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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Jan 2012 01:56:28 -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/Jan/16/t1326697025zt2c2yk07k0518x.htm/, Retrieved Sun, 28 Apr 2024 03:23:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161185, Retrieved Sun, 28 Apr 2024 03:23:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact206
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-01-16 06:56:28] [be958d63cbc449c3910bbbf4c2665e23] [Current]
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Dataseries X:
123,06
123,39
124,02
124,05
123,99
124,46
124,46
124,6
124,84
124,84
124,99
125,02
128,27
128,38
128,47
128,52
128,71
128,92
128,92
128,82
128,97
129,04
128,95
129,39
129,39
129,48
130,16
129,89
129,85
129,9
129,9
129,57
129,54
129,57
128,97
129,01
129,01
128,72
128,32
128,39
128,33
128,44
128,44
128,6
128,3
128,56
128,01
128,01
128,01
128,26
128,38
128,36
128,48
128,46
128,46
129,56
129,66
129,47
129,41
129,48
129,48
130,17
129,77
129,87
129,97
130,05
130,05
129,89
130,33
130,6
131,46
131,73




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=161185&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=161185&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161185&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
alpha0.919515806148139
beta0.0886193593925807
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.919515806148139 \tabularnewline
beta & 0.0886193593925807 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161185&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]0.919515806148139[/C][/ROW]
[ROW][C]beta[/C][C]0.0886193593925807[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161185&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161185&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
alpha0.919515806148139
beta0.0886193593925807
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3124.02123.720.299999999999997
4124.05124.350300812352-0.300300812352106
5123.99124.404144956529-0.414144956528659
6124.46124.3195602213380.140439778661516
7124.46124.756368918442-0.296368918441615
8124.6124.767374929374-0.167374929373764
9124.84124.883354087736-0.0433540877362901
10124.84125.109839579991-0.269839579990958
11124.99125.106079690927-0.116079690926824
12125.02125.234245475846-0.214245475845729
13128.27125.2546880698813.01531193011948
14128.38128.490468172384-0.110468172384088
15128.47128.843042354989-0.373042354989053
16128.52128.923777360694-0.403777360694335
17128.71128.943348476755-0.233348476755111
18128.92129.100616801037-0.180616801036848
19128.92129.291654831116-0.371654831116132
20128.82129.276745372276-0.45674537227552
21128.97129.146375050636-0.176375050636153
22129.04129.259437414907-0.219437414906878
23128.95129.315021979524-0.365021979524471
24129.39129.2069947256840.183005274316002
25129.39129.617799726747-0.227799726747122
26129.48129.632300342149-0.152300342149033
27130.16129.7038133520350.45618664796504
28129.89130.372013003702-0.482013003702349
29129.85130.138245500092-0.28824550009179
30129.9130.05916204604-0.159162046039825
31129.9130.085803246302-0.185803246302072
32129.57130.072806910963-0.502806910962931
33129.54129.727348518037-0.187348518037425
34129.57129.656692653318-0.0866926533175274
35128.97129.671527131471-0.701527131470755
36129.01129.063846316401-0.0538463164006941
37129.01129.047330478635-0.0373304786354254
38128.72129.042959269704-0.322959269704398
39128.32128.749630922434-0.429630922433518
40128.39128.323207011670.066792988330036
41128.33128.358695487077-0.0286954870771297
42128.44128.3040424937080.135957506291987
43128.44128.4118692862210.0281307137791202
44128.6128.42283992340.177160076599819
45128.3128.585281641019-0.285281641018969
46128.56128.2992541728290.260745827171291
47128.01128.536554961816-0.526554961815776
48128.01128.0070128987270.00298710127268009
49128.01127.9646365422970.045363457703246
50128.26127.9649224430290.295077556970682
51128.38128.2188693609330.16113063906721
52128.36128.362780007184-0.00278000718444105
53128.48128.355745689240.124254310760335
54128.46128.475646533374-0.0156465333740812
55128.46128.465631352507-0.0056313525065832
56129.56128.464366407281.09563359271993
57129.66129.5650117728070.0949882271931415
58129.47129.753288204714-0.283288204714069
59129.41129.570649200301-0.160649200301179
60129.48129.487687893304-0.00768789330433606
61129.48129.544750463214-0.064750463214267
62130.17129.5440667835220.625933216477875
63129.77130.229483022832-0.459483022832416
64129.87129.879400025936-0.00940002593628719
65129.97129.9424094797750.0275905202246918
66130.05130.0416805914970.00831940850341084
67130.05130.123909534211-0.0739095342109408
68129.89130.124505005428-0.234505005428275
69130.33129.9583213161420.371678683858249
70130.6130.3798200549560.220179945043924
71131.46130.6799550903550.780044909644545
72131.73131.5584582528810.171541747118596

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 124.02 & 123.72 & 0.299999999999997 \tabularnewline
4 & 124.05 & 124.350300812352 & -0.300300812352106 \tabularnewline
5 & 123.99 & 124.404144956529 & -0.414144956528659 \tabularnewline
6 & 124.46 & 124.319560221338 & 0.140439778661516 \tabularnewline
7 & 124.46 & 124.756368918442 & -0.296368918441615 \tabularnewline
8 & 124.6 & 124.767374929374 & -0.167374929373764 \tabularnewline
9 & 124.84 & 124.883354087736 & -0.0433540877362901 \tabularnewline
10 & 124.84 & 125.109839579991 & -0.269839579990958 \tabularnewline
11 & 124.99 & 125.106079690927 & -0.116079690926824 \tabularnewline
12 & 125.02 & 125.234245475846 & -0.214245475845729 \tabularnewline
13 & 128.27 & 125.254688069881 & 3.01531193011948 \tabularnewline
14 & 128.38 & 128.490468172384 & -0.110468172384088 \tabularnewline
15 & 128.47 & 128.843042354989 & -0.373042354989053 \tabularnewline
16 & 128.52 & 128.923777360694 & -0.403777360694335 \tabularnewline
17 & 128.71 & 128.943348476755 & -0.233348476755111 \tabularnewline
18 & 128.92 & 129.100616801037 & -0.180616801036848 \tabularnewline
19 & 128.92 & 129.291654831116 & -0.371654831116132 \tabularnewline
20 & 128.82 & 129.276745372276 & -0.45674537227552 \tabularnewline
21 & 128.97 & 129.146375050636 & -0.176375050636153 \tabularnewline
22 & 129.04 & 129.259437414907 & -0.219437414906878 \tabularnewline
23 & 128.95 & 129.315021979524 & -0.365021979524471 \tabularnewline
24 & 129.39 & 129.206994725684 & 0.183005274316002 \tabularnewline
25 & 129.39 & 129.617799726747 & -0.227799726747122 \tabularnewline
26 & 129.48 & 129.632300342149 & -0.152300342149033 \tabularnewline
27 & 130.16 & 129.703813352035 & 0.45618664796504 \tabularnewline
28 & 129.89 & 130.372013003702 & -0.482013003702349 \tabularnewline
29 & 129.85 & 130.138245500092 & -0.28824550009179 \tabularnewline
30 & 129.9 & 130.05916204604 & -0.159162046039825 \tabularnewline
31 & 129.9 & 130.085803246302 & -0.185803246302072 \tabularnewline
32 & 129.57 & 130.072806910963 & -0.502806910962931 \tabularnewline
33 & 129.54 & 129.727348518037 & -0.187348518037425 \tabularnewline
34 & 129.57 & 129.656692653318 & -0.0866926533175274 \tabularnewline
35 & 128.97 & 129.671527131471 & -0.701527131470755 \tabularnewline
36 & 129.01 & 129.063846316401 & -0.0538463164006941 \tabularnewline
37 & 129.01 & 129.047330478635 & -0.0373304786354254 \tabularnewline
38 & 128.72 & 129.042959269704 & -0.322959269704398 \tabularnewline
39 & 128.32 & 128.749630922434 & -0.429630922433518 \tabularnewline
40 & 128.39 & 128.32320701167 & 0.066792988330036 \tabularnewline
41 & 128.33 & 128.358695487077 & -0.0286954870771297 \tabularnewline
42 & 128.44 & 128.304042493708 & 0.135957506291987 \tabularnewline
43 & 128.44 & 128.411869286221 & 0.0281307137791202 \tabularnewline
44 & 128.6 & 128.4228399234 & 0.177160076599819 \tabularnewline
45 & 128.3 & 128.585281641019 & -0.285281641018969 \tabularnewline
46 & 128.56 & 128.299254172829 & 0.260745827171291 \tabularnewline
47 & 128.01 & 128.536554961816 & -0.526554961815776 \tabularnewline
48 & 128.01 & 128.007012898727 & 0.00298710127268009 \tabularnewline
49 & 128.01 & 127.964636542297 & 0.045363457703246 \tabularnewline
50 & 128.26 & 127.964922443029 & 0.295077556970682 \tabularnewline
51 & 128.38 & 128.218869360933 & 0.16113063906721 \tabularnewline
52 & 128.36 & 128.362780007184 & -0.00278000718444105 \tabularnewline
53 & 128.48 & 128.35574568924 & 0.124254310760335 \tabularnewline
54 & 128.46 & 128.475646533374 & -0.0156465333740812 \tabularnewline
55 & 128.46 & 128.465631352507 & -0.0056313525065832 \tabularnewline
56 & 129.56 & 128.46436640728 & 1.09563359271993 \tabularnewline
57 & 129.66 & 129.565011772807 & 0.0949882271931415 \tabularnewline
58 & 129.47 & 129.753288204714 & -0.283288204714069 \tabularnewline
59 & 129.41 & 129.570649200301 & -0.160649200301179 \tabularnewline
60 & 129.48 & 129.487687893304 & -0.00768789330433606 \tabularnewline
61 & 129.48 & 129.544750463214 & -0.064750463214267 \tabularnewline
62 & 130.17 & 129.544066783522 & 0.625933216477875 \tabularnewline
63 & 129.77 & 130.229483022832 & -0.459483022832416 \tabularnewline
64 & 129.87 & 129.879400025936 & -0.00940002593628719 \tabularnewline
65 & 129.97 & 129.942409479775 & 0.0275905202246918 \tabularnewline
66 & 130.05 & 130.041680591497 & 0.00831940850341084 \tabularnewline
67 & 130.05 & 130.123909534211 & -0.0739095342109408 \tabularnewline
68 & 129.89 & 130.124505005428 & -0.234505005428275 \tabularnewline
69 & 130.33 & 129.958321316142 & 0.371678683858249 \tabularnewline
70 & 130.6 & 130.379820054956 & 0.220179945043924 \tabularnewline
71 & 131.46 & 130.679955090355 & 0.780044909644545 \tabularnewline
72 & 131.73 & 131.558458252881 & 0.171541747118596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161185&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]124.02[/C][C]123.72[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]4[/C][C]124.05[/C][C]124.350300812352[/C][C]-0.300300812352106[/C][/ROW]
[ROW][C]5[/C][C]123.99[/C][C]124.404144956529[/C][C]-0.414144956528659[/C][/ROW]
[ROW][C]6[/C][C]124.46[/C][C]124.319560221338[/C][C]0.140439778661516[/C][/ROW]
[ROW][C]7[/C][C]124.46[/C][C]124.756368918442[/C][C]-0.296368918441615[/C][/ROW]
[ROW][C]8[/C][C]124.6[/C][C]124.767374929374[/C][C]-0.167374929373764[/C][/ROW]
[ROW][C]9[/C][C]124.84[/C][C]124.883354087736[/C][C]-0.0433540877362901[/C][/ROW]
[ROW][C]10[/C][C]124.84[/C][C]125.109839579991[/C][C]-0.269839579990958[/C][/ROW]
[ROW][C]11[/C][C]124.99[/C][C]125.106079690927[/C][C]-0.116079690926824[/C][/ROW]
[ROW][C]12[/C][C]125.02[/C][C]125.234245475846[/C][C]-0.214245475845729[/C][/ROW]
[ROW][C]13[/C][C]128.27[/C][C]125.254688069881[/C][C]3.01531193011948[/C][/ROW]
[ROW][C]14[/C][C]128.38[/C][C]128.490468172384[/C][C]-0.110468172384088[/C][/ROW]
[ROW][C]15[/C][C]128.47[/C][C]128.843042354989[/C][C]-0.373042354989053[/C][/ROW]
[ROW][C]16[/C][C]128.52[/C][C]128.923777360694[/C][C]-0.403777360694335[/C][/ROW]
[ROW][C]17[/C][C]128.71[/C][C]128.943348476755[/C][C]-0.233348476755111[/C][/ROW]
[ROW][C]18[/C][C]128.92[/C][C]129.100616801037[/C][C]-0.180616801036848[/C][/ROW]
[ROW][C]19[/C][C]128.92[/C][C]129.291654831116[/C][C]-0.371654831116132[/C][/ROW]
[ROW][C]20[/C][C]128.82[/C][C]129.276745372276[/C][C]-0.45674537227552[/C][/ROW]
[ROW][C]21[/C][C]128.97[/C][C]129.146375050636[/C][C]-0.176375050636153[/C][/ROW]
[ROW][C]22[/C][C]129.04[/C][C]129.259437414907[/C][C]-0.219437414906878[/C][/ROW]
[ROW][C]23[/C][C]128.95[/C][C]129.315021979524[/C][C]-0.365021979524471[/C][/ROW]
[ROW][C]24[/C][C]129.39[/C][C]129.206994725684[/C][C]0.183005274316002[/C][/ROW]
[ROW][C]25[/C][C]129.39[/C][C]129.617799726747[/C][C]-0.227799726747122[/C][/ROW]
[ROW][C]26[/C][C]129.48[/C][C]129.632300342149[/C][C]-0.152300342149033[/C][/ROW]
[ROW][C]27[/C][C]130.16[/C][C]129.703813352035[/C][C]0.45618664796504[/C][/ROW]
[ROW][C]28[/C][C]129.89[/C][C]130.372013003702[/C][C]-0.482013003702349[/C][/ROW]
[ROW][C]29[/C][C]129.85[/C][C]130.138245500092[/C][C]-0.28824550009179[/C][/ROW]
[ROW][C]30[/C][C]129.9[/C][C]130.05916204604[/C][C]-0.159162046039825[/C][/ROW]
[ROW][C]31[/C][C]129.9[/C][C]130.085803246302[/C][C]-0.185803246302072[/C][/ROW]
[ROW][C]32[/C][C]129.57[/C][C]130.072806910963[/C][C]-0.502806910962931[/C][/ROW]
[ROW][C]33[/C][C]129.54[/C][C]129.727348518037[/C][C]-0.187348518037425[/C][/ROW]
[ROW][C]34[/C][C]129.57[/C][C]129.656692653318[/C][C]-0.0866926533175274[/C][/ROW]
[ROW][C]35[/C][C]128.97[/C][C]129.671527131471[/C][C]-0.701527131470755[/C][/ROW]
[ROW][C]36[/C][C]129.01[/C][C]129.063846316401[/C][C]-0.0538463164006941[/C][/ROW]
[ROW][C]37[/C][C]129.01[/C][C]129.047330478635[/C][C]-0.0373304786354254[/C][/ROW]
[ROW][C]38[/C][C]128.72[/C][C]129.042959269704[/C][C]-0.322959269704398[/C][/ROW]
[ROW][C]39[/C][C]128.32[/C][C]128.749630922434[/C][C]-0.429630922433518[/C][/ROW]
[ROW][C]40[/C][C]128.39[/C][C]128.32320701167[/C][C]0.066792988330036[/C][/ROW]
[ROW][C]41[/C][C]128.33[/C][C]128.358695487077[/C][C]-0.0286954870771297[/C][/ROW]
[ROW][C]42[/C][C]128.44[/C][C]128.304042493708[/C][C]0.135957506291987[/C][/ROW]
[ROW][C]43[/C][C]128.44[/C][C]128.411869286221[/C][C]0.0281307137791202[/C][/ROW]
[ROW][C]44[/C][C]128.6[/C][C]128.4228399234[/C][C]0.177160076599819[/C][/ROW]
[ROW][C]45[/C][C]128.3[/C][C]128.585281641019[/C][C]-0.285281641018969[/C][/ROW]
[ROW][C]46[/C][C]128.56[/C][C]128.299254172829[/C][C]0.260745827171291[/C][/ROW]
[ROW][C]47[/C][C]128.01[/C][C]128.536554961816[/C][C]-0.526554961815776[/C][/ROW]
[ROW][C]48[/C][C]128.01[/C][C]128.007012898727[/C][C]0.00298710127268009[/C][/ROW]
[ROW][C]49[/C][C]128.01[/C][C]127.964636542297[/C][C]0.045363457703246[/C][/ROW]
[ROW][C]50[/C][C]128.26[/C][C]127.964922443029[/C][C]0.295077556970682[/C][/ROW]
[ROW][C]51[/C][C]128.38[/C][C]128.218869360933[/C][C]0.16113063906721[/C][/ROW]
[ROW][C]52[/C][C]128.36[/C][C]128.362780007184[/C][C]-0.00278000718444105[/C][/ROW]
[ROW][C]53[/C][C]128.48[/C][C]128.35574568924[/C][C]0.124254310760335[/C][/ROW]
[ROW][C]54[/C][C]128.46[/C][C]128.475646533374[/C][C]-0.0156465333740812[/C][/ROW]
[ROW][C]55[/C][C]128.46[/C][C]128.465631352507[/C][C]-0.0056313525065832[/C][/ROW]
[ROW][C]56[/C][C]129.56[/C][C]128.46436640728[/C][C]1.09563359271993[/C][/ROW]
[ROW][C]57[/C][C]129.66[/C][C]129.565011772807[/C][C]0.0949882271931415[/C][/ROW]
[ROW][C]58[/C][C]129.47[/C][C]129.753288204714[/C][C]-0.283288204714069[/C][/ROW]
[ROW][C]59[/C][C]129.41[/C][C]129.570649200301[/C][C]-0.160649200301179[/C][/ROW]
[ROW][C]60[/C][C]129.48[/C][C]129.487687893304[/C][C]-0.00768789330433606[/C][/ROW]
[ROW][C]61[/C][C]129.48[/C][C]129.544750463214[/C][C]-0.064750463214267[/C][/ROW]
[ROW][C]62[/C][C]130.17[/C][C]129.544066783522[/C][C]0.625933216477875[/C][/ROW]
[ROW][C]63[/C][C]129.77[/C][C]130.229483022832[/C][C]-0.459483022832416[/C][/ROW]
[ROW][C]64[/C][C]129.87[/C][C]129.879400025936[/C][C]-0.00940002593628719[/C][/ROW]
[ROW][C]65[/C][C]129.97[/C][C]129.942409479775[/C][C]0.0275905202246918[/C][/ROW]
[ROW][C]66[/C][C]130.05[/C][C]130.041680591497[/C][C]0.00831940850341084[/C][/ROW]
[ROW][C]67[/C][C]130.05[/C][C]130.123909534211[/C][C]-0.0739095342109408[/C][/ROW]
[ROW][C]68[/C][C]129.89[/C][C]130.124505005428[/C][C]-0.234505005428275[/C][/ROW]
[ROW][C]69[/C][C]130.33[/C][C]129.958321316142[/C][C]0.371678683858249[/C][/ROW]
[ROW][C]70[/C][C]130.6[/C][C]130.379820054956[/C][C]0.220179945043924[/C][/ROW]
[ROW][C]71[/C][C]131.46[/C][C]130.679955090355[/C][C]0.780044909644545[/C][/ROW]
[ROW][C]72[/C][C]131.73[/C][C]131.558458252881[/C][C]0.171541747118596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161185&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161185&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
3124.02123.720.299999999999997
4124.05124.350300812352-0.300300812352106
5123.99124.404144956529-0.414144956528659
6124.46124.3195602213380.140439778661516
7124.46124.756368918442-0.296368918441615
8124.6124.767374929374-0.167374929373764
9124.84124.883354087736-0.0433540877362901
10124.84125.109839579991-0.269839579990958
11124.99125.106079690927-0.116079690926824
12125.02125.234245475846-0.214245475845729
13128.27125.2546880698813.01531193011948
14128.38128.490468172384-0.110468172384088
15128.47128.843042354989-0.373042354989053
16128.52128.923777360694-0.403777360694335
17128.71128.943348476755-0.233348476755111
18128.92129.100616801037-0.180616801036848
19128.92129.291654831116-0.371654831116132
20128.82129.276745372276-0.45674537227552
21128.97129.146375050636-0.176375050636153
22129.04129.259437414907-0.219437414906878
23128.95129.315021979524-0.365021979524471
24129.39129.2069947256840.183005274316002
25129.39129.617799726747-0.227799726747122
26129.48129.632300342149-0.152300342149033
27130.16129.7038133520350.45618664796504
28129.89130.372013003702-0.482013003702349
29129.85130.138245500092-0.28824550009179
30129.9130.05916204604-0.159162046039825
31129.9130.085803246302-0.185803246302072
32129.57130.072806910963-0.502806910962931
33129.54129.727348518037-0.187348518037425
34129.57129.656692653318-0.0866926533175274
35128.97129.671527131471-0.701527131470755
36129.01129.063846316401-0.0538463164006941
37129.01129.047330478635-0.0373304786354254
38128.72129.042959269704-0.322959269704398
39128.32128.749630922434-0.429630922433518
40128.39128.323207011670.066792988330036
41128.33128.358695487077-0.0286954870771297
42128.44128.3040424937080.135957506291987
43128.44128.4118692862210.0281307137791202
44128.6128.42283992340.177160076599819
45128.3128.585281641019-0.285281641018969
46128.56128.2992541728290.260745827171291
47128.01128.536554961816-0.526554961815776
48128.01128.0070128987270.00298710127268009
49128.01127.9646365422970.045363457703246
50128.26127.9649224430290.295077556970682
51128.38128.2188693609330.16113063906721
52128.36128.362780007184-0.00278000718444105
53128.48128.355745689240.124254310760335
54128.46128.475646533374-0.0156465333740812
55128.46128.465631352507-0.0056313525065832
56129.56128.464366407281.09563359271993
57129.66129.5650117728070.0949882271931415
58129.47129.753288204714-0.283288204714069
59129.41129.570649200301-0.160649200301179
60129.48129.487687893304-0.00768789330433606
61129.48129.544750463214-0.064750463214267
62130.17129.5440667835220.625933216477875
63129.77130.229483022832-0.459483022832416
64129.87129.879400025936-0.00940002593628719
65129.97129.9424094797750.0275905202246918
66130.05130.0416805914970.00831940850341084
67130.05130.123909534211-0.0739095342109408
68129.89130.124505005428-0.234505005428275
69130.33129.9583213161420.371678683858249
70130.6130.3798200549560.220179945043924
71131.46130.6799550903550.780044909644545
72131.73131.5584582528810.171541747118596







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73131.891411544857130.953007950397132.829815139318
74132.066629488943130.738860883637133.394398094249
75132.241847433029130.570068807095133.913626058963
76132.417065377115130.420087958887134.414042795344
77132.592283321201130.278436057068134.906130585334
78132.767501265287130.139869361702135.395133168872
79132.942719209373130.00141096744135.884027451306
80133.117937153459129.861233603878136.374640703039
81133.293155097545129.718156423944136.868153771146
82133.468373041631129.57138942845137.365356654811
83133.643590985717129.420391973897137.866789997537
84133.818808929803129.264789173531138.372828686075

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 131.891411544857 & 130.953007950397 & 132.829815139318 \tabularnewline
74 & 132.066629488943 & 130.738860883637 & 133.394398094249 \tabularnewline
75 & 132.241847433029 & 130.570068807095 & 133.913626058963 \tabularnewline
76 & 132.417065377115 & 130.420087958887 & 134.414042795344 \tabularnewline
77 & 132.592283321201 & 130.278436057068 & 134.906130585334 \tabularnewline
78 & 132.767501265287 & 130.139869361702 & 135.395133168872 \tabularnewline
79 & 132.942719209373 & 130.00141096744 & 135.884027451306 \tabularnewline
80 & 133.117937153459 & 129.861233603878 & 136.374640703039 \tabularnewline
81 & 133.293155097545 & 129.718156423944 & 136.868153771146 \tabularnewline
82 & 133.468373041631 & 129.57138942845 & 137.365356654811 \tabularnewline
83 & 133.643590985717 & 129.420391973897 & 137.866789997537 \tabularnewline
84 & 133.818808929803 & 129.264789173531 & 138.372828686075 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161185&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]131.891411544857[/C][C]130.953007950397[/C][C]132.829815139318[/C][/ROW]
[ROW][C]74[/C][C]132.066629488943[/C][C]130.738860883637[/C][C]133.394398094249[/C][/ROW]
[ROW][C]75[/C][C]132.241847433029[/C][C]130.570068807095[/C][C]133.913626058963[/C][/ROW]
[ROW][C]76[/C][C]132.417065377115[/C][C]130.420087958887[/C][C]134.414042795344[/C][/ROW]
[ROW][C]77[/C][C]132.592283321201[/C][C]130.278436057068[/C][C]134.906130585334[/C][/ROW]
[ROW][C]78[/C][C]132.767501265287[/C][C]130.139869361702[/C][C]135.395133168872[/C][/ROW]
[ROW][C]79[/C][C]132.942719209373[/C][C]130.00141096744[/C][C]135.884027451306[/C][/ROW]
[ROW][C]80[/C][C]133.117937153459[/C][C]129.861233603878[/C][C]136.374640703039[/C][/ROW]
[ROW][C]81[/C][C]133.293155097545[/C][C]129.718156423944[/C][C]136.868153771146[/C][/ROW]
[ROW][C]82[/C][C]133.468373041631[/C][C]129.57138942845[/C][C]137.365356654811[/C][/ROW]
[ROW][C]83[/C][C]133.643590985717[/C][C]129.420391973897[/C][C]137.866789997537[/C][/ROW]
[ROW][C]84[/C][C]133.818808929803[/C][C]129.264789173531[/C][C]138.372828686075[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161185&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161185&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
73131.891411544857130.953007950397132.829815139318
74132.066629488943130.738860883637133.394398094249
75132.241847433029130.570068807095133.913626058963
76132.417065377115130.420087958887134.414042795344
77132.592283321201130.278436057068134.906130585334
78132.767501265287130.139869361702135.395133168872
79132.942719209373130.00141096744135.884027451306
80133.117937153459129.861233603878136.374640703039
81133.293155097545129.718156423944136.868153771146
82133.468373041631129.57138942845137.365356654811
83133.643590985717129.420391973897137.866789997537
84133.818808929803129.264789173531138.372828686075



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')