Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 09 Jan 2017 15:26:15 +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/2017/Jan/09/t1483975626u8yohxhog1okx6c.htm/, Retrieved Tue, 14 May 2024 06:54:04 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 06:54:04 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
91,16
91,17
91,17
91,38
92,68
92,72
92,79
92,81
92,81
92,81
92,81
92,81
92,81
92,82
92,82
92,88
93,38
93,89
94,1
94,18
94,3
94,31
94,36
94,38
94,38
94,5
94,57
94,89
96,71
97,57
97,88
97,97
98,4
98,51
98,46
98,46
98,48
98,6
98,6
98,71
99,13
99,2
99,3
100,18
101,37
101,77
102,28
102,38
102,35
103,23
105,37
106,62
107
107,24
107,31
107,35
107,42
107,58
107,64
107,64
107,68
108,51
110,37
111,31
111,57
111,66
111,69
111,9
111,95
112,04
112,13
112,14




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=&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=&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.082068491689949
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.082068491689949 \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]0.082068491689949[/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
beta0.082068491689949
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
391.1791.18-0.0100000000000051
491.3891.17917931508310.200820684916891
592.6891.40566036579441.27433963420563
692.7292.8102434974744-0.0902434974743613
792.7992.8428373497518-0.0528373497517975
892.8192.9085010681528-0.0985010681527854
992.8192.9204172340596-0.110417234059639
1092.8192.9113554582038-0.101355458203784
1192.8192.9030373686245-0.0930373686244508
1292.8192.8954019321106-0.0854019321106421
1392.8192.8883931243549-0.0783931243549176
1492.8292.8819595188803-0.0619595188802577
1592.8292.8868745946199-0.0668745946199039
1692.8892.8813862975071-0.00138629750706798
1793.3892.94127252616160.43872747383837
1893.8993.47727822820250.412721771797507
1994.194.02114968150150.0788503184984819
2094.1894.23762080821-0.057620808209947
2194.394.3128919553902-0.0128919553902307
2294.3194.4318339320564-0.121833932056404
2394.3694.4318352050159-0.071835205015887
2494.3894.47593979809-0.0959397980899865
2594.3894.4880661635677-0.108066163567699
2694.594.4791973365210.0208026634790173
2794.5794.6009045797358-0.0309045797358465
2894.8994.66836828749060.221631712509406
2996.7195.00655726784691.70344273215308
3097.5796.96635624355490.603643756445081
3197.8897.87589637616440.00410362383557583
3297.9798.1862331543831-0.216233154383076
3398.498.25848722554950.141512774450504
3498.5198.7001009655035-0.190100965503504
3598.4698.7944996659958-0.33449966599585
3698.4698.7170477829368-0.257047782936766
3798.4898.6959522590989-0.215952259098884
3898.698.6982293829176-0.0982293829176228
3998.698.8101678456219-0.210167845621925
4098.7198.79291968753-0.0829196875300084
4199.1398.8961145938430.233885406156986
4299.299.3353092163546-0.135309216354614
4399.399.3942045930566-0.0942045930566451
44100.1899.48647336419420.693526635805796
45101.37100.4233900491420.946609950858388
46101.77101.6910769000270.0789230999727408
47102.28102.0975539998020.182446000198496
48102.38102.622527067853-0.242527067852663
49102.35102.7026232372-0.352623237200007
50103.23102.6436839799880.586316020011836
51105.37103.5718020514041.7981979485958
52106.62105.8593774448050.760622555194587
53107107.171800590656-0.171800590655593
54107.24107.537701175309-0.297701175309058
55107.31107.753269288877-0.443269288877104
56107.35107.786890846926-0.436890846926502
57107.42107.791035874086-0.371035874086076
58107.58107.830585519537-0.250585519536983
59107.64107.970020343909-0.33002034390924
60107.64108.002936072058-0.362936072057607
61107.68107.973150456044-0.293150456043961
62108.51107.9890920402780.520907959721782
63110.37108.8618421708421.50815782915812
64111.31110.8456144091110.464385590888725
65111.57111.823725834118-0.253725834118057
66111.66112.062902937609-0.402902937609198
67111.69112.119837301222-0.429837301222165
68111.9112.114561202239-0.214561202238784
69111.95112.306952487996-0.356952487995869
70112.04112.327657935701-0.287657935701077
71112.13112.394050282795-0.264050282795452
72112.14112.462380074356-0.322380074356104

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 91.17 & 91.18 & -0.0100000000000051 \tabularnewline
4 & 91.38 & 91.1791793150831 & 0.200820684916891 \tabularnewline
5 & 92.68 & 91.4056603657944 & 1.27433963420563 \tabularnewline
6 & 92.72 & 92.8102434974744 & -0.0902434974743613 \tabularnewline
7 & 92.79 & 92.8428373497518 & -0.0528373497517975 \tabularnewline
8 & 92.81 & 92.9085010681528 & -0.0985010681527854 \tabularnewline
9 & 92.81 & 92.9204172340596 & -0.110417234059639 \tabularnewline
10 & 92.81 & 92.9113554582038 & -0.101355458203784 \tabularnewline
11 & 92.81 & 92.9030373686245 & -0.0930373686244508 \tabularnewline
12 & 92.81 & 92.8954019321106 & -0.0854019321106421 \tabularnewline
13 & 92.81 & 92.8883931243549 & -0.0783931243549176 \tabularnewline
14 & 92.82 & 92.8819595188803 & -0.0619595188802577 \tabularnewline
15 & 92.82 & 92.8868745946199 & -0.0668745946199039 \tabularnewline
16 & 92.88 & 92.8813862975071 & -0.00138629750706798 \tabularnewline
17 & 93.38 & 92.9412725261616 & 0.43872747383837 \tabularnewline
18 & 93.89 & 93.4772782282025 & 0.412721771797507 \tabularnewline
19 & 94.1 & 94.0211496815015 & 0.0788503184984819 \tabularnewline
20 & 94.18 & 94.23762080821 & -0.057620808209947 \tabularnewline
21 & 94.3 & 94.3128919553902 & -0.0128919553902307 \tabularnewline
22 & 94.31 & 94.4318339320564 & -0.121833932056404 \tabularnewline
23 & 94.36 & 94.4318352050159 & -0.071835205015887 \tabularnewline
24 & 94.38 & 94.47593979809 & -0.0959397980899865 \tabularnewline
25 & 94.38 & 94.4880661635677 & -0.108066163567699 \tabularnewline
26 & 94.5 & 94.479197336521 & 0.0208026634790173 \tabularnewline
27 & 94.57 & 94.6009045797358 & -0.0309045797358465 \tabularnewline
28 & 94.89 & 94.6683682874906 & 0.221631712509406 \tabularnewline
29 & 96.71 & 95.0065572678469 & 1.70344273215308 \tabularnewline
30 & 97.57 & 96.9663562435549 & 0.603643756445081 \tabularnewline
31 & 97.88 & 97.8758963761644 & 0.00410362383557583 \tabularnewline
32 & 97.97 & 98.1862331543831 & -0.216233154383076 \tabularnewline
33 & 98.4 & 98.2584872255495 & 0.141512774450504 \tabularnewline
34 & 98.51 & 98.7001009655035 & -0.190100965503504 \tabularnewline
35 & 98.46 & 98.7944996659958 & -0.33449966599585 \tabularnewline
36 & 98.46 & 98.7170477829368 & -0.257047782936766 \tabularnewline
37 & 98.48 & 98.6959522590989 & -0.215952259098884 \tabularnewline
38 & 98.6 & 98.6982293829176 & -0.0982293829176228 \tabularnewline
39 & 98.6 & 98.8101678456219 & -0.210167845621925 \tabularnewline
40 & 98.71 & 98.79291968753 & -0.0829196875300084 \tabularnewline
41 & 99.13 & 98.896114593843 & 0.233885406156986 \tabularnewline
42 & 99.2 & 99.3353092163546 & -0.135309216354614 \tabularnewline
43 & 99.3 & 99.3942045930566 & -0.0942045930566451 \tabularnewline
44 & 100.18 & 99.4864733641942 & 0.693526635805796 \tabularnewline
45 & 101.37 & 100.423390049142 & 0.946609950858388 \tabularnewline
46 & 101.77 & 101.691076900027 & 0.0789230999727408 \tabularnewline
47 & 102.28 & 102.097553999802 & 0.182446000198496 \tabularnewline
48 & 102.38 & 102.622527067853 & -0.242527067852663 \tabularnewline
49 & 102.35 & 102.7026232372 & -0.352623237200007 \tabularnewline
50 & 103.23 & 102.643683979988 & 0.586316020011836 \tabularnewline
51 & 105.37 & 103.571802051404 & 1.7981979485958 \tabularnewline
52 & 106.62 & 105.859377444805 & 0.760622555194587 \tabularnewline
53 & 107 & 107.171800590656 & -0.171800590655593 \tabularnewline
54 & 107.24 & 107.537701175309 & -0.297701175309058 \tabularnewline
55 & 107.31 & 107.753269288877 & -0.443269288877104 \tabularnewline
56 & 107.35 & 107.786890846926 & -0.436890846926502 \tabularnewline
57 & 107.42 & 107.791035874086 & -0.371035874086076 \tabularnewline
58 & 107.58 & 107.830585519537 & -0.250585519536983 \tabularnewline
59 & 107.64 & 107.970020343909 & -0.33002034390924 \tabularnewline
60 & 107.64 & 108.002936072058 & -0.362936072057607 \tabularnewline
61 & 107.68 & 107.973150456044 & -0.293150456043961 \tabularnewline
62 & 108.51 & 107.989092040278 & 0.520907959721782 \tabularnewline
63 & 110.37 & 108.861842170842 & 1.50815782915812 \tabularnewline
64 & 111.31 & 110.845614409111 & 0.464385590888725 \tabularnewline
65 & 111.57 & 111.823725834118 & -0.253725834118057 \tabularnewline
66 & 111.66 & 112.062902937609 & -0.402902937609198 \tabularnewline
67 & 111.69 & 112.119837301222 & -0.429837301222165 \tabularnewline
68 & 111.9 & 112.114561202239 & -0.214561202238784 \tabularnewline
69 & 111.95 & 112.306952487996 & -0.356952487995869 \tabularnewline
70 & 112.04 & 112.327657935701 & -0.287657935701077 \tabularnewline
71 & 112.13 & 112.394050282795 & -0.264050282795452 \tabularnewline
72 & 112.14 & 112.462380074356 & -0.322380074356104 \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]91.17[/C][C]91.18[/C][C]-0.0100000000000051[/C][/ROW]
[ROW][C]4[/C][C]91.38[/C][C]91.1791793150831[/C][C]0.200820684916891[/C][/ROW]
[ROW][C]5[/C][C]92.68[/C][C]91.4056603657944[/C][C]1.27433963420563[/C][/ROW]
[ROW][C]6[/C][C]92.72[/C][C]92.8102434974744[/C][C]-0.0902434974743613[/C][/ROW]
[ROW][C]7[/C][C]92.79[/C][C]92.8428373497518[/C][C]-0.0528373497517975[/C][/ROW]
[ROW][C]8[/C][C]92.81[/C][C]92.9085010681528[/C][C]-0.0985010681527854[/C][/ROW]
[ROW][C]9[/C][C]92.81[/C][C]92.9204172340596[/C][C]-0.110417234059639[/C][/ROW]
[ROW][C]10[/C][C]92.81[/C][C]92.9113554582038[/C][C]-0.101355458203784[/C][/ROW]
[ROW][C]11[/C][C]92.81[/C][C]92.9030373686245[/C][C]-0.0930373686244508[/C][/ROW]
[ROW][C]12[/C][C]92.81[/C][C]92.8954019321106[/C][C]-0.0854019321106421[/C][/ROW]
[ROW][C]13[/C][C]92.81[/C][C]92.8883931243549[/C][C]-0.0783931243549176[/C][/ROW]
[ROW][C]14[/C][C]92.82[/C][C]92.8819595188803[/C][C]-0.0619595188802577[/C][/ROW]
[ROW][C]15[/C][C]92.82[/C][C]92.8868745946199[/C][C]-0.0668745946199039[/C][/ROW]
[ROW][C]16[/C][C]92.88[/C][C]92.8813862975071[/C][C]-0.00138629750706798[/C][/ROW]
[ROW][C]17[/C][C]93.38[/C][C]92.9412725261616[/C][C]0.43872747383837[/C][/ROW]
[ROW][C]18[/C][C]93.89[/C][C]93.4772782282025[/C][C]0.412721771797507[/C][/ROW]
[ROW][C]19[/C][C]94.1[/C][C]94.0211496815015[/C][C]0.0788503184984819[/C][/ROW]
[ROW][C]20[/C][C]94.18[/C][C]94.23762080821[/C][C]-0.057620808209947[/C][/ROW]
[ROW][C]21[/C][C]94.3[/C][C]94.3128919553902[/C][C]-0.0128919553902307[/C][/ROW]
[ROW][C]22[/C][C]94.31[/C][C]94.4318339320564[/C][C]-0.121833932056404[/C][/ROW]
[ROW][C]23[/C][C]94.36[/C][C]94.4318352050159[/C][C]-0.071835205015887[/C][/ROW]
[ROW][C]24[/C][C]94.38[/C][C]94.47593979809[/C][C]-0.0959397980899865[/C][/ROW]
[ROW][C]25[/C][C]94.38[/C][C]94.4880661635677[/C][C]-0.108066163567699[/C][/ROW]
[ROW][C]26[/C][C]94.5[/C][C]94.479197336521[/C][C]0.0208026634790173[/C][/ROW]
[ROW][C]27[/C][C]94.57[/C][C]94.6009045797358[/C][C]-0.0309045797358465[/C][/ROW]
[ROW][C]28[/C][C]94.89[/C][C]94.6683682874906[/C][C]0.221631712509406[/C][/ROW]
[ROW][C]29[/C][C]96.71[/C][C]95.0065572678469[/C][C]1.70344273215308[/C][/ROW]
[ROW][C]30[/C][C]97.57[/C][C]96.9663562435549[/C][C]0.603643756445081[/C][/ROW]
[ROW][C]31[/C][C]97.88[/C][C]97.8758963761644[/C][C]0.00410362383557583[/C][/ROW]
[ROW][C]32[/C][C]97.97[/C][C]98.1862331543831[/C][C]-0.216233154383076[/C][/ROW]
[ROW][C]33[/C][C]98.4[/C][C]98.2584872255495[/C][C]0.141512774450504[/C][/ROW]
[ROW][C]34[/C][C]98.51[/C][C]98.7001009655035[/C][C]-0.190100965503504[/C][/ROW]
[ROW][C]35[/C][C]98.46[/C][C]98.7944996659958[/C][C]-0.33449966599585[/C][/ROW]
[ROW][C]36[/C][C]98.46[/C][C]98.7170477829368[/C][C]-0.257047782936766[/C][/ROW]
[ROW][C]37[/C][C]98.48[/C][C]98.6959522590989[/C][C]-0.215952259098884[/C][/ROW]
[ROW][C]38[/C][C]98.6[/C][C]98.6982293829176[/C][C]-0.0982293829176228[/C][/ROW]
[ROW][C]39[/C][C]98.6[/C][C]98.8101678456219[/C][C]-0.210167845621925[/C][/ROW]
[ROW][C]40[/C][C]98.71[/C][C]98.79291968753[/C][C]-0.0829196875300084[/C][/ROW]
[ROW][C]41[/C][C]99.13[/C][C]98.896114593843[/C][C]0.233885406156986[/C][/ROW]
[ROW][C]42[/C][C]99.2[/C][C]99.3353092163546[/C][C]-0.135309216354614[/C][/ROW]
[ROW][C]43[/C][C]99.3[/C][C]99.3942045930566[/C][C]-0.0942045930566451[/C][/ROW]
[ROW][C]44[/C][C]100.18[/C][C]99.4864733641942[/C][C]0.693526635805796[/C][/ROW]
[ROW][C]45[/C][C]101.37[/C][C]100.423390049142[/C][C]0.946609950858388[/C][/ROW]
[ROW][C]46[/C][C]101.77[/C][C]101.691076900027[/C][C]0.0789230999727408[/C][/ROW]
[ROW][C]47[/C][C]102.28[/C][C]102.097553999802[/C][C]0.182446000198496[/C][/ROW]
[ROW][C]48[/C][C]102.38[/C][C]102.622527067853[/C][C]-0.242527067852663[/C][/ROW]
[ROW][C]49[/C][C]102.35[/C][C]102.7026232372[/C][C]-0.352623237200007[/C][/ROW]
[ROW][C]50[/C][C]103.23[/C][C]102.643683979988[/C][C]0.586316020011836[/C][/ROW]
[ROW][C]51[/C][C]105.37[/C][C]103.571802051404[/C][C]1.7981979485958[/C][/ROW]
[ROW][C]52[/C][C]106.62[/C][C]105.859377444805[/C][C]0.760622555194587[/C][/ROW]
[ROW][C]53[/C][C]107[/C][C]107.171800590656[/C][C]-0.171800590655593[/C][/ROW]
[ROW][C]54[/C][C]107.24[/C][C]107.537701175309[/C][C]-0.297701175309058[/C][/ROW]
[ROW][C]55[/C][C]107.31[/C][C]107.753269288877[/C][C]-0.443269288877104[/C][/ROW]
[ROW][C]56[/C][C]107.35[/C][C]107.786890846926[/C][C]-0.436890846926502[/C][/ROW]
[ROW][C]57[/C][C]107.42[/C][C]107.791035874086[/C][C]-0.371035874086076[/C][/ROW]
[ROW][C]58[/C][C]107.58[/C][C]107.830585519537[/C][C]-0.250585519536983[/C][/ROW]
[ROW][C]59[/C][C]107.64[/C][C]107.970020343909[/C][C]-0.33002034390924[/C][/ROW]
[ROW][C]60[/C][C]107.64[/C][C]108.002936072058[/C][C]-0.362936072057607[/C][/ROW]
[ROW][C]61[/C][C]107.68[/C][C]107.973150456044[/C][C]-0.293150456043961[/C][/ROW]
[ROW][C]62[/C][C]108.51[/C][C]107.989092040278[/C][C]0.520907959721782[/C][/ROW]
[ROW][C]63[/C][C]110.37[/C][C]108.861842170842[/C][C]1.50815782915812[/C][/ROW]
[ROW][C]64[/C][C]111.31[/C][C]110.845614409111[/C][C]0.464385590888725[/C][/ROW]
[ROW][C]65[/C][C]111.57[/C][C]111.823725834118[/C][C]-0.253725834118057[/C][/ROW]
[ROW][C]66[/C][C]111.66[/C][C]112.062902937609[/C][C]-0.402902937609198[/C][/ROW]
[ROW][C]67[/C][C]111.69[/C][C]112.119837301222[/C][C]-0.429837301222165[/C][/ROW]
[ROW][C]68[/C][C]111.9[/C][C]112.114561202239[/C][C]-0.214561202238784[/C][/ROW]
[ROW][C]69[/C][C]111.95[/C][C]112.306952487996[/C][C]-0.356952487995869[/C][/ROW]
[ROW][C]70[/C][C]112.04[/C][C]112.327657935701[/C][C]-0.287657935701077[/C][/ROW]
[ROW][C]71[/C][C]112.13[/C][C]112.394050282795[/C][C]-0.264050282795452[/C][/ROW]
[ROW][C]72[/C][C]112.14[/C][C]112.462380074356[/C][C]-0.322380074356104[/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
391.1791.18-0.0100000000000051
491.3891.17917931508310.200820684916891
592.6891.40566036579441.27433963420563
692.7292.8102434974744-0.0902434974743613
792.7992.8428373497518-0.0528373497517975
892.8192.9085010681528-0.0985010681527854
992.8192.9204172340596-0.110417234059639
1092.8192.9113554582038-0.101355458203784
1192.8192.9030373686245-0.0930373686244508
1292.8192.8954019321106-0.0854019321106421
1392.8192.8883931243549-0.0783931243549176
1492.8292.8819595188803-0.0619595188802577
1592.8292.8868745946199-0.0668745946199039
1692.8892.8813862975071-0.00138629750706798
1793.3892.94127252616160.43872747383837
1893.8993.47727822820250.412721771797507
1994.194.02114968150150.0788503184984819
2094.1894.23762080821-0.057620808209947
2194.394.3128919553902-0.0128919553902307
2294.3194.4318339320564-0.121833932056404
2394.3694.4318352050159-0.071835205015887
2494.3894.47593979809-0.0959397980899865
2594.3894.4880661635677-0.108066163567699
2694.594.4791973365210.0208026634790173
2794.5794.6009045797358-0.0309045797358465
2894.8994.66836828749060.221631712509406
2996.7195.00655726784691.70344273215308
3097.5796.96635624355490.603643756445081
3197.8897.87589637616440.00410362383557583
3297.9798.1862331543831-0.216233154383076
3398.498.25848722554950.141512774450504
3498.5198.7001009655035-0.190100965503504
3598.4698.7944996659958-0.33449966599585
3698.4698.7170477829368-0.257047782936766
3798.4898.6959522590989-0.215952259098884
3898.698.6982293829176-0.0982293829176228
3998.698.8101678456219-0.210167845621925
4098.7198.79291968753-0.0829196875300084
4199.1398.8961145938430.233885406156986
4299.299.3353092163546-0.135309216354614
4399.399.3942045930566-0.0942045930566451
44100.1899.48647336419420.693526635805796
45101.37100.4233900491420.946609950858388
46101.77101.6910769000270.0789230999727408
47102.28102.0975539998020.182446000198496
48102.38102.622527067853-0.242527067852663
49102.35102.7026232372-0.352623237200007
50103.23102.6436839799880.586316020011836
51105.37103.5718020514041.7981979485958
52106.62105.8593774448050.760622555194587
53107107.171800590656-0.171800590655593
54107.24107.537701175309-0.297701175309058
55107.31107.753269288877-0.443269288877104
56107.35107.786890846926-0.436890846926502
57107.42107.791035874086-0.371035874086076
58107.58107.830585519537-0.250585519536983
59107.64107.970020343909-0.33002034390924
60107.64108.002936072058-0.362936072057607
61107.68107.973150456044-0.293150456043961
62108.51107.9890920402780.520907959721782
63110.37108.8618421708421.50815782915812
64111.31110.8456144091110.464385590888725
65111.57111.823725834118-0.253725834118057
66111.66112.062902937609-0.402902937609198
67111.69112.119837301222-0.429837301222165
68111.9112.114561202239-0.214561202238784
69111.95112.306952487996-0.356952487995869
70112.04112.327657935701-0.287657935701077
71112.13112.394050282795-0.264050282795452
72112.14112.462380074356-0.322380074356104







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73112.445922827903111.497900022768113.393945633038
74112.751845655806111.355040223862114.148651087749
75113.057768483708111.277582797086114.837954170331
76113.363691311611111.227142509592115.50024011363
77113.669614139514111.189591744398116.14963653463
78113.975536967417111.158059634525116.793014300309
79114.28145979532111.128691224909117.43422836573
80114.587382623223111.099126462358118.075638784087
81114.893305451125111.067834339094118.718776563157
82115.199228279028111.033781032212119.364675525844
83115.505151106931110.996248556778120.014053657084
84115.811073934834110.954728590524120.667419279144

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 112.445922827903 & 111.497900022768 & 113.393945633038 \tabularnewline
74 & 112.751845655806 & 111.355040223862 & 114.148651087749 \tabularnewline
75 & 113.057768483708 & 111.277582797086 & 114.837954170331 \tabularnewline
76 & 113.363691311611 & 111.227142509592 & 115.50024011363 \tabularnewline
77 & 113.669614139514 & 111.189591744398 & 116.14963653463 \tabularnewline
78 & 113.975536967417 & 111.158059634525 & 116.793014300309 \tabularnewline
79 & 114.28145979532 & 111.128691224909 & 117.43422836573 \tabularnewline
80 & 114.587382623223 & 111.099126462358 & 118.075638784087 \tabularnewline
81 & 114.893305451125 & 111.067834339094 & 118.718776563157 \tabularnewline
82 & 115.199228279028 & 111.033781032212 & 119.364675525844 \tabularnewline
83 & 115.505151106931 & 110.996248556778 & 120.014053657084 \tabularnewline
84 & 115.811073934834 & 110.954728590524 & 120.667419279144 \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]112.445922827903[/C][C]111.497900022768[/C][C]113.393945633038[/C][/ROW]
[ROW][C]74[/C][C]112.751845655806[/C][C]111.355040223862[/C][C]114.148651087749[/C][/ROW]
[ROW][C]75[/C][C]113.057768483708[/C][C]111.277582797086[/C][C]114.837954170331[/C][/ROW]
[ROW][C]76[/C][C]113.363691311611[/C][C]111.227142509592[/C][C]115.50024011363[/C][/ROW]
[ROW][C]77[/C][C]113.669614139514[/C][C]111.189591744398[/C][C]116.14963653463[/C][/ROW]
[ROW][C]78[/C][C]113.975536967417[/C][C]111.158059634525[/C][C]116.793014300309[/C][/ROW]
[ROW][C]79[/C][C]114.28145979532[/C][C]111.128691224909[/C][C]117.43422836573[/C][/ROW]
[ROW][C]80[/C][C]114.587382623223[/C][C]111.099126462358[/C][C]118.075638784087[/C][/ROW]
[ROW][C]81[/C][C]114.893305451125[/C][C]111.067834339094[/C][C]118.718776563157[/C][/ROW]
[ROW][C]82[/C][C]115.199228279028[/C][C]111.033781032212[/C][C]119.364675525844[/C][/ROW]
[ROW][C]83[/C][C]115.505151106931[/C][C]110.996248556778[/C][C]120.014053657084[/C][/ROW]
[ROW][C]84[/C][C]115.811073934834[/C][C]110.954728590524[/C][C]120.667419279144[/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
73112.445922827903111.497900022768113.393945633038
74112.751845655806111.355040223862114.148651087749
75113.057768483708111.277582797086114.837954170331
76113.363691311611111.227142509592115.50024011363
77113.669614139514111.189591744398116.14963653463
78113.975536967417111.158059634525116.793014300309
79114.28145979532111.128691224909117.43422836573
80114.587382623223111.099126462358118.075638784087
81114.893305451125111.067834339094118.718776563157
82115.199228279028111.033781032212119.364675525844
83115.505151106931110.996248556778120.014053657084
84115.811073934834110.954728590524120.667419279144



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')