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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 04:20:53 -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/2012/Dec/21/t1356081694nv9hz373xxbmsj8.htm/, Retrieved Wed, 24 Apr 2024 01:40:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203361, Retrieved Wed, 24 Apr 2024 01:40:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact43
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-21 09:20:53] [5af040df2efe5a417a92383fa6aaebd4] [Current]
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Dataseries X:
99.42
99.42
99.42
99.42
99.42
109.26
110.00
110.00
109.26
100.07
100.07
100.05
100.05
100.05
100.05
100.05
100.05
108.77
111.32
111.60
108.52
103.13
102.87
102.75
102.75
102.75
102.75
102.75
102.75
115.22
115.53
115.40
111.99
107.93
107.43
106.98
106.98
106.98
106.98
106.98
106.98
113.71
118.77
118.54
116.16
110.52
110.06
109.90
109.90
110.72
110.09
110.07
112.45
113.06
119.83
119.84
113.73
110.50
110.12
109.86
110.36
110.36
110.59
112.52
112.10
115.90
122.96
121.26
114.55
111.57
110.65
109.77




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203361&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203361&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203361&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.408032483432256
beta0
gamma0.881226574770473

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.408032483432256 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.881226574770473 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203361&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]0.408032483432256[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.881226574770473[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203361&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203361&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
alpha0.408032483432256
beta0
gamma0.881226574770473







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13100.0599.85599358974360.194006410256435
14100.0599.88898900595680.161010994043224
15100.0599.9943545538840.0556454461160456
16100.0599.99589420228890.0541057977111308
17100.0599.84930562413150.200694375868466
18108.77108.4975299475630.27247005243747
19111.32110.8921244118870.427875588112599
20111.6111.0897127162060.510287283793815
21108.52110.580927669378-2.06092766937763
22103.13100.5730033997682.55699660023161
23102.87101.639342238191.23065776181012
24102.75102.1911584131640.558841586835712
25102.75102.561306666170.188693333829633
26102.75102.574921868050.175078131949732
27102.75102.6310625361370.118937463863205
28102.75102.6576242145760.0923757854240392
29102.75102.6031200667820.146879933217676
30115.22111.2668286700363.95317132996375
31115.53115.2443372817170.28566271828322
32115.4115.4268887953-0.0268887952997972
33111.99113.357624876445-1.36762487644479
34107.93106.0415655292071.88843447079267
35107.43106.1432146897361.28678531026362
36106.98106.3674747766960.612525223304445
37106.98106.5664370823260.413562917674057
38106.98106.664703906680.315296093319716
39106.98106.7487718568110.231228143188929
40106.98106.8072956810450.172704318954516
41106.98106.8140006821380.165999317862045
42113.71117.471091096334-3.76109109633356
43118.77116.3877466530922.38225334690782
44118.54117.2627304042291.27726959577124
45116.16115.0262004308361.13379956916407
46110.52110.4293513139840.090648686016408
47110.06109.4835906749010.576409325099291
48109.9109.066261448430.833738551570335
49109.9109.2516957974190.6483042025815
50110.72109.3944830646041.32551693539581
51110.09109.8468992564580.243100743541547
52110.07109.8797380950490.190261904950688
53112.45109.8901094474052.55989055259546
54113.06119.475389051941-6.41538905194076
55119.83120.51372656901-0.683726569009735
56119.84119.5612678520070.27873214799277
57113.73116.842459947588-3.11245994758805
58110.5109.9688315256890.531168474310547
59110.12109.4562179538080.663782046191827
60109.86109.2087773584680.651222641532016
61110.36109.2230060672121.13699393278777
62110.36109.9184677245510.441532275449362
63110.59109.4455389281111.1444610718886
64112.52109.8185982831332.7014017168671
65112.1112.0897308220370.0102691779629396
66115.9115.952660102136-0.0526601021363007
67122.96122.5771624758140.3828375241863
68121.26122.5619703694-1.30197036939995
69114.55117.429143676901-2.87914367690134
70111.57112.55144199136-0.981441991359532
71110.65111.490813080007-0.840813080007266
72109.77110.62289709104-0.85289709103975

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 100.05 & 99.8559935897436 & 0.194006410256435 \tabularnewline
14 & 100.05 & 99.8889890059568 & 0.161010994043224 \tabularnewline
15 & 100.05 & 99.994354553884 & 0.0556454461160456 \tabularnewline
16 & 100.05 & 99.9958942022889 & 0.0541057977111308 \tabularnewline
17 & 100.05 & 99.8493056241315 & 0.200694375868466 \tabularnewline
18 & 108.77 & 108.497529947563 & 0.27247005243747 \tabularnewline
19 & 111.32 & 110.892124411887 & 0.427875588112599 \tabularnewline
20 & 111.6 & 111.089712716206 & 0.510287283793815 \tabularnewline
21 & 108.52 & 110.580927669378 & -2.06092766937763 \tabularnewline
22 & 103.13 & 100.573003399768 & 2.55699660023161 \tabularnewline
23 & 102.87 & 101.63934223819 & 1.23065776181012 \tabularnewline
24 & 102.75 & 102.191158413164 & 0.558841586835712 \tabularnewline
25 & 102.75 & 102.56130666617 & 0.188693333829633 \tabularnewline
26 & 102.75 & 102.57492186805 & 0.175078131949732 \tabularnewline
27 & 102.75 & 102.631062536137 & 0.118937463863205 \tabularnewline
28 & 102.75 & 102.657624214576 & 0.0923757854240392 \tabularnewline
29 & 102.75 & 102.603120066782 & 0.146879933217676 \tabularnewline
30 & 115.22 & 111.266828670036 & 3.95317132996375 \tabularnewline
31 & 115.53 & 115.244337281717 & 0.28566271828322 \tabularnewline
32 & 115.4 & 115.4268887953 & -0.0268887952997972 \tabularnewline
33 & 111.99 & 113.357624876445 & -1.36762487644479 \tabularnewline
34 & 107.93 & 106.041565529207 & 1.88843447079267 \tabularnewline
35 & 107.43 & 106.143214689736 & 1.28678531026362 \tabularnewline
36 & 106.98 & 106.367474776696 & 0.612525223304445 \tabularnewline
37 & 106.98 & 106.566437082326 & 0.413562917674057 \tabularnewline
38 & 106.98 & 106.66470390668 & 0.315296093319716 \tabularnewline
39 & 106.98 & 106.748771856811 & 0.231228143188929 \tabularnewline
40 & 106.98 & 106.807295681045 & 0.172704318954516 \tabularnewline
41 & 106.98 & 106.814000682138 & 0.165999317862045 \tabularnewline
42 & 113.71 & 117.471091096334 & -3.76109109633356 \tabularnewline
43 & 118.77 & 116.387746653092 & 2.38225334690782 \tabularnewline
44 & 118.54 & 117.262730404229 & 1.27726959577124 \tabularnewline
45 & 116.16 & 115.026200430836 & 1.13379956916407 \tabularnewline
46 & 110.52 & 110.429351313984 & 0.090648686016408 \tabularnewline
47 & 110.06 & 109.483590674901 & 0.576409325099291 \tabularnewline
48 & 109.9 & 109.06626144843 & 0.833738551570335 \tabularnewline
49 & 109.9 & 109.251695797419 & 0.6483042025815 \tabularnewline
50 & 110.72 & 109.394483064604 & 1.32551693539581 \tabularnewline
51 & 110.09 & 109.846899256458 & 0.243100743541547 \tabularnewline
52 & 110.07 & 109.879738095049 & 0.190261904950688 \tabularnewline
53 & 112.45 & 109.890109447405 & 2.55989055259546 \tabularnewline
54 & 113.06 & 119.475389051941 & -6.41538905194076 \tabularnewline
55 & 119.83 & 120.51372656901 & -0.683726569009735 \tabularnewline
56 & 119.84 & 119.561267852007 & 0.27873214799277 \tabularnewline
57 & 113.73 & 116.842459947588 & -3.11245994758805 \tabularnewline
58 & 110.5 & 109.968831525689 & 0.531168474310547 \tabularnewline
59 & 110.12 & 109.456217953808 & 0.663782046191827 \tabularnewline
60 & 109.86 & 109.208777358468 & 0.651222641532016 \tabularnewline
61 & 110.36 & 109.223006067212 & 1.13699393278777 \tabularnewline
62 & 110.36 & 109.918467724551 & 0.441532275449362 \tabularnewline
63 & 110.59 & 109.445538928111 & 1.1444610718886 \tabularnewline
64 & 112.52 & 109.818598283133 & 2.7014017168671 \tabularnewline
65 & 112.1 & 112.089730822037 & 0.0102691779629396 \tabularnewline
66 & 115.9 & 115.952660102136 & -0.0526601021363007 \tabularnewline
67 & 122.96 & 122.577162475814 & 0.3828375241863 \tabularnewline
68 & 121.26 & 122.5619703694 & -1.30197036939995 \tabularnewline
69 & 114.55 & 117.429143676901 & -2.87914367690134 \tabularnewline
70 & 111.57 & 112.55144199136 & -0.981441991359532 \tabularnewline
71 & 110.65 & 111.490813080007 & -0.840813080007266 \tabularnewline
72 & 109.77 & 110.62289709104 & -0.85289709103975 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203361&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]100.05[/C][C]99.8559935897436[/C][C]0.194006410256435[/C][/ROW]
[ROW][C]14[/C][C]100.05[/C][C]99.8889890059568[/C][C]0.161010994043224[/C][/ROW]
[ROW][C]15[/C][C]100.05[/C][C]99.994354553884[/C][C]0.0556454461160456[/C][/ROW]
[ROW][C]16[/C][C]100.05[/C][C]99.9958942022889[/C][C]0.0541057977111308[/C][/ROW]
[ROW][C]17[/C][C]100.05[/C][C]99.8493056241315[/C][C]0.200694375868466[/C][/ROW]
[ROW][C]18[/C][C]108.77[/C][C]108.497529947563[/C][C]0.27247005243747[/C][/ROW]
[ROW][C]19[/C][C]111.32[/C][C]110.892124411887[/C][C]0.427875588112599[/C][/ROW]
[ROW][C]20[/C][C]111.6[/C][C]111.089712716206[/C][C]0.510287283793815[/C][/ROW]
[ROW][C]21[/C][C]108.52[/C][C]110.580927669378[/C][C]-2.06092766937763[/C][/ROW]
[ROW][C]22[/C][C]103.13[/C][C]100.573003399768[/C][C]2.55699660023161[/C][/ROW]
[ROW][C]23[/C][C]102.87[/C][C]101.63934223819[/C][C]1.23065776181012[/C][/ROW]
[ROW][C]24[/C][C]102.75[/C][C]102.191158413164[/C][C]0.558841586835712[/C][/ROW]
[ROW][C]25[/C][C]102.75[/C][C]102.56130666617[/C][C]0.188693333829633[/C][/ROW]
[ROW][C]26[/C][C]102.75[/C][C]102.57492186805[/C][C]0.175078131949732[/C][/ROW]
[ROW][C]27[/C][C]102.75[/C][C]102.631062536137[/C][C]0.118937463863205[/C][/ROW]
[ROW][C]28[/C][C]102.75[/C][C]102.657624214576[/C][C]0.0923757854240392[/C][/ROW]
[ROW][C]29[/C][C]102.75[/C][C]102.603120066782[/C][C]0.146879933217676[/C][/ROW]
[ROW][C]30[/C][C]115.22[/C][C]111.266828670036[/C][C]3.95317132996375[/C][/ROW]
[ROW][C]31[/C][C]115.53[/C][C]115.244337281717[/C][C]0.28566271828322[/C][/ROW]
[ROW][C]32[/C][C]115.4[/C][C]115.4268887953[/C][C]-0.0268887952997972[/C][/ROW]
[ROW][C]33[/C][C]111.99[/C][C]113.357624876445[/C][C]-1.36762487644479[/C][/ROW]
[ROW][C]34[/C][C]107.93[/C][C]106.041565529207[/C][C]1.88843447079267[/C][/ROW]
[ROW][C]35[/C][C]107.43[/C][C]106.143214689736[/C][C]1.28678531026362[/C][/ROW]
[ROW][C]36[/C][C]106.98[/C][C]106.367474776696[/C][C]0.612525223304445[/C][/ROW]
[ROW][C]37[/C][C]106.98[/C][C]106.566437082326[/C][C]0.413562917674057[/C][/ROW]
[ROW][C]38[/C][C]106.98[/C][C]106.66470390668[/C][C]0.315296093319716[/C][/ROW]
[ROW][C]39[/C][C]106.98[/C][C]106.748771856811[/C][C]0.231228143188929[/C][/ROW]
[ROW][C]40[/C][C]106.98[/C][C]106.807295681045[/C][C]0.172704318954516[/C][/ROW]
[ROW][C]41[/C][C]106.98[/C][C]106.814000682138[/C][C]0.165999317862045[/C][/ROW]
[ROW][C]42[/C][C]113.71[/C][C]117.471091096334[/C][C]-3.76109109633356[/C][/ROW]
[ROW][C]43[/C][C]118.77[/C][C]116.387746653092[/C][C]2.38225334690782[/C][/ROW]
[ROW][C]44[/C][C]118.54[/C][C]117.262730404229[/C][C]1.27726959577124[/C][/ROW]
[ROW][C]45[/C][C]116.16[/C][C]115.026200430836[/C][C]1.13379956916407[/C][/ROW]
[ROW][C]46[/C][C]110.52[/C][C]110.429351313984[/C][C]0.090648686016408[/C][/ROW]
[ROW][C]47[/C][C]110.06[/C][C]109.483590674901[/C][C]0.576409325099291[/C][/ROW]
[ROW][C]48[/C][C]109.9[/C][C]109.06626144843[/C][C]0.833738551570335[/C][/ROW]
[ROW][C]49[/C][C]109.9[/C][C]109.251695797419[/C][C]0.6483042025815[/C][/ROW]
[ROW][C]50[/C][C]110.72[/C][C]109.394483064604[/C][C]1.32551693539581[/C][/ROW]
[ROW][C]51[/C][C]110.09[/C][C]109.846899256458[/C][C]0.243100743541547[/C][/ROW]
[ROW][C]52[/C][C]110.07[/C][C]109.879738095049[/C][C]0.190261904950688[/C][/ROW]
[ROW][C]53[/C][C]112.45[/C][C]109.890109447405[/C][C]2.55989055259546[/C][/ROW]
[ROW][C]54[/C][C]113.06[/C][C]119.475389051941[/C][C]-6.41538905194076[/C][/ROW]
[ROW][C]55[/C][C]119.83[/C][C]120.51372656901[/C][C]-0.683726569009735[/C][/ROW]
[ROW][C]56[/C][C]119.84[/C][C]119.561267852007[/C][C]0.27873214799277[/C][/ROW]
[ROW][C]57[/C][C]113.73[/C][C]116.842459947588[/C][C]-3.11245994758805[/C][/ROW]
[ROW][C]58[/C][C]110.5[/C][C]109.968831525689[/C][C]0.531168474310547[/C][/ROW]
[ROW][C]59[/C][C]110.12[/C][C]109.456217953808[/C][C]0.663782046191827[/C][/ROW]
[ROW][C]60[/C][C]109.86[/C][C]109.208777358468[/C][C]0.651222641532016[/C][/ROW]
[ROW][C]61[/C][C]110.36[/C][C]109.223006067212[/C][C]1.13699393278777[/C][/ROW]
[ROW][C]62[/C][C]110.36[/C][C]109.918467724551[/C][C]0.441532275449362[/C][/ROW]
[ROW][C]63[/C][C]110.59[/C][C]109.445538928111[/C][C]1.1444610718886[/C][/ROW]
[ROW][C]64[/C][C]112.52[/C][C]109.818598283133[/C][C]2.7014017168671[/C][/ROW]
[ROW][C]65[/C][C]112.1[/C][C]112.089730822037[/C][C]0.0102691779629396[/C][/ROW]
[ROW][C]66[/C][C]115.9[/C][C]115.952660102136[/C][C]-0.0526601021363007[/C][/ROW]
[ROW][C]67[/C][C]122.96[/C][C]122.577162475814[/C][C]0.3828375241863[/C][/ROW]
[ROW][C]68[/C][C]121.26[/C][C]122.5619703694[/C][C]-1.30197036939995[/C][/ROW]
[ROW][C]69[/C][C]114.55[/C][C]117.429143676901[/C][C]-2.87914367690134[/C][/ROW]
[ROW][C]70[/C][C]111.57[/C][C]112.55144199136[/C][C]-0.981441991359532[/C][/ROW]
[ROW][C]71[/C][C]110.65[/C][C]111.490813080007[/C][C]-0.840813080007266[/C][/ROW]
[ROW][C]72[/C][C]109.77[/C][C]110.62289709104[/C][C]-0.85289709103975[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203361&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203361&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
13100.0599.85599358974360.194006410256435
14100.0599.88898900595680.161010994043224
15100.0599.9943545538840.0556454461160456
16100.0599.99589420228890.0541057977111308
17100.0599.84930562413150.200694375868466
18108.77108.4975299475630.27247005243747
19111.32110.8921244118870.427875588112599
20111.6111.0897127162060.510287283793815
21108.52110.580927669378-2.06092766937763
22103.13100.5730033997682.55699660023161
23102.87101.639342238191.23065776181012
24102.75102.1911584131640.558841586835712
25102.75102.561306666170.188693333829633
26102.75102.574921868050.175078131949732
27102.75102.6310625361370.118937463863205
28102.75102.6576242145760.0923757854240392
29102.75102.6031200667820.146879933217676
30115.22111.2668286700363.95317132996375
31115.53115.2443372817170.28566271828322
32115.4115.4268887953-0.0268887952997972
33111.99113.357624876445-1.36762487644479
34107.93106.0415655292071.88843447079267
35107.43106.1432146897361.28678531026362
36106.98106.3674747766960.612525223304445
37106.98106.5664370823260.413562917674057
38106.98106.664703906680.315296093319716
39106.98106.7487718568110.231228143188929
40106.98106.8072956810450.172704318954516
41106.98106.8140006821380.165999317862045
42113.71117.471091096334-3.76109109633356
43118.77116.3877466530922.38225334690782
44118.54117.2627304042291.27726959577124
45116.16115.0262004308361.13379956916407
46110.52110.4293513139840.090648686016408
47110.06109.4835906749010.576409325099291
48109.9109.066261448430.833738551570335
49109.9109.2516957974190.6483042025815
50110.72109.3944830646041.32551693539581
51110.09109.8468992564580.243100743541547
52110.07109.8797380950490.190261904950688
53112.45109.8901094474052.55989055259546
54113.06119.475389051941-6.41538905194076
55119.83120.51372656901-0.683726569009735
56119.84119.5612678520070.27873214799277
57113.73116.842459947588-3.11245994758805
58110.5109.9688315256890.531168474310547
59110.12109.4562179538080.663782046191827
60109.86109.2087773584680.651222641532016
61110.36109.2230060672121.13699393278777
62110.36109.9184677245510.441532275449362
63110.59109.4455389281111.1444610718886
64112.52109.8185982831332.7014017168671
65112.1112.0897308220370.0102691779629396
66115.9115.952660102136-0.0526601021363007
67122.96122.5771624758140.3828375241863
68121.26122.5619703694-1.30197036939995
69114.55117.429143676901-2.87914367690134
70111.57112.55144199136-0.981441991359532
71110.65111.490813080007-0.840813080007266
72109.77110.62289709104-0.85289709103975







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73110.276802330692107.229685637481113.323919023904
74110.145540735606106.854527030237113.436554440975
75109.859140511849106.341098119295113.377182904403
76110.577412348923106.846129279698114.308695418149
77110.342435745294106.409456669635114.275414820952
78114.168347335832110.043523039399118.293171632266
79121.041517347814116.7333824215125.349652274128
80119.991222410113115.507264603642124.475180216583
81114.566897625097109.913755817985119.220039432208
82111.85393041451107.0375438287116.670317000319
83111.267121843545106.292844930178116.241398756911
84110.735981188645105.608673720029115.863288657261

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 110.276802330692 & 107.229685637481 & 113.323919023904 \tabularnewline
74 & 110.145540735606 & 106.854527030237 & 113.436554440975 \tabularnewline
75 & 109.859140511849 & 106.341098119295 & 113.377182904403 \tabularnewline
76 & 110.577412348923 & 106.846129279698 & 114.308695418149 \tabularnewline
77 & 110.342435745294 & 106.409456669635 & 114.275414820952 \tabularnewline
78 & 114.168347335832 & 110.043523039399 & 118.293171632266 \tabularnewline
79 & 121.041517347814 & 116.7333824215 & 125.349652274128 \tabularnewline
80 & 119.991222410113 & 115.507264603642 & 124.475180216583 \tabularnewline
81 & 114.566897625097 & 109.913755817985 & 119.220039432208 \tabularnewline
82 & 111.85393041451 & 107.0375438287 & 116.670317000319 \tabularnewline
83 & 111.267121843545 & 106.292844930178 & 116.241398756911 \tabularnewline
84 & 110.735981188645 & 105.608673720029 & 115.863288657261 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203361&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]110.276802330692[/C][C]107.229685637481[/C][C]113.323919023904[/C][/ROW]
[ROW][C]74[/C][C]110.145540735606[/C][C]106.854527030237[/C][C]113.436554440975[/C][/ROW]
[ROW][C]75[/C][C]109.859140511849[/C][C]106.341098119295[/C][C]113.377182904403[/C][/ROW]
[ROW][C]76[/C][C]110.577412348923[/C][C]106.846129279698[/C][C]114.308695418149[/C][/ROW]
[ROW][C]77[/C][C]110.342435745294[/C][C]106.409456669635[/C][C]114.275414820952[/C][/ROW]
[ROW][C]78[/C][C]114.168347335832[/C][C]110.043523039399[/C][C]118.293171632266[/C][/ROW]
[ROW][C]79[/C][C]121.041517347814[/C][C]116.7333824215[/C][C]125.349652274128[/C][/ROW]
[ROW][C]80[/C][C]119.991222410113[/C][C]115.507264603642[/C][C]124.475180216583[/C][/ROW]
[ROW][C]81[/C][C]114.566897625097[/C][C]109.913755817985[/C][C]119.220039432208[/C][/ROW]
[ROW][C]82[/C][C]111.85393041451[/C][C]107.0375438287[/C][C]116.670317000319[/C][/ROW]
[ROW][C]83[/C][C]111.267121843545[/C][C]106.292844930178[/C][C]116.241398756911[/C][/ROW]
[ROW][C]84[/C][C]110.735981188645[/C][C]105.608673720029[/C][C]115.863288657261[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203361&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203361&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
73110.276802330692107.229685637481113.323919023904
74110.145540735606106.854527030237113.436554440975
75109.859140511849106.341098119295113.377182904403
76110.577412348923106.846129279698114.308695418149
77110.342435745294106.409456669635114.275414820952
78114.168347335832110.043523039399118.293171632266
79121.041517347814116.7333824215125.349652274128
80119.991222410113115.507264603642124.475180216583
81114.566897625097109.913755817985119.220039432208
82111.85393041451107.0375438287116.670317000319
83111.267121843545106.292844930178116.241398756911
84110.735981188645105.608673720029115.863288657261



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')