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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 29 Nov 2014 11:49:55 +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/2014/Nov/29/t14172618698jclduo7ylyuzgx.htm/, Retrieved Sun, 19 May 2024 15:37:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261092, Retrieved Sun, 19 May 2024 15:37:56 +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] [] [2014-11-29 11:49:55] [e9c24c4a54e855481a8eaf4353236c0f] [Current]
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Dataseries X:
24175
23658
26727
24397
25829
25503
24914
24875
25461
27647
28382
25259
28100
27900
28078
28479
28156
29219
28782
27078
30031
29579
26532
23995
22067
21818
23787
21551
21309
22395
22906
21430
23492
24144
24438
24689
24569
23754
28473
27051
27081
29635
27715
26373
28009
29472
30005
29777
28886
28549
33348
29017
30924
30435
29431
30290
31286
30622
31742
30391
30740
32086
33947
31312
33239
32362
32170
32665
31412
34891
33919
30706
32846
31368
33130
31665
33139
32201
32230
30287
31918
33853
32232
31484




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261092&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261092&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261092&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.564784640120011
beta0.0788517054574182
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.564784640120011 \tabularnewline
beta & 0.0788517054574182 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261092&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]0.564784640120011[/C][/ROW]
[ROW][C]beta[/C][C]0.0788517054574182[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261092&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261092&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
alpha0.564784640120011
beta0.0788517054574182
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
326727231413586
42439724809.0174757437-412.017475743727
52582924200.66720836631628.33279163373
62550324817.1919829301685.808017069896
72491424931.9351752888-17.9351752888215
82487524648.4162927554226.583707244565
92546124513.0886507024947.911349297632
102764724827.37028540492819.62971459514
112838226324.33974757452057.66025242551
122525927482.5968805133-2223.59688051329
132810026123.83956481351976.1604351865
142790027225.0474607195674.952539280483
152807827621.4116164487456.588383551269
162847927914.7808641118564.219135888197
172815628294.0653734464-138.065373446381
182921928270.56174353948.438256470028
192878228902.9366446613-120.936644661295
202707828925.9592065023-1847.95920650231
213003127891.28850808032139.71149191972
222957929204.0833781696374.916621830369
232653229536.8458365208-3004.84583652077
242399527826.9518692638-3831.9518692638
252206725479.2680850609-3412.26808506094
262181823216.6525170312-1398.65251703119
272378722029.0081771251757.99182287501
282155122702.4788905711-1151.47889057114
292130921681.4450060249-372.445006024911
302239521083.81094126451311.18905873552
312290621495.46033371871410.53966628134
322143022026.0387241711-596.038724171085
332349221396.78833362262095.21166637738
342414422380.82346900021763.17653099977
352443823255.85197278291182.1480272171
362468923855.3705567656833.629443234415
372456924295.1762448202273.823755179787
382375424431.0068094746-677.006809474598
392847323999.67289747624473.32710252385
402705126676.3846578602374.61534213979
412708127054.890178291326.1098217087128
422963527237.72791464572397.27208535435
432771528866.5223481704-1151.5223481704
442637328439.7300311872-2066.73003118718
452800927404.0022374408604.997762559215
462947227904.16837495561567.83162504441
473000529017.9504664566987.049533543381
482977729847.6732464319-70.6732464318666
492888630076.8630680129-1190.86306801293
502854929620.3527120884-1071.3527120884
513334829183.62809919534164.37190080468
522901731889.4174323005-2872.41743230046
533092430493.0153297192430.984670280839
543043530981.5175661493-546.517566149279
552943130893.6028136288-1462.60281362876
563029030223.161291134266.8387088657801
573128630419.5014590796866.498540920438
583062231106.066064617-484.066064616982
593174231008.2950149888733.704985011231
603039131630.9773374612-1239.9773374612
613074031083.7327611924-343.732761192445
623208631027.36548082741058.6345191726
633394731810.17917559432136.82082440568
643131233297.0976092726-1985.09760927263
653323932367.61502613871.384973869986
663236233090.2363913824-728.236391382408
673217032876.9847310625-706.984731062519
683266532644.250659971420.7493400286039
693141232823.4536702491-1411.45367024908
703489132130.91241345372760.08758654632
713391933917.31196529021.68803470983403
723070634145.884994265-3439.88499426503
733284632277.5178019274568.482198072601
743136832698.3317499308-1330.33174993082
753313031987.47944274871142.52055725134
763166532724.1374116121-1059.13741161211
773313932170.1649055601968.835094439874
783220132804.7064484643-603.706448464349
793223032524.2150788957-294.21507889573
803028732405.4170385014-2118.41703850136
813191831161.9956747897756.004325210306
823385331575.67141861492277.32858138514
833223232949.9868145573-717.986814557291
843148432600.6190911197-1116.61909111968

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 26727 & 23141 & 3586 \tabularnewline
4 & 24397 & 24809.0174757437 & -412.017475743727 \tabularnewline
5 & 25829 & 24200.6672083663 & 1628.33279163373 \tabularnewline
6 & 25503 & 24817.1919829301 & 685.808017069896 \tabularnewline
7 & 24914 & 24931.9351752888 & -17.9351752888215 \tabularnewline
8 & 24875 & 24648.4162927554 & 226.583707244565 \tabularnewline
9 & 25461 & 24513.0886507024 & 947.911349297632 \tabularnewline
10 & 27647 & 24827.3702854049 & 2819.62971459514 \tabularnewline
11 & 28382 & 26324.3397475745 & 2057.66025242551 \tabularnewline
12 & 25259 & 27482.5968805133 & -2223.59688051329 \tabularnewline
13 & 28100 & 26123.8395648135 & 1976.1604351865 \tabularnewline
14 & 27900 & 27225.0474607195 & 674.952539280483 \tabularnewline
15 & 28078 & 27621.4116164487 & 456.588383551269 \tabularnewline
16 & 28479 & 27914.7808641118 & 564.219135888197 \tabularnewline
17 & 28156 & 28294.0653734464 & -138.065373446381 \tabularnewline
18 & 29219 & 28270.56174353 & 948.438256470028 \tabularnewline
19 & 28782 & 28902.9366446613 & -120.936644661295 \tabularnewline
20 & 27078 & 28925.9592065023 & -1847.95920650231 \tabularnewline
21 & 30031 & 27891.2885080803 & 2139.71149191972 \tabularnewline
22 & 29579 & 29204.0833781696 & 374.916621830369 \tabularnewline
23 & 26532 & 29536.8458365208 & -3004.84583652077 \tabularnewline
24 & 23995 & 27826.9518692638 & -3831.9518692638 \tabularnewline
25 & 22067 & 25479.2680850609 & -3412.26808506094 \tabularnewline
26 & 21818 & 23216.6525170312 & -1398.65251703119 \tabularnewline
27 & 23787 & 22029.008177125 & 1757.99182287501 \tabularnewline
28 & 21551 & 22702.4788905711 & -1151.47889057114 \tabularnewline
29 & 21309 & 21681.4450060249 & -372.445006024911 \tabularnewline
30 & 22395 & 21083.8109412645 & 1311.18905873552 \tabularnewline
31 & 22906 & 21495.4603337187 & 1410.53966628134 \tabularnewline
32 & 21430 & 22026.0387241711 & -596.038724171085 \tabularnewline
33 & 23492 & 21396.7883336226 & 2095.21166637738 \tabularnewline
34 & 24144 & 22380.8234690002 & 1763.17653099977 \tabularnewline
35 & 24438 & 23255.8519727829 & 1182.1480272171 \tabularnewline
36 & 24689 & 23855.3705567656 & 833.629443234415 \tabularnewline
37 & 24569 & 24295.1762448202 & 273.823755179787 \tabularnewline
38 & 23754 & 24431.0068094746 & -677.006809474598 \tabularnewline
39 & 28473 & 23999.6728974762 & 4473.32710252385 \tabularnewline
40 & 27051 & 26676.3846578602 & 374.61534213979 \tabularnewline
41 & 27081 & 27054.8901782913 & 26.1098217087128 \tabularnewline
42 & 29635 & 27237.7279146457 & 2397.27208535435 \tabularnewline
43 & 27715 & 28866.5223481704 & -1151.5223481704 \tabularnewline
44 & 26373 & 28439.7300311872 & -2066.73003118718 \tabularnewline
45 & 28009 & 27404.0022374408 & 604.997762559215 \tabularnewline
46 & 29472 & 27904.1683749556 & 1567.83162504441 \tabularnewline
47 & 30005 & 29017.9504664566 & 987.049533543381 \tabularnewline
48 & 29777 & 29847.6732464319 & -70.6732464318666 \tabularnewline
49 & 28886 & 30076.8630680129 & -1190.86306801293 \tabularnewline
50 & 28549 & 29620.3527120884 & -1071.3527120884 \tabularnewline
51 & 33348 & 29183.6280991953 & 4164.37190080468 \tabularnewline
52 & 29017 & 31889.4174323005 & -2872.41743230046 \tabularnewline
53 & 30924 & 30493.0153297192 & 430.984670280839 \tabularnewline
54 & 30435 & 30981.5175661493 & -546.517566149279 \tabularnewline
55 & 29431 & 30893.6028136288 & -1462.60281362876 \tabularnewline
56 & 30290 & 30223.1612911342 & 66.8387088657801 \tabularnewline
57 & 31286 & 30419.5014590796 & 866.498540920438 \tabularnewline
58 & 30622 & 31106.066064617 & -484.066064616982 \tabularnewline
59 & 31742 & 31008.2950149888 & 733.704985011231 \tabularnewline
60 & 30391 & 31630.9773374612 & -1239.9773374612 \tabularnewline
61 & 30740 & 31083.7327611924 & -343.732761192445 \tabularnewline
62 & 32086 & 31027.3654808274 & 1058.6345191726 \tabularnewline
63 & 33947 & 31810.1791755943 & 2136.82082440568 \tabularnewline
64 & 31312 & 33297.0976092726 & -1985.09760927263 \tabularnewline
65 & 33239 & 32367.61502613 & 871.384973869986 \tabularnewline
66 & 32362 & 33090.2363913824 & -728.236391382408 \tabularnewline
67 & 32170 & 32876.9847310625 & -706.984731062519 \tabularnewline
68 & 32665 & 32644.2506599714 & 20.7493400286039 \tabularnewline
69 & 31412 & 32823.4536702491 & -1411.45367024908 \tabularnewline
70 & 34891 & 32130.9124134537 & 2760.08758654632 \tabularnewline
71 & 33919 & 33917.3119652902 & 1.68803470983403 \tabularnewline
72 & 30706 & 34145.884994265 & -3439.88499426503 \tabularnewline
73 & 32846 & 32277.5178019274 & 568.482198072601 \tabularnewline
74 & 31368 & 32698.3317499308 & -1330.33174993082 \tabularnewline
75 & 33130 & 31987.4794427487 & 1142.52055725134 \tabularnewline
76 & 31665 & 32724.1374116121 & -1059.13741161211 \tabularnewline
77 & 33139 & 32170.1649055601 & 968.835094439874 \tabularnewline
78 & 32201 & 32804.7064484643 & -603.706448464349 \tabularnewline
79 & 32230 & 32524.2150788957 & -294.21507889573 \tabularnewline
80 & 30287 & 32405.4170385014 & -2118.41703850136 \tabularnewline
81 & 31918 & 31161.9956747897 & 756.004325210306 \tabularnewline
82 & 33853 & 31575.6714186149 & 2277.32858138514 \tabularnewline
83 & 32232 & 32949.9868145573 & -717.986814557291 \tabularnewline
84 & 31484 & 32600.6190911197 & -1116.61909111968 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261092&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]26727[/C][C]23141[/C][C]3586[/C][/ROW]
[ROW][C]4[/C][C]24397[/C][C]24809.0174757437[/C][C]-412.017475743727[/C][/ROW]
[ROW][C]5[/C][C]25829[/C][C]24200.6672083663[/C][C]1628.33279163373[/C][/ROW]
[ROW][C]6[/C][C]25503[/C][C]24817.1919829301[/C][C]685.808017069896[/C][/ROW]
[ROW][C]7[/C][C]24914[/C][C]24931.9351752888[/C][C]-17.9351752888215[/C][/ROW]
[ROW][C]8[/C][C]24875[/C][C]24648.4162927554[/C][C]226.583707244565[/C][/ROW]
[ROW][C]9[/C][C]25461[/C][C]24513.0886507024[/C][C]947.911349297632[/C][/ROW]
[ROW][C]10[/C][C]27647[/C][C]24827.3702854049[/C][C]2819.62971459514[/C][/ROW]
[ROW][C]11[/C][C]28382[/C][C]26324.3397475745[/C][C]2057.66025242551[/C][/ROW]
[ROW][C]12[/C][C]25259[/C][C]27482.5968805133[/C][C]-2223.59688051329[/C][/ROW]
[ROW][C]13[/C][C]28100[/C][C]26123.8395648135[/C][C]1976.1604351865[/C][/ROW]
[ROW][C]14[/C][C]27900[/C][C]27225.0474607195[/C][C]674.952539280483[/C][/ROW]
[ROW][C]15[/C][C]28078[/C][C]27621.4116164487[/C][C]456.588383551269[/C][/ROW]
[ROW][C]16[/C][C]28479[/C][C]27914.7808641118[/C][C]564.219135888197[/C][/ROW]
[ROW][C]17[/C][C]28156[/C][C]28294.0653734464[/C][C]-138.065373446381[/C][/ROW]
[ROW][C]18[/C][C]29219[/C][C]28270.56174353[/C][C]948.438256470028[/C][/ROW]
[ROW][C]19[/C][C]28782[/C][C]28902.9366446613[/C][C]-120.936644661295[/C][/ROW]
[ROW][C]20[/C][C]27078[/C][C]28925.9592065023[/C][C]-1847.95920650231[/C][/ROW]
[ROW][C]21[/C][C]30031[/C][C]27891.2885080803[/C][C]2139.71149191972[/C][/ROW]
[ROW][C]22[/C][C]29579[/C][C]29204.0833781696[/C][C]374.916621830369[/C][/ROW]
[ROW][C]23[/C][C]26532[/C][C]29536.8458365208[/C][C]-3004.84583652077[/C][/ROW]
[ROW][C]24[/C][C]23995[/C][C]27826.9518692638[/C][C]-3831.9518692638[/C][/ROW]
[ROW][C]25[/C][C]22067[/C][C]25479.2680850609[/C][C]-3412.26808506094[/C][/ROW]
[ROW][C]26[/C][C]21818[/C][C]23216.6525170312[/C][C]-1398.65251703119[/C][/ROW]
[ROW][C]27[/C][C]23787[/C][C]22029.008177125[/C][C]1757.99182287501[/C][/ROW]
[ROW][C]28[/C][C]21551[/C][C]22702.4788905711[/C][C]-1151.47889057114[/C][/ROW]
[ROW][C]29[/C][C]21309[/C][C]21681.4450060249[/C][C]-372.445006024911[/C][/ROW]
[ROW][C]30[/C][C]22395[/C][C]21083.8109412645[/C][C]1311.18905873552[/C][/ROW]
[ROW][C]31[/C][C]22906[/C][C]21495.4603337187[/C][C]1410.53966628134[/C][/ROW]
[ROW][C]32[/C][C]21430[/C][C]22026.0387241711[/C][C]-596.038724171085[/C][/ROW]
[ROW][C]33[/C][C]23492[/C][C]21396.7883336226[/C][C]2095.21166637738[/C][/ROW]
[ROW][C]34[/C][C]24144[/C][C]22380.8234690002[/C][C]1763.17653099977[/C][/ROW]
[ROW][C]35[/C][C]24438[/C][C]23255.8519727829[/C][C]1182.1480272171[/C][/ROW]
[ROW][C]36[/C][C]24689[/C][C]23855.3705567656[/C][C]833.629443234415[/C][/ROW]
[ROW][C]37[/C][C]24569[/C][C]24295.1762448202[/C][C]273.823755179787[/C][/ROW]
[ROW][C]38[/C][C]23754[/C][C]24431.0068094746[/C][C]-677.006809474598[/C][/ROW]
[ROW][C]39[/C][C]28473[/C][C]23999.6728974762[/C][C]4473.32710252385[/C][/ROW]
[ROW][C]40[/C][C]27051[/C][C]26676.3846578602[/C][C]374.61534213979[/C][/ROW]
[ROW][C]41[/C][C]27081[/C][C]27054.8901782913[/C][C]26.1098217087128[/C][/ROW]
[ROW][C]42[/C][C]29635[/C][C]27237.7279146457[/C][C]2397.27208535435[/C][/ROW]
[ROW][C]43[/C][C]27715[/C][C]28866.5223481704[/C][C]-1151.5223481704[/C][/ROW]
[ROW][C]44[/C][C]26373[/C][C]28439.7300311872[/C][C]-2066.73003118718[/C][/ROW]
[ROW][C]45[/C][C]28009[/C][C]27404.0022374408[/C][C]604.997762559215[/C][/ROW]
[ROW][C]46[/C][C]29472[/C][C]27904.1683749556[/C][C]1567.83162504441[/C][/ROW]
[ROW][C]47[/C][C]30005[/C][C]29017.9504664566[/C][C]987.049533543381[/C][/ROW]
[ROW][C]48[/C][C]29777[/C][C]29847.6732464319[/C][C]-70.6732464318666[/C][/ROW]
[ROW][C]49[/C][C]28886[/C][C]30076.8630680129[/C][C]-1190.86306801293[/C][/ROW]
[ROW][C]50[/C][C]28549[/C][C]29620.3527120884[/C][C]-1071.3527120884[/C][/ROW]
[ROW][C]51[/C][C]33348[/C][C]29183.6280991953[/C][C]4164.37190080468[/C][/ROW]
[ROW][C]52[/C][C]29017[/C][C]31889.4174323005[/C][C]-2872.41743230046[/C][/ROW]
[ROW][C]53[/C][C]30924[/C][C]30493.0153297192[/C][C]430.984670280839[/C][/ROW]
[ROW][C]54[/C][C]30435[/C][C]30981.5175661493[/C][C]-546.517566149279[/C][/ROW]
[ROW][C]55[/C][C]29431[/C][C]30893.6028136288[/C][C]-1462.60281362876[/C][/ROW]
[ROW][C]56[/C][C]30290[/C][C]30223.1612911342[/C][C]66.8387088657801[/C][/ROW]
[ROW][C]57[/C][C]31286[/C][C]30419.5014590796[/C][C]866.498540920438[/C][/ROW]
[ROW][C]58[/C][C]30622[/C][C]31106.066064617[/C][C]-484.066064616982[/C][/ROW]
[ROW][C]59[/C][C]31742[/C][C]31008.2950149888[/C][C]733.704985011231[/C][/ROW]
[ROW][C]60[/C][C]30391[/C][C]31630.9773374612[/C][C]-1239.9773374612[/C][/ROW]
[ROW][C]61[/C][C]30740[/C][C]31083.7327611924[/C][C]-343.732761192445[/C][/ROW]
[ROW][C]62[/C][C]32086[/C][C]31027.3654808274[/C][C]1058.6345191726[/C][/ROW]
[ROW][C]63[/C][C]33947[/C][C]31810.1791755943[/C][C]2136.82082440568[/C][/ROW]
[ROW][C]64[/C][C]31312[/C][C]33297.0976092726[/C][C]-1985.09760927263[/C][/ROW]
[ROW][C]65[/C][C]33239[/C][C]32367.61502613[/C][C]871.384973869986[/C][/ROW]
[ROW][C]66[/C][C]32362[/C][C]33090.2363913824[/C][C]-728.236391382408[/C][/ROW]
[ROW][C]67[/C][C]32170[/C][C]32876.9847310625[/C][C]-706.984731062519[/C][/ROW]
[ROW][C]68[/C][C]32665[/C][C]32644.2506599714[/C][C]20.7493400286039[/C][/ROW]
[ROW][C]69[/C][C]31412[/C][C]32823.4536702491[/C][C]-1411.45367024908[/C][/ROW]
[ROW][C]70[/C][C]34891[/C][C]32130.9124134537[/C][C]2760.08758654632[/C][/ROW]
[ROW][C]71[/C][C]33919[/C][C]33917.3119652902[/C][C]1.68803470983403[/C][/ROW]
[ROW][C]72[/C][C]30706[/C][C]34145.884994265[/C][C]-3439.88499426503[/C][/ROW]
[ROW][C]73[/C][C]32846[/C][C]32277.5178019274[/C][C]568.482198072601[/C][/ROW]
[ROW][C]74[/C][C]31368[/C][C]32698.3317499308[/C][C]-1330.33174993082[/C][/ROW]
[ROW][C]75[/C][C]33130[/C][C]31987.4794427487[/C][C]1142.52055725134[/C][/ROW]
[ROW][C]76[/C][C]31665[/C][C]32724.1374116121[/C][C]-1059.13741161211[/C][/ROW]
[ROW][C]77[/C][C]33139[/C][C]32170.1649055601[/C][C]968.835094439874[/C][/ROW]
[ROW][C]78[/C][C]32201[/C][C]32804.7064484643[/C][C]-603.706448464349[/C][/ROW]
[ROW][C]79[/C][C]32230[/C][C]32524.2150788957[/C][C]-294.21507889573[/C][/ROW]
[ROW][C]80[/C][C]30287[/C][C]32405.4170385014[/C][C]-2118.41703850136[/C][/ROW]
[ROW][C]81[/C][C]31918[/C][C]31161.9956747897[/C][C]756.004325210306[/C][/ROW]
[ROW][C]82[/C][C]33853[/C][C]31575.6714186149[/C][C]2277.32858138514[/C][/ROW]
[ROW][C]83[/C][C]32232[/C][C]32949.9868145573[/C][C]-717.986814557291[/C][/ROW]
[ROW][C]84[/C][C]31484[/C][C]32600.6190911197[/C][C]-1116.61909111968[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261092&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261092&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
326727231413586
42439724809.0174757437-412.017475743727
52582924200.66720836631628.33279163373
62550324817.1919829301685.808017069896
72491424931.9351752888-17.9351752888215
82487524648.4162927554226.583707244565
92546124513.0886507024947.911349297632
102764724827.37028540492819.62971459514
112838226324.33974757452057.66025242551
122525927482.5968805133-2223.59688051329
132810026123.83956481351976.1604351865
142790027225.0474607195674.952539280483
152807827621.4116164487456.588383551269
162847927914.7808641118564.219135888197
172815628294.0653734464-138.065373446381
182921928270.56174353948.438256470028
192878228902.9366446613-120.936644661295
202707828925.9592065023-1847.95920650231
213003127891.28850808032139.71149191972
222957929204.0833781696374.916621830369
232653229536.8458365208-3004.84583652077
242399527826.9518692638-3831.9518692638
252206725479.2680850609-3412.26808506094
262181823216.6525170312-1398.65251703119
272378722029.0081771251757.99182287501
282155122702.4788905711-1151.47889057114
292130921681.4450060249-372.445006024911
302239521083.81094126451311.18905873552
312290621495.46033371871410.53966628134
322143022026.0387241711-596.038724171085
332349221396.78833362262095.21166637738
342414422380.82346900021763.17653099977
352443823255.85197278291182.1480272171
362468923855.3705567656833.629443234415
372456924295.1762448202273.823755179787
382375424431.0068094746-677.006809474598
392847323999.67289747624473.32710252385
402705126676.3846578602374.61534213979
412708127054.890178291326.1098217087128
422963527237.72791464572397.27208535435
432771528866.5223481704-1151.5223481704
442637328439.7300311872-2066.73003118718
452800927404.0022374408604.997762559215
462947227904.16837495561567.83162504441
473000529017.9504664566987.049533543381
482977729847.6732464319-70.6732464318666
492888630076.8630680129-1190.86306801293
502854929620.3527120884-1071.3527120884
513334829183.62809919534164.37190080468
522901731889.4174323005-2872.41743230046
533092430493.0153297192430.984670280839
543043530981.5175661493-546.517566149279
552943130893.6028136288-1462.60281362876
563029030223.161291134266.8387088657801
573128630419.5014590796866.498540920438
583062231106.066064617-484.066064616982
593174231008.2950149888733.704985011231
603039131630.9773374612-1239.9773374612
613074031083.7327611924-343.732761192445
623208631027.36548082741058.6345191726
633394731810.17917559432136.82082440568
643131233297.0976092726-1985.09760927263
653323932367.61502613871.384973869986
663236233090.2363913824-728.236391382408
673217032876.9847310625-706.984731062519
683266532644.250659971420.7493400286039
693141232823.4536702491-1411.45367024908
703489132130.91241345372760.08758654632
713391933917.31196529021.68803470983403
723070634145.884994265-3439.88499426503
733284632277.5178019274568.482198072601
743136832698.3317499308-1330.33174993082
753313031987.47944274871142.52055725134
763166532724.1374116121-1059.13741161211
773313932170.1649055601968.835094439874
783220132804.7064484643-603.706448464349
793223032524.2150788957-294.21507889573
803028732405.4170385014-2118.41703850136
813191831161.9956747897756.004325210306
823385331575.67141861492277.32858138514
833223232949.9868145573-717.986814557291
843148432600.6190911197-1116.61909111968







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8531976.382207063928727.247193713135225.5172204148
8631982.794634537328178.018011709835787.5712573649
8731989.207062010827631.496337650236346.9177863713
8831995.619489484227082.503774838436908.7352041299
8932002.031916957626527.966716192137476.097117723
9032008.44434443125965.963974984738050.9247138773
9132014.856771904425395.25569087438634.4578529348
9232021.269199377824815.027941934739227.510456821
9332027.681626851224224.744510074339830.6187436282
9432034.094054324723624.056176680140444.1319319692
9532040.506481798123012.74284436641068.2701192302
9632046.918909271522390.675328774441703.1624897686

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 31976.3822070639 & 28727.2471937131 & 35225.5172204148 \tabularnewline
86 & 31982.7946345373 & 28178.0180117098 & 35787.5712573649 \tabularnewline
87 & 31989.2070620108 & 27631.4963376502 & 36346.9177863713 \tabularnewline
88 & 31995.6194894842 & 27082.5037748384 & 36908.7352041299 \tabularnewline
89 & 32002.0319169576 & 26527.9667161921 & 37476.097117723 \tabularnewline
90 & 32008.444344431 & 25965.9639749847 & 38050.9247138773 \tabularnewline
91 & 32014.8567719044 & 25395.255690874 & 38634.4578529348 \tabularnewline
92 & 32021.2691993778 & 24815.0279419347 & 39227.510456821 \tabularnewline
93 & 32027.6816268512 & 24224.7445100743 & 39830.6187436282 \tabularnewline
94 & 32034.0940543247 & 23624.0561766801 & 40444.1319319692 \tabularnewline
95 & 32040.5064817981 & 23012.742844366 & 41068.2701192302 \tabularnewline
96 & 32046.9189092715 & 22390.6753287744 & 41703.1624897686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261092&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]31976.3822070639[/C][C]28727.2471937131[/C][C]35225.5172204148[/C][/ROW]
[ROW][C]86[/C][C]31982.7946345373[/C][C]28178.0180117098[/C][C]35787.5712573649[/C][/ROW]
[ROW][C]87[/C][C]31989.2070620108[/C][C]27631.4963376502[/C][C]36346.9177863713[/C][/ROW]
[ROW][C]88[/C][C]31995.6194894842[/C][C]27082.5037748384[/C][C]36908.7352041299[/C][/ROW]
[ROW][C]89[/C][C]32002.0319169576[/C][C]26527.9667161921[/C][C]37476.097117723[/C][/ROW]
[ROW][C]90[/C][C]32008.444344431[/C][C]25965.9639749847[/C][C]38050.9247138773[/C][/ROW]
[ROW][C]91[/C][C]32014.8567719044[/C][C]25395.255690874[/C][C]38634.4578529348[/C][/ROW]
[ROW][C]92[/C][C]32021.2691993778[/C][C]24815.0279419347[/C][C]39227.510456821[/C][/ROW]
[ROW][C]93[/C][C]32027.6816268512[/C][C]24224.7445100743[/C][C]39830.6187436282[/C][/ROW]
[ROW][C]94[/C][C]32034.0940543247[/C][C]23624.0561766801[/C][C]40444.1319319692[/C][/ROW]
[ROW][C]95[/C][C]32040.5064817981[/C][C]23012.742844366[/C][C]41068.2701192302[/C][/ROW]
[ROW][C]96[/C][C]32046.9189092715[/C][C]22390.6753287744[/C][C]41703.1624897686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261092&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261092&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
8531976.382207063928727.247193713135225.5172204148
8631982.794634537328178.018011709835787.5712573649
8731989.207062010827631.496337650236346.9177863713
8831995.619489484227082.503774838436908.7352041299
8932002.031916957626527.966716192137476.097117723
9032008.44434443125965.963974984738050.9247138773
9132014.856771904425395.25569087438634.4578529348
9232021.269199377824815.027941934739227.510456821
9332027.681626851224224.744510074339830.6187436282
9432034.094054324723624.056176680140444.1319319692
9532040.506481798123012.74284436641068.2701192302
9632046.918909271522390.675328774441703.1624897686



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')