Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 26 Nov 2016 19:22:22 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/26/t1480188161543voxh35woapia.htm/, Retrieved Fri, 03 May 2024 17:51:06 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 03 May 2024 17:51:06 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
97.78
97.73
97.61
97.69
97.68
97.67
97.67
97.96
98.27
99.52
99.59
99.75
99.75
99.8
99.99
100.25
100.08
100.08
100.08
100.06
101
101.81
101.82
101.96
101.96
101.93
102.03
102.11
102.07
102.34
102.34
102.33
102.77
103.08
103.38
103.44
99.1
99.15
99.21
99.01
99.08
99.11
100.11
100.31
100.55
101.38
101.49
101.5
100.69
100.8
100.58
100.34
100.38
100.33
101.06
101.15
101.36
101.98
102.24
102.34
101.91
101.8
101.8
101.73
101.8
101.81
102.28
101.7
101.7
102.37
102.43
102.41




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.00942378258373058
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00942378258373058 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.00942378258373058[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
beta0.00942378258373058
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
397.6197.68-0.0700000000000074
497.6997.55934033521910.13065966478085
597.6897.64057164349250.0394283565075142
697.6797.63094320775190.0390567922481324
797.6797.62131127047040.048688729529573
897.9697.62177010247180.338229897528208
998.2797.91495750748940.355042492510592
1099.5298.22830335074681.29169664925318
1199.5999.49047601913350.0995239808664934
1299.7599.56141391149110.188586088508927
1399.7599.72319110578750.0268088942125075
1499.899.72344374697790.0765562530221331
1599.9999.77416519646180.215834803538229
16100.2599.96619917672430.283800823275698
17100.08100.22887365398-0.148873653979948
18100.08100.0574707010320.022529298967612
19100.08100.0576830122480.0223169877523759
20100.06100.0578933226880.00210667731187186
21101100.0379131755570.962086824442906
22101.81100.9869796726170.823020327382693
23101.82101.8047356372450.0152643627554312
24101.96101.814879485280.145120514719551
25101.96101.956247069460.00375293054040071
26101.93101.956282436261-0.0262824362610559
27102.03101.9260347562960.103965243704025
28102.11102.0270145021490.082985497851098
29102.07102.107796539438-0.0377965394382613
30102.34102.0674403530680.272559646931839
31102.34102.340008895922-8.8959219510798e-06
32102.33102.340008812089-0.0100088120887278
33102.77102.329914491220.440085508780328
34103.08102.7740617613730.305938238627334
35103.38103.0869448568180.293055143182457
36103.44103.3897065447720.0502934552280578
3799.1103.450180499359-4.3501804993594
3899.1599.06918534413340.0808146558665612
3999.2199.11994692387990.0900530761200713
4099.0199.1807955644903-0.170795564490248
4199.0898.97918602422420.10081397577575
4299.1199.05013607321340.0598639267866474
43100.1199.0807002178441.029299782156
44100.31100.0904001152050.219599884795485
45100.55100.2924695767740.257530423225745
46101.38100.5348964874910.845103512508587
47101.49101.3728605592540.117139440745959
48101.5101.4839644558760.0160355441243922
49100.69101.494115571357-0.804115571357059
50100.8100.676537761040.123462238959604
51100.58100.787701242338-0.207701242337649
52100.34100.565743910987-0.225743910987489
53100.38100.3236165494510.056383450549248
54100.33100.36414789483-0.034147894830042
55101.06100.3138260924930.746173907506531
56101.15101.0508578731670.0991421268325468
57101.36101.1417921670160.218207832984376
58101.98101.3538485101920.626151489808265
59102.24101.9797492256960.260250774303827
60102.34102.242201772410.0977982275895499
61101.91102.343123401644-0.433123401644337
62101.8101.909041740875-0.109041740875313
63101.8101.7980141552170.00198584478324904
64101.73101.798032869386-0.0680328693862293
65101.8101.7273917424170.0726082575834113
66101.81101.798075986850.0119240131501641
67102.28101.8081883561570.471811643842713
68101.7102.282634606509-0.58263460650933
69101.7101.6971439846520.00285601534817204
70102.37101.697170899120.672829100880463
71102.43102.3735114942820.0564885057177662
72102.41102.434043829679-0.0240438296786039

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 97.61 & 97.68 & -0.0700000000000074 \tabularnewline
4 & 97.69 & 97.5593403352191 & 0.13065966478085 \tabularnewline
5 & 97.68 & 97.6405716434925 & 0.0394283565075142 \tabularnewline
6 & 97.67 & 97.6309432077519 & 0.0390567922481324 \tabularnewline
7 & 97.67 & 97.6213112704704 & 0.048688729529573 \tabularnewline
8 & 97.96 & 97.6217701024718 & 0.338229897528208 \tabularnewline
9 & 98.27 & 97.9149575074894 & 0.355042492510592 \tabularnewline
10 & 99.52 & 98.2283033507468 & 1.29169664925318 \tabularnewline
11 & 99.59 & 99.4904760191335 & 0.0995239808664934 \tabularnewline
12 & 99.75 & 99.5614139114911 & 0.188586088508927 \tabularnewline
13 & 99.75 & 99.7231911057875 & 0.0268088942125075 \tabularnewline
14 & 99.8 & 99.7234437469779 & 0.0765562530221331 \tabularnewline
15 & 99.99 & 99.7741651964618 & 0.215834803538229 \tabularnewline
16 & 100.25 & 99.9661991767243 & 0.283800823275698 \tabularnewline
17 & 100.08 & 100.22887365398 & -0.148873653979948 \tabularnewline
18 & 100.08 & 100.057470701032 & 0.022529298967612 \tabularnewline
19 & 100.08 & 100.057683012248 & 0.0223169877523759 \tabularnewline
20 & 100.06 & 100.057893322688 & 0.00210667731187186 \tabularnewline
21 & 101 & 100.037913175557 & 0.962086824442906 \tabularnewline
22 & 101.81 & 100.986979672617 & 0.823020327382693 \tabularnewline
23 & 101.82 & 101.804735637245 & 0.0152643627554312 \tabularnewline
24 & 101.96 & 101.81487948528 & 0.145120514719551 \tabularnewline
25 & 101.96 & 101.95624706946 & 0.00375293054040071 \tabularnewline
26 & 101.93 & 101.956282436261 & -0.0262824362610559 \tabularnewline
27 & 102.03 & 101.926034756296 & 0.103965243704025 \tabularnewline
28 & 102.11 & 102.027014502149 & 0.082985497851098 \tabularnewline
29 & 102.07 & 102.107796539438 & -0.0377965394382613 \tabularnewline
30 & 102.34 & 102.067440353068 & 0.272559646931839 \tabularnewline
31 & 102.34 & 102.340008895922 & -8.8959219510798e-06 \tabularnewline
32 & 102.33 & 102.340008812089 & -0.0100088120887278 \tabularnewline
33 & 102.77 & 102.32991449122 & 0.440085508780328 \tabularnewline
34 & 103.08 & 102.774061761373 & 0.305938238627334 \tabularnewline
35 & 103.38 & 103.086944856818 & 0.293055143182457 \tabularnewline
36 & 103.44 & 103.389706544772 & 0.0502934552280578 \tabularnewline
37 & 99.1 & 103.450180499359 & -4.3501804993594 \tabularnewline
38 & 99.15 & 99.0691853441334 & 0.0808146558665612 \tabularnewline
39 & 99.21 & 99.1199469238799 & 0.0900530761200713 \tabularnewline
40 & 99.01 & 99.1807955644903 & -0.170795564490248 \tabularnewline
41 & 99.08 & 98.9791860242242 & 0.10081397577575 \tabularnewline
42 & 99.11 & 99.0501360732134 & 0.0598639267866474 \tabularnewline
43 & 100.11 & 99.080700217844 & 1.029299782156 \tabularnewline
44 & 100.31 & 100.090400115205 & 0.219599884795485 \tabularnewline
45 & 100.55 & 100.292469576774 & 0.257530423225745 \tabularnewline
46 & 101.38 & 100.534896487491 & 0.845103512508587 \tabularnewline
47 & 101.49 & 101.372860559254 & 0.117139440745959 \tabularnewline
48 & 101.5 & 101.483964455876 & 0.0160355441243922 \tabularnewline
49 & 100.69 & 101.494115571357 & -0.804115571357059 \tabularnewline
50 & 100.8 & 100.67653776104 & 0.123462238959604 \tabularnewline
51 & 100.58 & 100.787701242338 & -0.207701242337649 \tabularnewline
52 & 100.34 & 100.565743910987 & -0.225743910987489 \tabularnewline
53 & 100.38 & 100.323616549451 & 0.056383450549248 \tabularnewline
54 & 100.33 & 100.36414789483 & -0.034147894830042 \tabularnewline
55 & 101.06 & 100.313826092493 & 0.746173907506531 \tabularnewline
56 & 101.15 & 101.050857873167 & 0.0991421268325468 \tabularnewline
57 & 101.36 & 101.141792167016 & 0.218207832984376 \tabularnewline
58 & 101.98 & 101.353848510192 & 0.626151489808265 \tabularnewline
59 & 102.24 & 101.979749225696 & 0.260250774303827 \tabularnewline
60 & 102.34 & 102.24220177241 & 0.0977982275895499 \tabularnewline
61 & 101.91 & 102.343123401644 & -0.433123401644337 \tabularnewline
62 & 101.8 & 101.909041740875 & -0.109041740875313 \tabularnewline
63 & 101.8 & 101.798014155217 & 0.00198584478324904 \tabularnewline
64 & 101.73 & 101.798032869386 & -0.0680328693862293 \tabularnewline
65 & 101.8 & 101.727391742417 & 0.0726082575834113 \tabularnewline
66 & 101.81 & 101.79807598685 & 0.0119240131501641 \tabularnewline
67 & 102.28 & 101.808188356157 & 0.471811643842713 \tabularnewline
68 & 101.7 & 102.282634606509 & -0.58263460650933 \tabularnewline
69 & 101.7 & 101.697143984652 & 0.00285601534817204 \tabularnewline
70 & 102.37 & 101.69717089912 & 0.672829100880463 \tabularnewline
71 & 102.43 & 102.373511494282 & 0.0564885057177662 \tabularnewline
72 & 102.41 & 102.434043829679 & -0.0240438296786039 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]97.61[/C][C]97.68[/C][C]-0.0700000000000074[/C][/ROW]
[ROW][C]4[/C][C]97.69[/C][C]97.5593403352191[/C][C]0.13065966478085[/C][/ROW]
[ROW][C]5[/C][C]97.68[/C][C]97.6405716434925[/C][C]0.0394283565075142[/C][/ROW]
[ROW][C]6[/C][C]97.67[/C][C]97.6309432077519[/C][C]0.0390567922481324[/C][/ROW]
[ROW][C]7[/C][C]97.67[/C][C]97.6213112704704[/C][C]0.048688729529573[/C][/ROW]
[ROW][C]8[/C][C]97.96[/C][C]97.6217701024718[/C][C]0.338229897528208[/C][/ROW]
[ROW][C]9[/C][C]98.27[/C][C]97.9149575074894[/C][C]0.355042492510592[/C][/ROW]
[ROW][C]10[/C][C]99.52[/C][C]98.2283033507468[/C][C]1.29169664925318[/C][/ROW]
[ROW][C]11[/C][C]99.59[/C][C]99.4904760191335[/C][C]0.0995239808664934[/C][/ROW]
[ROW][C]12[/C][C]99.75[/C][C]99.5614139114911[/C][C]0.188586088508927[/C][/ROW]
[ROW][C]13[/C][C]99.75[/C][C]99.7231911057875[/C][C]0.0268088942125075[/C][/ROW]
[ROW][C]14[/C][C]99.8[/C][C]99.7234437469779[/C][C]0.0765562530221331[/C][/ROW]
[ROW][C]15[/C][C]99.99[/C][C]99.7741651964618[/C][C]0.215834803538229[/C][/ROW]
[ROW][C]16[/C][C]100.25[/C][C]99.9661991767243[/C][C]0.283800823275698[/C][/ROW]
[ROW][C]17[/C][C]100.08[/C][C]100.22887365398[/C][C]-0.148873653979948[/C][/ROW]
[ROW][C]18[/C][C]100.08[/C][C]100.057470701032[/C][C]0.022529298967612[/C][/ROW]
[ROW][C]19[/C][C]100.08[/C][C]100.057683012248[/C][C]0.0223169877523759[/C][/ROW]
[ROW][C]20[/C][C]100.06[/C][C]100.057893322688[/C][C]0.00210667731187186[/C][/ROW]
[ROW][C]21[/C][C]101[/C][C]100.037913175557[/C][C]0.962086824442906[/C][/ROW]
[ROW][C]22[/C][C]101.81[/C][C]100.986979672617[/C][C]0.823020327382693[/C][/ROW]
[ROW][C]23[/C][C]101.82[/C][C]101.804735637245[/C][C]0.0152643627554312[/C][/ROW]
[ROW][C]24[/C][C]101.96[/C][C]101.81487948528[/C][C]0.145120514719551[/C][/ROW]
[ROW][C]25[/C][C]101.96[/C][C]101.95624706946[/C][C]0.00375293054040071[/C][/ROW]
[ROW][C]26[/C][C]101.93[/C][C]101.956282436261[/C][C]-0.0262824362610559[/C][/ROW]
[ROW][C]27[/C][C]102.03[/C][C]101.926034756296[/C][C]0.103965243704025[/C][/ROW]
[ROW][C]28[/C][C]102.11[/C][C]102.027014502149[/C][C]0.082985497851098[/C][/ROW]
[ROW][C]29[/C][C]102.07[/C][C]102.107796539438[/C][C]-0.0377965394382613[/C][/ROW]
[ROW][C]30[/C][C]102.34[/C][C]102.067440353068[/C][C]0.272559646931839[/C][/ROW]
[ROW][C]31[/C][C]102.34[/C][C]102.340008895922[/C][C]-8.8959219510798e-06[/C][/ROW]
[ROW][C]32[/C][C]102.33[/C][C]102.340008812089[/C][C]-0.0100088120887278[/C][/ROW]
[ROW][C]33[/C][C]102.77[/C][C]102.32991449122[/C][C]0.440085508780328[/C][/ROW]
[ROW][C]34[/C][C]103.08[/C][C]102.774061761373[/C][C]0.305938238627334[/C][/ROW]
[ROW][C]35[/C][C]103.38[/C][C]103.086944856818[/C][C]0.293055143182457[/C][/ROW]
[ROW][C]36[/C][C]103.44[/C][C]103.389706544772[/C][C]0.0502934552280578[/C][/ROW]
[ROW][C]37[/C][C]99.1[/C][C]103.450180499359[/C][C]-4.3501804993594[/C][/ROW]
[ROW][C]38[/C][C]99.15[/C][C]99.0691853441334[/C][C]0.0808146558665612[/C][/ROW]
[ROW][C]39[/C][C]99.21[/C][C]99.1199469238799[/C][C]0.0900530761200713[/C][/ROW]
[ROW][C]40[/C][C]99.01[/C][C]99.1807955644903[/C][C]-0.170795564490248[/C][/ROW]
[ROW][C]41[/C][C]99.08[/C][C]98.9791860242242[/C][C]0.10081397577575[/C][/ROW]
[ROW][C]42[/C][C]99.11[/C][C]99.0501360732134[/C][C]0.0598639267866474[/C][/ROW]
[ROW][C]43[/C][C]100.11[/C][C]99.080700217844[/C][C]1.029299782156[/C][/ROW]
[ROW][C]44[/C][C]100.31[/C][C]100.090400115205[/C][C]0.219599884795485[/C][/ROW]
[ROW][C]45[/C][C]100.55[/C][C]100.292469576774[/C][C]0.257530423225745[/C][/ROW]
[ROW][C]46[/C][C]101.38[/C][C]100.534896487491[/C][C]0.845103512508587[/C][/ROW]
[ROW][C]47[/C][C]101.49[/C][C]101.372860559254[/C][C]0.117139440745959[/C][/ROW]
[ROW][C]48[/C][C]101.5[/C][C]101.483964455876[/C][C]0.0160355441243922[/C][/ROW]
[ROW][C]49[/C][C]100.69[/C][C]101.494115571357[/C][C]-0.804115571357059[/C][/ROW]
[ROW][C]50[/C][C]100.8[/C][C]100.67653776104[/C][C]0.123462238959604[/C][/ROW]
[ROW][C]51[/C][C]100.58[/C][C]100.787701242338[/C][C]-0.207701242337649[/C][/ROW]
[ROW][C]52[/C][C]100.34[/C][C]100.565743910987[/C][C]-0.225743910987489[/C][/ROW]
[ROW][C]53[/C][C]100.38[/C][C]100.323616549451[/C][C]0.056383450549248[/C][/ROW]
[ROW][C]54[/C][C]100.33[/C][C]100.36414789483[/C][C]-0.034147894830042[/C][/ROW]
[ROW][C]55[/C][C]101.06[/C][C]100.313826092493[/C][C]0.746173907506531[/C][/ROW]
[ROW][C]56[/C][C]101.15[/C][C]101.050857873167[/C][C]0.0991421268325468[/C][/ROW]
[ROW][C]57[/C][C]101.36[/C][C]101.141792167016[/C][C]0.218207832984376[/C][/ROW]
[ROW][C]58[/C][C]101.98[/C][C]101.353848510192[/C][C]0.626151489808265[/C][/ROW]
[ROW][C]59[/C][C]102.24[/C][C]101.979749225696[/C][C]0.260250774303827[/C][/ROW]
[ROW][C]60[/C][C]102.34[/C][C]102.24220177241[/C][C]0.0977982275895499[/C][/ROW]
[ROW][C]61[/C][C]101.91[/C][C]102.343123401644[/C][C]-0.433123401644337[/C][/ROW]
[ROW][C]62[/C][C]101.8[/C][C]101.909041740875[/C][C]-0.109041740875313[/C][/ROW]
[ROW][C]63[/C][C]101.8[/C][C]101.798014155217[/C][C]0.00198584478324904[/C][/ROW]
[ROW][C]64[/C][C]101.73[/C][C]101.798032869386[/C][C]-0.0680328693862293[/C][/ROW]
[ROW][C]65[/C][C]101.8[/C][C]101.727391742417[/C][C]0.0726082575834113[/C][/ROW]
[ROW][C]66[/C][C]101.81[/C][C]101.79807598685[/C][C]0.0119240131501641[/C][/ROW]
[ROW][C]67[/C][C]102.28[/C][C]101.808188356157[/C][C]0.471811643842713[/C][/ROW]
[ROW][C]68[/C][C]101.7[/C][C]102.282634606509[/C][C]-0.58263460650933[/C][/ROW]
[ROW][C]69[/C][C]101.7[/C][C]101.697143984652[/C][C]0.00285601534817204[/C][/ROW]
[ROW][C]70[/C][C]102.37[/C][C]101.69717089912[/C][C]0.672829100880463[/C][/ROW]
[ROW][C]71[/C][C]102.43[/C][C]102.373511494282[/C][C]0.0564885057177662[/C][/ROW]
[ROW][C]72[/C][C]102.41[/C][C]102.434043829679[/C][C]-0.0240438296786039[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
397.6197.68-0.0700000000000074
497.6997.55934033521910.13065966478085
597.6897.64057164349250.0394283565075142
697.6797.63094320775190.0390567922481324
797.6797.62131127047040.048688729529573
897.9697.62177010247180.338229897528208
998.2797.91495750748940.355042492510592
1099.5298.22830335074681.29169664925318
1199.5999.49047601913350.0995239808664934
1299.7599.56141391149110.188586088508927
1399.7599.72319110578750.0268088942125075
1499.899.72344374697790.0765562530221331
1599.9999.77416519646180.215834803538229
16100.2599.96619917672430.283800823275698
17100.08100.22887365398-0.148873653979948
18100.08100.0574707010320.022529298967612
19100.08100.0576830122480.0223169877523759
20100.06100.0578933226880.00210667731187186
21101100.0379131755570.962086824442906
22101.81100.9869796726170.823020327382693
23101.82101.8047356372450.0152643627554312
24101.96101.814879485280.145120514719551
25101.96101.956247069460.00375293054040071
26101.93101.956282436261-0.0262824362610559
27102.03101.9260347562960.103965243704025
28102.11102.0270145021490.082985497851098
29102.07102.107796539438-0.0377965394382613
30102.34102.0674403530680.272559646931839
31102.34102.340008895922-8.8959219510798e-06
32102.33102.340008812089-0.0100088120887278
33102.77102.329914491220.440085508780328
34103.08102.7740617613730.305938238627334
35103.38103.0869448568180.293055143182457
36103.44103.3897065447720.0502934552280578
3799.1103.450180499359-4.3501804993594
3899.1599.06918534413340.0808146558665612
3999.2199.11994692387990.0900530761200713
4099.0199.1807955644903-0.170795564490248
4199.0898.97918602422420.10081397577575
4299.1199.05013607321340.0598639267866474
43100.1199.0807002178441.029299782156
44100.31100.0904001152050.219599884795485
45100.55100.2924695767740.257530423225745
46101.38100.5348964874910.845103512508587
47101.49101.3728605592540.117139440745959
48101.5101.4839644558760.0160355441243922
49100.69101.494115571357-0.804115571357059
50100.8100.676537761040.123462238959604
51100.58100.787701242338-0.207701242337649
52100.34100.565743910987-0.225743910987489
53100.38100.3236165494510.056383450549248
54100.33100.36414789483-0.034147894830042
55101.06100.3138260924930.746173907506531
56101.15101.0508578731670.0991421268325468
57101.36101.1417921670160.218207832984376
58101.98101.3538485101920.626151489808265
59102.24101.9797492256960.260250774303827
60102.34102.242201772410.0977982275895499
61101.91102.343123401644-0.433123401644337
62101.8101.909041740875-0.109041740875313
63101.8101.7980141552170.00198584478324904
64101.73101.798032869386-0.0680328693862293
65101.8101.7273917424170.0726082575834113
66101.81101.798075986850.0119240131501641
67102.28101.8081883561570.471811643842713
68101.7102.282634606509-0.58263460650933
69101.7101.6971439846520.00285601534817204
70102.37101.697170899120.672829100880463
71102.43102.3735114942820.0564885057177662
72102.41102.434043829679-0.0240438296786039







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102.413817245855101.171474070979103.656160420731
74102.41763449171100.652398009015104.182870974405
75102.421451737566100.249309025516104.593594449616
76102.42526898342199.9053239317049104.945214035137
77102.42908622927699.598522454904105.259650003648
78102.43290347513199.3177176464279105.548089303835
79102.43672072098799.056295955095105.817145486878
80102.44053796684298.8099688700245106.071107063659
81102.44435521269798.5757717524919106.312938672902
82102.44817245855298.3515563186436106.544788598461
83102.45198970440898.1357084891933106.768270919622
84102.45580695026397.9269802461144106.984633654411

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102.413817245855 & 101.171474070979 & 103.656160420731 \tabularnewline
74 & 102.41763449171 & 100.652398009015 & 104.182870974405 \tabularnewline
75 & 102.421451737566 & 100.249309025516 & 104.593594449616 \tabularnewline
76 & 102.425268983421 & 99.9053239317049 & 104.945214035137 \tabularnewline
77 & 102.429086229276 & 99.598522454904 & 105.259650003648 \tabularnewline
78 & 102.432903475131 & 99.3177176464279 & 105.548089303835 \tabularnewline
79 & 102.436720720987 & 99.056295955095 & 105.817145486878 \tabularnewline
80 & 102.440537966842 & 98.8099688700245 & 106.071107063659 \tabularnewline
81 & 102.444355212697 & 98.5757717524919 & 106.312938672902 \tabularnewline
82 & 102.448172458552 & 98.3515563186436 & 106.544788598461 \tabularnewline
83 & 102.451989704408 & 98.1357084891933 & 106.768270919622 \tabularnewline
84 & 102.455806950263 & 97.9269802461144 & 106.984633654411 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]102.413817245855[/C][C]101.171474070979[/C][C]103.656160420731[/C][/ROW]
[ROW][C]74[/C][C]102.41763449171[/C][C]100.652398009015[/C][C]104.182870974405[/C][/ROW]
[ROW][C]75[/C][C]102.421451737566[/C][C]100.249309025516[/C][C]104.593594449616[/C][/ROW]
[ROW][C]76[/C][C]102.425268983421[/C][C]99.9053239317049[/C][C]104.945214035137[/C][/ROW]
[ROW][C]77[/C][C]102.429086229276[/C][C]99.598522454904[/C][C]105.259650003648[/C][/ROW]
[ROW][C]78[/C][C]102.432903475131[/C][C]99.3177176464279[/C][C]105.548089303835[/C][/ROW]
[ROW][C]79[/C][C]102.436720720987[/C][C]99.056295955095[/C][C]105.817145486878[/C][/ROW]
[ROW][C]80[/C][C]102.440537966842[/C][C]98.8099688700245[/C][C]106.071107063659[/C][/ROW]
[ROW][C]81[/C][C]102.444355212697[/C][C]98.5757717524919[/C][C]106.312938672902[/C][/ROW]
[ROW][C]82[/C][C]102.448172458552[/C][C]98.3515563186436[/C][C]106.544788598461[/C][/ROW]
[ROW][C]83[/C][C]102.451989704408[/C][C]98.1357084891933[/C][C]106.768270919622[/C][/ROW]
[ROW][C]84[/C][C]102.455806950263[/C][C]97.9269802461144[/C][C]106.984633654411[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
73102.413817245855101.171474070979103.656160420731
74102.41763449171100.652398009015104.182870974405
75102.421451737566100.249309025516104.593594449616
76102.42526898342199.9053239317049104.945214035137
77102.42908622927699.598522454904105.259650003648
78102.43290347513199.3177176464279105.548089303835
79102.43672072098799.056295955095105.817145486878
80102.44053796684298.8099688700245106.071107063659
81102.44435521269798.5757717524919106.312938672902
82102.44817245855298.3515563186436106.544788598461
83102.45198970440898.1357084891933106.768270919622
84102.45580695026397.9269802461144106.984633654411



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')