Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 06 Jun 2010 18:49:12 +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/2010/Jun/06/t1275850173lguz0w4xau2xvtx.htm/, Retrieved Sat, 27 Apr 2024 21:31:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77763, Retrieved Sat, 27 Apr 2024 21:31:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Opgave 6 Oefening 2] [2010-05-05 09:51:48] [e895dcb2cc7dd335cb0a684691a903a1]
- RMP     [Exponential Smoothing] [Opgave 10 oefening 2] [2010-06-06 18:49:12] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
22577.0
22792.0
23932.0
22321.0
21102.0
22824.0
23129.0
23604.0
24746.0
26911.0
27909.0
28922.0
29800.0
30506.0
30771.0
31976.0
33749.0
34371.0
33246.0
35072.0
35762.0
36179.0
37433.0
38298.0
37559.0
37511.0
39364.0
40084.0
42712.0
41938.0
40799.0
38568.0
41134.0
43955.0
43607.0
45082.0
46464.0
46496.0
46774.0
47890.0
45740.0
42660.0
39190.0
39010.0
41150.0
42530.0
44710.0
46620.0
44560.0
46120.0
48060.0
51970.0
57720.0
63490.0
65370.0
64260.0
58700.0
58630.0
59803.0
59266.0
60570.0
63062.0
63846.0
64726.0
63460.0
65220.0
66659.0
66871.0
65672.0
67182.0
68292.0
68318.0
69530.0
70500.0
72044.0
73811.0
76018.0
77818.0
79455.0
81408.0
81815.0




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77763&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77763&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77763&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0311447030224647
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0311447030224647 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77763&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]0.0311447030224647[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77763&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77763&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
beta0.0311447030224647
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32393223007925
42232124175.8088502958-1854.80885029578
52110222507.0413794899-1405.04137948988
62282421244.28178299141579.71821700861
72312923015.4816377193113.518362280698
82360423324.0171334001279.982866599868
92474623807.7371166318938.262883368236
102691124978.95903549131932.04096450873
112790927204.1318775581704.868122441872
122892228224.0847859016697.915214098415
132980029258.8211479795541.178852020461
143050630153.6760026078352.323997392246
153077130870.6490288742-99.6490288742243
163197631132.5454894635843.454510536543
173374932363.81462970711385.18537029292
183437134179.9558166959191.04418330409
193324634807.9058310491-1561.90583104909
203507233634.2607377921437.73926220799
213576235505.0387001372256.961299862785
223617936203.0416835097-24.0416835097058
233743336619.2929124166813.70708758336
243829837898.6355780067399.364421993305
253755938776.0736643274-1217.07366432741
263751137999.1682664955-488.168266495471
273936437935.96441081051428.03558918952
284008439833.4401551413250.559844858697
294271240561.24376709882150.75623290122
304193843256.2284312462-1318.2284312462
314079942441.1725982393-1642.17259823927
323856841251.0276203555-2683.02762035548
334113438936.46552191842197.53447808156
344395541570.90708061992384.09291938008
354360744466.158946572-859.158946571966
364508244091.4006963319990.59930366811
374646445597.2526174589866.747382541107
384649647006.2472072836-510.247207283639
394677447022.3557095447-248.355709544747
404789047292.620744727597.379255272957
414574048427.2259442243-2687.22594422429
424266046193.5330902372-3533.53309023717
433919043003.4822515217-3813.48225152168
443901039414.7124793166-404.7124793166
454115039222.10782933881927.8921706612
464253041422.15145845341107.84854154663
474471042836.65507227371873.34492772628
484662045074.99984370641545.00015629361
494456047033.1184147438-2473.11841474382
504612044896.09387617721223.90612382277
514806046494.21206893111565.78793106893
525197048482.97806904043487.02193095963
535772052501.58033151295218.41966848707
546349058414.10646233455075.89353766546
556537064342.19365913881027.80634086121
566426066254.2043823895-1994.20438238951
575870065082.0954791339-6382.0954791339
585863059323.3270107753-693.327010775254
595980359231.7335469272571.266453072793
605926660422.5254709549-1156.52547095485
616057059849.505828624720.494171375947
626306261175.9454056211886.05459437903
636384663726.686015847119.313984152941
646472664514.40201445211.59798555007
656346065400.99217087-1940.99217087004
666522064074.54054613941145.45945386063
676665965870.2155406541788.784459345872
686687167333.7819983892-462.781998389197
696567267531.3687904852-1859.36879048521
706718266274.4593016963907.540698303681
716829267812.7243872258479.275612774218
726831868937.6512838515-619.651283851548
736953068944.3524286385585.647571361493
747050070174.5922483244325.407751675622
757204471154.7269761115889.273023888469
767381172726.42312034641084.57687965357
777601874527.20194516831490.79805483173
787781876780.63240785251037.36759214754
797945578612.940913435842.059086564972
808140880276.16659361351131.83340638653
818181582264.4172089263-449.417208926272

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 23932 & 23007 & 925 \tabularnewline
4 & 22321 & 24175.8088502958 & -1854.80885029578 \tabularnewline
5 & 21102 & 22507.0413794899 & -1405.04137948988 \tabularnewline
6 & 22824 & 21244.2817829914 & 1579.71821700861 \tabularnewline
7 & 23129 & 23015.4816377193 & 113.518362280698 \tabularnewline
8 & 23604 & 23324.0171334001 & 279.982866599868 \tabularnewline
9 & 24746 & 23807.7371166318 & 938.262883368236 \tabularnewline
10 & 26911 & 24978.9590354913 & 1932.04096450873 \tabularnewline
11 & 27909 & 27204.1318775581 & 704.868122441872 \tabularnewline
12 & 28922 & 28224.0847859016 & 697.915214098415 \tabularnewline
13 & 29800 & 29258.8211479795 & 541.178852020461 \tabularnewline
14 & 30506 & 30153.6760026078 & 352.323997392246 \tabularnewline
15 & 30771 & 30870.6490288742 & -99.6490288742243 \tabularnewline
16 & 31976 & 31132.5454894635 & 843.454510536543 \tabularnewline
17 & 33749 & 32363.8146297071 & 1385.18537029292 \tabularnewline
18 & 34371 & 34179.9558166959 & 191.04418330409 \tabularnewline
19 & 33246 & 34807.9058310491 & -1561.90583104909 \tabularnewline
20 & 35072 & 33634.260737792 & 1437.73926220799 \tabularnewline
21 & 35762 & 35505.0387001372 & 256.961299862785 \tabularnewline
22 & 36179 & 36203.0416835097 & -24.0416835097058 \tabularnewline
23 & 37433 & 36619.2929124166 & 813.70708758336 \tabularnewline
24 & 38298 & 37898.6355780067 & 399.364421993305 \tabularnewline
25 & 37559 & 38776.0736643274 & -1217.07366432741 \tabularnewline
26 & 37511 & 37999.1682664955 & -488.168266495471 \tabularnewline
27 & 39364 & 37935.9644108105 & 1428.03558918952 \tabularnewline
28 & 40084 & 39833.4401551413 & 250.559844858697 \tabularnewline
29 & 42712 & 40561.2437670988 & 2150.75623290122 \tabularnewline
30 & 41938 & 43256.2284312462 & -1318.2284312462 \tabularnewline
31 & 40799 & 42441.1725982393 & -1642.17259823927 \tabularnewline
32 & 38568 & 41251.0276203555 & -2683.02762035548 \tabularnewline
33 & 41134 & 38936.4655219184 & 2197.53447808156 \tabularnewline
34 & 43955 & 41570.9070806199 & 2384.09291938008 \tabularnewline
35 & 43607 & 44466.158946572 & -859.158946571966 \tabularnewline
36 & 45082 & 44091.4006963319 & 990.59930366811 \tabularnewline
37 & 46464 & 45597.2526174589 & 866.747382541107 \tabularnewline
38 & 46496 & 47006.2472072836 & -510.247207283639 \tabularnewline
39 & 46774 & 47022.3557095447 & -248.355709544747 \tabularnewline
40 & 47890 & 47292.620744727 & 597.379255272957 \tabularnewline
41 & 45740 & 48427.2259442243 & -2687.22594422429 \tabularnewline
42 & 42660 & 46193.5330902372 & -3533.53309023717 \tabularnewline
43 & 39190 & 43003.4822515217 & -3813.48225152168 \tabularnewline
44 & 39010 & 39414.7124793166 & -404.7124793166 \tabularnewline
45 & 41150 & 39222.1078293388 & 1927.8921706612 \tabularnewline
46 & 42530 & 41422.1514584534 & 1107.84854154663 \tabularnewline
47 & 44710 & 42836.6550722737 & 1873.34492772628 \tabularnewline
48 & 46620 & 45074.9998437064 & 1545.00015629361 \tabularnewline
49 & 44560 & 47033.1184147438 & -2473.11841474382 \tabularnewline
50 & 46120 & 44896.0938761772 & 1223.90612382277 \tabularnewline
51 & 48060 & 46494.2120689311 & 1565.78793106893 \tabularnewline
52 & 51970 & 48482.9780690404 & 3487.02193095963 \tabularnewline
53 & 57720 & 52501.5803315129 & 5218.41966848707 \tabularnewline
54 & 63490 & 58414.1064623345 & 5075.89353766546 \tabularnewline
55 & 65370 & 64342.1936591388 & 1027.80634086121 \tabularnewline
56 & 64260 & 66254.2043823895 & -1994.20438238951 \tabularnewline
57 & 58700 & 65082.0954791339 & -6382.0954791339 \tabularnewline
58 & 58630 & 59323.3270107753 & -693.327010775254 \tabularnewline
59 & 59803 & 59231.7335469272 & 571.266453072793 \tabularnewline
60 & 59266 & 60422.5254709549 & -1156.52547095485 \tabularnewline
61 & 60570 & 59849.505828624 & 720.494171375947 \tabularnewline
62 & 63062 & 61175.945405621 & 1886.05459437903 \tabularnewline
63 & 63846 & 63726.686015847 & 119.313984152941 \tabularnewline
64 & 64726 & 64514.40201445 & 211.59798555007 \tabularnewline
65 & 63460 & 65400.99217087 & -1940.99217087004 \tabularnewline
66 & 65220 & 64074.5405461394 & 1145.45945386063 \tabularnewline
67 & 66659 & 65870.2155406541 & 788.784459345872 \tabularnewline
68 & 66871 & 67333.7819983892 & -462.781998389197 \tabularnewline
69 & 65672 & 67531.3687904852 & -1859.36879048521 \tabularnewline
70 & 67182 & 66274.4593016963 & 907.540698303681 \tabularnewline
71 & 68292 & 67812.7243872258 & 479.275612774218 \tabularnewline
72 & 68318 & 68937.6512838515 & -619.651283851548 \tabularnewline
73 & 69530 & 68944.3524286385 & 585.647571361493 \tabularnewline
74 & 70500 & 70174.5922483244 & 325.407751675622 \tabularnewline
75 & 72044 & 71154.7269761115 & 889.273023888469 \tabularnewline
76 & 73811 & 72726.4231203464 & 1084.57687965357 \tabularnewline
77 & 76018 & 74527.2019451683 & 1490.79805483173 \tabularnewline
78 & 77818 & 76780.6324078525 & 1037.36759214754 \tabularnewline
79 & 79455 & 78612.940913435 & 842.059086564972 \tabularnewline
80 & 81408 & 80276.1665936135 & 1131.83340638653 \tabularnewline
81 & 81815 & 82264.4172089263 & -449.417208926272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77763&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]23932[/C][C]23007[/C][C]925[/C][/ROW]
[ROW][C]4[/C][C]22321[/C][C]24175.8088502958[/C][C]-1854.80885029578[/C][/ROW]
[ROW][C]5[/C][C]21102[/C][C]22507.0413794899[/C][C]-1405.04137948988[/C][/ROW]
[ROW][C]6[/C][C]22824[/C][C]21244.2817829914[/C][C]1579.71821700861[/C][/ROW]
[ROW][C]7[/C][C]23129[/C][C]23015.4816377193[/C][C]113.518362280698[/C][/ROW]
[ROW][C]8[/C][C]23604[/C][C]23324.0171334001[/C][C]279.982866599868[/C][/ROW]
[ROW][C]9[/C][C]24746[/C][C]23807.7371166318[/C][C]938.262883368236[/C][/ROW]
[ROW][C]10[/C][C]26911[/C][C]24978.9590354913[/C][C]1932.04096450873[/C][/ROW]
[ROW][C]11[/C][C]27909[/C][C]27204.1318775581[/C][C]704.868122441872[/C][/ROW]
[ROW][C]12[/C][C]28922[/C][C]28224.0847859016[/C][C]697.915214098415[/C][/ROW]
[ROW][C]13[/C][C]29800[/C][C]29258.8211479795[/C][C]541.178852020461[/C][/ROW]
[ROW][C]14[/C][C]30506[/C][C]30153.6760026078[/C][C]352.323997392246[/C][/ROW]
[ROW][C]15[/C][C]30771[/C][C]30870.6490288742[/C][C]-99.6490288742243[/C][/ROW]
[ROW][C]16[/C][C]31976[/C][C]31132.5454894635[/C][C]843.454510536543[/C][/ROW]
[ROW][C]17[/C][C]33749[/C][C]32363.8146297071[/C][C]1385.18537029292[/C][/ROW]
[ROW][C]18[/C][C]34371[/C][C]34179.9558166959[/C][C]191.04418330409[/C][/ROW]
[ROW][C]19[/C][C]33246[/C][C]34807.9058310491[/C][C]-1561.90583104909[/C][/ROW]
[ROW][C]20[/C][C]35072[/C][C]33634.260737792[/C][C]1437.73926220799[/C][/ROW]
[ROW][C]21[/C][C]35762[/C][C]35505.0387001372[/C][C]256.961299862785[/C][/ROW]
[ROW][C]22[/C][C]36179[/C][C]36203.0416835097[/C][C]-24.0416835097058[/C][/ROW]
[ROW][C]23[/C][C]37433[/C][C]36619.2929124166[/C][C]813.70708758336[/C][/ROW]
[ROW][C]24[/C][C]38298[/C][C]37898.6355780067[/C][C]399.364421993305[/C][/ROW]
[ROW][C]25[/C][C]37559[/C][C]38776.0736643274[/C][C]-1217.07366432741[/C][/ROW]
[ROW][C]26[/C][C]37511[/C][C]37999.1682664955[/C][C]-488.168266495471[/C][/ROW]
[ROW][C]27[/C][C]39364[/C][C]37935.9644108105[/C][C]1428.03558918952[/C][/ROW]
[ROW][C]28[/C][C]40084[/C][C]39833.4401551413[/C][C]250.559844858697[/C][/ROW]
[ROW][C]29[/C][C]42712[/C][C]40561.2437670988[/C][C]2150.75623290122[/C][/ROW]
[ROW][C]30[/C][C]41938[/C][C]43256.2284312462[/C][C]-1318.2284312462[/C][/ROW]
[ROW][C]31[/C][C]40799[/C][C]42441.1725982393[/C][C]-1642.17259823927[/C][/ROW]
[ROW][C]32[/C][C]38568[/C][C]41251.0276203555[/C][C]-2683.02762035548[/C][/ROW]
[ROW][C]33[/C][C]41134[/C][C]38936.4655219184[/C][C]2197.53447808156[/C][/ROW]
[ROW][C]34[/C][C]43955[/C][C]41570.9070806199[/C][C]2384.09291938008[/C][/ROW]
[ROW][C]35[/C][C]43607[/C][C]44466.158946572[/C][C]-859.158946571966[/C][/ROW]
[ROW][C]36[/C][C]45082[/C][C]44091.4006963319[/C][C]990.59930366811[/C][/ROW]
[ROW][C]37[/C][C]46464[/C][C]45597.2526174589[/C][C]866.747382541107[/C][/ROW]
[ROW][C]38[/C][C]46496[/C][C]47006.2472072836[/C][C]-510.247207283639[/C][/ROW]
[ROW][C]39[/C][C]46774[/C][C]47022.3557095447[/C][C]-248.355709544747[/C][/ROW]
[ROW][C]40[/C][C]47890[/C][C]47292.620744727[/C][C]597.379255272957[/C][/ROW]
[ROW][C]41[/C][C]45740[/C][C]48427.2259442243[/C][C]-2687.22594422429[/C][/ROW]
[ROW][C]42[/C][C]42660[/C][C]46193.5330902372[/C][C]-3533.53309023717[/C][/ROW]
[ROW][C]43[/C][C]39190[/C][C]43003.4822515217[/C][C]-3813.48225152168[/C][/ROW]
[ROW][C]44[/C][C]39010[/C][C]39414.7124793166[/C][C]-404.7124793166[/C][/ROW]
[ROW][C]45[/C][C]41150[/C][C]39222.1078293388[/C][C]1927.8921706612[/C][/ROW]
[ROW][C]46[/C][C]42530[/C][C]41422.1514584534[/C][C]1107.84854154663[/C][/ROW]
[ROW][C]47[/C][C]44710[/C][C]42836.6550722737[/C][C]1873.34492772628[/C][/ROW]
[ROW][C]48[/C][C]46620[/C][C]45074.9998437064[/C][C]1545.00015629361[/C][/ROW]
[ROW][C]49[/C][C]44560[/C][C]47033.1184147438[/C][C]-2473.11841474382[/C][/ROW]
[ROW][C]50[/C][C]46120[/C][C]44896.0938761772[/C][C]1223.90612382277[/C][/ROW]
[ROW][C]51[/C][C]48060[/C][C]46494.2120689311[/C][C]1565.78793106893[/C][/ROW]
[ROW][C]52[/C][C]51970[/C][C]48482.9780690404[/C][C]3487.02193095963[/C][/ROW]
[ROW][C]53[/C][C]57720[/C][C]52501.5803315129[/C][C]5218.41966848707[/C][/ROW]
[ROW][C]54[/C][C]63490[/C][C]58414.1064623345[/C][C]5075.89353766546[/C][/ROW]
[ROW][C]55[/C][C]65370[/C][C]64342.1936591388[/C][C]1027.80634086121[/C][/ROW]
[ROW][C]56[/C][C]64260[/C][C]66254.2043823895[/C][C]-1994.20438238951[/C][/ROW]
[ROW][C]57[/C][C]58700[/C][C]65082.0954791339[/C][C]-6382.0954791339[/C][/ROW]
[ROW][C]58[/C][C]58630[/C][C]59323.3270107753[/C][C]-693.327010775254[/C][/ROW]
[ROW][C]59[/C][C]59803[/C][C]59231.7335469272[/C][C]571.266453072793[/C][/ROW]
[ROW][C]60[/C][C]59266[/C][C]60422.5254709549[/C][C]-1156.52547095485[/C][/ROW]
[ROW][C]61[/C][C]60570[/C][C]59849.505828624[/C][C]720.494171375947[/C][/ROW]
[ROW][C]62[/C][C]63062[/C][C]61175.945405621[/C][C]1886.05459437903[/C][/ROW]
[ROW][C]63[/C][C]63846[/C][C]63726.686015847[/C][C]119.313984152941[/C][/ROW]
[ROW][C]64[/C][C]64726[/C][C]64514.40201445[/C][C]211.59798555007[/C][/ROW]
[ROW][C]65[/C][C]63460[/C][C]65400.99217087[/C][C]-1940.99217087004[/C][/ROW]
[ROW][C]66[/C][C]65220[/C][C]64074.5405461394[/C][C]1145.45945386063[/C][/ROW]
[ROW][C]67[/C][C]66659[/C][C]65870.2155406541[/C][C]788.784459345872[/C][/ROW]
[ROW][C]68[/C][C]66871[/C][C]67333.7819983892[/C][C]-462.781998389197[/C][/ROW]
[ROW][C]69[/C][C]65672[/C][C]67531.3687904852[/C][C]-1859.36879048521[/C][/ROW]
[ROW][C]70[/C][C]67182[/C][C]66274.4593016963[/C][C]907.540698303681[/C][/ROW]
[ROW][C]71[/C][C]68292[/C][C]67812.7243872258[/C][C]479.275612774218[/C][/ROW]
[ROW][C]72[/C][C]68318[/C][C]68937.6512838515[/C][C]-619.651283851548[/C][/ROW]
[ROW][C]73[/C][C]69530[/C][C]68944.3524286385[/C][C]585.647571361493[/C][/ROW]
[ROW][C]74[/C][C]70500[/C][C]70174.5922483244[/C][C]325.407751675622[/C][/ROW]
[ROW][C]75[/C][C]72044[/C][C]71154.7269761115[/C][C]889.273023888469[/C][/ROW]
[ROW][C]76[/C][C]73811[/C][C]72726.4231203464[/C][C]1084.57687965357[/C][/ROW]
[ROW][C]77[/C][C]76018[/C][C]74527.2019451683[/C][C]1490.79805483173[/C][/ROW]
[ROW][C]78[/C][C]77818[/C][C]76780.6324078525[/C][C]1037.36759214754[/C][/ROW]
[ROW][C]79[/C][C]79455[/C][C]78612.940913435[/C][C]842.059086564972[/C][/ROW]
[ROW][C]80[/C][C]81408[/C][C]80276.1665936135[/C][C]1131.83340638653[/C][/ROW]
[ROW][C]81[/C][C]81815[/C][C]82264.4172089263[/C][C]-449.417208926272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77763&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77763&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
32393223007925
42232124175.8088502958-1854.80885029578
52110222507.0413794899-1405.04137948988
62282421244.28178299141579.71821700861
72312923015.4816377193113.518362280698
82360423324.0171334001279.982866599868
92474623807.7371166318938.262883368236
102691124978.95903549131932.04096450873
112790927204.1318775581704.868122441872
122892228224.0847859016697.915214098415
132980029258.8211479795541.178852020461
143050630153.6760026078352.323997392246
153077130870.6490288742-99.6490288742243
163197631132.5454894635843.454510536543
173374932363.81462970711385.18537029292
183437134179.9558166959191.04418330409
193324634807.9058310491-1561.90583104909
203507233634.2607377921437.73926220799
213576235505.0387001372256.961299862785
223617936203.0416835097-24.0416835097058
233743336619.2929124166813.70708758336
243829837898.6355780067399.364421993305
253755938776.0736643274-1217.07366432741
263751137999.1682664955-488.168266495471
273936437935.96441081051428.03558918952
284008439833.4401551413250.559844858697
294271240561.24376709882150.75623290122
304193843256.2284312462-1318.2284312462
314079942441.1725982393-1642.17259823927
323856841251.0276203555-2683.02762035548
334113438936.46552191842197.53447808156
344395541570.90708061992384.09291938008
354360744466.158946572-859.158946571966
364508244091.4006963319990.59930366811
374646445597.2526174589866.747382541107
384649647006.2472072836-510.247207283639
394677447022.3557095447-248.355709544747
404789047292.620744727597.379255272957
414574048427.2259442243-2687.22594422429
424266046193.5330902372-3533.53309023717
433919043003.4822515217-3813.48225152168
443901039414.7124793166-404.7124793166
454115039222.10782933881927.8921706612
464253041422.15145845341107.84854154663
474471042836.65507227371873.34492772628
484662045074.99984370641545.00015629361
494456047033.1184147438-2473.11841474382
504612044896.09387617721223.90612382277
514806046494.21206893111565.78793106893
525197048482.97806904043487.02193095963
535772052501.58033151295218.41966848707
546349058414.10646233455075.89353766546
556537064342.19365913881027.80634086121
566426066254.2043823895-1994.20438238951
575870065082.0954791339-6382.0954791339
585863059323.3270107753-693.327010775254
595980359231.7335469272571.266453072793
605926660422.5254709549-1156.52547095485
616057059849.505828624720.494171375947
626306261175.9454056211886.05459437903
636384663726.686015847119.313984152941
646472664514.40201445211.59798555007
656346065400.99217087-1940.99217087004
666522064074.54054613941145.45945386063
676665965870.2155406541788.784459345872
686687167333.7819983892-462.781998389197
696567267531.3687904852-1859.36879048521
706718266274.4593016963907.540698303681
716829267812.7243872258479.275612774218
726831868937.6512838515-619.651283851548
736953068944.3524286385585.647571361493
747050070174.5922483244325.407751675622
757204471154.7269761115889.273023888469
767381172726.42312034641084.57687965357
777601874527.20194516831490.79805483173
787781876780.63240785251037.36759214754
797945578612.940913435842.059086564972
808140880276.16659361351131.83340638653
818181582264.4172089263-449.417208926272







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8282657.42024342179199.521185098786115.3193017435
8383499.840486842278532.896900243988466.7840734405
8484342.260730263378164.592512090390519.9289484363
8585184.680973684377941.792703747692427.569243621
8686027.101217105477806.31884847194247.8835857399
8786869.521460526577728.827945921996010.214975131
8887711.941703947677692.177607605297731.70580029
8988554.361947368777685.3857703499423.3381243974
9089396.782190789877700.9544634141101092.609918165
9190239.202434210877733.5197918933102744.885076528
9291081.62267763277779.1050199977104384.140335266
9391924.04292105377834.6775768833106013.408265223

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
82 & 82657.420243421 & 79199.5211850987 & 86115.3193017435 \tabularnewline
83 & 83499.8404868422 & 78532.8969002439 & 88466.7840734405 \tabularnewline
84 & 84342.2607302633 & 78164.5925120903 & 90519.9289484363 \tabularnewline
85 & 85184.6809736843 & 77941.7927037476 & 92427.569243621 \tabularnewline
86 & 86027.1012171054 & 77806.318848471 & 94247.8835857399 \tabularnewline
87 & 86869.5214605265 & 77728.8279459219 & 96010.214975131 \tabularnewline
88 & 87711.9417039476 & 77692.1776076052 & 97731.70580029 \tabularnewline
89 & 88554.3619473687 & 77685.38577034 & 99423.3381243974 \tabularnewline
90 & 89396.7821907898 & 77700.9544634141 & 101092.609918165 \tabularnewline
91 & 90239.2024342108 & 77733.5197918933 & 102744.885076528 \tabularnewline
92 & 91081.622677632 & 77779.1050199977 & 104384.140335266 \tabularnewline
93 & 91924.042921053 & 77834.6775768833 & 106013.408265223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77763&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]82[/C][C]82657.420243421[/C][C]79199.5211850987[/C][C]86115.3193017435[/C][/ROW]
[ROW][C]83[/C][C]83499.8404868422[/C][C]78532.8969002439[/C][C]88466.7840734405[/C][/ROW]
[ROW][C]84[/C][C]84342.2607302633[/C][C]78164.5925120903[/C][C]90519.9289484363[/C][/ROW]
[ROW][C]85[/C][C]85184.6809736843[/C][C]77941.7927037476[/C][C]92427.569243621[/C][/ROW]
[ROW][C]86[/C][C]86027.1012171054[/C][C]77806.318848471[/C][C]94247.8835857399[/C][/ROW]
[ROW][C]87[/C][C]86869.5214605265[/C][C]77728.8279459219[/C][C]96010.214975131[/C][/ROW]
[ROW][C]88[/C][C]87711.9417039476[/C][C]77692.1776076052[/C][C]97731.70580029[/C][/ROW]
[ROW][C]89[/C][C]88554.3619473687[/C][C]77685.38577034[/C][C]99423.3381243974[/C][/ROW]
[ROW][C]90[/C][C]89396.7821907898[/C][C]77700.9544634141[/C][C]101092.609918165[/C][/ROW]
[ROW][C]91[/C][C]90239.2024342108[/C][C]77733.5197918933[/C][C]102744.885076528[/C][/ROW]
[ROW][C]92[/C][C]91081.622677632[/C][C]77779.1050199977[/C][C]104384.140335266[/C][/ROW]
[ROW][C]93[/C][C]91924.042921053[/C][C]77834.6775768833[/C][C]106013.408265223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77763&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77763&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
8282657.42024342179199.521185098786115.3193017435
8383499.840486842278532.896900243988466.7840734405
8484342.260730263378164.592512090390519.9289484363
8585184.680973684377941.792703747692427.569243621
8686027.101217105477806.31884847194247.8835857399
8786869.521460526577728.827945921996010.214975131
8887711.941703947677692.177607605297731.70580029
8988554.361947368777685.3857703499423.3381243974
9089396.782190789877700.9544634141101092.609918165
9190239.202434210877733.5197918933102744.885076528
9291081.62267763277779.1050199977104384.140335266
9391924.04292105377834.6775768833106013.408265223



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')