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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 12:02:26 +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/2016/Apr/25/t1461582299d5rhjevs5tdzleo.htm/, Retrieved Sun, 05 May 2024 23:58:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294691, Retrieved Sun, 05 May 2024 23:58:20 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 11:02:26] [e5ae4b5dd737e4828f1ae85ef60fb5e4] [Current]
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Dataseries X:
87
93
89
88
90
91
91
90
90
90
88
85
91
93
94
90
91
93
93
92
92
92
94
93
95
98
98
95
97
100
100
100
98
98
98
99
97
100
104
96
99
102
101
101
99
99
101
102
103
102
104
103
103
102
101
101
103
103
103
103
103
104
98
102
103
103
102
103
102
102
103
103




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=294691&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=294691&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294691&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
alpha0.220599106985876
beta0.080087863820834
gamma0.699236496119895

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.220599106985876 \tabularnewline
beta & 0.080087863820834 \tabularnewline
gamma & 0.699236496119895 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294691&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]0.220599106985876[/C][/ROW]
[ROW][C]beta[/C][C]0.080087863820834[/C][/ROW]
[ROW][C]gamma[/C][C]0.699236496119895[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294691&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294691&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
alpha0.220599106985876
beta0.080087863820834
gamma0.699236496119895







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139189.9316239316241.068376068376
149392.21881610338750.781183896612546
159493.45645535756310.543544642436885
169089.65127457685320.348725423146774
179190.64261122426540.357388775734634
189392.39217309825620.607826901743778
199393.2910533995859-0.291053399585948
209292.3198327114907-0.319832711490747
219292.2949460821646-0.294946082164614
229292.187005183478-0.18700518347795
239490.26623873853563.73376126146437
249388.27635539234724.72364460765277
259596.1288763798494-1.12887637984939
269897.93162715129660.0683728487034188
279899.0267036218215-1.0267036218215
289594.8854044086720.114595591327969
299795.94212777330841.0578722266916
3010098.10739063697621.89260936302384
3110098.94720448481271.05279551518727
3210098.42788201299931.57211798700068
339899.0384772082916-1.03847720829158
349899.0167603780397-1.01676037803971
359899.2264723312487-1.22647233124874
369996.77096461034692.22903538965309
3797100.928691235161-3.92869123516094
38100102.761877247494-2.76187724749383
39104102.5813876818561.41861231814418
409699.5903021776202-3.5903021776202
4199100.267132573849-1.26713257384921
42102102.25667658371-0.25667658370989
43101102.008956807927-1.00895680792709
44101101.12569458572-0.125694585720368
459999.7168791316949-0.716879131694924
469999.5614856270227-0.561485627022719
4710199.54892799881351.45107200118646
4810299.40617814886222.59382185113782
49103100.1338413171622.86615868283845
50102104.067245648232-2.06724564823169
51104106.295953601346-2.29595360134643
5210399.6676817664673.33231823353303
53103103.172063608824-0.172063608823976
54102106.00754339405-4.00754339404985
55101104.509816793309-3.50981679330886
56101103.49946166263-2.4994616626297
57103101.1460996183161.85390038168381
58103101.5892150965931.41078490340675
59103103.090108231866-0.0901082318656137
60103103.184483863683-0.184483863683155
61103103.352916028415-0.352916028415379
62104103.7359300059240.264069994075783
6398106.243838380735-8.24383838073506
64102101.1552689645490.844731035451048
65103101.941578521961.05842147804009
66103102.7204852166790.279514783321318
67102102.277738474124-0.277738474124064
68103102.4261128617220.573887138278224
69102103.072653015336-1.07265301533589
70102102.526382356619-0.526382356619422
71103102.6454489786270.354551021372743
72103102.6578145469310.342185453068694

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 91 & 89.931623931624 & 1.068376068376 \tabularnewline
14 & 93 & 92.2188161033875 & 0.781183896612546 \tabularnewline
15 & 94 & 93.4564553575631 & 0.543544642436885 \tabularnewline
16 & 90 & 89.6512745768532 & 0.348725423146774 \tabularnewline
17 & 91 & 90.6426112242654 & 0.357388775734634 \tabularnewline
18 & 93 & 92.3921730982562 & 0.607826901743778 \tabularnewline
19 & 93 & 93.2910533995859 & -0.291053399585948 \tabularnewline
20 & 92 & 92.3198327114907 & -0.319832711490747 \tabularnewline
21 & 92 & 92.2949460821646 & -0.294946082164614 \tabularnewline
22 & 92 & 92.187005183478 & -0.18700518347795 \tabularnewline
23 & 94 & 90.2662387385356 & 3.73376126146437 \tabularnewline
24 & 93 & 88.2763553923472 & 4.72364460765277 \tabularnewline
25 & 95 & 96.1288763798494 & -1.12887637984939 \tabularnewline
26 & 98 & 97.9316271512966 & 0.0683728487034188 \tabularnewline
27 & 98 & 99.0267036218215 & -1.0267036218215 \tabularnewline
28 & 95 & 94.885404408672 & 0.114595591327969 \tabularnewline
29 & 97 & 95.9421277733084 & 1.0578722266916 \tabularnewline
30 & 100 & 98.1073906369762 & 1.89260936302384 \tabularnewline
31 & 100 & 98.9472044848127 & 1.05279551518727 \tabularnewline
32 & 100 & 98.4278820129993 & 1.57211798700068 \tabularnewline
33 & 98 & 99.0384772082916 & -1.03847720829158 \tabularnewline
34 & 98 & 99.0167603780397 & -1.01676037803971 \tabularnewline
35 & 98 & 99.2264723312487 & -1.22647233124874 \tabularnewline
36 & 99 & 96.7709646103469 & 2.22903538965309 \tabularnewline
37 & 97 & 100.928691235161 & -3.92869123516094 \tabularnewline
38 & 100 & 102.761877247494 & -2.76187724749383 \tabularnewline
39 & 104 & 102.581387681856 & 1.41861231814418 \tabularnewline
40 & 96 & 99.5903021776202 & -3.5903021776202 \tabularnewline
41 & 99 & 100.267132573849 & -1.26713257384921 \tabularnewline
42 & 102 & 102.25667658371 & -0.25667658370989 \tabularnewline
43 & 101 & 102.008956807927 & -1.00895680792709 \tabularnewline
44 & 101 & 101.12569458572 & -0.125694585720368 \tabularnewline
45 & 99 & 99.7168791316949 & -0.716879131694924 \tabularnewline
46 & 99 & 99.5614856270227 & -0.561485627022719 \tabularnewline
47 & 101 & 99.5489279988135 & 1.45107200118646 \tabularnewline
48 & 102 & 99.4061781488622 & 2.59382185113782 \tabularnewline
49 & 103 & 100.133841317162 & 2.86615868283845 \tabularnewline
50 & 102 & 104.067245648232 & -2.06724564823169 \tabularnewline
51 & 104 & 106.295953601346 & -2.29595360134643 \tabularnewline
52 & 103 & 99.667681766467 & 3.33231823353303 \tabularnewline
53 & 103 & 103.172063608824 & -0.172063608823976 \tabularnewline
54 & 102 & 106.00754339405 & -4.00754339404985 \tabularnewline
55 & 101 & 104.509816793309 & -3.50981679330886 \tabularnewline
56 & 101 & 103.49946166263 & -2.4994616626297 \tabularnewline
57 & 103 & 101.146099618316 & 1.85390038168381 \tabularnewline
58 & 103 & 101.589215096593 & 1.41078490340675 \tabularnewline
59 & 103 & 103.090108231866 & -0.0901082318656137 \tabularnewline
60 & 103 & 103.184483863683 & -0.184483863683155 \tabularnewline
61 & 103 & 103.352916028415 & -0.352916028415379 \tabularnewline
62 & 104 & 103.735930005924 & 0.264069994075783 \tabularnewline
63 & 98 & 106.243838380735 & -8.24383838073506 \tabularnewline
64 & 102 & 101.155268964549 & 0.844731035451048 \tabularnewline
65 & 103 & 101.94157852196 & 1.05842147804009 \tabularnewline
66 & 103 & 102.720485216679 & 0.279514783321318 \tabularnewline
67 & 102 & 102.277738474124 & -0.277738474124064 \tabularnewline
68 & 103 & 102.426112861722 & 0.573887138278224 \tabularnewline
69 & 102 & 103.072653015336 & -1.07265301533589 \tabularnewline
70 & 102 & 102.526382356619 & -0.526382356619422 \tabularnewline
71 & 103 & 102.645448978627 & 0.354551021372743 \tabularnewline
72 & 103 & 102.657814546931 & 0.342185453068694 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294691&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]91[/C][C]89.931623931624[/C][C]1.068376068376[/C][/ROW]
[ROW][C]14[/C][C]93[/C][C]92.2188161033875[/C][C]0.781183896612546[/C][/ROW]
[ROW][C]15[/C][C]94[/C][C]93.4564553575631[/C][C]0.543544642436885[/C][/ROW]
[ROW][C]16[/C][C]90[/C][C]89.6512745768532[/C][C]0.348725423146774[/C][/ROW]
[ROW][C]17[/C][C]91[/C][C]90.6426112242654[/C][C]0.357388775734634[/C][/ROW]
[ROW][C]18[/C][C]93[/C][C]92.3921730982562[/C][C]0.607826901743778[/C][/ROW]
[ROW][C]19[/C][C]93[/C][C]93.2910533995859[/C][C]-0.291053399585948[/C][/ROW]
[ROW][C]20[/C][C]92[/C][C]92.3198327114907[/C][C]-0.319832711490747[/C][/ROW]
[ROW][C]21[/C][C]92[/C][C]92.2949460821646[/C][C]-0.294946082164614[/C][/ROW]
[ROW][C]22[/C][C]92[/C][C]92.187005183478[/C][C]-0.18700518347795[/C][/ROW]
[ROW][C]23[/C][C]94[/C][C]90.2662387385356[/C][C]3.73376126146437[/C][/ROW]
[ROW][C]24[/C][C]93[/C][C]88.2763553923472[/C][C]4.72364460765277[/C][/ROW]
[ROW][C]25[/C][C]95[/C][C]96.1288763798494[/C][C]-1.12887637984939[/C][/ROW]
[ROW][C]26[/C][C]98[/C][C]97.9316271512966[/C][C]0.0683728487034188[/C][/ROW]
[ROW][C]27[/C][C]98[/C][C]99.0267036218215[/C][C]-1.0267036218215[/C][/ROW]
[ROW][C]28[/C][C]95[/C][C]94.885404408672[/C][C]0.114595591327969[/C][/ROW]
[ROW][C]29[/C][C]97[/C][C]95.9421277733084[/C][C]1.0578722266916[/C][/ROW]
[ROW][C]30[/C][C]100[/C][C]98.1073906369762[/C][C]1.89260936302384[/C][/ROW]
[ROW][C]31[/C][C]100[/C][C]98.9472044848127[/C][C]1.05279551518727[/C][/ROW]
[ROW][C]32[/C][C]100[/C][C]98.4278820129993[/C][C]1.57211798700068[/C][/ROW]
[ROW][C]33[/C][C]98[/C][C]99.0384772082916[/C][C]-1.03847720829158[/C][/ROW]
[ROW][C]34[/C][C]98[/C][C]99.0167603780397[/C][C]-1.01676037803971[/C][/ROW]
[ROW][C]35[/C][C]98[/C][C]99.2264723312487[/C][C]-1.22647233124874[/C][/ROW]
[ROW][C]36[/C][C]99[/C][C]96.7709646103469[/C][C]2.22903538965309[/C][/ROW]
[ROW][C]37[/C][C]97[/C][C]100.928691235161[/C][C]-3.92869123516094[/C][/ROW]
[ROW][C]38[/C][C]100[/C][C]102.761877247494[/C][C]-2.76187724749383[/C][/ROW]
[ROW][C]39[/C][C]104[/C][C]102.581387681856[/C][C]1.41861231814418[/C][/ROW]
[ROW][C]40[/C][C]96[/C][C]99.5903021776202[/C][C]-3.5903021776202[/C][/ROW]
[ROW][C]41[/C][C]99[/C][C]100.267132573849[/C][C]-1.26713257384921[/C][/ROW]
[ROW][C]42[/C][C]102[/C][C]102.25667658371[/C][C]-0.25667658370989[/C][/ROW]
[ROW][C]43[/C][C]101[/C][C]102.008956807927[/C][C]-1.00895680792709[/C][/ROW]
[ROW][C]44[/C][C]101[/C][C]101.12569458572[/C][C]-0.125694585720368[/C][/ROW]
[ROW][C]45[/C][C]99[/C][C]99.7168791316949[/C][C]-0.716879131694924[/C][/ROW]
[ROW][C]46[/C][C]99[/C][C]99.5614856270227[/C][C]-0.561485627022719[/C][/ROW]
[ROW][C]47[/C][C]101[/C][C]99.5489279988135[/C][C]1.45107200118646[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]99.4061781488622[/C][C]2.59382185113782[/C][/ROW]
[ROW][C]49[/C][C]103[/C][C]100.133841317162[/C][C]2.86615868283845[/C][/ROW]
[ROW][C]50[/C][C]102[/C][C]104.067245648232[/C][C]-2.06724564823169[/C][/ROW]
[ROW][C]51[/C][C]104[/C][C]106.295953601346[/C][C]-2.29595360134643[/C][/ROW]
[ROW][C]52[/C][C]103[/C][C]99.667681766467[/C][C]3.33231823353303[/C][/ROW]
[ROW][C]53[/C][C]103[/C][C]103.172063608824[/C][C]-0.172063608823976[/C][/ROW]
[ROW][C]54[/C][C]102[/C][C]106.00754339405[/C][C]-4.00754339404985[/C][/ROW]
[ROW][C]55[/C][C]101[/C][C]104.509816793309[/C][C]-3.50981679330886[/C][/ROW]
[ROW][C]56[/C][C]101[/C][C]103.49946166263[/C][C]-2.4994616626297[/C][/ROW]
[ROW][C]57[/C][C]103[/C][C]101.146099618316[/C][C]1.85390038168381[/C][/ROW]
[ROW][C]58[/C][C]103[/C][C]101.589215096593[/C][C]1.41078490340675[/C][/ROW]
[ROW][C]59[/C][C]103[/C][C]103.090108231866[/C][C]-0.0901082318656137[/C][/ROW]
[ROW][C]60[/C][C]103[/C][C]103.184483863683[/C][C]-0.184483863683155[/C][/ROW]
[ROW][C]61[/C][C]103[/C][C]103.352916028415[/C][C]-0.352916028415379[/C][/ROW]
[ROW][C]62[/C][C]104[/C][C]103.735930005924[/C][C]0.264069994075783[/C][/ROW]
[ROW][C]63[/C][C]98[/C][C]106.243838380735[/C][C]-8.24383838073506[/C][/ROW]
[ROW][C]64[/C][C]102[/C][C]101.155268964549[/C][C]0.844731035451048[/C][/ROW]
[ROW][C]65[/C][C]103[/C][C]101.94157852196[/C][C]1.05842147804009[/C][/ROW]
[ROW][C]66[/C][C]103[/C][C]102.720485216679[/C][C]0.279514783321318[/C][/ROW]
[ROW][C]67[/C][C]102[/C][C]102.277738474124[/C][C]-0.277738474124064[/C][/ROW]
[ROW][C]68[/C][C]103[/C][C]102.426112861722[/C][C]0.573887138278224[/C][/ROW]
[ROW][C]69[/C][C]102[/C][C]103.072653015336[/C][C]-1.07265301533589[/C][/ROW]
[ROW][C]70[/C][C]102[/C][C]102.526382356619[/C][C]-0.526382356619422[/C][/ROW]
[ROW][C]71[/C][C]103[/C][C]102.645448978627[/C][C]0.354551021372743[/C][/ROW]
[ROW][C]72[/C][C]103[/C][C]102.657814546931[/C][C]0.342185453068694[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294691&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294691&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
139189.9316239316241.068376068376
149392.21881610338750.781183896612546
159493.45645535756310.543544642436885
169089.65127457685320.348725423146774
179190.64261122426540.357388775734634
189392.39217309825620.607826901743778
199393.2910533995859-0.291053399585948
209292.3198327114907-0.319832711490747
219292.2949460821646-0.294946082164614
229292.187005183478-0.18700518347795
239490.26623873853563.73376126146437
249388.27635539234724.72364460765277
259596.1288763798494-1.12887637984939
269897.93162715129660.0683728487034188
279899.0267036218215-1.0267036218215
289594.8854044086720.114595591327969
299795.94212777330841.0578722266916
3010098.10739063697621.89260936302384
3110098.94720448481271.05279551518727
3210098.42788201299931.57211798700068
339899.0384772082916-1.03847720829158
349899.0167603780397-1.01676037803971
359899.2264723312487-1.22647233124874
369996.77096461034692.22903538965309
3797100.928691235161-3.92869123516094
38100102.761877247494-2.76187724749383
39104102.5813876818561.41861231814418
409699.5903021776202-3.5903021776202
4199100.267132573849-1.26713257384921
42102102.25667658371-0.25667658370989
43101102.008956807927-1.00895680792709
44101101.12569458572-0.125694585720368
459999.7168791316949-0.716879131694924
469999.5614856270227-0.561485627022719
4710199.54892799881351.45107200118646
4810299.40617814886222.59382185113782
49103100.1338413171622.86615868283845
50102104.067245648232-2.06724564823169
51104106.295953601346-2.29595360134643
5210399.6676817664673.33231823353303
53103103.172063608824-0.172063608823976
54102106.00754339405-4.00754339404985
55101104.509816793309-3.50981679330886
56101103.49946166263-2.4994616626297
57103101.1460996183161.85390038168381
58103101.5892150965931.41078490340675
59103103.090108231866-0.0901082318656137
60103103.184483863683-0.184483863683155
61103103.352916028415-0.352916028415379
62104103.7359300059240.264069994075783
6398106.243838380735-8.24383838073506
64102101.1552689645490.844731035451048
65103101.941578521961.05842147804009
66103102.7204852166790.279514783321318
67102102.277738474124-0.277738474124064
68103102.4261128617220.573887138278224
69102103.072653015336-1.07265301533589
70102102.526382356619-0.526382356619422
71103102.6454489786270.354551021372743
72103102.6578145469310.342185453068694







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102.73127308537998.70457354848106.757972622279
74103.41526025603199.2758388159916107.55468169607
75101.11043426434796.844654061997105.376214466696
76102.82144004820598.4156888227455107.227191273665
77103.55078958834898.9915987273978108.109980449298
78103.66594578700598.9400876487177108.391803925293
79102.84713431530897.9416977963787107.752570834238
80103.51509906185598.4175447196896108.612653404021
81103.12175843940397.8199553777902108.423561501017
82103.11283339231597.595080606051108.630586178578
83103.84042491335398.0954599299466109.585389896759
84103.77388328382597.7908808330874109.756885734563

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102.731273085379 & 98.70457354848 & 106.757972622279 \tabularnewline
74 & 103.415260256031 & 99.2758388159916 & 107.55468169607 \tabularnewline
75 & 101.110434264347 & 96.844654061997 & 105.376214466696 \tabularnewline
76 & 102.821440048205 & 98.4156888227455 & 107.227191273665 \tabularnewline
77 & 103.550789588348 & 98.9915987273978 & 108.109980449298 \tabularnewline
78 & 103.665945787005 & 98.9400876487177 & 108.391803925293 \tabularnewline
79 & 102.847134315308 & 97.9416977963787 & 107.752570834238 \tabularnewline
80 & 103.515099061855 & 98.4175447196896 & 108.612653404021 \tabularnewline
81 & 103.121758439403 & 97.8199553777902 & 108.423561501017 \tabularnewline
82 & 103.112833392315 & 97.595080606051 & 108.630586178578 \tabularnewline
83 & 103.840424913353 & 98.0954599299466 & 109.585389896759 \tabularnewline
84 & 103.773883283825 & 97.7908808330874 & 109.756885734563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294691&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]102.731273085379[/C][C]98.70457354848[/C][C]106.757972622279[/C][/ROW]
[ROW][C]74[/C][C]103.415260256031[/C][C]99.2758388159916[/C][C]107.55468169607[/C][/ROW]
[ROW][C]75[/C][C]101.110434264347[/C][C]96.844654061997[/C][C]105.376214466696[/C][/ROW]
[ROW][C]76[/C][C]102.821440048205[/C][C]98.4156888227455[/C][C]107.227191273665[/C][/ROW]
[ROW][C]77[/C][C]103.550789588348[/C][C]98.9915987273978[/C][C]108.109980449298[/C][/ROW]
[ROW][C]78[/C][C]103.665945787005[/C][C]98.9400876487177[/C][C]108.391803925293[/C][/ROW]
[ROW][C]79[/C][C]102.847134315308[/C][C]97.9416977963787[/C][C]107.752570834238[/C][/ROW]
[ROW][C]80[/C][C]103.515099061855[/C][C]98.4175447196896[/C][C]108.612653404021[/C][/ROW]
[ROW][C]81[/C][C]103.121758439403[/C][C]97.8199553777902[/C][C]108.423561501017[/C][/ROW]
[ROW][C]82[/C][C]103.112833392315[/C][C]97.595080606051[/C][C]108.630586178578[/C][/ROW]
[ROW][C]83[/C][C]103.840424913353[/C][C]98.0954599299466[/C][C]109.585389896759[/C][/ROW]
[ROW][C]84[/C][C]103.773883283825[/C][C]97.7908808330874[/C][C]109.756885734563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294691&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294691&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
73102.73127308537998.70457354848106.757972622279
74103.41526025603199.2758388159916107.55468169607
75101.11043426434796.844654061997105.376214466696
76102.82144004820598.4156888227455107.227191273665
77103.55078958834898.9915987273978108.109980449298
78103.66594578700598.9400876487177108.391803925293
79102.84713431530897.9416977963787107.752570834238
80103.51509906185598.4175447196896108.612653404021
81103.12175843940397.8199553777902108.423561501017
82103.11283339231597.595080606051108.630586178578
83103.84042491335398.0954599299466109.585389896759
84103.77388328382597.7908808330874109.756885734563



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