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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Jan 2013 20:47:40 -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/2013/Jan/15/t1358300947saqqn9xclb6wmqz.htm/, Retrieved Sun, 28 Apr 2024 02:07:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205599, Retrieved Sun, 28 Apr 2024 02:07:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Gemiddelde prijs ...] [2013-01-16 01:47:40] [5ebf8d45d440e2351c3182f635b9c69f] [Current]
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Dataseries X:
434,49
434,43
434,07
434,52
433,52
433,52
433,52
433,26
433,63
434,67
432,87
432,49
432,5
430,88
431,64
433,7
434,47
434,38
434,9
435,3
435,37
436,61
436,08
436,08
436,08
435,99
437,72
438,73
437,7
438,13
438,13
438,31
439,67
442
442,61
442,27
442,27
443,72
443,83
444,01
445,01
444,9
444,86
445,36
447,99
449,08
448,66
447,65
447,69
448,17
450,62
450,38
449,18
448,73
448,73
449,55
449,71
449,93
452,23
452,98
452,88
452,37
452,76
452,96
455,21
453,6
453,6
453,86
454,21
454,62
456,28
456,17




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205599&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]2 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=205599&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205599&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0451179389646938
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0451179389646938 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205599&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0451179389646938[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205599&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205599&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
alpha1
beta0.0451179389646938
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3434.07434.37-0.300000000000011
4434.52433.9964646183110.523535381689385
5433.52434.470085455707-0.950085455707494
6433.52433.4272195581060.0927804418943197
7433.52433.431405620420.0885943795798312
8433.26433.435402816231-0.175402816230644
9433.63433.1674890026740.462510997326262
10434.67433.5583565456221.11164345437845
11432.87434.648511607147-1.77851160714675
12432.49432.768268829008-0.278268829007516
13432.5432.3757139129650.124286087035443
14430.88432.391321445054-1.51132144505357
15431.64430.703133736340.936866263660363
16433.7431.5054032112422.19459678875847
17434.47433.6644188952090.805581104791202
18434.38434.470765054326-0.0907650543259706
19434.9434.3766699221450.523330077855235
20435.3434.9202814966560.379718503344236
21435.37435.3374136129130.0325863870865533
22436.61435.4088838435371.20111615646294
23436.08436.703075728974-0.623075728973902
24436.08436.144963836264-0.0649638362636438
25436.08436.142032801864-0.062032801864234
26435.99436.139234009696-0.149234009695874
27437.72436.0425008787551.67749912124503
28438.73437.8481861817210.88181381827934
29437.7438.897971803752-1.19797180375201
30438.13437.8139217850290.316078214971128
31438.13438.25818258264-0.128182582640022
32438.31438.25239924870.0576007512999013
33439.67438.4349980758821.23500192411842
34442439.8507188173152.14928118268472
35442.61442.2776899545340.332310045466443
36442.27442.902683098882-0.632683098882353
37442.27442.534137741443-0.264137741442937
38443.72442.5222203909461.19777960905384
39443.83444.026261738241-0.196261738240707
40444.01444.127406813114-0.117406813113632
41445.01444.3021096596860.707890340314464
42444.9445.334048212854-0.434048212853554
43444.86445.204464852078-0.344464852078261
44445.36445.1489233079070.211076692093286
45447.99445.6584466532172.33155334678253
46449.08448.3936415348110.686358465189471
47448.66449.514608614151-0.854608614150777
48447.65449.056050434859-1.40605043485891
49447.69447.982612337158-0.292612337157607
50448.17448.0094102715890.160589728410571
51450.62448.4966557491542.12334425084578
52450.38451.042456665465-0.662456665464902
53449.18450.772567986066-1.59256798606572
54448.73449.500714600873-0.770714600873248
55448.73449.015941546552-0.285941546551896
56449.55449.0030404533070.546959546692904
57449.71449.847718140751-0.137718140750962
58449.93450.001504582082-0.0715045820821842
59452.23450.2182784427122.0117215572879
60452.98452.6090431731480.370956826852193
61452.88453.37577998062-0.495779980620284
62452.37453.253411409715-0.883411409714711
63452.76452.703553707650.0564462923495057
64452.96453.096100448023-0.136100448023512
65455.21453.2899598763161.92004012368352
66453.6455.626588129427-2.02658812942656
67453.6453.925152649897-0.325152649896552
68453.86453.910482432484-0.0504824324843298
69454.21454.1682047691770.0417952308232543
70454.62454.520090483850.099909516150035
71456.28454.9345981953021.34540180469833
72456.17456.655299951809-0.485299951808997

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 434.07 & 434.37 & -0.300000000000011 \tabularnewline
4 & 434.52 & 433.996464618311 & 0.523535381689385 \tabularnewline
5 & 433.52 & 434.470085455707 & -0.950085455707494 \tabularnewline
6 & 433.52 & 433.427219558106 & 0.0927804418943197 \tabularnewline
7 & 433.52 & 433.43140562042 & 0.0885943795798312 \tabularnewline
8 & 433.26 & 433.435402816231 & -0.175402816230644 \tabularnewline
9 & 433.63 & 433.167489002674 & 0.462510997326262 \tabularnewline
10 & 434.67 & 433.558356545622 & 1.11164345437845 \tabularnewline
11 & 432.87 & 434.648511607147 & -1.77851160714675 \tabularnewline
12 & 432.49 & 432.768268829008 & -0.278268829007516 \tabularnewline
13 & 432.5 & 432.375713912965 & 0.124286087035443 \tabularnewline
14 & 430.88 & 432.391321445054 & -1.51132144505357 \tabularnewline
15 & 431.64 & 430.70313373634 & 0.936866263660363 \tabularnewline
16 & 433.7 & 431.505403211242 & 2.19459678875847 \tabularnewline
17 & 434.47 & 433.664418895209 & 0.805581104791202 \tabularnewline
18 & 434.38 & 434.470765054326 & -0.0907650543259706 \tabularnewline
19 & 434.9 & 434.376669922145 & 0.523330077855235 \tabularnewline
20 & 435.3 & 434.920281496656 & 0.379718503344236 \tabularnewline
21 & 435.37 & 435.337413612913 & 0.0325863870865533 \tabularnewline
22 & 436.61 & 435.408883843537 & 1.20111615646294 \tabularnewline
23 & 436.08 & 436.703075728974 & -0.623075728973902 \tabularnewline
24 & 436.08 & 436.144963836264 & -0.0649638362636438 \tabularnewline
25 & 436.08 & 436.142032801864 & -0.062032801864234 \tabularnewline
26 & 435.99 & 436.139234009696 & -0.149234009695874 \tabularnewline
27 & 437.72 & 436.042500878755 & 1.67749912124503 \tabularnewline
28 & 438.73 & 437.848186181721 & 0.88181381827934 \tabularnewline
29 & 437.7 & 438.897971803752 & -1.19797180375201 \tabularnewline
30 & 438.13 & 437.813921785029 & 0.316078214971128 \tabularnewline
31 & 438.13 & 438.25818258264 & -0.128182582640022 \tabularnewline
32 & 438.31 & 438.2523992487 & 0.0576007512999013 \tabularnewline
33 & 439.67 & 438.434998075882 & 1.23500192411842 \tabularnewline
34 & 442 & 439.850718817315 & 2.14928118268472 \tabularnewline
35 & 442.61 & 442.277689954534 & 0.332310045466443 \tabularnewline
36 & 442.27 & 442.902683098882 & -0.632683098882353 \tabularnewline
37 & 442.27 & 442.534137741443 & -0.264137741442937 \tabularnewline
38 & 443.72 & 442.522220390946 & 1.19777960905384 \tabularnewline
39 & 443.83 & 444.026261738241 & -0.196261738240707 \tabularnewline
40 & 444.01 & 444.127406813114 & -0.117406813113632 \tabularnewline
41 & 445.01 & 444.302109659686 & 0.707890340314464 \tabularnewline
42 & 444.9 & 445.334048212854 & -0.434048212853554 \tabularnewline
43 & 444.86 & 445.204464852078 & -0.344464852078261 \tabularnewline
44 & 445.36 & 445.148923307907 & 0.211076692093286 \tabularnewline
45 & 447.99 & 445.658446653217 & 2.33155334678253 \tabularnewline
46 & 449.08 & 448.393641534811 & 0.686358465189471 \tabularnewline
47 & 448.66 & 449.514608614151 & -0.854608614150777 \tabularnewline
48 & 447.65 & 449.056050434859 & -1.40605043485891 \tabularnewline
49 & 447.69 & 447.982612337158 & -0.292612337157607 \tabularnewline
50 & 448.17 & 448.009410271589 & 0.160589728410571 \tabularnewline
51 & 450.62 & 448.496655749154 & 2.12334425084578 \tabularnewline
52 & 450.38 & 451.042456665465 & -0.662456665464902 \tabularnewline
53 & 449.18 & 450.772567986066 & -1.59256798606572 \tabularnewline
54 & 448.73 & 449.500714600873 & -0.770714600873248 \tabularnewline
55 & 448.73 & 449.015941546552 & -0.285941546551896 \tabularnewline
56 & 449.55 & 449.003040453307 & 0.546959546692904 \tabularnewline
57 & 449.71 & 449.847718140751 & -0.137718140750962 \tabularnewline
58 & 449.93 & 450.001504582082 & -0.0715045820821842 \tabularnewline
59 & 452.23 & 450.218278442712 & 2.0117215572879 \tabularnewline
60 & 452.98 & 452.609043173148 & 0.370956826852193 \tabularnewline
61 & 452.88 & 453.37577998062 & -0.495779980620284 \tabularnewline
62 & 452.37 & 453.253411409715 & -0.883411409714711 \tabularnewline
63 & 452.76 & 452.70355370765 & 0.0564462923495057 \tabularnewline
64 & 452.96 & 453.096100448023 & -0.136100448023512 \tabularnewline
65 & 455.21 & 453.289959876316 & 1.92004012368352 \tabularnewline
66 & 453.6 & 455.626588129427 & -2.02658812942656 \tabularnewline
67 & 453.6 & 453.925152649897 & -0.325152649896552 \tabularnewline
68 & 453.86 & 453.910482432484 & -0.0504824324843298 \tabularnewline
69 & 454.21 & 454.168204769177 & 0.0417952308232543 \tabularnewline
70 & 454.62 & 454.52009048385 & 0.099909516150035 \tabularnewline
71 & 456.28 & 454.934598195302 & 1.34540180469833 \tabularnewline
72 & 456.17 & 456.655299951809 & -0.485299951808997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205599&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]434.07[/C][C]434.37[/C][C]-0.300000000000011[/C][/ROW]
[ROW][C]4[/C][C]434.52[/C][C]433.996464618311[/C][C]0.523535381689385[/C][/ROW]
[ROW][C]5[/C][C]433.52[/C][C]434.470085455707[/C][C]-0.950085455707494[/C][/ROW]
[ROW][C]6[/C][C]433.52[/C][C]433.427219558106[/C][C]0.0927804418943197[/C][/ROW]
[ROW][C]7[/C][C]433.52[/C][C]433.43140562042[/C][C]0.0885943795798312[/C][/ROW]
[ROW][C]8[/C][C]433.26[/C][C]433.435402816231[/C][C]-0.175402816230644[/C][/ROW]
[ROW][C]9[/C][C]433.63[/C][C]433.167489002674[/C][C]0.462510997326262[/C][/ROW]
[ROW][C]10[/C][C]434.67[/C][C]433.558356545622[/C][C]1.11164345437845[/C][/ROW]
[ROW][C]11[/C][C]432.87[/C][C]434.648511607147[/C][C]-1.77851160714675[/C][/ROW]
[ROW][C]12[/C][C]432.49[/C][C]432.768268829008[/C][C]-0.278268829007516[/C][/ROW]
[ROW][C]13[/C][C]432.5[/C][C]432.375713912965[/C][C]0.124286087035443[/C][/ROW]
[ROW][C]14[/C][C]430.88[/C][C]432.391321445054[/C][C]-1.51132144505357[/C][/ROW]
[ROW][C]15[/C][C]431.64[/C][C]430.70313373634[/C][C]0.936866263660363[/C][/ROW]
[ROW][C]16[/C][C]433.7[/C][C]431.505403211242[/C][C]2.19459678875847[/C][/ROW]
[ROW][C]17[/C][C]434.47[/C][C]433.664418895209[/C][C]0.805581104791202[/C][/ROW]
[ROW][C]18[/C][C]434.38[/C][C]434.470765054326[/C][C]-0.0907650543259706[/C][/ROW]
[ROW][C]19[/C][C]434.9[/C][C]434.376669922145[/C][C]0.523330077855235[/C][/ROW]
[ROW][C]20[/C][C]435.3[/C][C]434.920281496656[/C][C]0.379718503344236[/C][/ROW]
[ROW][C]21[/C][C]435.37[/C][C]435.337413612913[/C][C]0.0325863870865533[/C][/ROW]
[ROW][C]22[/C][C]436.61[/C][C]435.408883843537[/C][C]1.20111615646294[/C][/ROW]
[ROW][C]23[/C][C]436.08[/C][C]436.703075728974[/C][C]-0.623075728973902[/C][/ROW]
[ROW][C]24[/C][C]436.08[/C][C]436.144963836264[/C][C]-0.0649638362636438[/C][/ROW]
[ROW][C]25[/C][C]436.08[/C][C]436.142032801864[/C][C]-0.062032801864234[/C][/ROW]
[ROW][C]26[/C][C]435.99[/C][C]436.139234009696[/C][C]-0.149234009695874[/C][/ROW]
[ROW][C]27[/C][C]437.72[/C][C]436.042500878755[/C][C]1.67749912124503[/C][/ROW]
[ROW][C]28[/C][C]438.73[/C][C]437.848186181721[/C][C]0.88181381827934[/C][/ROW]
[ROW][C]29[/C][C]437.7[/C][C]438.897971803752[/C][C]-1.19797180375201[/C][/ROW]
[ROW][C]30[/C][C]438.13[/C][C]437.813921785029[/C][C]0.316078214971128[/C][/ROW]
[ROW][C]31[/C][C]438.13[/C][C]438.25818258264[/C][C]-0.128182582640022[/C][/ROW]
[ROW][C]32[/C][C]438.31[/C][C]438.2523992487[/C][C]0.0576007512999013[/C][/ROW]
[ROW][C]33[/C][C]439.67[/C][C]438.434998075882[/C][C]1.23500192411842[/C][/ROW]
[ROW][C]34[/C][C]442[/C][C]439.850718817315[/C][C]2.14928118268472[/C][/ROW]
[ROW][C]35[/C][C]442.61[/C][C]442.277689954534[/C][C]0.332310045466443[/C][/ROW]
[ROW][C]36[/C][C]442.27[/C][C]442.902683098882[/C][C]-0.632683098882353[/C][/ROW]
[ROW][C]37[/C][C]442.27[/C][C]442.534137741443[/C][C]-0.264137741442937[/C][/ROW]
[ROW][C]38[/C][C]443.72[/C][C]442.522220390946[/C][C]1.19777960905384[/C][/ROW]
[ROW][C]39[/C][C]443.83[/C][C]444.026261738241[/C][C]-0.196261738240707[/C][/ROW]
[ROW][C]40[/C][C]444.01[/C][C]444.127406813114[/C][C]-0.117406813113632[/C][/ROW]
[ROW][C]41[/C][C]445.01[/C][C]444.302109659686[/C][C]0.707890340314464[/C][/ROW]
[ROW][C]42[/C][C]444.9[/C][C]445.334048212854[/C][C]-0.434048212853554[/C][/ROW]
[ROW][C]43[/C][C]444.86[/C][C]445.204464852078[/C][C]-0.344464852078261[/C][/ROW]
[ROW][C]44[/C][C]445.36[/C][C]445.148923307907[/C][C]0.211076692093286[/C][/ROW]
[ROW][C]45[/C][C]447.99[/C][C]445.658446653217[/C][C]2.33155334678253[/C][/ROW]
[ROW][C]46[/C][C]449.08[/C][C]448.393641534811[/C][C]0.686358465189471[/C][/ROW]
[ROW][C]47[/C][C]448.66[/C][C]449.514608614151[/C][C]-0.854608614150777[/C][/ROW]
[ROW][C]48[/C][C]447.65[/C][C]449.056050434859[/C][C]-1.40605043485891[/C][/ROW]
[ROW][C]49[/C][C]447.69[/C][C]447.982612337158[/C][C]-0.292612337157607[/C][/ROW]
[ROW][C]50[/C][C]448.17[/C][C]448.009410271589[/C][C]0.160589728410571[/C][/ROW]
[ROW][C]51[/C][C]450.62[/C][C]448.496655749154[/C][C]2.12334425084578[/C][/ROW]
[ROW][C]52[/C][C]450.38[/C][C]451.042456665465[/C][C]-0.662456665464902[/C][/ROW]
[ROW][C]53[/C][C]449.18[/C][C]450.772567986066[/C][C]-1.59256798606572[/C][/ROW]
[ROW][C]54[/C][C]448.73[/C][C]449.500714600873[/C][C]-0.770714600873248[/C][/ROW]
[ROW][C]55[/C][C]448.73[/C][C]449.015941546552[/C][C]-0.285941546551896[/C][/ROW]
[ROW][C]56[/C][C]449.55[/C][C]449.003040453307[/C][C]0.546959546692904[/C][/ROW]
[ROW][C]57[/C][C]449.71[/C][C]449.847718140751[/C][C]-0.137718140750962[/C][/ROW]
[ROW][C]58[/C][C]449.93[/C][C]450.001504582082[/C][C]-0.0715045820821842[/C][/ROW]
[ROW][C]59[/C][C]452.23[/C][C]450.218278442712[/C][C]2.0117215572879[/C][/ROW]
[ROW][C]60[/C][C]452.98[/C][C]452.609043173148[/C][C]0.370956826852193[/C][/ROW]
[ROW][C]61[/C][C]452.88[/C][C]453.37577998062[/C][C]-0.495779980620284[/C][/ROW]
[ROW][C]62[/C][C]452.37[/C][C]453.253411409715[/C][C]-0.883411409714711[/C][/ROW]
[ROW][C]63[/C][C]452.76[/C][C]452.70355370765[/C][C]0.0564462923495057[/C][/ROW]
[ROW][C]64[/C][C]452.96[/C][C]453.096100448023[/C][C]-0.136100448023512[/C][/ROW]
[ROW][C]65[/C][C]455.21[/C][C]453.289959876316[/C][C]1.92004012368352[/C][/ROW]
[ROW][C]66[/C][C]453.6[/C][C]455.626588129427[/C][C]-2.02658812942656[/C][/ROW]
[ROW][C]67[/C][C]453.6[/C][C]453.925152649897[/C][C]-0.325152649896552[/C][/ROW]
[ROW][C]68[/C][C]453.86[/C][C]453.910482432484[/C][C]-0.0504824324843298[/C][/ROW]
[ROW][C]69[/C][C]454.21[/C][C]454.168204769177[/C][C]0.0417952308232543[/C][/ROW]
[ROW][C]70[/C][C]454.62[/C][C]454.52009048385[/C][C]0.099909516150035[/C][/ROW]
[ROW][C]71[/C][C]456.28[/C][C]454.934598195302[/C][C]1.34540180469833[/C][/ROW]
[ROW][C]72[/C][C]456.17[/C][C]456.655299951809[/C][C]-0.485299951808997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205599&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205599&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
3434.07434.37-0.300000000000011
4434.52433.9964646183110.523535381689385
5433.52434.470085455707-0.950085455707494
6433.52433.4272195581060.0927804418943197
7433.52433.431405620420.0885943795798312
8433.26433.435402816231-0.175402816230644
9433.63433.1674890026740.462510997326262
10434.67433.5583565456221.11164345437845
11432.87434.648511607147-1.77851160714675
12432.49432.768268829008-0.278268829007516
13432.5432.3757139129650.124286087035443
14430.88432.391321445054-1.51132144505357
15431.64430.703133736340.936866263660363
16433.7431.5054032112422.19459678875847
17434.47433.6644188952090.805581104791202
18434.38434.470765054326-0.0907650543259706
19434.9434.3766699221450.523330077855235
20435.3434.9202814966560.379718503344236
21435.37435.3374136129130.0325863870865533
22436.61435.4088838435371.20111615646294
23436.08436.703075728974-0.623075728973902
24436.08436.144963836264-0.0649638362636438
25436.08436.142032801864-0.062032801864234
26435.99436.139234009696-0.149234009695874
27437.72436.0425008787551.67749912124503
28438.73437.8481861817210.88181381827934
29437.7438.897971803752-1.19797180375201
30438.13437.8139217850290.316078214971128
31438.13438.25818258264-0.128182582640022
32438.31438.25239924870.0576007512999013
33439.67438.4349980758821.23500192411842
34442439.8507188173152.14928118268472
35442.61442.2776899545340.332310045466443
36442.27442.902683098882-0.632683098882353
37442.27442.534137741443-0.264137741442937
38443.72442.5222203909461.19777960905384
39443.83444.026261738241-0.196261738240707
40444.01444.127406813114-0.117406813113632
41445.01444.3021096596860.707890340314464
42444.9445.334048212854-0.434048212853554
43444.86445.204464852078-0.344464852078261
44445.36445.1489233079070.211076692093286
45447.99445.6584466532172.33155334678253
46449.08448.3936415348110.686358465189471
47448.66449.514608614151-0.854608614150777
48447.65449.056050434859-1.40605043485891
49447.69447.982612337158-0.292612337157607
50448.17448.0094102715890.160589728410571
51450.62448.4966557491542.12334425084578
52450.38451.042456665465-0.662456665464902
53449.18450.772567986066-1.59256798606572
54448.73449.500714600873-0.770714600873248
55448.73449.015941546552-0.285941546551896
56449.55449.0030404533070.546959546692904
57449.71449.847718140751-0.137718140750962
58449.93450.001504582082-0.0715045820821842
59452.23450.2182784427122.0117215572879
60452.98452.6090431731480.370956826852193
61452.88453.37577998062-0.495779980620284
62452.37453.253411409715-0.883411409714711
63452.76452.703553707650.0564462923495057
64452.96453.096100448023-0.136100448023512
65455.21453.2899598763161.92004012368352
66453.6455.626588129427-2.02658812942656
67453.6453.925152649897-0.325152649896552
68453.86453.910482432484-0.0504824324843298
69454.21454.1682047691770.0417952308232543
70454.62454.520090483850.099909516150035
71456.28454.9345981953021.34540180469833
72456.17456.655299951809-0.485299951808997







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73456.523404218204454.660316265103458.386492171305
74456.876808436407454.181910151667459.571706721148
75457.230212654611453.855561286164460.604864023059
76457.583616872815453.6008271812461.56640656443
77457.937021091019453.387336036144462.486706145894
78458.290425309222453.199898352457463.380952265988
79458.643829527426453.029718978916464.257940075937
80458.99723374563452.871216810883465.123250680377
81459.350637963834452.720620231916465.980655695751
82459.704042182037452.575260806562466.832823557513
83460.057446400241452.433183712451467.681709088031
84460.410850618445452.292917399265468.528783837625

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 456.523404218204 & 454.660316265103 & 458.386492171305 \tabularnewline
74 & 456.876808436407 & 454.181910151667 & 459.571706721148 \tabularnewline
75 & 457.230212654611 & 453.855561286164 & 460.604864023059 \tabularnewline
76 & 457.583616872815 & 453.6008271812 & 461.56640656443 \tabularnewline
77 & 457.937021091019 & 453.387336036144 & 462.486706145894 \tabularnewline
78 & 458.290425309222 & 453.199898352457 & 463.380952265988 \tabularnewline
79 & 458.643829527426 & 453.029718978916 & 464.257940075937 \tabularnewline
80 & 458.99723374563 & 452.871216810883 & 465.123250680377 \tabularnewline
81 & 459.350637963834 & 452.720620231916 & 465.980655695751 \tabularnewline
82 & 459.704042182037 & 452.575260806562 & 466.832823557513 \tabularnewline
83 & 460.057446400241 & 452.433183712451 & 467.681709088031 \tabularnewline
84 & 460.410850618445 & 452.292917399265 & 468.528783837625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205599&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]456.523404218204[/C][C]454.660316265103[/C][C]458.386492171305[/C][/ROW]
[ROW][C]74[/C][C]456.876808436407[/C][C]454.181910151667[/C][C]459.571706721148[/C][/ROW]
[ROW][C]75[/C][C]457.230212654611[/C][C]453.855561286164[/C][C]460.604864023059[/C][/ROW]
[ROW][C]76[/C][C]457.583616872815[/C][C]453.6008271812[/C][C]461.56640656443[/C][/ROW]
[ROW][C]77[/C][C]457.937021091019[/C][C]453.387336036144[/C][C]462.486706145894[/C][/ROW]
[ROW][C]78[/C][C]458.290425309222[/C][C]453.199898352457[/C][C]463.380952265988[/C][/ROW]
[ROW][C]79[/C][C]458.643829527426[/C][C]453.029718978916[/C][C]464.257940075937[/C][/ROW]
[ROW][C]80[/C][C]458.99723374563[/C][C]452.871216810883[/C][C]465.123250680377[/C][/ROW]
[ROW][C]81[/C][C]459.350637963834[/C][C]452.720620231916[/C][C]465.980655695751[/C][/ROW]
[ROW][C]82[/C][C]459.704042182037[/C][C]452.575260806562[/C][C]466.832823557513[/C][/ROW]
[ROW][C]83[/C][C]460.057446400241[/C][C]452.433183712451[/C][C]467.681709088031[/C][/ROW]
[ROW][C]84[/C][C]460.410850618445[/C][C]452.292917399265[/C][C]468.528783837625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205599&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205599&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
73456.523404218204454.660316265103458.386492171305
74456.876808436407454.181910151667459.571706721148
75457.230212654611453.855561286164460.604864023059
76457.583616872815453.6008271812461.56640656443
77457.937021091019453.387336036144462.486706145894
78458.290425309222453.199898352457463.380952265988
79458.643829527426453.029718978916464.257940075937
80458.99723374563452.871216810883465.123250680377
81459.350637963834452.720620231916465.980655695751
82459.704042182037452.575260806562466.832823557513
83460.057446400241452.433183712451467.681709088031
84460.410850618445452.292917399265468.528783837625



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')