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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 23 May 2013 16:04:56 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/23/t1369339558hrwi5yfjy9zvtxq.htm/, Retrieved Mon, 29 Apr 2024 17:19:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210382, Retrieved Mon, 29 Apr 2024 17:19:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2013-05-23 20:04:56] [a0dc50058fa7049d3ca1c49ed2014afb] [Current]
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Dataseries X:
109,77
109,77
109,77
109,77
109,77
109,77
109,77
109,77
109,77
109,77
109,77
109,77
109,86
110,12
110,5
113,73
119,84
119,83
113,06
112,45
110,07
110,09
110,72
109,9
109,9
110,06
110,52
116,16
118,54
118,77
113,71
106,98
106,98
106,98
106,98
106,98
106,98
107,43
107,93
111,99
115,4
115,53
115,22
102,75
102,75
102,75
102,75
102,75
102,75
102,87
103,13
108,52
111,6
111,32
108,77
100,05
100,05
100,05
100,05
100,05
100,05
100,07
100,07
109,26
110
110
109,26
99,42
99,42
99,42
99,42
99,42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210382&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]3 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=210382&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210382&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.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=210382&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=210382&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210382&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
2109.77109.770
3109.77109.770
4109.77109.770
5109.77109.770
6109.77109.770
7109.77109.770
8109.77109.770
9109.77109.770
10109.77109.770
11109.77109.770
12109.77109.770
13109.86109.770.0900000000000034
14110.12109.8599940503730.260005949626532
15110.5110.1199828117970.380017188203254
16113.73110.4999748782183.23002512178158
17119.84113.7297864728546.11021352714589
18119.83119.839596072351-0.00959607235051863
19113.06119.830000634367-6.77000063436718
20112.45113.06044754417-0.610447544170285
21110.07112.450040354832-2.38004035483222
22110.09110.0701573372360.0198426627642618
23110.72110.0899986882620.630001311738141
24109.9110.719958352528-0.819958352527621
25109.9109.900054204955-5.42049551199852e-05
26110.06109.9000000035830.159999996416673
27110.52110.0599894228860.460010577113579
28116.16110.5199695900995.64003040990144
29118.54116.1596271547282.38037284527235
30118.77118.5398426407840.230157359215681
31113.71118.769984784996-5.05998478499635
32106.98113.710334500219-6.73033450021862
33106.98106.980444921963-0.000444921962696299
34106.98106.980000029412-2.9412433377729e-08
35106.98106.980000000002-1.94688709598267e-12
36106.98106.980
37106.98106.980
38107.43106.980.450000000000003
39107.93107.4299702518670.500029748132604
40111.99107.9299669445534.06003305544722
41115.4111.9897316035523.41026839644829
42115.53115.3997745575190.130225442481077
43115.22115.529991391192-0.309991391191716
44102.75115.220020492589-12.4700204925889
45102.75102.750824355163-0.000824355162762913
46102.75102.750000054496-5.44956151316001e-08
47102.75102.750000000004-3.60955709766131e-12
48102.75102.750
49102.75102.750
50102.87102.750.120000000000005
51103.13102.8699920671650.26000793283535
52108.52103.1299828116665.39001718833437
53111.6108.5196436823423.08035631765796
54111.32111.599796367004-0.279796367003954
55108.77111.320018496488-2.55001849648762
56100.05108.770168573974-8.72016857397419
57100.05100.050576463847-0.000576463846897468
58100.05100.050000038108-3.81082685407819e-08
59100.05100.050000000003-2.51532128459075e-12
60100.05100.050
61100.05100.050
62100.07100.050.019999999999996
63100.07100.0699986778611.322139226545e-06
64109.26100.0699999999139.19000000008741
65110109.2593924770250.740607522974827
66110109.9999510406874.89593128918386e-05
67109.26109.999999996763-0.739999996763444
6899.42109.260048919151-9.84004891915119
6999.4299.4206504957336-0.00065049573359488
7099.4299.4200000430023-4.30023021635861e-08
7199.4299.4200000000028-2.8421709430404e-12
7299.4299.420

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 109.77 & 109.77 & 0 \tabularnewline
3 & 109.77 & 109.77 & 0 \tabularnewline
4 & 109.77 & 109.77 & 0 \tabularnewline
5 & 109.77 & 109.77 & 0 \tabularnewline
6 & 109.77 & 109.77 & 0 \tabularnewline
7 & 109.77 & 109.77 & 0 \tabularnewline
8 & 109.77 & 109.77 & 0 \tabularnewline
9 & 109.77 & 109.77 & 0 \tabularnewline
10 & 109.77 & 109.77 & 0 \tabularnewline
11 & 109.77 & 109.77 & 0 \tabularnewline
12 & 109.77 & 109.77 & 0 \tabularnewline
13 & 109.86 & 109.77 & 0.0900000000000034 \tabularnewline
14 & 110.12 & 109.859994050373 & 0.260005949626532 \tabularnewline
15 & 110.5 & 110.119982811797 & 0.380017188203254 \tabularnewline
16 & 113.73 & 110.499974878218 & 3.23002512178158 \tabularnewline
17 & 119.84 & 113.729786472854 & 6.11021352714589 \tabularnewline
18 & 119.83 & 119.839596072351 & -0.00959607235051863 \tabularnewline
19 & 113.06 & 119.830000634367 & -6.77000063436718 \tabularnewline
20 & 112.45 & 113.06044754417 & -0.610447544170285 \tabularnewline
21 & 110.07 & 112.450040354832 & -2.38004035483222 \tabularnewline
22 & 110.09 & 110.070157337236 & 0.0198426627642618 \tabularnewline
23 & 110.72 & 110.089998688262 & 0.630001311738141 \tabularnewline
24 & 109.9 & 110.719958352528 & -0.819958352527621 \tabularnewline
25 & 109.9 & 109.900054204955 & -5.42049551199852e-05 \tabularnewline
26 & 110.06 & 109.900000003583 & 0.159999996416673 \tabularnewline
27 & 110.52 & 110.059989422886 & 0.460010577113579 \tabularnewline
28 & 116.16 & 110.519969590099 & 5.64003040990144 \tabularnewline
29 & 118.54 & 116.159627154728 & 2.38037284527235 \tabularnewline
30 & 118.77 & 118.539842640784 & 0.230157359215681 \tabularnewline
31 & 113.71 & 118.769984784996 & -5.05998478499635 \tabularnewline
32 & 106.98 & 113.710334500219 & -6.73033450021862 \tabularnewline
33 & 106.98 & 106.980444921963 & -0.000444921962696299 \tabularnewline
34 & 106.98 & 106.980000029412 & -2.9412433377729e-08 \tabularnewline
35 & 106.98 & 106.980000000002 & -1.94688709598267e-12 \tabularnewline
36 & 106.98 & 106.98 & 0 \tabularnewline
37 & 106.98 & 106.98 & 0 \tabularnewline
38 & 107.43 & 106.98 & 0.450000000000003 \tabularnewline
39 & 107.93 & 107.429970251867 & 0.500029748132604 \tabularnewline
40 & 111.99 & 107.929966944553 & 4.06003305544722 \tabularnewline
41 & 115.4 & 111.989731603552 & 3.41026839644829 \tabularnewline
42 & 115.53 & 115.399774557519 & 0.130225442481077 \tabularnewline
43 & 115.22 & 115.529991391192 & -0.309991391191716 \tabularnewline
44 & 102.75 & 115.220020492589 & -12.4700204925889 \tabularnewline
45 & 102.75 & 102.750824355163 & -0.000824355162762913 \tabularnewline
46 & 102.75 & 102.750000054496 & -5.44956151316001e-08 \tabularnewline
47 & 102.75 & 102.750000000004 & -3.60955709766131e-12 \tabularnewline
48 & 102.75 & 102.75 & 0 \tabularnewline
49 & 102.75 & 102.75 & 0 \tabularnewline
50 & 102.87 & 102.75 & 0.120000000000005 \tabularnewline
51 & 103.13 & 102.869992067165 & 0.26000793283535 \tabularnewline
52 & 108.52 & 103.129982811666 & 5.39001718833437 \tabularnewline
53 & 111.6 & 108.519643682342 & 3.08035631765796 \tabularnewline
54 & 111.32 & 111.599796367004 & -0.279796367003954 \tabularnewline
55 & 108.77 & 111.320018496488 & -2.55001849648762 \tabularnewline
56 & 100.05 & 108.770168573974 & -8.72016857397419 \tabularnewline
57 & 100.05 & 100.050576463847 & -0.000576463846897468 \tabularnewline
58 & 100.05 & 100.050000038108 & -3.81082685407819e-08 \tabularnewline
59 & 100.05 & 100.050000000003 & -2.51532128459075e-12 \tabularnewline
60 & 100.05 & 100.05 & 0 \tabularnewline
61 & 100.05 & 100.05 & 0 \tabularnewline
62 & 100.07 & 100.05 & 0.019999999999996 \tabularnewline
63 & 100.07 & 100.069998677861 & 1.322139226545e-06 \tabularnewline
64 & 109.26 & 100.069999999913 & 9.19000000008741 \tabularnewline
65 & 110 & 109.259392477025 & 0.740607522974827 \tabularnewline
66 & 110 & 109.999951040687 & 4.89593128918386e-05 \tabularnewline
67 & 109.26 & 109.999999996763 & -0.739999996763444 \tabularnewline
68 & 99.42 & 109.260048919151 & -9.84004891915119 \tabularnewline
69 & 99.42 & 99.4206504957336 & -0.00065049573359488 \tabularnewline
70 & 99.42 & 99.4200000430023 & -4.30023021635861e-08 \tabularnewline
71 & 99.42 & 99.4200000000028 & -2.8421709430404e-12 \tabularnewline
72 & 99.42 & 99.42 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210382&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]109.77[/C][C]109.77[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]109.77[/C][C]109.77[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]109.77[/C][C]109.77[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]109.77[/C][C]109.77[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]109.77[/C][C]109.77[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]109.77[/C][C]109.77[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]109.77[/C][C]109.77[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]109.77[/C][C]109.77[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]109.77[/C][C]109.77[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]109.77[/C][C]109.77[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]109.77[/C][C]109.77[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]109.86[/C][C]109.77[/C][C]0.0900000000000034[/C][/ROW]
[ROW][C]14[/C][C]110.12[/C][C]109.859994050373[/C][C]0.260005949626532[/C][/ROW]
[ROW][C]15[/C][C]110.5[/C][C]110.119982811797[/C][C]0.380017188203254[/C][/ROW]
[ROW][C]16[/C][C]113.73[/C][C]110.499974878218[/C][C]3.23002512178158[/C][/ROW]
[ROW][C]17[/C][C]119.84[/C][C]113.729786472854[/C][C]6.11021352714589[/C][/ROW]
[ROW][C]18[/C][C]119.83[/C][C]119.839596072351[/C][C]-0.00959607235051863[/C][/ROW]
[ROW][C]19[/C][C]113.06[/C][C]119.830000634367[/C][C]-6.77000063436718[/C][/ROW]
[ROW][C]20[/C][C]112.45[/C][C]113.06044754417[/C][C]-0.610447544170285[/C][/ROW]
[ROW][C]21[/C][C]110.07[/C][C]112.450040354832[/C][C]-2.38004035483222[/C][/ROW]
[ROW][C]22[/C][C]110.09[/C][C]110.070157337236[/C][C]0.0198426627642618[/C][/ROW]
[ROW][C]23[/C][C]110.72[/C][C]110.089998688262[/C][C]0.630001311738141[/C][/ROW]
[ROW][C]24[/C][C]109.9[/C][C]110.719958352528[/C][C]-0.819958352527621[/C][/ROW]
[ROW][C]25[/C][C]109.9[/C][C]109.900054204955[/C][C]-5.42049551199852e-05[/C][/ROW]
[ROW][C]26[/C][C]110.06[/C][C]109.900000003583[/C][C]0.159999996416673[/C][/ROW]
[ROW][C]27[/C][C]110.52[/C][C]110.059989422886[/C][C]0.460010577113579[/C][/ROW]
[ROW][C]28[/C][C]116.16[/C][C]110.519969590099[/C][C]5.64003040990144[/C][/ROW]
[ROW][C]29[/C][C]118.54[/C][C]116.159627154728[/C][C]2.38037284527235[/C][/ROW]
[ROW][C]30[/C][C]118.77[/C][C]118.539842640784[/C][C]0.230157359215681[/C][/ROW]
[ROW][C]31[/C][C]113.71[/C][C]118.769984784996[/C][C]-5.05998478499635[/C][/ROW]
[ROW][C]32[/C][C]106.98[/C][C]113.710334500219[/C][C]-6.73033450021862[/C][/ROW]
[ROW][C]33[/C][C]106.98[/C][C]106.980444921963[/C][C]-0.000444921962696299[/C][/ROW]
[ROW][C]34[/C][C]106.98[/C][C]106.980000029412[/C][C]-2.9412433377729e-08[/C][/ROW]
[ROW][C]35[/C][C]106.98[/C][C]106.980000000002[/C][C]-1.94688709598267e-12[/C][/ROW]
[ROW][C]36[/C][C]106.98[/C][C]106.98[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]106.98[/C][C]106.98[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]107.43[/C][C]106.98[/C][C]0.450000000000003[/C][/ROW]
[ROW][C]39[/C][C]107.93[/C][C]107.429970251867[/C][C]0.500029748132604[/C][/ROW]
[ROW][C]40[/C][C]111.99[/C][C]107.929966944553[/C][C]4.06003305544722[/C][/ROW]
[ROW][C]41[/C][C]115.4[/C][C]111.989731603552[/C][C]3.41026839644829[/C][/ROW]
[ROW][C]42[/C][C]115.53[/C][C]115.399774557519[/C][C]0.130225442481077[/C][/ROW]
[ROW][C]43[/C][C]115.22[/C][C]115.529991391192[/C][C]-0.309991391191716[/C][/ROW]
[ROW][C]44[/C][C]102.75[/C][C]115.220020492589[/C][C]-12.4700204925889[/C][/ROW]
[ROW][C]45[/C][C]102.75[/C][C]102.750824355163[/C][C]-0.000824355162762913[/C][/ROW]
[ROW][C]46[/C][C]102.75[/C][C]102.750000054496[/C][C]-5.44956151316001e-08[/C][/ROW]
[ROW][C]47[/C][C]102.75[/C][C]102.750000000004[/C][C]-3.60955709766131e-12[/C][/ROW]
[ROW][C]48[/C][C]102.75[/C][C]102.75[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]102.75[/C][C]102.75[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]102.87[/C][C]102.75[/C][C]0.120000000000005[/C][/ROW]
[ROW][C]51[/C][C]103.13[/C][C]102.869992067165[/C][C]0.26000793283535[/C][/ROW]
[ROW][C]52[/C][C]108.52[/C][C]103.129982811666[/C][C]5.39001718833437[/C][/ROW]
[ROW][C]53[/C][C]111.6[/C][C]108.519643682342[/C][C]3.08035631765796[/C][/ROW]
[ROW][C]54[/C][C]111.32[/C][C]111.599796367004[/C][C]-0.279796367003954[/C][/ROW]
[ROW][C]55[/C][C]108.77[/C][C]111.320018496488[/C][C]-2.55001849648762[/C][/ROW]
[ROW][C]56[/C][C]100.05[/C][C]108.770168573974[/C][C]-8.72016857397419[/C][/ROW]
[ROW][C]57[/C][C]100.05[/C][C]100.050576463847[/C][C]-0.000576463846897468[/C][/ROW]
[ROW][C]58[/C][C]100.05[/C][C]100.050000038108[/C][C]-3.81082685407819e-08[/C][/ROW]
[ROW][C]59[/C][C]100.05[/C][C]100.050000000003[/C][C]-2.51532128459075e-12[/C][/ROW]
[ROW][C]60[/C][C]100.05[/C][C]100.05[/C][C]0[/C][/ROW]
[ROW][C]61[/C][C]100.05[/C][C]100.05[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]100.07[/C][C]100.05[/C][C]0.019999999999996[/C][/ROW]
[ROW][C]63[/C][C]100.07[/C][C]100.069998677861[/C][C]1.322139226545e-06[/C][/ROW]
[ROW][C]64[/C][C]109.26[/C][C]100.069999999913[/C][C]9.19000000008741[/C][/ROW]
[ROW][C]65[/C][C]110[/C][C]109.259392477025[/C][C]0.740607522974827[/C][/ROW]
[ROW][C]66[/C][C]110[/C][C]109.999951040687[/C][C]4.89593128918386e-05[/C][/ROW]
[ROW][C]67[/C][C]109.26[/C][C]109.999999996763[/C][C]-0.739999996763444[/C][/ROW]
[ROW][C]68[/C][C]99.42[/C][C]109.260048919151[/C][C]-9.84004891915119[/C][/ROW]
[ROW][C]69[/C][C]99.42[/C][C]99.4206504957336[/C][C]-0.00065049573359488[/C][/ROW]
[ROW][C]70[/C][C]99.42[/C][C]99.4200000430023[/C][C]-4.30023021635861e-08[/C][/ROW]
[ROW][C]71[/C][C]99.42[/C][C]99.4200000000028[/C][C]-2.8421709430404e-12[/C][/ROW]
[ROW][C]72[/C][C]99.42[/C][C]99.42[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210382&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210382&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
2109.77109.770
3109.77109.770
4109.77109.770
5109.77109.770
6109.77109.770
7109.77109.770
8109.77109.770
9109.77109.770
10109.77109.770
11109.77109.770
12109.77109.770
13109.86109.770.0900000000000034
14110.12109.8599940503730.260005949626532
15110.5110.1199828117970.380017188203254
16113.73110.4999748782183.23002512178158
17119.84113.7297864728546.11021352714589
18119.83119.839596072351-0.00959607235051863
19113.06119.830000634367-6.77000063436718
20112.45113.06044754417-0.610447544170285
21110.07112.450040354832-2.38004035483222
22110.09110.0701573372360.0198426627642618
23110.72110.0899986882620.630001311738141
24109.9110.719958352528-0.819958352527621
25109.9109.900054204955-5.42049551199852e-05
26110.06109.9000000035830.159999996416673
27110.52110.0599894228860.460010577113579
28116.16110.5199695900995.64003040990144
29118.54116.1596271547282.38037284527235
30118.77118.5398426407840.230157359215681
31113.71118.769984784996-5.05998478499635
32106.98113.710334500219-6.73033450021862
33106.98106.980444921963-0.000444921962696299
34106.98106.980000029412-2.9412433377729e-08
35106.98106.980000000002-1.94688709598267e-12
36106.98106.980
37106.98106.980
38107.43106.980.450000000000003
39107.93107.4299702518670.500029748132604
40111.99107.9299669445534.06003305544722
41115.4111.9897316035523.41026839644829
42115.53115.3997745575190.130225442481077
43115.22115.529991391192-0.309991391191716
44102.75115.220020492589-12.4700204925889
45102.75102.750824355163-0.000824355162762913
46102.75102.750000054496-5.44956151316001e-08
47102.75102.750000000004-3.60955709766131e-12
48102.75102.750
49102.75102.750
50102.87102.750.120000000000005
51103.13102.8699920671650.26000793283535
52108.52103.1299828116665.39001718833437
53111.6108.5196436823423.08035631765796
54111.32111.599796367004-0.279796367003954
55108.77111.320018496488-2.55001849648762
56100.05108.770168573974-8.72016857397419
57100.05100.050576463847-0.000576463846897468
58100.05100.050000038108-3.81082685407819e-08
59100.05100.050000000003-2.51532128459075e-12
60100.05100.050
61100.05100.050
62100.07100.050.019999999999996
63100.07100.0699986778611.322139226545e-06
64109.26100.0699999999139.19000000008741
65110109.2593924770250.740607522974827
66110109.9999510406874.89593128918386e-05
67109.26109.999999996763-0.739999996763444
6899.42109.260048919151-9.84004891915119
6999.4299.4206504957336-0.00065049573359488
7099.4299.4200000430023-4.30023021635861e-08
7199.4299.4200000000028-2.8421709430404e-12
7299.4299.420







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7399.4293.2402674482379105.599732551762
7499.4290.6808272783099108.15917272169
7599.4288.7168609600849110.123139039915
7699.4287.0611476764233111.778852323577
7799.4285.602428715429113.237571284571
7899.4284.2836423914991114.556357608501
7999.4283.0708909386277115.769109061372
8099.4281.9420878664278116.897912133572
8199.4280.8818917362884117.958108263712
8299.4279.8791324797153118.960867520285
8399.4278.9253775615763119.914622438424
8499.4278.0140757185829120.825924281417

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 99.42 & 93.2402674482379 & 105.599732551762 \tabularnewline
74 & 99.42 & 90.6808272783099 & 108.15917272169 \tabularnewline
75 & 99.42 & 88.7168609600849 & 110.123139039915 \tabularnewline
76 & 99.42 & 87.0611476764233 & 111.778852323577 \tabularnewline
77 & 99.42 & 85.602428715429 & 113.237571284571 \tabularnewline
78 & 99.42 & 84.2836423914991 & 114.556357608501 \tabularnewline
79 & 99.42 & 83.0708909386277 & 115.769109061372 \tabularnewline
80 & 99.42 & 81.9420878664278 & 116.897912133572 \tabularnewline
81 & 99.42 & 80.8818917362884 & 117.958108263712 \tabularnewline
82 & 99.42 & 79.8791324797153 & 118.960867520285 \tabularnewline
83 & 99.42 & 78.9253775615763 & 119.914622438424 \tabularnewline
84 & 99.42 & 78.0140757185829 & 120.825924281417 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210382&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]99.42[/C][C]93.2402674482379[/C][C]105.599732551762[/C][/ROW]
[ROW][C]74[/C][C]99.42[/C][C]90.6808272783099[/C][C]108.15917272169[/C][/ROW]
[ROW][C]75[/C][C]99.42[/C][C]88.7168609600849[/C][C]110.123139039915[/C][/ROW]
[ROW][C]76[/C][C]99.42[/C][C]87.0611476764233[/C][C]111.778852323577[/C][/ROW]
[ROW][C]77[/C][C]99.42[/C][C]85.602428715429[/C][C]113.237571284571[/C][/ROW]
[ROW][C]78[/C][C]99.42[/C][C]84.2836423914991[/C][C]114.556357608501[/C][/ROW]
[ROW][C]79[/C][C]99.42[/C][C]83.0708909386277[/C][C]115.769109061372[/C][/ROW]
[ROW][C]80[/C][C]99.42[/C][C]81.9420878664278[/C][C]116.897912133572[/C][/ROW]
[ROW][C]81[/C][C]99.42[/C][C]80.8818917362884[/C][C]117.958108263712[/C][/ROW]
[ROW][C]82[/C][C]99.42[/C][C]79.8791324797153[/C][C]118.960867520285[/C][/ROW]
[ROW][C]83[/C][C]99.42[/C][C]78.9253775615763[/C][C]119.914622438424[/C][/ROW]
[ROW][C]84[/C][C]99.42[/C][C]78.0140757185829[/C][C]120.825924281417[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210382&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210382&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
7399.4293.2402674482379105.599732551762
7499.4290.6808272783099108.15917272169
7599.4288.7168609600849110.123139039915
7699.4287.0611476764233111.778852323577
7799.4285.602428715429113.237571284571
7899.4284.2836423914991114.556357608501
7999.4283.0708909386277115.769109061372
8099.4281.9420878664278116.897912133572
8199.4280.8818917362884117.958108263712
8299.4279.8791324797153118.960867520285
8399.4278.9253775615763119.914622438424
8499.4278.0140757185829120.825924281417



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