROW][C]62[/C][C]115.89[/C][C]113.650017865005[/C][C]2.23998213499475[/C][/ROW]
[ROW][C]63[/C][C]116.55[/C][C]115.889851921588[/C][C]0.660148078412419[/C][/ROW]
[ROW][C]64[/C][C]117.78[/C][C]116.549956359616[/C][C]1.23004364038351[/C][/ROW]
[ROW][C]65[/C][C]117.36[/C][C]117.779918685553[/C][C]-0.419918685552602[/C][/ROW]
[ROW][C]66[/C][C]121.09[/C][C]117.360027759548[/C][C]3.72997224045169[/C][/ROW]
[ROW][C]67[/C][C]124.26[/C][C]121.089753422869[/C][C]3.17024657713074[/C][/ROW]
[ROW][C]68[/C][C]121.88[/C][C]124.259790424632[/C][C]-2.37979042463206[/C][/ROW]
[ROW][C]69[/C][C]119.52[/C][C]121.880157320714[/C][C]-2.36015732071363[/C][/ROW]
[ROW][C]70[/C][C]122.49[/C][C]119.520156022829[/C][C]2.96984397717121[/C][/ROW]
[ROW][C]71[/C][C]120.86[/C][C]122.489803672639[/C][C]-1.62980367263897[/C][/ROW]
[ROW][C]72[/C][C]120.31[/C][C]120.860107741368[/C][C]-0.550107741368393[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232891&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232891&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
2112.28110.122.16
3113.77112.2798572089631.49014279103652
4114.38113.7699014911880.610098508811902
5119.06114.3799596682414.68004033175855
6119.94119.0596906167550.880309383245333
7120.98119.9399418054221.04005819457838
8122.33120.9799312449131.35006875508687
9121.7122.329910751057-0.629910751056983
10123.73121.7000416414862.02995835851432
11121.73123.729865805621-1.99986580562125
12119.75121.730132205052-1.98013220505152
13117.4119.750130900523-2.35013090052314
14120.99117.4001553600133.58984463998738
15125.18120.9897626862794.19023731372089
16126.41125.1797229961441.23027700385614
17129.38126.4099186701262.97008132987435
18131.93129.3798036569482.55019634305171
19129.34131.929831414269-2.5898314142689
20128.58129.340171205885-0.7601712058852
21125.37128.580050252609-3.21005025260854
22123.25125.370212206668-2.12021220666799
23122.78123.250140160786-0.4701401607864
24120.37122.780031079537-2.41003107953743
25116.83120.370159319831-3.54015931983143
26116.39116.830234029175-0.440234029175329
27120.69116.3900291025344.29997089746604
28123.51120.689715741992.82028425800993
29127.43123.5098135595783.92018644042244
30125.99127.429740848387-1.43974084838651
31120.62125.990095176893-5.3700951768926
32113.71120.620355000674-6.91035500067433
33110.79113.710456822571-2.92045682257094
34108.15110.790193062526-2.64019306252629
35111.22108.1501745351413.06982546485925
36112.65111.2197970631671.43020293683337
37112.47112.64990545363-0.179905453629743
38117.48112.4700118930035.00998810699714
39122.46117.479668804914.98033119509016
40123.46122.4596707654381.00032923456183
41122.33123.459933871274-1.12993387127395
42129.2122.3300746964956.86992530350523
43129.22129.1995458501130.0204541498865467
44131.17129.2199986478381.95000135216168
45120.22131.169871091336-10.949871091336
46120.38120.2207238627050.159276137294952
47115.32120.379989470739-5.05998947073854
48112.25115.320334500528-3.07033450052838
49109.83112.250202970484-2.42020297048417
50107.05109.830159992264-2.78015999226423
51112.87107.0501837879295.81981621207085
52113.68112.8696152696350.810384730365413
53115.08113.6799464279281.40005357207204
54120.61115.0799074467135.53009255328737
55119.14120.609634422385-1.46963442238531
56118.63119.140097153066-0.510097153065971
57115.78118.630033720973-2.85003372097277
58117.26115.7801884070691.47981159293096
59117.61117.2599021741520.350097825847783
60113.92117.609976856097-3.68997685609655
61113.65113.920243933157-0.270243933157417
62115.89113.6500178650052.23998213499475
63116.55115.8898519215880.660148078412419
64117.78116.5499563596161.23004364038351
65117.36117.779918685553-0.419918685552602
66121.09117.3600277595483.72997224045169
67124.26121.0897534228693.17024657713074
68121.88124.259790424632-2.37979042463206
69119.52121.880157320714-2.36015732071363
70122.49119.5201560228292.96984397717121
71120.86122.489803672639-1.62980367263897
72120.31120.860107741368-0.550107741368393







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73120.310036365951114.09266667897126.527406052932
74120.310036365951111.517638456493129.10243427541
75120.310036365951109.541710768538131.078361963365
76120.310036365951107.875913504021132.744159227881
77120.310036365951106.40831033933134.211762392572
78120.310036365951105.081492059522135.538580672381
79120.310036365951103.86135444713136.758718284772
80120.310036365951102.725676495879137.894396236024
81120.310036365951101.65902333143138.961049400472
82120.310036365951100.650156854939139.969915876964
83120.31003636595199.690593173634140.929479558268
84120.31003636595198.7737411243165141.846331607586

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 120.310036365951 & 114.09266667897 & 126.527406052932 \tabularnewline
74 & 120.310036365951 & 111.517638456493 & 129.10243427541 \tabularnewline
75 & 120.310036365951 & 109.541710768538 & 131.078361963365 \tabularnewline
76 & 120.310036365951 & 107.875913504021 & 132.744159227881 \tabularnewline
77 & 120.310036365951 & 106.40831033933 & 134.211762392572 \tabularnewline
78 & 120.310036365951 & 105.081492059522 & 135.538580672381 \tabularnewline
79 & 120.310036365951 & 103.86135444713 & 136.758718284772 \tabularnewline
80 & 120.310036365951 & 102.725676495879 & 137.894396236024 \tabularnewline
81 & 120.310036365951 & 101.65902333143 & 138.961049400472 \tabularnewline
82 & 120.310036365951 & 100.650156854939 & 139.969915876964 \tabularnewline
83 & 120.310036365951 & 99.690593173634 & 140.929479558268 \tabularnewline
84 & 120.310036365951 & 98.7737411243165 & 141.846331607586 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232891&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]120.310036365951[/C][C]114.09266667897[/C][C]126.527406052932[/C][/ROW]
[ROW][C]74[/C][C]120.310036365951[/C][C]111.517638456493[/C][C]129.10243427541[/C][/ROW]
[ROW][C]75[/C][C]120.310036365951[/C][C]109.541710768538[/C][C]131.078361963365[/C][/ROW]
[ROW][C]76[/C][C]120.310036365951[/C][C]107.875913504021[/C][C]132.744159227881[/C][/ROW]
[ROW][C]77[/C][C]120.310036365951[/C][C]106.40831033933[/C][C]134.211762392572[/C][/ROW]
[ROW][C]78[/C][C]120.310036365951[/C][C]105.081492059522[/C][C]135.538580672381[/C][/ROW]
[ROW][C]79[/C][C]120.310036365951[/C][C]103.86135444713[/C][C]136.758718284772[/C][/ROW]
[ROW][C]80[/C][C]120.310036365951[/C][C]102.725676495879[/C][C]137.894396236024[/C][/ROW]
[ROW][C]81[/C][C]120.310036365951[/C][C]101.65902333143[/C][C]138.961049400472[/C][/ROW]
[ROW][C]82[/C][C]120.310036365951[/C][C]100.650156854939[/C][C]139.969915876964[/C][/ROW]
[ROW][C]83[/C][C]120.310036365951[/C][C]99.690593173634[/C][C]140.929479558268[/C][/ROW]
[ROW][C]84[/C][C]120.310036365951[/C][C]98.7737411243165[/C][C]141.846331607586[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232891&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232891&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
73120.310036365951114.09266667897126.527406052932
74120.310036365951111.517638456493129.10243427541
75120.310036365951109.541710768538131.078361963365
76120.310036365951107.875913504021132.744159227881
77120.310036365951106.40831033933134.211762392572
78120.310036365951105.081492059522135.538580672381
79120.310036365951103.86135444713136.758718284772
80120.310036365951102.725676495879137.894396236024
81120.310036365951101.65902333143138.961049400472
82120.310036365951100.650156854939139.969915876964
83120.31003636595199.690593173634140.929479558268
84120.31003636595198.7737411243165141.846331607586



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')