Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 06 Jun 2009 08:27:52 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/06/t12442985311htsfc9ee4p66hw.htm/, Retrieved Sun, 28 Apr 2024 19:51:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42010, Retrieved Sun, 28 Apr 2024 19:51:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Ben Eysackers, op...] [2009-06-06 14:27:52] [2b08e9b5345c911f5a04c663d4ad43d5] [Current]
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Dataseries X:
46
33
34
25
33
18
26
21
23
24
26
32
47
45
47
43
48
48
43
44
46
36
32
18
31
37
32
29
29
40
26
29
19
30
12
24
40
43
49
49
48
33
46
46
43
44
38
38
39
47
41
36
38
11
24
30
18
21
22
15
15
16
26
39
28
25
25
13
20
13
10
19
31
36
26
33
42
44
45
42
60
42
63
71




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42010&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42010&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42010&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.770094354773406
beta0.00308092481798597
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.770094354773406 \tabularnewline
beta & 0.00308092481798597 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42010&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]0.770094354773406[/C][/ROW]
[ROW][C]beta[/C][C]0.00308092481798597[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42010&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42010&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
alpha0.770094354773406
beta0.00308092481798597
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134736.057637861091310.9423621389087
144542.47814430007622.52185569992385
154745.91940984811661.0805901518834
164342.81199294708370.188007052916312
174848.7905776544218-0.790577654421796
184850.2640287424153-2.26402874241529
194340.14260503229172.85739496770831
204434.64042082258349.35957917741658
214645.40879189735830.59120810264168
223647.0515459369091-11.0515459369091
233241.1804620027384-9.18046200273838
241841.0580182564942-23.0580182564942
253134.1925531755259-3.19255317552587
263730.70235500421056.29764499578953
273237.0085270935604-5.00852709356036
282930.7125533282961-1.71255332829606
292933.8115427512704-4.81154275127042
304031.92743194478018.07256805521995
312631.7731366027537-5.77313660275368
322922.66361893470516.33638106529493
331930.1976331330650-11.1976331330650
343022.63552604250877.36447395749127
351230.4856433037945-18.4856433037945
362420.15548359099073.84451640900933
374033.86842008876256.13157991123752
384336.93956057262586.0604394273742
394942.98873791565766.01126208434241
404943.47026351305745.52973648694257
414853.9199901029233-5.91999010292332
423351.3365903810986-18.3365903810986
434630.982084226229715.0179157737703
444634.727449039710711.2725509602893
454346.9839975693075-3.98399756930755
464445.0172850121569-1.01728501215685
473847.0249415113234-9.02494151132343
483847.9268770335403-9.9268770335403
493957.7376485077695-18.7376485077695
504741.21236875297445.78763124702562
514146.9819512891653-5.98195128916534
523638.775022580714-2.77502258071402
533841.6640069362547-3.66400693625471
541140.6440713520483-29.6440713520483
552415.37947569937238.62052430062773
563018.369584576213611.6304154237864
571829.8904874376668-11.8904874376668
582121.7151636263480-0.715163626348044
592222.9711162989545-0.97111629895446
601527.0381213660788-12.0381213660788
611526.283383542732-11.2833835427320
621617.5381210367758-1.53812103677583
632617.68065739426998.31934260573013
643922.532063227276716.4679367727233
652840.0448912488407-12.0448912488407
662532.4286864783348-7.42868647833483
672522.4679956986732.53200430132701
681320.2441149134746-7.24411491347459
692016.42840048002553.57159951997445
701320.1198125513801-7.11981255138008
711016.1398077524889-6.1398077524889
721914.37215030994224.62784969005781
733126.46021894903524.53978105096484
743628.83989705413847.16010294586158
752635.5854394083182-9.5854394083182
763326.13084007379416.8691599262059
774235.82205733344546.17794266655459
784442.29649393177441.70350606822559
794535.97937999624359.02062000375651
804234.92677967963347.07322032036662
816043.658452970319416.3415470296806
824257.2809909808047-15.2809909808047
836348.245827072891714.7541729271083
847170.60553118699010.394468813009908

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 47 & 36.0576378610913 & 10.9423621389087 \tabularnewline
14 & 45 & 42.4781443000762 & 2.52185569992385 \tabularnewline
15 & 47 & 45.9194098481166 & 1.0805901518834 \tabularnewline
16 & 43 & 42.8119929470837 & 0.188007052916312 \tabularnewline
17 & 48 & 48.7905776544218 & -0.790577654421796 \tabularnewline
18 & 48 & 50.2640287424153 & -2.26402874241529 \tabularnewline
19 & 43 & 40.1426050322917 & 2.85739496770831 \tabularnewline
20 & 44 & 34.6404208225834 & 9.35957917741658 \tabularnewline
21 & 46 & 45.4087918973583 & 0.59120810264168 \tabularnewline
22 & 36 & 47.0515459369091 & -11.0515459369091 \tabularnewline
23 & 32 & 41.1804620027384 & -9.18046200273838 \tabularnewline
24 & 18 & 41.0580182564942 & -23.0580182564942 \tabularnewline
25 & 31 & 34.1925531755259 & -3.19255317552587 \tabularnewline
26 & 37 & 30.7023550042105 & 6.29764499578953 \tabularnewline
27 & 32 & 37.0085270935604 & -5.00852709356036 \tabularnewline
28 & 29 & 30.7125533282961 & -1.71255332829606 \tabularnewline
29 & 29 & 33.8115427512704 & -4.81154275127042 \tabularnewline
30 & 40 & 31.9274319447801 & 8.07256805521995 \tabularnewline
31 & 26 & 31.7731366027537 & -5.77313660275368 \tabularnewline
32 & 29 & 22.6636189347051 & 6.33638106529493 \tabularnewline
33 & 19 & 30.1976331330650 & -11.1976331330650 \tabularnewline
34 & 30 & 22.6355260425087 & 7.36447395749127 \tabularnewline
35 & 12 & 30.4856433037945 & -18.4856433037945 \tabularnewline
36 & 24 & 20.1554835909907 & 3.84451640900933 \tabularnewline
37 & 40 & 33.8684200887625 & 6.13157991123752 \tabularnewline
38 & 43 & 36.9395605726258 & 6.0604394273742 \tabularnewline
39 & 49 & 42.9887379156576 & 6.01126208434241 \tabularnewline
40 & 49 & 43.4702635130574 & 5.52973648694257 \tabularnewline
41 & 48 & 53.9199901029233 & -5.91999010292332 \tabularnewline
42 & 33 & 51.3365903810986 & -18.3365903810986 \tabularnewline
43 & 46 & 30.9820842262297 & 15.0179157737703 \tabularnewline
44 & 46 & 34.7274490397107 & 11.2725509602893 \tabularnewline
45 & 43 & 46.9839975693075 & -3.98399756930755 \tabularnewline
46 & 44 & 45.0172850121569 & -1.01728501215685 \tabularnewline
47 & 38 & 47.0249415113234 & -9.02494151132343 \tabularnewline
48 & 38 & 47.9268770335403 & -9.9268770335403 \tabularnewline
49 & 39 & 57.7376485077695 & -18.7376485077695 \tabularnewline
50 & 47 & 41.2123687529744 & 5.78763124702562 \tabularnewline
51 & 41 & 46.9819512891653 & -5.98195128916534 \tabularnewline
52 & 36 & 38.775022580714 & -2.77502258071402 \tabularnewline
53 & 38 & 41.6640069362547 & -3.66400693625471 \tabularnewline
54 & 11 & 40.6440713520483 & -29.6440713520483 \tabularnewline
55 & 24 & 15.3794756993723 & 8.62052430062773 \tabularnewline
56 & 30 & 18.3695845762136 & 11.6304154237864 \tabularnewline
57 & 18 & 29.8904874376668 & -11.8904874376668 \tabularnewline
58 & 21 & 21.7151636263480 & -0.715163626348044 \tabularnewline
59 & 22 & 22.9711162989545 & -0.97111629895446 \tabularnewline
60 & 15 & 27.0381213660788 & -12.0381213660788 \tabularnewline
61 & 15 & 26.283383542732 & -11.2833835427320 \tabularnewline
62 & 16 & 17.5381210367758 & -1.53812103677583 \tabularnewline
63 & 26 & 17.6806573942699 & 8.31934260573013 \tabularnewline
64 & 39 & 22.5320632272767 & 16.4679367727233 \tabularnewline
65 & 28 & 40.0448912488407 & -12.0448912488407 \tabularnewline
66 & 25 & 32.4286864783348 & -7.42868647833483 \tabularnewline
67 & 25 & 22.467995698673 & 2.53200430132701 \tabularnewline
68 & 13 & 20.2441149134746 & -7.24411491347459 \tabularnewline
69 & 20 & 16.4284004800255 & 3.57159951997445 \tabularnewline
70 & 13 & 20.1198125513801 & -7.11981255138008 \tabularnewline
71 & 10 & 16.1398077524889 & -6.1398077524889 \tabularnewline
72 & 19 & 14.3721503099422 & 4.62784969005781 \tabularnewline
73 & 31 & 26.4602189490352 & 4.53978105096484 \tabularnewline
74 & 36 & 28.8398970541384 & 7.16010294586158 \tabularnewline
75 & 26 & 35.5854394083182 & -9.5854394083182 \tabularnewline
76 & 33 & 26.1308400737941 & 6.8691599262059 \tabularnewline
77 & 42 & 35.8220573334454 & 6.17794266655459 \tabularnewline
78 & 44 & 42.2964939317744 & 1.70350606822559 \tabularnewline
79 & 45 & 35.9793799962435 & 9.02062000375651 \tabularnewline
80 & 42 & 34.9267796796334 & 7.07322032036662 \tabularnewline
81 & 60 & 43.6584529703194 & 16.3415470296806 \tabularnewline
82 & 42 & 57.2809909808047 & -15.2809909808047 \tabularnewline
83 & 63 & 48.2458270728917 & 14.7541729271083 \tabularnewline
84 & 71 & 70.6055311869901 & 0.394468813009908 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42010&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]13[/C][C]47[/C][C]36.0576378610913[/C][C]10.9423621389087[/C][/ROW]
[ROW][C]14[/C][C]45[/C][C]42.4781443000762[/C][C]2.52185569992385[/C][/ROW]
[ROW][C]15[/C][C]47[/C][C]45.9194098481166[/C][C]1.0805901518834[/C][/ROW]
[ROW][C]16[/C][C]43[/C][C]42.8119929470837[/C][C]0.188007052916312[/C][/ROW]
[ROW][C]17[/C][C]48[/C][C]48.7905776544218[/C][C]-0.790577654421796[/C][/ROW]
[ROW][C]18[/C][C]48[/C][C]50.2640287424153[/C][C]-2.26402874241529[/C][/ROW]
[ROW][C]19[/C][C]43[/C][C]40.1426050322917[/C][C]2.85739496770831[/C][/ROW]
[ROW][C]20[/C][C]44[/C][C]34.6404208225834[/C][C]9.35957917741658[/C][/ROW]
[ROW][C]21[/C][C]46[/C][C]45.4087918973583[/C][C]0.59120810264168[/C][/ROW]
[ROW][C]22[/C][C]36[/C][C]47.0515459369091[/C][C]-11.0515459369091[/C][/ROW]
[ROW][C]23[/C][C]32[/C][C]41.1804620027384[/C][C]-9.18046200273838[/C][/ROW]
[ROW][C]24[/C][C]18[/C][C]41.0580182564942[/C][C]-23.0580182564942[/C][/ROW]
[ROW][C]25[/C][C]31[/C][C]34.1925531755259[/C][C]-3.19255317552587[/C][/ROW]
[ROW][C]26[/C][C]37[/C][C]30.7023550042105[/C][C]6.29764499578953[/C][/ROW]
[ROW][C]27[/C][C]32[/C][C]37.0085270935604[/C][C]-5.00852709356036[/C][/ROW]
[ROW][C]28[/C][C]29[/C][C]30.7125533282961[/C][C]-1.71255332829606[/C][/ROW]
[ROW][C]29[/C][C]29[/C][C]33.8115427512704[/C][C]-4.81154275127042[/C][/ROW]
[ROW][C]30[/C][C]40[/C][C]31.9274319447801[/C][C]8.07256805521995[/C][/ROW]
[ROW][C]31[/C][C]26[/C][C]31.7731366027537[/C][C]-5.77313660275368[/C][/ROW]
[ROW][C]32[/C][C]29[/C][C]22.6636189347051[/C][C]6.33638106529493[/C][/ROW]
[ROW][C]33[/C][C]19[/C][C]30.1976331330650[/C][C]-11.1976331330650[/C][/ROW]
[ROW][C]34[/C][C]30[/C][C]22.6355260425087[/C][C]7.36447395749127[/C][/ROW]
[ROW][C]35[/C][C]12[/C][C]30.4856433037945[/C][C]-18.4856433037945[/C][/ROW]
[ROW][C]36[/C][C]24[/C][C]20.1554835909907[/C][C]3.84451640900933[/C][/ROW]
[ROW][C]37[/C][C]40[/C][C]33.8684200887625[/C][C]6.13157991123752[/C][/ROW]
[ROW][C]38[/C][C]43[/C][C]36.9395605726258[/C][C]6.0604394273742[/C][/ROW]
[ROW][C]39[/C][C]49[/C][C]42.9887379156576[/C][C]6.01126208434241[/C][/ROW]
[ROW][C]40[/C][C]49[/C][C]43.4702635130574[/C][C]5.52973648694257[/C][/ROW]
[ROW][C]41[/C][C]48[/C][C]53.9199901029233[/C][C]-5.91999010292332[/C][/ROW]
[ROW][C]42[/C][C]33[/C][C]51.3365903810986[/C][C]-18.3365903810986[/C][/ROW]
[ROW][C]43[/C][C]46[/C][C]30.9820842262297[/C][C]15.0179157737703[/C][/ROW]
[ROW][C]44[/C][C]46[/C][C]34.7274490397107[/C][C]11.2725509602893[/C][/ROW]
[ROW][C]45[/C][C]43[/C][C]46.9839975693075[/C][C]-3.98399756930755[/C][/ROW]
[ROW][C]46[/C][C]44[/C][C]45.0172850121569[/C][C]-1.01728501215685[/C][/ROW]
[ROW][C]47[/C][C]38[/C][C]47.0249415113234[/C][C]-9.02494151132343[/C][/ROW]
[ROW][C]48[/C][C]38[/C][C]47.9268770335403[/C][C]-9.9268770335403[/C][/ROW]
[ROW][C]49[/C][C]39[/C][C]57.7376485077695[/C][C]-18.7376485077695[/C][/ROW]
[ROW][C]50[/C][C]47[/C][C]41.2123687529744[/C][C]5.78763124702562[/C][/ROW]
[ROW][C]51[/C][C]41[/C][C]46.9819512891653[/C][C]-5.98195128916534[/C][/ROW]
[ROW][C]52[/C][C]36[/C][C]38.775022580714[/C][C]-2.77502258071402[/C][/ROW]
[ROW][C]53[/C][C]38[/C][C]41.6640069362547[/C][C]-3.66400693625471[/C][/ROW]
[ROW][C]54[/C][C]11[/C][C]40.6440713520483[/C][C]-29.6440713520483[/C][/ROW]
[ROW][C]55[/C][C]24[/C][C]15.3794756993723[/C][C]8.62052430062773[/C][/ROW]
[ROW][C]56[/C][C]30[/C][C]18.3695845762136[/C][C]11.6304154237864[/C][/ROW]
[ROW][C]57[/C][C]18[/C][C]29.8904874376668[/C][C]-11.8904874376668[/C][/ROW]
[ROW][C]58[/C][C]21[/C][C]21.7151636263480[/C][C]-0.715163626348044[/C][/ROW]
[ROW][C]59[/C][C]22[/C][C]22.9711162989545[/C][C]-0.97111629895446[/C][/ROW]
[ROW][C]60[/C][C]15[/C][C]27.0381213660788[/C][C]-12.0381213660788[/C][/ROW]
[ROW][C]61[/C][C]15[/C][C]26.283383542732[/C][C]-11.2833835427320[/C][/ROW]
[ROW][C]62[/C][C]16[/C][C]17.5381210367758[/C][C]-1.53812103677583[/C][/ROW]
[ROW][C]63[/C][C]26[/C][C]17.6806573942699[/C][C]8.31934260573013[/C][/ROW]
[ROW][C]64[/C][C]39[/C][C]22.5320632272767[/C][C]16.4679367727233[/C][/ROW]
[ROW][C]65[/C][C]28[/C][C]40.0448912488407[/C][C]-12.0448912488407[/C][/ROW]
[ROW][C]66[/C][C]25[/C][C]32.4286864783348[/C][C]-7.42868647833483[/C][/ROW]
[ROW][C]67[/C][C]25[/C][C]22.467995698673[/C][C]2.53200430132701[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]20.2441149134746[/C][C]-7.24411491347459[/C][/ROW]
[ROW][C]69[/C][C]20[/C][C]16.4284004800255[/C][C]3.57159951997445[/C][/ROW]
[ROW][C]70[/C][C]13[/C][C]20.1198125513801[/C][C]-7.11981255138008[/C][/ROW]
[ROW][C]71[/C][C]10[/C][C]16.1398077524889[/C][C]-6.1398077524889[/C][/ROW]
[ROW][C]72[/C][C]19[/C][C]14.3721503099422[/C][C]4.62784969005781[/C][/ROW]
[ROW][C]73[/C][C]31[/C][C]26.4602189490352[/C][C]4.53978105096484[/C][/ROW]
[ROW][C]74[/C][C]36[/C][C]28.8398970541384[/C][C]7.16010294586158[/C][/ROW]
[ROW][C]75[/C][C]26[/C][C]35.5854394083182[/C][C]-9.5854394083182[/C][/ROW]
[ROW][C]76[/C][C]33[/C][C]26.1308400737941[/C][C]6.8691599262059[/C][/ROW]
[ROW][C]77[/C][C]42[/C][C]35.8220573334454[/C][C]6.17794266655459[/C][/ROW]
[ROW][C]78[/C][C]44[/C][C]42.2964939317744[/C][C]1.70350606822559[/C][/ROW]
[ROW][C]79[/C][C]45[/C][C]35.9793799962435[/C][C]9.02062000375651[/C][/ROW]
[ROW][C]80[/C][C]42[/C][C]34.9267796796334[/C][C]7.07322032036662[/C][/ROW]
[ROW][C]81[/C][C]60[/C][C]43.6584529703194[/C][C]16.3415470296806[/C][/ROW]
[ROW][C]82[/C][C]42[/C][C]57.2809909808047[/C][C]-15.2809909808047[/C][/ROW]
[ROW][C]83[/C][C]63[/C][C]48.2458270728917[/C][C]14.7541729271083[/C][/ROW]
[ROW][C]84[/C][C]71[/C][C]70.6055311869901[/C][C]0.394468813009908[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42010&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42010&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
134736.057637861091310.9423621389087
144542.47814430007622.52185569992385
154745.91940984811661.0805901518834
164342.81199294708370.188007052916312
174848.7905776544218-0.790577654421796
184850.2640287424153-2.26402874241529
194340.14260503229172.85739496770831
204434.64042082258349.35957917741658
214645.40879189735830.59120810264168
223647.0515459369091-11.0515459369091
233241.1804620027384-9.18046200273838
241841.0580182564942-23.0580182564942
253134.1925531755259-3.19255317552587
263730.70235500421056.29764499578953
273237.0085270935604-5.00852709356036
282930.7125533282961-1.71255332829606
292933.8115427512704-4.81154275127042
304031.92743194478018.07256805521995
312631.7731366027537-5.77313660275368
322922.66361893470516.33638106529493
331930.1976331330650-11.1976331330650
343022.63552604250877.36447395749127
351230.4856433037945-18.4856433037945
362420.15548359099073.84451640900933
374033.86842008876256.13157991123752
384336.93956057262586.0604394273742
394942.98873791565766.01126208434241
404943.47026351305745.52973648694257
414853.9199901029233-5.91999010292332
423351.3365903810986-18.3365903810986
434630.982084226229715.0179157737703
444634.727449039710711.2725509602893
454346.9839975693075-3.98399756930755
464445.0172850121569-1.01728501215685
473847.0249415113234-9.02494151132343
483847.9268770335403-9.9268770335403
493957.7376485077695-18.7376485077695
504741.21236875297445.78763124702562
514146.9819512891653-5.98195128916534
523638.775022580714-2.77502258071402
533841.6640069362547-3.66400693625471
541140.6440713520483-29.6440713520483
552415.37947569937238.62052430062773
563018.369584576213611.6304154237864
571829.8904874376668-11.8904874376668
582121.7151636263480-0.715163626348044
592222.9711162989545-0.97111629895446
601527.0381213660788-12.0381213660788
611526.283383542732-11.2833835427320
621617.5381210367758-1.53812103677583
632617.68065739426998.31934260573013
643922.532063227276716.4679367727233
652840.0448912488407-12.0448912488407
662532.4286864783348-7.42868647833483
672522.4679956986732.53200430132701
681320.2441149134746-7.24411491347459
692016.42840048002553.57159951997445
701320.1198125513801-7.11981255138008
711016.1398077524889-6.1398077524889
721914.37215030994224.62784969005781
733126.46021894903524.53978105096484
743628.83989705413847.16010294586158
752635.5854394083182-9.5854394083182
763326.13084007379416.8691599262059
774235.82205733344546.17794266655459
784442.29649393177441.70350606822559
794535.97937999624359.02062000375651
804234.92677967963347.07322032036662
816043.658452970319416.3415470296806
824257.2809909808047-15.2809909808047
836348.245827072891714.7541729271083
847170.60553118699010.394468813009908







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85100.26297339180585.7994225502783114.726524233332
8693.36241886420273.7236598143192113.001177914085
8794.398881651064770.0465346184716118.751228683658
8884.69996249188258.7341826226396110.665742361125
8994.369192556881262.3566150954734126.381770018289
9096.625497546117861.1752602937451132.075734798490
9178.44880090271946.5546361139309110.342965691507
9263.13408199776833.942312418087292.3258515774488
9367.759022926178433.5893163466899101.928729505667
9468.800604442332931.5851829369906106.016025947675
9572.449131773329831.0975794990895113.80068404757
9685.554146874425436.1588133095561134.949480439295

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 100.262973391805 & 85.7994225502783 & 114.726524233332 \tabularnewline
86 & 93.362418864202 & 73.7236598143192 & 113.001177914085 \tabularnewline
87 & 94.3988816510647 & 70.0465346184716 & 118.751228683658 \tabularnewline
88 & 84.699962491882 & 58.7341826226396 & 110.665742361125 \tabularnewline
89 & 94.3691925568812 & 62.3566150954734 & 126.381770018289 \tabularnewline
90 & 96.6254975461178 & 61.1752602937451 & 132.075734798490 \tabularnewline
91 & 78.448800902719 & 46.5546361139309 & 110.342965691507 \tabularnewline
92 & 63.134081997768 & 33.9423124180872 & 92.3258515774488 \tabularnewline
93 & 67.7590229261784 & 33.5893163466899 & 101.928729505667 \tabularnewline
94 & 68.8006044423329 & 31.5851829369906 & 106.016025947675 \tabularnewline
95 & 72.4491317733298 & 31.0975794990895 & 113.80068404757 \tabularnewline
96 & 85.5541468744254 & 36.1588133095561 & 134.949480439295 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42010&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]85[/C][C]100.262973391805[/C][C]85.7994225502783[/C][C]114.726524233332[/C][/ROW]
[ROW][C]86[/C][C]93.362418864202[/C][C]73.7236598143192[/C][C]113.001177914085[/C][/ROW]
[ROW][C]87[/C][C]94.3988816510647[/C][C]70.0465346184716[/C][C]118.751228683658[/C][/ROW]
[ROW][C]88[/C][C]84.699962491882[/C][C]58.7341826226396[/C][C]110.665742361125[/C][/ROW]
[ROW][C]89[/C][C]94.3691925568812[/C][C]62.3566150954734[/C][C]126.381770018289[/C][/ROW]
[ROW][C]90[/C][C]96.6254975461178[/C][C]61.1752602937451[/C][C]132.075734798490[/C][/ROW]
[ROW][C]91[/C][C]78.448800902719[/C][C]46.5546361139309[/C][C]110.342965691507[/C][/ROW]
[ROW][C]92[/C][C]63.134081997768[/C][C]33.9423124180872[/C][C]92.3258515774488[/C][/ROW]
[ROW][C]93[/C][C]67.7590229261784[/C][C]33.5893163466899[/C][C]101.928729505667[/C][/ROW]
[ROW][C]94[/C][C]68.8006044423329[/C][C]31.5851829369906[/C][C]106.016025947675[/C][/ROW]
[ROW][C]95[/C][C]72.4491317733298[/C][C]31.0975794990895[/C][C]113.80068404757[/C][/ROW]
[ROW][C]96[/C][C]85.5541468744254[/C][C]36.1588133095561[/C][C]134.949480439295[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42010&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42010&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
85100.26297339180585.7994225502783114.726524233332
8693.36241886420273.7236598143192113.001177914085
8794.398881651064770.0465346184716118.751228683658
8884.69996249188258.7341826226396110.665742361125
8994.369192556881262.3566150954734126.381770018289
9096.625497546117861.1752602937451132.075734798490
9178.44880090271946.5546361139309110.342965691507
9263.13408199776833.942312418087292.3258515774488
9367.759022926178433.5893163466899101.928729505667
9468.800604442332931.5851829369906106.016025947675
9572.449131773329831.0975794990895113.80068404757
9685.554146874425436.1588133095561134.949480439295



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')