Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 10 Jan 2017 10:42:28 +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/2017/Jan/10/t14840452940yw83tho99sxfa5.htm/, Retrieved Thu, 16 May 2024 03:22:01 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Thu, 16 May 2024 03:22:01 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
122,9
122,82
120,26
118,82
126,69
125,79
123,96
128,7
127,74
127,55
126,16
124,74
122,32
120,92
117,09
115,77
117,88
117,77
122,61
127,31
124,62
119,07
116,92
115,07
113,84
112,89
111,86
111,58
107,72
106,49
108,53
108,62
107,92
106,43
117,66
115,11
113,98
112,16
109,72
117,99
112,57
113,66
118,18
115,66
114,72
110,46
108,38
106,52
107,01
105,89
103,76
103,71
101,07
100,4
102,24
99,18
98,14
96,22
94,38
94,62
94,71
94,97
93,69
106,42
105,73
105,18
104,8
102,77
100,29
99,3
96,63
95,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.907108086500555
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.907108086500555 \tabularnewline
beta & 0 \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]0.907108086500555[/C][/ROW]
[ROW][C]beta[/C][C]0[/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
alpha0.907108086500555
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3120.26122.74-2.47999999999998
4118.82120.410371945479-1.59037194547862
5126.69118.8877326931917.80226730680867
6125.79125.885232460236-0.0952324602363603
7123.96125.718846325459-1.75884632545862
8128.7124.0433826007234.6566173992767
9127.74128.187437899346-0.447437899346355
10127.55127.701563362642-0.151563362642435
11126.16127.484079010772-1.32407901077225
12124.74126.202996232935-1.46299623293508
13122.32124.79590051952-2.47590051951981
14120.92122.469991136892-1.54999113689244
15117.09120.983981642613-3.8939816426131
16115.77117.371719405914-1.60171940591404
17117.88115.8387867805052.04121321949546
18117.77117.6103877981810.159612201819314
19122.61117.6751733171554.93482668284487
20127.31122.0715945066425.23840549335759
21124.62126.743394490036-2.12339449003599
22119.07124.737246177294-5.66724617729361
23116.92119.516441341681-2.5964413416812
24115.07117.081188404518-2.01118840451784
25113.84115.176823139304-1.33682313930353
26112.89113.88418005942-0.994180059420231
27111.86112.902351288083-1.04235128808253
28111.58111.876826005689-0.296826005688573
29107.72111.527572735645-3.8075727356448
30106.49107.993692717202-1.50369271720236
31108.53106.5496808938161.98031910618391
32108.62108.2660443688870.353955631112953
33107.92108.507120384132-0.587120384132007
34106.43107.894538735937-1.46453873593653
35117.66106.48604380557511.1739561944248
36115.11116.542029827741-1.43202982774089
37113.98115.163023990887-1.18302399088712
38112.16114.009893362229-1.84989336222925
39109.72112.251840134187-2.53184013418739
40117.99109.8751874747398.11481252526065
41112.57117.156199536839-4.58619953683927
42113.66112.9160208506670.743979149332745
43118.18113.5108903532154.66910964678523
44115.66117.666277470571-2.00627747057139
45114.72115.766366953252-1.04636695325219
46110.46114.73719902851-4.27719902851017
47108.38110.777317202176-2.39731720217627
48106.52108.522691382175-2.00269138217529
49107.01106.6260338346390.383966165360903
50105.89106.894332648181-1.00433264818058
51103.76105.903294381479-2.14329438147945
52103.71103.879094716288-0.169094716288228
53101.07103.645707531759-2.57570753175865
54100.4101.22926240124-0.829262401239973
55102.24100.3970317712441.84296822875568
5699.18101.988803154712-2.80880315471218
5798.1499.3609150996845-1.22091509968449
5896.2298.17341313983-1.95341313983005
5994.3896.3214562844138-1.94145628441376
6094.6294.48034558923470.139654410765303
6194.7194.52702723455540.182972765444632
6294.9794.61300330969950.356996690300463
6393.6994.856837894325-1.16683789432501
64106.4293.718389804747512.7016101952525
65105.73105.1601231244390.569876875561079
66105.18105.59706304657-0.417063046570021
67104.8105.138741784446-0.338741784445787
68102.77104.751466372539-1.98146637253937
69100.29102.87406220288-2.58406220287996
7099.3100.450038482627-1.15003848262711
7196.6399.3268292752492-2.69682927524921
7295.596.8005136317592-1.3005136317592

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 120.26 & 122.74 & -2.47999999999998 \tabularnewline
4 & 118.82 & 120.410371945479 & -1.59037194547862 \tabularnewline
5 & 126.69 & 118.887732693191 & 7.80226730680867 \tabularnewline
6 & 125.79 & 125.885232460236 & -0.0952324602363603 \tabularnewline
7 & 123.96 & 125.718846325459 & -1.75884632545862 \tabularnewline
8 & 128.7 & 124.043382600723 & 4.6566173992767 \tabularnewline
9 & 127.74 & 128.187437899346 & -0.447437899346355 \tabularnewline
10 & 127.55 & 127.701563362642 & -0.151563362642435 \tabularnewline
11 & 126.16 & 127.484079010772 & -1.32407901077225 \tabularnewline
12 & 124.74 & 126.202996232935 & -1.46299623293508 \tabularnewline
13 & 122.32 & 124.79590051952 & -2.47590051951981 \tabularnewline
14 & 120.92 & 122.469991136892 & -1.54999113689244 \tabularnewline
15 & 117.09 & 120.983981642613 & -3.8939816426131 \tabularnewline
16 & 115.77 & 117.371719405914 & -1.60171940591404 \tabularnewline
17 & 117.88 & 115.838786780505 & 2.04121321949546 \tabularnewline
18 & 117.77 & 117.610387798181 & 0.159612201819314 \tabularnewline
19 & 122.61 & 117.675173317155 & 4.93482668284487 \tabularnewline
20 & 127.31 & 122.071594506642 & 5.23840549335759 \tabularnewline
21 & 124.62 & 126.743394490036 & -2.12339449003599 \tabularnewline
22 & 119.07 & 124.737246177294 & -5.66724617729361 \tabularnewline
23 & 116.92 & 119.516441341681 & -2.5964413416812 \tabularnewline
24 & 115.07 & 117.081188404518 & -2.01118840451784 \tabularnewline
25 & 113.84 & 115.176823139304 & -1.33682313930353 \tabularnewline
26 & 112.89 & 113.88418005942 & -0.994180059420231 \tabularnewline
27 & 111.86 & 112.902351288083 & -1.04235128808253 \tabularnewline
28 & 111.58 & 111.876826005689 & -0.296826005688573 \tabularnewline
29 & 107.72 & 111.527572735645 & -3.8075727356448 \tabularnewline
30 & 106.49 & 107.993692717202 & -1.50369271720236 \tabularnewline
31 & 108.53 & 106.549680893816 & 1.98031910618391 \tabularnewline
32 & 108.62 & 108.266044368887 & 0.353955631112953 \tabularnewline
33 & 107.92 & 108.507120384132 & -0.587120384132007 \tabularnewline
34 & 106.43 & 107.894538735937 & -1.46453873593653 \tabularnewline
35 & 117.66 & 106.486043805575 & 11.1739561944248 \tabularnewline
36 & 115.11 & 116.542029827741 & -1.43202982774089 \tabularnewline
37 & 113.98 & 115.163023990887 & -1.18302399088712 \tabularnewline
38 & 112.16 & 114.009893362229 & -1.84989336222925 \tabularnewline
39 & 109.72 & 112.251840134187 & -2.53184013418739 \tabularnewline
40 & 117.99 & 109.875187474739 & 8.11481252526065 \tabularnewline
41 & 112.57 & 117.156199536839 & -4.58619953683927 \tabularnewline
42 & 113.66 & 112.916020850667 & 0.743979149332745 \tabularnewline
43 & 118.18 & 113.510890353215 & 4.66910964678523 \tabularnewline
44 & 115.66 & 117.666277470571 & -2.00627747057139 \tabularnewline
45 & 114.72 & 115.766366953252 & -1.04636695325219 \tabularnewline
46 & 110.46 & 114.73719902851 & -4.27719902851017 \tabularnewline
47 & 108.38 & 110.777317202176 & -2.39731720217627 \tabularnewline
48 & 106.52 & 108.522691382175 & -2.00269138217529 \tabularnewline
49 & 107.01 & 106.626033834639 & 0.383966165360903 \tabularnewline
50 & 105.89 & 106.894332648181 & -1.00433264818058 \tabularnewline
51 & 103.76 & 105.903294381479 & -2.14329438147945 \tabularnewline
52 & 103.71 & 103.879094716288 & -0.169094716288228 \tabularnewline
53 & 101.07 & 103.645707531759 & -2.57570753175865 \tabularnewline
54 & 100.4 & 101.22926240124 & -0.829262401239973 \tabularnewline
55 & 102.24 & 100.397031771244 & 1.84296822875568 \tabularnewline
56 & 99.18 & 101.988803154712 & -2.80880315471218 \tabularnewline
57 & 98.14 & 99.3609150996845 & -1.22091509968449 \tabularnewline
58 & 96.22 & 98.17341313983 & -1.95341313983005 \tabularnewline
59 & 94.38 & 96.3214562844138 & -1.94145628441376 \tabularnewline
60 & 94.62 & 94.4803455892347 & 0.139654410765303 \tabularnewline
61 & 94.71 & 94.5270272345554 & 0.182972765444632 \tabularnewline
62 & 94.97 & 94.6130033096995 & 0.356996690300463 \tabularnewline
63 & 93.69 & 94.856837894325 & -1.16683789432501 \tabularnewline
64 & 106.42 & 93.7183898047475 & 12.7016101952525 \tabularnewline
65 & 105.73 & 105.160123124439 & 0.569876875561079 \tabularnewline
66 & 105.18 & 105.59706304657 & -0.417063046570021 \tabularnewline
67 & 104.8 & 105.138741784446 & -0.338741784445787 \tabularnewline
68 & 102.77 & 104.751466372539 & -1.98146637253937 \tabularnewline
69 & 100.29 & 102.87406220288 & -2.58406220287996 \tabularnewline
70 & 99.3 & 100.450038482627 & -1.15003848262711 \tabularnewline
71 & 96.63 & 99.3268292752492 & -2.69682927524921 \tabularnewline
72 & 95.5 & 96.8005136317592 & -1.3005136317592 \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]3[/C][C]120.26[/C][C]122.74[/C][C]-2.47999999999998[/C][/ROW]
[ROW][C]4[/C][C]118.82[/C][C]120.410371945479[/C][C]-1.59037194547862[/C][/ROW]
[ROW][C]5[/C][C]126.69[/C][C]118.887732693191[/C][C]7.80226730680867[/C][/ROW]
[ROW][C]6[/C][C]125.79[/C][C]125.885232460236[/C][C]-0.0952324602363603[/C][/ROW]
[ROW][C]7[/C][C]123.96[/C][C]125.718846325459[/C][C]-1.75884632545862[/C][/ROW]
[ROW][C]8[/C][C]128.7[/C][C]124.043382600723[/C][C]4.6566173992767[/C][/ROW]
[ROW][C]9[/C][C]127.74[/C][C]128.187437899346[/C][C]-0.447437899346355[/C][/ROW]
[ROW][C]10[/C][C]127.55[/C][C]127.701563362642[/C][C]-0.151563362642435[/C][/ROW]
[ROW][C]11[/C][C]126.16[/C][C]127.484079010772[/C][C]-1.32407901077225[/C][/ROW]
[ROW][C]12[/C][C]124.74[/C][C]126.202996232935[/C][C]-1.46299623293508[/C][/ROW]
[ROW][C]13[/C][C]122.32[/C][C]124.79590051952[/C][C]-2.47590051951981[/C][/ROW]
[ROW][C]14[/C][C]120.92[/C][C]122.469991136892[/C][C]-1.54999113689244[/C][/ROW]
[ROW][C]15[/C][C]117.09[/C][C]120.983981642613[/C][C]-3.8939816426131[/C][/ROW]
[ROW][C]16[/C][C]115.77[/C][C]117.371719405914[/C][C]-1.60171940591404[/C][/ROW]
[ROW][C]17[/C][C]117.88[/C][C]115.838786780505[/C][C]2.04121321949546[/C][/ROW]
[ROW][C]18[/C][C]117.77[/C][C]117.610387798181[/C][C]0.159612201819314[/C][/ROW]
[ROW][C]19[/C][C]122.61[/C][C]117.675173317155[/C][C]4.93482668284487[/C][/ROW]
[ROW][C]20[/C][C]127.31[/C][C]122.071594506642[/C][C]5.23840549335759[/C][/ROW]
[ROW][C]21[/C][C]124.62[/C][C]126.743394490036[/C][C]-2.12339449003599[/C][/ROW]
[ROW][C]22[/C][C]119.07[/C][C]124.737246177294[/C][C]-5.66724617729361[/C][/ROW]
[ROW][C]23[/C][C]116.92[/C][C]119.516441341681[/C][C]-2.5964413416812[/C][/ROW]
[ROW][C]24[/C][C]115.07[/C][C]117.081188404518[/C][C]-2.01118840451784[/C][/ROW]
[ROW][C]25[/C][C]113.84[/C][C]115.176823139304[/C][C]-1.33682313930353[/C][/ROW]
[ROW][C]26[/C][C]112.89[/C][C]113.88418005942[/C][C]-0.994180059420231[/C][/ROW]
[ROW][C]27[/C][C]111.86[/C][C]112.902351288083[/C][C]-1.04235128808253[/C][/ROW]
[ROW][C]28[/C][C]111.58[/C][C]111.876826005689[/C][C]-0.296826005688573[/C][/ROW]
[ROW][C]29[/C][C]107.72[/C][C]111.527572735645[/C][C]-3.8075727356448[/C][/ROW]
[ROW][C]30[/C][C]106.49[/C][C]107.993692717202[/C][C]-1.50369271720236[/C][/ROW]
[ROW][C]31[/C][C]108.53[/C][C]106.549680893816[/C][C]1.98031910618391[/C][/ROW]
[ROW][C]32[/C][C]108.62[/C][C]108.266044368887[/C][C]0.353955631112953[/C][/ROW]
[ROW][C]33[/C][C]107.92[/C][C]108.507120384132[/C][C]-0.587120384132007[/C][/ROW]
[ROW][C]34[/C][C]106.43[/C][C]107.894538735937[/C][C]-1.46453873593653[/C][/ROW]
[ROW][C]35[/C][C]117.66[/C][C]106.486043805575[/C][C]11.1739561944248[/C][/ROW]
[ROW][C]36[/C][C]115.11[/C][C]116.542029827741[/C][C]-1.43202982774089[/C][/ROW]
[ROW][C]37[/C][C]113.98[/C][C]115.163023990887[/C][C]-1.18302399088712[/C][/ROW]
[ROW][C]38[/C][C]112.16[/C][C]114.009893362229[/C][C]-1.84989336222925[/C][/ROW]
[ROW][C]39[/C][C]109.72[/C][C]112.251840134187[/C][C]-2.53184013418739[/C][/ROW]
[ROW][C]40[/C][C]117.99[/C][C]109.875187474739[/C][C]8.11481252526065[/C][/ROW]
[ROW][C]41[/C][C]112.57[/C][C]117.156199536839[/C][C]-4.58619953683927[/C][/ROW]
[ROW][C]42[/C][C]113.66[/C][C]112.916020850667[/C][C]0.743979149332745[/C][/ROW]
[ROW][C]43[/C][C]118.18[/C][C]113.510890353215[/C][C]4.66910964678523[/C][/ROW]
[ROW][C]44[/C][C]115.66[/C][C]117.666277470571[/C][C]-2.00627747057139[/C][/ROW]
[ROW][C]45[/C][C]114.72[/C][C]115.766366953252[/C][C]-1.04636695325219[/C][/ROW]
[ROW][C]46[/C][C]110.46[/C][C]114.73719902851[/C][C]-4.27719902851017[/C][/ROW]
[ROW][C]47[/C][C]108.38[/C][C]110.777317202176[/C][C]-2.39731720217627[/C][/ROW]
[ROW][C]48[/C][C]106.52[/C][C]108.522691382175[/C][C]-2.00269138217529[/C][/ROW]
[ROW][C]49[/C][C]107.01[/C][C]106.626033834639[/C][C]0.383966165360903[/C][/ROW]
[ROW][C]50[/C][C]105.89[/C][C]106.894332648181[/C][C]-1.00433264818058[/C][/ROW]
[ROW][C]51[/C][C]103.76[/C][C]105.903294381479[/C][C]-2.14329438147945[/C][/ROW]
[ROW][C]52[/C][C]103.71[/C][C]103.879094716288[/C][C]-0.169094716288228[/C][/ROW]
[ROW][C]53[/C][C]101.07[/C][C]103.645707531759[/C][C]-2.57570753175865[/C][/ROW]
[ROW][C]54[/C][C]100.4[/C][C]101.22926240124[/C][C]-0.829262401239973[/C][/ROW]
[ROW][C]55[/C][C]102.24[/C][C]100.397031771244[/C][C]1.84296822875568[/C][/ROW]
[ROW][C]56[/C][C]99.18[/C][C]101.988803154712[/C][C]-2.80880315471218[/C][/ROW]
[ROW][C]57[/C][C]98.14[/C][C]99.3609150996845[/C][C]-1.22091509968449[/C][/ROW]
[ROW][C]58[/C][C]96.22[/C][C]98.17341313983[/C][C]-1.95341313983005[/C][/ROW]
[ROW][C]59[/C][C]94.38[/C][C]96.3214562844138[/C][C]-1.94145628441376[/C][/ROW]
[ROW][C]60[/C][C]94.62[/C][C]94.4803455892347[/C][C]0.139654410765303[/C][/ROW]
[ROW][C]61[/C][C]94.71[/C][C]94.5270272345554[/C][C]0.182972765444632[/C][/ROW]
[ROW][C]62[/C][C]94.97[/C][C]94.6130033096995[/C][C]0.356996690300463[/C][/ROW]
[ROW][C]63[/C][C]93.69[/C][C]94.856837894325[/C][C]-1.16683789432501[/C][/ROW]
[ROW][C]64[/C][C]106.42[/C][C]93.7183898047475[/C][C]12.7016101952525[/C][/ROW]
[ROW][C]65[/C][C]105.73[/C][C]105.160123124439[/C][C]0.569876875561079[/C][/ROW]
[ROW][C]66[/C][C]105.18[/C][C]105.59706304657[/C][C]-0.417063046570021[/C][/ROW]
[ROW][C]67[/C][C]104.8[/C][C]105.138741784446[/C][C]-0.338741784445787[/C][/ROW]
[ROW][C]68[/C][C]102.77[/C][C]104.751466372539[/C][C]-1.98146637253937[/C][/ROW]
[ROW][C]69[/C][C]100.29[/C][C]102.87406220288[/C][C]-2.58406220287996[/C][/ROW]
[ROW][C]70[/C][C]99.3[/C][C]100.450038482627[/C][C]-1.15003848262711[/C][/ROW]
[ROW][C]71[/C][C]96.63[/C][C]99.3268292752492[/C][C]-2.69682927524921[/C][/ROW]
[ROW][C]72[/C][C]95.5[/C][C]96.8005136317592[/C][C]-1.3005136317592[/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
3120.26122.74-2.47999999999998
4118.82120.410371945479-1.59037194547862
5126.69118.8877326931917.80226730680867
6125.79125.885232460236-0.0952324602363603
7123.96125.718846325459-1.75884632545862
8128.7124.0433826007234.6566173992767
9127.74128.187437899346-0.447437899346355
10127.55127.701563362642-0.151563362642435
11126.16127.484079010772-1.32407901077225
12124.74126.202996232935-1.46299623293508
13122.32124.79590051952-2.47590051951981
14120.92122.469991136892-1.54999113689244
15117.09120.983981642613-3.8939816426131
16115.77117.371719405914-1.60171940591404
17117.88115.8387867805052.04121321949546
18117.77117.6103877981810.159612201819314
19122.61117.6751733171554.93482668284487
20127.31122.0715945066425.23840549335759
21124.62126.743394490036-2.12339449003599
22119.07124.737246177294-5.66724617729361
23116.92119.516441341681-2.5964413416812
24115.07117.081188404518-2.01118840451784
25113.84115.176823139304-1.33682313930353
26112.89113.88418005942-0.994180059420231
27111.86112.902351288083-1.04235128808253
28111.58111.876826005689-0.296826005688573
29107.72111.527572735645-3.8075727356448
30106.49107.993692717202-1.50369271720236
31108.53106.5496808938161.98031910618391
32108.62108.2660443688870.353955631112953
33107.92108.507120384132-0.587120384132007
34106.43107.894538735937-1.46453873593653
35117.66106.48604380557511.1739561944248
36115.11116.542029827741-1.43202982774089
37113.98115.163023990887-1.18302399088712
38112.16114.009893362229-1.84989336222925
39109.72112.251840134187-2.53184013418739
40117.99109.8751874747398.11481252526065
41112.57117.156199536839-4.58619953683927
42113.66112.9160208506670.743979149332745
43118.18113.5108903532154.66910964678523
44115.66117.666277470571-2.00627747057139
45114.72115.766366953252-1.04636695325219
46110.46114.73719902851-4.27719902851017
47108.38110.777317202176-2.39731720217627
48106.52108.522691382175-2.00269138217529
49107.01106.6260338346390.383966165360903
50105.89106.894332648181-1.00433264818058
51103.76105.903294381479-2.14329438147945
52103.71103.879094716288-0.169094716288228
53101.07103.645707531759-2.57570753175865
54100.4101.22926240124-0.829262401239973
55102.24100.3970317712441.84296822875568
5699.18101.988803154712-2.80880315471218
5798.1499.3609150996845-1.22091509968449
5896.2298.17341313983-1.95341313983005
5994.3896.3214562844138-1.94145628441376
6094.6294.48034558923470.139654410765303
6194.7194.52702723455540.182972765444632
6294.9794.61300330969950.356996690300463
6393.6994.856837894325-1.16683789432501
64106.4293.718389804747512.7016101952525
65105.73105.1601231244390.569876875561079
66105.18105.59706304657-0.417063046570021
67104.8105.138741784446-0.338741784445787
68102.77104.751466372539-1.98146637253937
69100.29102.87406220288-2.58406220287996
7099.3100.450038482627-1.15003848262711
7196.6399.3268292752492-2.69682927524921
7295.596.8005136317592-1.3005136317592







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7395.540807199786289.0977545375116101.983859862061
7495.460807199786286.7618626734161104.159751726156
7595.380807199786284.9008098650115105.860804534561
7695.300807199786283.3012633584185107.300351041154
7795.220807199786281.8736067193511108.568007680221
7895.140807199786180.5700670357126109.71154736386
7995.060807199786179.3615977549457110.760016644627
8094.980807199786178.2289748983037111.732639501268
8194.900807199786177.1586936356977112.642920763874
8294.820807199786176.1408365899315113.500777809641
8394.740807199786175.1678664332827114.313747966289
8494.660807199786174.2338955753365115.087718824236

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 95.5408071997862 & 89.0977545375116 & 101.983859862061 \tabularnewline
74 & 95.4608071997862 & 86.7618626734161 & 104.159751726156 \tabularnewline
75 & 95.3808071997862 & 84.9008098650115 & 105.860804534561 \tabularnewline
76 & 95.3008071997862 & 83.3012633584185 & 107.300351041154 \tabularnewline
77 & 95.2208071997862 & 81.8736067193511 & 108.568007680221 \tabularnewline
78 & 95.1408071997861 & 80.5700670357126 & 109.71154736386 \tabularnewline
79 & 95.0608071997861 & 79.3615977549457 & 110.760016644627 \tabularnewline
80 & 94.9808071997861 & 78.2289748983037 & 111.732639501268 \tabularnewline
81 & 94.9008071997861 & 77.1586936356977 & 112.642920763874 \tabularnewline
82 & 94.8208071997861 & 76.1408365899315 & 113.500777809641 \tabularnewline
83 & 94.7408071997861 & 75.1678664332827 & 114.313747966289 \tabularnewline
84 & 94.6608071997861 & 74.2338955753365 & 115.087718824236 \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]95.5408071997862[/C][C]89.0977545375116[/C][C]101.983859862061[/C][/ROW]
[ROW][C]74[/C][C]95.4608071997862[/C][C]86.7618626734161[/C][C]104.159751726156[/C][/ROW]
[ROW][C]75[/C][C]95.3808071997862[/C][C]84.9008098650115[/C][C]105.860804534561[/C][/ROW]
[ROW][C]76[/C][C]95.3008071997862[/C][C]83.3012633584185[/C][C]107.300351041154[/C][/ROW]
[ROW][C]77[/C][C]95.2208071997862[/C][C]81.8736067193511[/C][C]108.568007680221[/C][/ROW]
[ROW][C]78[/C][C]95.1408071997861[/C][C]80.5700670357126[/C][C]109.71154736386[/C][/ROW]
[ROW][C]79[/C][C]95.0608071997861[/C][C]79.3615977549457[/C][C]110.760016644627[/C][/ROW]
[ROW][C]80[/C][C]94.9808071997861[/C][C]78.2289748983037[/C][C]111.732639501268[/C][/ROW]
[ROW][C]81[/C][C]94.9008071997861[/C][C]77.1586936356977[/C][C]112.642920763874[/C][/ROW]
[ROW][C]82[/C][C]94.8208071997861[/C][C]76.1408365899315[/C][C]113.500777809641[/C][/ROW]
[ROW][C]83[/C][C]94.7408071997861[/C][C]75.1678664332827[/C][C]114.313747966289[/C][/ROW]
[ROW][C]84[/C][C]94.6608071997861[/C][C]74.2338955753365[/C][C]115.087718824236[/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
7395.540807199786289.0977545375116101.983859862061
7495.460807199786286.7618626734161104.159751726156
7595.380807199786284.9008098650115105.860804534561
7695.300807199786283.3012633584185107.300351041154
7795.220807199786281.8736067193511108.568007680221
7895.140807199786180.5700670357126109.71154736386
7995.060807199786179.3615977549457110.760016644627
8094.980807199786178.2289748983037111.732639501268
8194.900807199786177.1586936356977112.642920763874
8294.820807199786176.1408365899315113.500777809641
8394.740807199786175.1678664332827114.313747966289
8494.660807199786174.2338955753365115.087718824236



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')