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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 25 Apr 2016 21:21:05 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/25/t14616156984qy8oxislwxkfpg.htm/, Retrieved Sun, 05 May 2024 23:01:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294785, Retrieved Sun, 05 May 2024 23:01:17 +0000

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No (this computation is public)

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Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [Exponential Smoot...] [2016-04-25 20:21:05] [4e1138fa3bff5f7fc8fdb388bb0b126b] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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=294785&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=294785&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294785&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.447755635358466
beta	0.0078697426446501
gamma	0.819858905941707

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.447755635358466 \tabularnewline
beta & 0.0078697426446501 \tabularnewline
gamma & 0.819858905941707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294785&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]0.447755635358466[/C][/ROW]
[ROW][C]beta[/C][C]0.0078697426446501[/C][/ROW]
[ROW][C]gamma[/C][C]0.819858905941707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294785&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294785&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
Parameter	Value
alpha	0.447755635358466
beta	0.0078697426446501
gamma	0.819858905941707

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	98.24	99.2732861677437	-1.03328616774373
14	98.37	98.9000434471212	-0.530043447121201
15	99.68	99.9098309541678	-0.229830954167838
16	97.8	97.8741243424041	-0.0741243424041471
17	98.34	98.2919921865452	0.0480078134547881
18	98.06	97.9245231284466	0.135476871553408
19	97.19	97.4620194039223	-0.272019403922272
20	99.44	98.123418625267	1.31658137473302
21	99.04	99.2516011307798	-0.211601130779826
22	100.81	100.485441139547	0.324558860452555
23	98.49	98.0287574844625	0.461242515537506
24	101.03	100.705432452984	0.324567547015761
25	98.59	97.3415914357495	1.24840856425048
26	101.07	98.2241452640279	2.8458547359721
27	99.28	100.91902196856	-1.6390219685602
28	101.65	98.3303257249456	3.31967427505442
29	100.59	100.364242705282	0.225757294717639
30	101.84	100.139823975569	1.70017602443144
31	100.27	100.210402808245	0.0595971917546478
32	100.04	101.822402413525	-1.78240241352459
33	97.78	100.895301084947	-3.11530108494733
34	97.59	101.093795181215	-3.50379518121527
35	97.68	97.015535342383	0.664464657617046
36	100.56	99.6938715751385	0.866128424861515
37	98.9	97.0182181997098	1.88178180029018
38	100.08	98.8900491672387	1.1899508327613
39	101.7	98.8143106699258	2.8856893300742
40	100.9	100.493580321002	0.406419678998361
41	100.67	99.8324474552409	0.837552544759092
42	100.51	100.549861797768	-0.0398617977681681
43	100.01	99.1150105218265	0.894989478173528
44	99.8	100.258908595325	-0.458908595324615
45	97.7	99.3112743833923	-1.6112743833923
46	98.14	100.004428201685	-1.86442820168524
47	101.77	98.560214779439	3.20978522056097
48	99.82	102.561161807728	-2.7411618077285
49	100.03	98.7180489957554	1.31195100424459
50	101.83	100.038157771268	1.79184222873161
51	98.25	101.001773551389	-2.75177355138851
52	99.88	99.0409489170222	0.839051082977747
53	98.96	98.7733999224361	0.186600077563881
54	98.37	98.7972769897466	-0.427276989746616
55	97.52	97.6222586179196	-0.102258617919645
56	99.59	97.6920248358331	1.89797516416692
57	97.99	97.2873308966536	0.702669103346352
58	100.68	98.8987648058108	1.78123519418918
59	100.39	101.408996529912	-1.01899652991167
60	99.31	100.813010356489	-1.5030103564891
61	96.93	99.3654256284456	-2.43542562844564
62	102.06	99.198013230138	2.86198676986196
63	97.9	98.589478560809	-0.689478560808965
64	102.29	99.1814837797023	3.1085162202977
65	100.55	99.6435190936605	0.90648090633951
66	100.77	99.7266637607407	1.04333623925929
67	100.68	99.3668765483542	1.31312345164577
68	100.75	101.024616298808	-0.274616298808155
69	100.21	99.0993880165897	1.11061198341027
70	99.85	101.429435809302	-1.57943580930244
71	100.59	101.176290379519	-0.58629037951917
72	101.45	100.560818918131	0.889181081868557

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 98.24 & 99.2732861677437 & -1.03328616774373 \tabularnewline
14 & 98.37 & 98.9000434471212 & -0.530043447121201 \tabularnewline
15 & 99.68 & 99.9098309541678 & -0.229830954167838 \tabularnewline
16 & 97.8 & 97.8741243424041 & -0.0741243424041471 \tabularnewline
17 & 98.34 & 98.2919921865452 & 0.0480078134547881 \tabularnewline
18 & 98.06 & 97.9245231284466 & 0.135476871553408 \tabularnewline
19 & 97.19 & 97.4620194039223 & -0.272019403922272 \tabularnewline
20 & 99.44 & 98.123418625267 & 1.31658137473302 \tabularnewline
21 & 99.04 & 99.2516011307798 & -0.211601130779826 \tabularnewline
22 & 100.81 & 100.485441139547 & 0.324558860452555 \tabularnewline
23 & 98.49 & 98.0287574844625 & 0.461242515537506 \tabularnewline
24 & 101.03 & 100.705432452984 & 0.324567547015761 \tabularnewline
25 & 98.59 & 97.3415914357495 & 1.24840856425048 \tabularnewline
26 & 101.07 & 98.2241452640279 & 2.8458547359721 \tabularnewline
27 & 99.28 & 100.91902196856 & -1.6390219685602 \tabularnewline
28 & 101.65 & 98.3303257249456 & 3.31967427505442 \tabularnewline
29 & 100.59 & 100.364242705282 & 0.225757294717639 \tabularnewline
30 & 101.84 & 100.139823975569 & 1.70017602443144 \tabularnewline
31 & 100.27 & 100.210402808245 & 0.0595971917546478 \tabularnewline
32 & 100.04 & 101.822402413525 & -1.78240241352459 \tabularnewline
33 & 97.78 & 100.895301084947 & -3.11530108494733 \tabularnewline
34 & 97.59 & 101.093795181215 & -3.50379518121527 \tabularnewline
35 & 97.68 & 97.015535342383 & 0.664464657617046 \tabularnewline
36 & 100.56 & 99.6938715751385 & 0.866128424861515 \tabularnewline
37 & 98.9 & 97.0182181997098 & 1.88178180029018 \tabularnewline
38 & 100.08 & 98.8900491672387 & 1.1899508327613 \tabularnewline
39 & 101.7 & 98.8143106699258 & 2.8856893300742 \tabularnewline
40 & 100.9 & 100.493580321002 & 0.406419678998361 \tabularnewline
41 & 100.67 & 99.8324474552409 & 0.837552544759092 \tabularnewline
42 & 100.51 & 100.549861797768 & -0.0398617977681681 \tabularnewline
43 & 100.01 & 99.1150105218265 & 0.894989478173528 \tabularnewline
44 & 99.8 & 100.258908595325 & -0.458908595324615 \tabularnewline
45 & 97.7 & 99.3112743833923 & -1.6112743833923 \tabularnewline
46 & 98.14 & 100.004428201685 & -1.86442820168524 \tabularnewline
47 & 101.77 & 98.560214779439 & 3.20978522056097 \tabularnewline
48 & 99.82 & 102.561161807728 & -2.7411618077285 \tabularnewline
49 & 100.03 & 98.7180489957554 & 1.31195100424459 \tabularnewline
50 & 101.83 & 100.038157771268 & 1.79184222873161 \tabularnewline
51 & 98.25 & 101.001773551389 & -2.75177355138851 \tabularnewline
52 & 99.88 & 99.0409489170222 & 0.839051082977747 \tabularnewline
53 & 98.96 & 98.7733999224361 & 0.186600077563881 \tabularnewline
54 & 98.37 & 98.7972769897466 & -0.427276989746616 \tabularnewline
55 & 97.52 & 97.6222586179196 & -0.102258617919645 \tabularnewline
56 & 99.59 & 97.6920248358331 & 1.89797516416692 \tabularnewline
57 & 97.99 & 97.2873308966536 & 0.702669103346352 \tabularnewline
58 & 100.68 & 98.8987648058108 & 1.78123519418918 \tabularnewline
59 & 100.39 & 101.408996529912 & -1.01899652991167 \tabularnewline
60 & 99.31 & 100.813010356489 & -1.5030103564891 \tabularnewline
61 & 96.93 & 99.3654256284456 & -2.43542562844564 \tabularnewline
62 & 102.06 & 99.198013230138 & 2.86198676986196 \tabularnewline
63 & 97.9 & 98.589478560809 & -0.689478560808965 \tabularnewline
64 & 102.29 & 99.1814837797023 & 3.1085162202977 \tabularnewline
65 & 100.55 & 99.6435190936605 & 0.90648090633951 \tabularnewline
66 & 100.77 & 99.7266637607407 & 1.04333623925929 \tabularnewline
67 & 100.68 & 99.3668765483542 & 1.31312345164577 \tabularnewline
68 & 100.75 & 101.024616298808 & -0.274616298808155 \tabularnewline
69 & 100.21 & 99.0993880165897 & 1.11061198341027 \tabularnewline
70 & 99.85 & 101.429435809302 & -1.57943580930244 \tabularnewline
71 & 100.59 & 101.176290379519 & -0.58629037951917 \tabularnewline
72 & 101.45 & 100.560818918131 & 0.889181081868557 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294785&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]98.24[/C][C]99.2732861677437[/C][C]-1.03328616774373[/C][/ROW]
[ROW][C]14[/C][C]98.37[/C][C]98.9000434471212[/C][C]-0.530043447121201[/C][/ROW]
[ROW][C]15[/C][C]99.68[/C][C]99.9098309541678[/C][C]-0.229830954167838[/C][/ROW]
[ROW][C]16[/C][C]97.8[/C][C]97.8741243424041[/C][C]-0.0741243424041471[/C][/ROW]
[ROW][C]17[/C][C]98.34[/C][C]98.2919921865452[/C][C]0.0480078134547881[/C][/ROW]
[ROW][C]18[/C][C]98.06[/C][C]97.9245231284466[/C][C]0.135476871553408[/C][/ROW]
[ROW][C]19[/C][C]97.19[/C][C]97.4620194039223[/C][C]-0.272019403922272[/C][/ROW]
[ROW][C]20[/C][C]99.44[/C][C]98.123418625267[/C][C]1.31658137473302[/C][/ROW]
[ROW][C]21[/C][C]99.04[/C][C]99.2516011307798[/C][C]-0.211601130779826[/C][/ROW]
[ROW][C]22[/C][C]100.81[/C][C]100.485441139547[/C][C]0.324558860452555[/C][/ROW]
[ROW][C]23[/C][C]98.49[/C][C]98.0287574844625[/C][C]0.461242515537506[/C][/ROW]
[ROW][C]24[/C][C]101.03[/C][C]100.705432452984[/C][C]0.324567547015761[/C][/ROW]
[ROW][C]25[/C][C]98.59[/C][C]97.3415914357495[/C][C]1.24840856425048[/C][/ROW]
[ROW][C]26[/C][C]101.07[/C][C]98.2241452640279[/C][C]2.8458547359721[/C][/ROW]
[ROW][C]27[/C][C]99.28[/C][C]100.91902196856[/C][C]-1.6390219685602[/C][/ROW]
[ROW][C]28[/C][C]101.65[/C][C]98.3303257249456[/C][C]3.31967427505442[/C][/ROW]
[ROW][C]29[/C][C]100.59[/C][C]100.364242705282[/C][C]0.225757294717639[/C][/ROW]
[ROW][C]30[/C][C]101.84[/C][C]100.139823975569[/C][C]1.70017602443144[/C][/ROW]
[ROW][C]31[/C][C]100.27[/C][C]100.210402808245[/C][C]0.0595971917546478[/C][/ROW]
[ROW][C]32[/C][C]100.04[/C][C]101.822402413525[/C][C]-1.78240241352459[/C][/ROW]
[ROW][C]33[/C][C]97.78[/C][C]100.895301084947[/C][C]-3.11530108494733[/C][/ROW]
[ROW][C]34[/C][C]97.59[/C][C]101.093795181215[/C][C]-3.50379518121527[/C][/ROW]
[ROW][C]35[/C][C]97.68[/C][C]97.015535342383[/C][C]0.664464657617046[/C][/ROW]
[ROW][C]36[/C][C]100.56[/C][C]99.6938715751385[/C][C]0.866128424861515[/C][/ROW]
[ROW][C]37[/C][C]98.9[/C][C]97.0182181997098[/C][C]1.88178180029018[/C][/ROW]
[ROW][C]38[/C][C]100.08[/C][C]98.8900491672387[/C][C]1.1899508327613[/C][/ROW]
[ROW][C]39[/C][C]101.7[/C][C]98.8143106699258[/C][C]2.8856893300742[/C][/ROW]
[ROW][C]40[/C][C]100.9[/C][C]100.493580321002[/C][C]0.406419678998361[/C][/ROW]
[ROW][C]41[/C][C]100.67[/C][C]99.8324474552409[/C][C]0.837552544759092[/C][/ROW]
[ROW][C]42[/C][C]100.51[/C][C]100.549861797768[/C][C]-0.0398617977681681[/C][/ROW]
[ROW][C]43[/C][C]100.01[/C][C]99.1150105218265[/C][C]0.894989478173528[/C][/ROW]
[ROW][C]44[/C][C]99.8[/C][C]100.258908595325[/C][C]-0.458908595324615[/C][/ROW]
[ROW][C]45[/C][C]97.7[/C][C]99.3112743833923[/C][C]-1.6112743833923[/C][/ROW]
[ROW][C]46[/C][C]98.14[/C][C]100.004428201685[/C][C]-1.86442820168524[/C][/ROW]
[ROW][C]47[/C][C]101.77[/C][C]98.560214779439[/C][C]3.20978522056097[/C][/ROW]
[ROW][C]48[/C][C]99.82[/C][C]102.561161807728[/C][C]-2.7411618077285[/C][/ROW]
[ROW][C]49[/C][C]100.03[/C][C]98.7180489957554[/C][C]1.31195100424459[/C][/ROW]
[ROW][C]50[/C][C]101.83[/C][C]100.038157771268[/C][C]1.79184222873161[/C][/ROW]
[ROW][C]51[/C][C]98.25[/C][C]101.001773551389[/C][C]-2.75177355138851[/C][/ROW]
[ROW][C]52[/C][C]99.88[/C][C]99.0409489170222[/C][C]0.839051082977747[/C][/ROW]
[ROW][C]53[/C][C]98.96[/C][C]98.7733999224361[/C][C]0.186600077563881[/C][/ROW]
[ROW][C]54[/C][C]98.37[/C][C]98.7972769897466[/C][C]-0.427276989746616[/C][/ROW]
[ROW][C]55[/C][C]97.52[/C][C]97.6222586179196[/C][C]-0.102258617919645[/C][/ROW]
[ROW][C]56[/C][C]99.59[/C][C]97.6920248358331[/C][C]1.89797516416692[/C][/ROW]
[ROW][C]57[/C][C]97.99[/C][C]97.2873308966536[/C][C]0.702669103346352[/C][/ROW]
[ROW][C]58[/C][C]100.68[/C][C]98.8987648058108[/C][C]1.78123519418918[/C][/ROW]
[ROW][C]59[/C][C]100.39[/C][C]101.408996529912[/C][C]-1.01899652991167[/C][/ROW]
[ROW][C]60[/C][C]99.31[/C][C]100.813010356489[/C][C]-1.5030103564891[/C][/ROW]
[ROW][C]61[/C][C]96.93[/C][C]99.3654256284456[/C][C]-2.43542562844564[/C][/ROW]
[ROW][C]62[/C][C]102.06[/C][C]99.198013230138[/C][C]2.86198676986196[/C][/ROW]
[ROW][C]63[/C][C]97.9[/C][C]98.589478560809[/C][C]-0.689478560808965[/C][/ROW]
[ROW][C]64[/C][C]102.29[/C][C]99.1814837797023[/C][C]3.1085162202977[/C][/ROW]
[ROW][C]65[/C][C]100.55[/C][C]99.6435190936605[/C][C]0.90648090633951[/C][/ROW]
[ROW][C]66[/C][C]100.77[/C][C]99.7266637607407[/C][C]1.04333623925929[/C][/ROW]
[ROW][C]67[/C][C]100.68[/C][C]99.3668765483542[/C][C]1.31312345164577[/C][/ROW]
[ROW][C]68[/C][C]100.75[/C][C]101.024616298808[/C][C]-0.274616298808155[/C][/ROW]
[ROW][C]69[/C][C]100.21[/C][C]99.0993880165897[/C][C]1.11061198341027[/C][/ROW]
[ROW][C]70[/C][C]99.85[/C][C]101.429435809302[/C][C]-1.57943580930244[/C][/ROW]
[ROW][C]71[/C][C]100.59[/C][C]101.176290379519[/C][C]-0.58629037951917[/C][/ROW]
[ROW][C]72[/C][C]101.45[/C][C]100.560818918131[/C][C]0.889181081868557[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294785&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294785&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
t	Observed	Fitted	Residuals
13	98.24	99.2732861677437	-1.03328616774373
14	98.37	98.9000434471212	-0.530043447121201
15	99.68	99.9098309541678	-0.229830954167838
16	97.8	97.8741243424041	-0.0741243424041471
17	98.34	98.2919921865452	0.0480078134547881
18	98.06	97.9245231284466	0.135476871553408
19	97.19	97.4620194039223	-0.272019403922272
20	99.44	98.123418625267	1.31658137473302
21	99.04	99.2516011307798	-0.211601130779826
22	100.81	100.485441139547	0.324558860452555
23	98.49	98.0287574844625	0.461242515537506
24	101.03	100.705432452984	0.324567547015761
25	98.59	97.3415914357495	1.24840856425048
26	101.07	98.2241452640279	2.8458547359721
27	99.28	100.91902196856	-1.6390219685602
28	101.65	98.3303257249456	3.31967427505442
29	100.59	100.364242705282	0.225757294717639
30	101.84	100.139823975569	1.70017602443144
31	100.27	100.210402808245	0.0595971917546478
32	100.04	101.822402413525	-1.78240241352459
33	97.78	100.895301084947	-3.11530108494733
34	97.59	101.093795181215	-3.50379518121527
35	97.68	97.015535342383	0.664464657617046
36	100.56	99.6938715751385	0.866128424861515
37	98.9	97.0182181997098	1.88178180029018
38	100.08	98.8900491672387	1.1899508327613
39	101.7	98.8143106699258	2.8856893300742
40	100.9	100.493580321002	0.406419678998361
41	100.67	99.8324474552409	0.837552544759092
42	100.51	100.549861797768	-0.0398617977681681
43	100.01	99.1150105218265	0.894989478173528
44	99.8	100.258908595325	-0.458908595324615
45	97.7	99.3112743833923	-1.6112743833923
46	98.14	100.004428201685	-1.86442820168524
47	101.77	98.560214779439	3.20978522056097
48	99.82	102.561161807728	-2.7411618077285
49	100.03	98.7180489957554	1.31195100424459
50	101.83	100.038157771268	1.79184222873161
51	98.25	101.001773551389	-2.75177355138851
52	99.88	99.0409489170222	0.839051082977747
53	98.96	98.7733999224361	0.186600077563881
54	98.37	98.7972769897466	-0.427276989746616
55	97.52	97.6222586179196	-0.102258617919645
56	99.59	97.6920248358331	1.89797516416692
57	97.99	97.2873308966536	0.702669103346352
58	100.68	98.8987648058108	1.78123519418918
59	100.39	101.408996529912	-1.01899652991167
60	99.31	100.813010356489	-1.5030103564891
61	96.93	99.3654256284456	-2.43542562844564
62	102.06	99.198013230138	2.86198676986196
63	97.9	98.589478560809	-0.689478560808965
64	102.29	99.1814837797023	3.1085162202977
65	100.55	99.6435190936605	0.90648090633951
66	100.77	99.7266637607407	1.04333623925929
67	100.68	99.3668765483542	1.31312345164577
68	100.75	101.024616298808	-0.274616298808155
69	100.21	99.0993880165897	1.11061198341027
70	99.85	101.429435809302	-1.57943580930244
71	100.59	101.176290379519	-0.58629037951917
72	101.45	100.560818918131	0.889181081868557

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	99.7529813676611	96.9488013053017	102.557161430021
74	103.177934175725	100.018913520732	106.336954830718
75	99.6504936618402	96.2276039800411	103.073383343639
76	102.31912556194	98.5667511683121	106.071499955568
77	100.394657216299	96.4127800995696	104.376534333028
78	100.13869858415	95.905712768541	104.371684399759
79	99.4368822696043	94.9763180755525	103.897446463656
80	99.781446842033	95.0721789948666	104.490714689199
81	98.6142306383794	93.7139867852002	103.514474491559
82	99.2094284738577	94.0630737328151	104.3557832149
83	100.105690987333	94.706162160783	105.505219813884
84	100.420200480203	63.5389310706237	137.301469889782

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 99.7529813676611 & 96.9488013053017 & 102.557161430021 \tabularnewline
74 & 103.177934175725 & 100.018913520732 & 106.336954830718 \tabularnewline
75 & 99.6504936618402 & 96.2276039800411 & 103.073383343639 \tabularnewline
76 & 102.31912556194 & 98.5667511683121 & 106.071499955568 \tabularnewline
77 & 100.394657216299 & 96.4127800995696 & 104.376534333028 \tabularnewline
78 & 100.13869858415 & 95.905712768541 & 104.371684399759 \tabularnewline
79 & 99.4368822696043 & 94.9763180755525 & 103.897446463656 \tabularnewline
80 & 99.781446842033 & 95.0721789948666 & 104.490714689199 \tabularnewline
81 & 98.6142306383794 & 93.7139867852002 & 103.514474491559 \tabularnewline
82 & 99.2094284738577 & 94.0630737328151 & 104.3557832149 \tabularnewline
83 & 100.105690987333 & 94.706162160783 & 105.505219813884 \tabularnewline
84 & 100.420200480203 & 63.5389310706237 & 137.301469889782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294785&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]99.7529813676611[/C][C]96.9488013053017[/C][C]102.557161430021[/C][/ROW]
[ROW][C]74[/C][C]103.177934175725[/C][C]100.018913520732[/C][C]106.336954830718[/C][/ROW]
[ROW][C]75[/C][C]99.6504936618402[/C][C]96.2276039800411[/C][C]103.073383343639[/C][/ROW]
[ROW][C]76[/C][C]102.31912556194[/C][C]98.5667511683121[/C][C]106.071499955568[/C][/ROW]
[ROW][C]77[/C][C]100.394657216299[/C][C]96.4127800995696[/C][C]104.376534333028[/C][/ROW]
[ROW][C]78[/C][C]100.13869858415[/C][C]95.905712768541[/C][C]104.371684399759[/C][/ROW]
[ROW][C]79[/C][C]99.4368822696043[/C][C]94.9763180755525[/C][C]103.897446463656[/C][/ROW]
[ROW][C]80[/C][C]99.781446842033[/C][C]95.0721789948666[/C][C]104.490714689199[/C][/ROW]
[ROW][C]81[/C][C]98.6142306383794[/C][C]93.7139867852002[/C][C]103.514474491559[/C][/ROW]
[ROW][C]82[/C][C]99.2094284738577[/C][C]94.0630737328151[/C][C]104.3557832149[/C][/ROW]
[ROW][C]83[/C][C]100.105690987333[/C][C]94.706162160783[/C][C]105.505219813884[/C][/ROW]
[ROW][C]84[/C][C]100.420200480203[/C][C]63.5389310706237[/C][C]137.301469889782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294785&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294785&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
t	Forecast	95% Lower Bound	95% Upper Bound
73	99.7529813676611	96.9488013053017	102.557161430021
74	103.177934175725	100.018913520732	106.336954830718
75	99.6504936618402	96.2276039800411	103.073383343639
76	102.31912556194	98.5667511683121	106.071499955568
77	100.394657216299	96.4127800995696	104.376534333028
78	100.13869858415	95.905712768541	104.371684399759
79	99.4368822696043	94.9763180755525	103.897446463656
80	99.781446842033	95.0721789948666	104.490714689199
81	98.6142306383794	93.7139867852002	103.514474491559
82	99.2094284738577	94.0630737328151	104.3557832149
83	100.105690987333	94.706162160783	105.505219813884
84	100.420200480203	63.5389310706237	137.301469889782

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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=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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code