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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 29 May 2012 05:19:48 -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/2012/May/29/t1338283227gvla6cc41iwispo.htm/, Retrieved Mon, 29 Apr 2024 19:17:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167956, Retrieved Mon, 29 Apr 2024 19:17:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 oef 2 (2)] [2012-05-29 09:19:48] [919141dca056cde38faaf6352f12d0de] [Current]
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Dataseries X:
115,43
115,55
117,14
119,09
119,55
119,8
121,32
121,48
119,63
118,61
118,82
119,93
118,7
119,99
116,67
116,84
115,17
114,21
114,77
115,59
116,64
118,79
125,63
127,42
131,17
137,68
144,41
146,09
151,26
156,56
158,38
154,21
158,06
154,83
150,89
149,22
148,34
143,88
134,48
133,73
130,08
123,11
122,08
126,83
123,17
123,82
125,6
126,32
129,15
130,09
133,81
136,83
138,34
138,67
137,86
138,56
141,65
142,42
143,12
146,17
147,8
151,87
157,12
158,97
161,4
165,81
165,1
164,64
167,88
167,14
169,83
169,71




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167956&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167956&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167956&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.558351615951655
beta0.953075715241967
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.558351615951655 \tabularnewline
beta & 0.953075715241967 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167956&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]0.558351615951655[/C][/ROW]
[ROW][C]beta[/C][C]0.953075715241967[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167956&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167956&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
alpha0.558351615951655
beta0.953075715241967
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3117.14115.671.47000000000001
4119.09117.3930393830711.69696061692852
5119.55120.14584250325-0.59584250325031
6119.8121.301376894354-1.50137689435388
7121.32121.152344930080.167655069920357
8121.48122.024437534562-0.544437534562476
9119.63122.209208905053-2.57920890505324
10118.61119.885332851412-1.2753328514122
11118.82117.6108079806831.20919201931656
12119.93117.3669947709072.56300522909318
13118.7119.24299208754-0.542992087539815
14119.99119.0957968023250.894203197675424
15116.67120.22691327993-3.55691327993013
16116.84116.979925419779-0.139925419778905
17115.17115.566356749795-0.396356749794677
18114.21113.7986874465960.411312553403874
19114.77112.7008621410292.06913785897137
20115.59113.6297808113251.96021918867521
21116.64115.5410178844371.09898211556326
22118.79117.5562066797691.23379332023141
23125.63120.3032323294655.32676767053545
24127.42128.170223512501-0.750223512501307
25131.17132.244884381586-1.07488438158552
26137.68135.5662691381182.11373086188195
27144.41141.7928471334242.61715286657591
28146.09149.693233090828-3.60323309082821
29151.26152.202991086746-0.94299108674636
30156.56155.6962855097830.863714490216893
31158.38160.657983756836-2.27798375683557
32154.21162.653277543504-8.44327754350383
33158.06156.7130679055591.34693209444072
34154.83156.956009393068-2.12600939306824
35150.89154.128469586846-3.23846958684578
36149.22148.9564298202320.26357017976818
37148.34145.8800188475632.45998115243702
38143.88145.339059820716-1.45905982071628
39134.48141.833457257253-7.35345725725327
40133.73131.1235560377572.60644396224328
41130.08127.361804473092.71819552690955
42123.11125.108941037106-1.99894103710584
43122.08119.158517575032.92148242497029
44126.83117.5100913665739.31990863342672
45123.17124.393838878909-1.22383887890932
46123.82124.739200398702-0.91920039870169
47125.6124.7655035586510.834496441349287
48126.32126.2150646040920.104935395907958
49129.15127.3131155751221.83688442487839
50130.09130.355703640609-0.265703640609246
51133.81132.0829137068221.72708629317833
52136.83135.8418725824640.988127417535679
53138.34139.714065930527-1.37406593052663
54138.67141.536113743976-2.8661137439758
55137.86140.999867906515-3.13986790651526
56138.56138.639885995365-0.0798859953646343
57141.65137.9459384875523.70406151244819
58142.42141.3358855779981.08411442200159
59143.12143.839893947062-0.719893947061621
60146.17144.9535387809591.21646121904124
61147.8147.7956921499760.00430785002436096
62151.87149.9633301548951.90666984510543
63157.12154.207792015962.91220798403961
64158.97160.563433177797-1.59343317779656
65161.4163.55539467426-2.15539467425984
66165.81165.0865878414770.723412158523502
67165.1168.610132223934-3.51013222393411
68164.64167.901948602385-3.26194860238533
69167.88165.5964883032822.28351169671816
70167.14167.602518591447-0.462518591446695
71169.83167.8291685306492.00083146935123
72169.71170.495979155962-0.785979155962082

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 117.14 & 115.67 & 1.47000000000001 \tabularnewline
4 & 119.09 & 117.393039383071 & 1.69696061692852 \tabularnewline
5 & 119.55 & 120.14584250325 & -0.59584250325031 \tabularnewline
6 & 119.8 & 121.301376894354 & -1.50137689435388 \tabularnewline
7 & 121.32 & 121.15234493008 & 0.167655069920357 \tabularnewline
8 & 121.48 & 122.024437534562 & -0.544437534562476 \tabularnewline
9 & 119.63 & 122.209208905053 & -2.57920890505324 \tabularnewline
10 & 118.61 & 119.885332851412 & -1.2753328514122 \tabularnewline
11 & 118.82 & 117.610807980683 & 1.20919201931656 \tabularnewline
12 & 119.93 & 117.366994770907 & 2.56300522909318 \tabularnewline
13 & 118.7 & 119.24299208754 & -0.542992087539815 \tabularnewline
14 & 119.99 & 119.095796802325 & 0.894203197675424 \tabularnewline
15 & 116.67 & 120.22691327993 & -3.55691327993013 \tabularnewline
16 & 116.84 & 116.979925419779 & -0.139925419778905 \tabularnewline
17 & 115.17 & 115.566356749795 & -0.396356749794677 \tabularnewline
18 & 114.21 & 113.798687446596 & 0.411312553403874 \tabularnewline
19 & 114.77 & 112.700862141029 & 2.06913785897137 \tabularnewline
20 & 115.59 & 113.629780811325 & 1.96021918867521 \tabularnewline
21 & 116.64 & 115.541017884437 & 1.09898211556326 \tabularnewline
22 & 118.79 & 117.556206679769 & 1.23379332023141 \tabularnewline
23 & 125.63 & 120.303232329465 & 5.32676767053545 \tabularnewline
24 & 127.42 & 128.170223512501 & -0.750223512501307 \tabularnewline
25 & 131.17 & 132.244884381586 & -1.07488438158552 \tabularnewline
26 & 137.68 & 135.566269138118 & 2.11373086188195 \tabularnewline
27 & 144.41 & 141.792847133424 & 2.61715286657591 \tabularnewline
28 & 146.09 & 149.693233090828 & -3.60323309082821 \tabularnewline
29 & 151.26 & 152.202991086746 & -0.94299108674636 \tabularnewline
30 & 156.56 & 155.696285509783 & 0.863714490216893 \tabularnewline
31 & 158.38 & 160.657983756836 & -2.27798375683557 \tabularnewline
32 & 154.21 & 162.653277543504 & -8.44327754350383 \tabularnewline
33 & 158.06 & 156.713067905559 & 1.34693209444072 \tabularnewline
34 & 154.83 & 156.956009393068 & -2.12600939306824 \tabularnewline
35 & 150.89 & 154.128469586846 & -3.23846958684578 \tabularnewline
36 & 149.22 & 148.956429820232 & 0.26357017976818 \tabularnewline
37 & 148.34 & 145.880018847563 & 2.45998115243702 \tabularnewline
38 & 143.88 & 145.339059820716 & -1.45905982071628 \tabularnewline
39 & 134.48 & 141.833457257253 & -7.35345725725327 \tabularnewline
40 & 133.73 & 131.123556037757 & 2.60644396224328 \tabularnewline
41 & 130.08 & 127.36180447309 & 2.71819552690955 \tabularnewline
42 & 123.11 & 125.108941037106 & -1.99894103710584 \tabularnewline
43 & 122.08 & 119.15851757503 & 2.92148242497029 \tabularnewline
44 & 126.83 & 117.510091366573 & 9.31990863342672 \tabularnewline
45 & 123.17 & 124.393838878909 & -1.22383887890932 \tabularnewline
46 & 123.82 & 124.739200398702 & -0.91920039870169 \tabularnewline
47 & 125.6 & 124.765503558651 & 0.834496441349287 \tabularnewline
48 & 126.32 & 126.215064604092 & 0.104935395907958 \tabularnewline
49 & 129.15 & 127.313115575122 & 1.83688442487839 \tabularnewline
50 & 130.09 & 130.355703640609 & -0.265703640609246 \tabularnewline
51 & 133.81 & 132.082913706822 & 1.72708629317833 \tabularnewline
52 & 136.83 & 135.841872582464 & 0.988127417535679 \tabularnewline
53 & 138.34 & 139.714065930527 & -1.37406593052663 \tabularnewline
54 & 138.67 & 141.536113743976 & -2.8661137439758 \tabularnewline
55 & 137.86 & 140.999867906515 & -3.13986790651526 \tabularnewline
56 & 138.56 & 138.639885995365 & -0.0798859953646343 \tabularnewline
57 & 141.65 & 137.945938487552 & 3.70406151244819 \tabularnewline
58 & 142.42 & 141.335885577998 & 1.08411442200159 \tabularnewline
59 & 143.12 & 143.839893947062 & -0.719893947061621 \tabularnewline
60 & 146.17 & 144.953538780959 & 1.21646121904124 \tabularnewline
61 & 147.8 & 147.795692149976 & 0.00430785002436096 \tabularnewline
62 & 151.87 & 149.963330154895 & 1.90666984510543 \tabularnewline
63 & 157.12 & 154.20779201596 & 2.91220798403961 \tabularnewline
64 & 158.97 & 160.563433177797 & -1.59343317779656 \tabularnewline
65 & 161.4 & 163.55539467426 & -2.15539467425984 \tabularnewline
66 & 165.81 & 165.086587841477 & 0.723412158523502 \tabularnewline
67 & 165.1 & 168.610132223934 & -3.51013222393411 \tabularnewline
68 & 164.64 & 167.901948602385 & -3.26194860238533 \tabularnewline
69 & 167.88 & 165.596488303282 & 2.28351169671816 \tabularnewline
70 & 167.14 & 167.602518591447 & -0.462518591446695 \tabularnewline
71 & 169.83 & 167.829168530649 & 2.00083146935123 \tabularnewline
72 & 169.71 & 170.495979155962 & -0.785979155962082 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167956&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]117.14[/C][C]115.67[/C][C]1.47000000000001[/C][/ROW]
[ROW][C]4[/C][C]119.09[/C][C]117.393039383071[/C][C]1.69696061692852[/C][/ROW]
[ROW][C]5[/C][C]119.55[/C][C]120.14584250325[/C][C]-0.59584250325031[/C][/ROW]
[ROW][C]6[/C][C]119.8[/C][C]121.301376894354[/C][C]-1.50137689435388[/C][/ROW]
[ROW][C]7[/C][C]121.32[/C][C]121.15234493008[/C][C]0.167655069920357[/C][/ROW]
[ROW][C]8[/C][C]121.48[/C][C]122.024437534562[/C][C]-0.544437534562476[/C][/ROW]
[ROW][C]9[/C][C]119.63[/C][C]122.209208905053[/C][C]-2.57920890505324[/C][/ROW]
[ROW][C]10[/C][C]118.61[/C][C]119.885332851412[/C][C]-1.2753328514122[/C][/ROW]
[ROW][C]11[/C][C]118.82[/C][C]117.610807980683[/C][C]1.20919201931656[/C][/ROW]
[ROW][C]12[/C][C]119.93[/C][C]117.366994770907[/C][C]2.56300522909318[/C][/ROW]
[ROW][C]13[/C][C]118.7[/C][C]119.24299208754[/C][C]-0.542992087539815[/C][/ROW]
[ROW][C]14[/C][C]119.99[/C][C]119.095796802325[/C][C]0.894203197675424[/C][/ROW]
[ROW][C]15[/C][C]116.67[/C][C]120.22691327993[/C][C]-3.55691327993013[/C][/ROW]
[ROW][C]16[/C][C]116.84[/C][C]116.979925419779[/C][C]-0.139925419778905[/C][/ROW]
[ROW][C]17[/C][C]115.17[/C][C]115.566356749795[/C][C]-0.396356749794677[/C][/ROW]
[ROW][C]18[/C][C]114.21[/C][C]113.798687446596[/C][C]0.411312553403874[/C][/ROW]
[ROW][C]19[/C][C]114.77[/C][C]112.700862141029[/C][C]2.06913785897137[/C][/ROW]
[ROW][C]20[/C][C]115.59[/C][C]113.629780811325[/C][C]1.96021918867521[/C][/ROW]
[ROW][C]21[/C][C]116.64[/C][C]115.541017884437[/C][C]1.09898211556326[/C][/ROW]
[ROW][C]22[/C][C]118.79[/C][C]117.556206679769[/C][C]1.23379332023141[/C][/ROW]
[ROW][C]23[/C][C]125.63[/C][C]120.303232329465[/C][C]5.32676767053545[/C][/ROW]
[ROW][C]24[/C][C]127.42[/C][C]128.170223512501[/C][C]-0.750223512501307[/C][/ROW]
[ROW][C]25[/C][C]131.17[/C][C]132.244884381586[/C][C]-1.07488438158552[/C][/ROW]
[ROW][C]26[/C][C]137.68[/C][C]135.566269138118[/C][C]2.11373086188195[/C][/ROW]
[ROW][C]27[/C][C]144.41[/C][C]141.792847133424[/C][C]2.61715286657591[/C][/ROW]
[ROW][C]28[/C][C]146.09[/C][C]149.693233090828[/C][C]-3.60323309082821[/C][/ROW]
[ROW][C]29[/C][C]151.26[/C][C]152.202991086746[/C][C]-0.94299108674636[/C][/ROW]
[ROW][C]30[/C][C]156.56[/C][C]155.696285509783[/C][C]0.863714490216893[/C][/ROW]
[ROW][C]31[/C][C]158.38[/C][C]160.657983756836[/C][C]-2.27798375683557[/C][/ROW]
[ROW][C]32[/C][C]154.21[/C][C]162.653277543504[/C][C]-8.44327754350383[/C][/ROW]
[ROW][C]33[/C][C]158.06[/C][C]156.713067905559[/C][C]1.34693209444072[/C][/ROW]
[ROW][C]34[/C][C]154.83[/C][C]156.956009393068[/C][C]-2.12600939306824[/C][/ROW]
[ROW][C]35[/C][C]150.89[/C][C]154.128469586846[/C][C]-3.23846958684578[/C][/ROW]
[ROW][C]36[/C][C]149.22[/C][C]148.956429820232[/C][C]0.26357017976818[/C][/ROW]
[ROW][C]37[/C][C]148.34[/C][C]145.880018847563[/C][C]2.45998115243702[/C][/ROW]
[ROW][C]38[/C][C]143.88[/C][C]145.339059820716[/C][C]-1.45905982071628[/C][/ROW]
[ROW][C]39[/C][C]134.48[/C][C]141.833457257253[/C][C]-7.35345725725327[/C][/ROW]
[ROW][C]40[/C][C]133.73[/C][C]131.123556037757[/C][C]2.60644396224328[/C][/ROW]
[ROW][C]41[/C][C]130.08[/C][C]127.36180447309[/C][C]2.71819552690955[/C][/ROW]
[ROW][C]42[/C][C]123.11[/C][C]125.108941037106[/C][C]-1.99894103710584[/C][/ROW]
[ROW][C]43[/C][C]122.08[/C][C]119.15851757503[/C][C]2.92148242497029[/C][/ROW]
[ROW][C]44[/C][C]126.83[/C][C]117.510091366573[/C][C]9.31990863342672[/C][/ROW]
[ROW][C]45[/C][C]123.17[/C][C]124.393838878909[/C][C]-1.22383887890932[/C][/ROW]
[ROW][C]46[/C][C]123.82[/C][C]124.739200398702[/C][C]-0.91920039870169[/C][/ROW]
[ROW][C]47[/C][C]125.6[/C][C]124.765503558651[/C][C]0.834496441349287[/C][/ROW]
[ROW][C]48[/C][C]126.32[/C][C]126.215064604092[/C][C]0.104935395907958[/C][/ROW]
[ROW][C]49[/C][C]129.15[/C][C]127.313115575122[/C][C]1.83688442487839[/C][/ROW]
[ROW][C]50[/C][C]130.09[/C][C]130.355703640609[/C][C]-0.265703640609246[/C][/ROW]
[ROW][C]51[/C][C]133.81[/C][C]132.082913706822[/C][C]1.72708629317833[/C][/ROW]
[ROW][C]52[/C][C]136.83[/C][C]135.841872582464[/C][C]0.988127417535679[/C][/ROW]
[ROW][C]53[/C][C]138.34[/C][C]139.714065930527[/C][C]-1.37406593052663[/C][/ROW]
[ROW][C]54[/C][C]138.67[/C][C]141.536113743976[/C][C]-2.8661137439758[/C][/ROW]
[ROW][C]55[/C][C]137.86[/C][C]140.999867906515[/C][C]-3.13986790651526[/C][/ROW]
[ROW][C]56[/C][C]138.56[/C][C]138.639885995365[/C][C]-0.0798859953646343[/C][/ROW]
[ROW][C]57[/C][C]141.65[/C][C]137.945938487552[/C][C]3.70406151244819[/C][/ROW]
[ROW][C]58[/C][C]142.42[/C][C]141.335885577998[/C][C]1.08411442200159[/C][/ROW]
[ROW][C]59[/C][C]143.12[/C][C]143.839893947062[/C][C]-0.719893947061621[/C][/ROW]
[ROW][C]60[/C][C]146.17[/C][C]144.953538780959[/C][C]1.21646121904124[/C][/ROW]
[ROW][C]61[/C][C]147.8[/C][C]147.795692149976[/C][C]0.00430785002436096[/C][/ROW]
[ROW][C]62[/C][C]151.87[/C][C]149.963330154895[/C][C]1.90666984510543[/C][/ROW]
[ROW][C]63[/C][C]157.12[/C][C]154.20779201596[/C][C]2.91220798403961[/C][/ROW]
[ROW][C]64[/C][C]158.97[/C][C]160.563433177797[/C][C]-1.59343317779656[/C][/ROW]
[ROW][C]65[/C][C]161.4[/C][C]163.55539467426[/C][C]-2.15539467425984[/C][/ROW]
[ROW][C]66[/C][C]165.81[/C][C]165.086587841477[/C][C]0.723412158523502[/C][/ROW]
[ROW][C]67[/C][C]165.1[/C][C]168.610132223934[/C][C]-3.51013222393411[/C][/ROW]
[ROW][C]68[/C][C]164.64[/C][C]167.901948602385[/C][C]-3.26194860238533[/C][/ROW]
[ROW][C]69[/C][C]167.88[/C][C]165.596488303282[/C][C]2.28351169671816[/C][/ROW]
[ROW][C]70[/C][C]167.14[/C][C]167.602518591447[/C][C]-0.462518591446695[/C][/ROW]
[ROW][C]71[/C][C]169.83[/C][C]167.829168530649[/C][C]2.00083146935123[/C][/ROW]
[ROW][C]72[/C][C]169.71[/C][C]170.495979155962[/C][C]-0.785979155962082[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167956&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167956&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
3117.14115.671.47000000000001
4119.09117.3930393830711.69696061692852
5119.55120.14584250325-0.59584250325031
6119.8121.301376894354-1.50137689435388
7121.32121.152344930080.167655069920357
8121.48122.024437534562-0.544437534562476
9119.63122.209208905053-2.57920890505324
10118.61119.885332851412-1.2753328514122
11118.82117.6108079806831.20919201931656
12119.93117.3669947709072.56300522909318
13118.7119.24299208754-0.542992087539815
14119.99119.0957968023250.894203197675424
15116.67120.22691327993-3.55691327993013
16116.84116.979925419779-0.139925419778905
17115.17115.566356749795-0.396356749794677
18114.21113.7986874465960.411312553403874
19114.77112.7008621410292.06913785897137
20115.59113.6297808113251.96021918867521
21116.64115.5410178844371.09898211556326
22118.79117.5562066797691.23379332023141
23125.63120.3032323294655.32676767053545
24127.42128.170223512501-0.750223512501307
25131.17132.244884381586-1.07488438158552
26137.68135.5662691381182.11373086188195
27144.41141.7928471334242.61715286657591
28146.09149.693233090828-3.60323309082821
29151.26152.202991086746-0.94299108674636
30156.56155.6962855097830.863714490216893
31158.38160.657983756836-2.27798375683557
32154.21162.653277543504-8.44327754350383
33158.06156.7130679055591.34693209444072
34154.83156.956009393068-2.12600939306824
35150.89154.128469586846-3.23846958684578
36149.22148.9564298202320.26357017976818
37148.34145.8800188475632.45998115243702
38143.88145.339059820716-1.45905982071628
39134.48141.833457257253-7.35345725725327
40133.73131.1235560377572.60644396224328
41130.08127.361804473092.71819552690955
42123.11125.108941037106-1.99894103710584
43122.08119.158517575032.92148242497029
44126.83117.5100913665739.31990863342672
45123.17124.393838878909-1.22383887890932
46123.82124.739200398702-0.91920039870169
47125.6124.7655035586510.834496441349287
48126.32126.2150646040920.104935395907958
49129.15127.3131155751221.83688442487839
50130.09130.355703640609-0.265703640609246
51133.81132.0829137068221.72708629317833
52136.83135.8418725824640.988127417535679
53138.34139.714065930527-1.37406593052663
54138.67141.536113743976-2.8661137439758
55137.86140.999867906515-3.13986790651526
56138.56138.639885995365-0.0798859953646343
57141.65137.9459384875523.70406151244819
58142.42141.3358855779981.08411442200159
59143.12143.839893947062-0.719893947061621
60146.17144.9535387809591.21646121904124
61147.8147.7956921499760.00430785002436096
62151.87149.9633301548951.90666984510543
63157.12154.207792015962.91220798403961
64158.97160.563433177797-1.59343317779656
65161.4163.55539467426-2.15539467425984
66165.81165.0865878414770.723412158523502
67165.1168.610132223934-3.51013222393411
68164.64167.901948602385-3.26194860238533
69167.88165.5964883032822.28351169671816
70167.14167.602518591447-0.462518591446695
71169.83167.8291685306492.00083146935123
72169.71170.495979155962-0.785979155962082







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73171.188509684166.048470403332176.328548964669
74172.319892943874164.714724533536179.925061354212
75173.451276203748162.163998189163184.738554218333
76174.582659463622158.768878111016190.396440816228
77175.714042723496154.718300412433196.709785034559
78176.84542598337150.113372374892203.577479591847
79177.976809243244145.016474490022210.937143996465
80179.108192503117139.470740169238218.745644836997
81180.239575762991133.508450448812226.970701077171
82181.370959022865127.155107969453235.586810076277
83182.502342282739120.431637227588244.57304733789
84183.633725542613113.355682481515253.911768603711

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 171.188509684 & 166.048470403332 & 176.328548964669 \tabularnewline
74 & 172.319892943874 & 164.714724533536 & 179.925061354212 \tabularnewline
75 & 173.451276203748 & 162.163998189163 & 184.738554218333 \tabularnewline
76 & 174.582659463622 & 158.768878111016 & 190.396440816228 \tabularnewline
77 & 175.714042723496 & 154.718300412433 & 196.709785034559 \tabularnewline
78 & 176.84542598337 & 150.113372374892 & 203.577479591847 \tabularnewline
79 & 177.976809243244 & 145.016474490022 & 210.937143996465 \tabularnewline
80 & 179.108192503117 & 139.470740169238 & 218.745644836997 \tabularnewline
81 & 180.239575762991 & 133.508450448812 & 226.970701077171 \tabularnewline
82 & 181.370959022865 & 127.155107969453 & 235.586810076277 \tabularnewline
83 & 182.502342282739 & 120.431637227588 & 244.57304733789 \tabularnewline
84 & 183.633725542613 & 113.355682481515 & 253.911768603711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167956&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]171.188509684[/C][C]166.048470403332[/C][C]176.328548964669[/C][/ROW]
[ROW][C]74[/C][C]172.319892943874[/C][C]164.714724533536[/C][C]179.925061354212[/C][/ROW]
[ROW][C]75[/C][C]173.451276203748[/C][C]162.163998189163[/C][C]184.738554218333[/C][/ROW]
[ROW][C]76[/C][C]174.582659463622[/C][C]158.768878111016[/C][C]190.396440816228[/C][/ROW]
[ROW][C]77[/C][C]175.714042723496[/C][C]154.718300412433[/C][C]196.709785034559[/C][/ROW]
[ROW][C]78[/C][C]176.84542598337[/C][C]150.113372374892[/C][C]203.577479591847[/C][/ROW]
[ROW][C]79[/C][C]177.976809243244[/C][C]145.016474490022[/C][C]210.937143996465[/C][/ROW]
[ROW][C]80[/C][C]179.108192503117[/C][C]139.470740169238[/C][C]218.745644836997[/C][/ROW]
[ROW][C]81[/C][C]180.239575762991[/C][C]133.508450448812[/C][C]226.970701077171[/C][/ROW]
[ROW][C]82[/C][C]181.370959022865[/C][C]127.155107969453[/C][C]235.586810076277[/C][/ROW]
[ROW][C]83[/C][C]182.502342282739[/C][C]120.431637227588[/C][C]244.57304733789[/C][/ROW]
[ROW][C]84[/C][C]183.633725542613[/C][C]113.355682481515[/C][C]253.911768603711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167956&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167956&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
73171.188509684166.048470403332176.328548964669
74172.319892943874164.714724533536179.925061354212
75173.451276203748162.163998189163184.738554218333
76174.582659463622158.768878111016190.396440816228
77175.714042723496154.718300412433196.709785034559
78176.84542598337150.113372374892203.577479591847
79177.976809243244145.016474490022210.937143996465
80179.108192503117139.470740169238218.745644836997
81180.239575762991133.508450448812226.970701077171
82181.370959022865127.155107969453235.586810076277
83182.502342282739120.431637227588244.57304733789
84183.633725542613113.355682481515253.911768603711



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')