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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 18 Aug 2008 07:43:58 -0600

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/2008/Aug/18/t1219067142842pcqje0634ng2.htm/, Retrieved Mon, 13 May 2024 20:42:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14641, Retrieved Mon, 13 May 2024 20:42:18 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

232

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

-       [Exponential Smoothing] [Exponential Smoot...] [2008-08-18 13:43:58] [b82ef19bb71ab1d2d730136b4505428a] [Current]

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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	'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=14641&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=14641&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14641&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	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.069731525720716
beta	0
gamma	0.163517945829889

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.069731525720716 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.163517945829889 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14641&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]0.069731525720716[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.163517945829889[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14641&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14641&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	0.069731525720716
beta	0
gamma	0.163517945829889

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	110.48	111.736474939613	-1.25647493961348
14	96.34	99.4988590250444	-3.15885902504442
15	100.43	103.470670299025	-3.04067029902475
16	90.88	95.0244730531934	-4.14447305319345
17	128.28	132.955055957219	-4.67505595721923
18	101.21	106.004473839159	-4.7944738391593
19	73.76	79.4293145299933	-5.66931452999331
20	73.64	78.9539845780263	-5.31398457802625
21	66.4	71.2592656590775	-4.85926565907747
22	57.34	61.738754984121	-4.39875498412105
23	113.59	118.43535642114	-4.84535642114002
24	123.53	127.924565658567	-4.39456565856659
25	102.87	108.020329796908	-5.15032979690821
26	102.99	95.2218071646726	7.7681928353274
27	95.8	99.973556784294	-4.17355678429402
28	98.43	91.2804560281997	7.14954397180034
29	102.65	129.917878039412	-27.2678780394124
30	129.55	101.373698645658	28.1763013543415
31	100.37	76.9645648871014	23.4054351128986
32	101.93	78.5707128129637	23.3592871870363
33	101.94	72.9445947182304	28.9954052817696
34	93.87	65.8548727537672	28.0151272462328
35	100.91	124.743808612160	-23.8338086121603
36	92.64	132.977496410041	-40.3374964100406
37	101.67	110.451941640415	-8.78194164041494
38	88.67	99.3652898654362	-10.6952898654362
39	129.86	101.01302637738	28.84697362262
40	98.07	96.3449177386338	1.72508226136623
41	166.45	129.368657303585	37.0813426964152
42	176.52	113.745571310364	62.774428689636
43	82.07	91.0232946249226	-8.95329462492265
44	92.18	90.3659991368132	1.81400086318679
45	95.02	84.0948367838307	10.9251632161693
46	84.69	75.595933698266	9.094066301734
47	103.01	125.278443640579	-22.268443640579
48	107.9	131.110818519944	-23.2108185199436
49	204.13	114.57962496119	89.55037503881
50	101.99	110.058785561811	-8.06878556181142
51	119.23	117.904666965965	1.3253330340346
52	95.65	107.191769832729	-11.5417698327285
53	160.95	144.668629975369	16.2813700246313
54	111.06	131.503449087175	-20.4434490871753
55	150.41	92.0673578668811	58.3426421331189
56	94.79	97.7405842294255	-2.95058422942544
57	160.34	92.523129925277	67.816870074723
58	104.08	87.7128339723569	16.3671660276431
59	101.07	133.131781552008	-32.0617815520083
60	111.5	138.137902126149	-26.6379021261493
61	136.9	138.520468284303	-1.62046828430348
62	141.71	112.792750670209	28.9172493297908
63	153.98	124.646716610305	29.3332833896947
64	134.27	113.929569643710	20.3404303562896
65	124.71	157.861957583486	-33.1519575834864
66	72.89	135.663297813462	-62.7732978134621
67	101.2	105.260074406501	-4.06007440650085
68	73.28	97.258208845431	-23.9782088454310
69	174.05	101.339299257699	72.7107007423006
70	111.9	89.0439554982013	22.8560445017987
71	97.06	127.548584540667	-30.4885845406669
72	105.23	133.489463161537	-28.2594631615372
73	109.13	137.564497103394	-28.4344971033939
74	84.04	114.612259280672	-30.5722592806718
75	118.82	122.381216287461	-3.56121628746060
76	90.84	108.002332525738	-17.1623325257381
77	144.28	141.182569439872	3.09743056012823
78	110.16	117.005767166331	-6.84576716633123
79	86.09	99.4336524196254	-13.3436524196254
80	59.87	87.7545700279856	-27.8845700279856
81	108.97	106.271154441870	2.69884555813042
82	94.93	81.5101067543454	13.4198932456546
83	87.36	111.242188853492	-23.8821888534922
84	143.52	117.982825638877	25.5371743611229
85	108.7	125.782555802500	-17.0825558025005
86	121.13	103.296719211739	17.8332807882614
87	210.25	118.549869121877	91.700130878123
88	110.2	108.744762619189	1.45523738081117
89	161.46	146.30505690287	15.1549430971299
90	99.41	121.456527986439	-22.0465279864389
91	132.72	101.836011346675	30.8839886533248
92	174.29	91.0290895851693	83.2609104148306
93	69.93	121.948232232915	-52.0182322329146
94	83.43	95.002517722281	-11.5725177222810
95	127.53	117.317612647034	10.2123873529658
96	187.58	133.953171842144	53.6268281578561

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 110.48 & 111.736474939613 & -1.25647493961348 \tabularnewline
14 & 96.34 & 99.4988590250444 & -3.15885902504442 \tabularnewline
15 & 100.43 & 103.470670299025 & -3.04067029902475 \tabularnewline
16 & 90.88 & 95.0244730531934 & -4.14447305319345 \tabularnewline
17 & 128.28 & 132.955055957219 & -4.67505595721923 \tabularnewline
18 & 101.21 & 106.004473839159 & -4.7944738391593 \tabularnewline
19 & 73.76 & 79.4293145299933 & -5.66931452999331 \tabularnewline
20 & 73.64 & 78.9539845780263 & -5.31398457802625 \tabularnewline
21 & 66.4 & 71.2592656590775 & -4.85926565907747 \tabularnewline
22 & 57.34 & 61.738754984121 & -4.39875498412105 \tabularnewline
23 & 113.59 & 118.43535642114 & -4.84535642114002 \tabularnewline
24 & 123.53 & 127.924565658567 & -4.39456565856659 \tabularnewline
25 & 102.87 & 108.020329796908 & -5.15032979690821 \tabularnewline
26 & 102.99 & 95.2218071646726 & 7.7681928353274 \tabularnewline
27 & 95.8 & 99.973556784294 & -4.17355678429402 \tabularnewline
28 & 98.43 & 91.2804560281997 & 7.14954397180034 \tabularnewline
29 & 102.65 & 129.917878039412 & -27.2678780394124 \tabularnewline
30 & 129.55 & 101.373698645658 & 28.1763013543415 \tabularnewline
31 & 100.37 & 76.9645648871014 & 23.4054351128986 \tabularnewline
32 & 101.93 & 78.5707128129637 & 23.3592871870363 \tabularnewline
33 & 101.94 & 72.9445947182304 & 28.9954052817696 \tabularnewline
34 & 93.87 & 65.8548727537672 & 28.0151272462328 \tabularnewline
35 & 100.91 & 124.743808612160 & -23.8338086121603 \tabularnewline
36 & 92.64 & 132.977496410041 & -40.3374964100406 \tabularnewline
37 & 101.67 & 110.451941640415 & -8.78194164041494 \tabularnewline
38 & 88.67 & 99.3652898654362 & -10.6952898654362 \tabularnewline
39 & 129.86 & 101.01302637738 & 28.84697362262 \tabularnewline
40 & 98.07 & 96.3449177386338 & 1.72508226136623 \tabularnewline
41 & 166.45 & 129.368657303585 & 37.0813426964152 \tabularnewline
42 & 176.52 & 113.745571310364 & 62.774428689636 \tabularnewline
43 & 82.07 & 91.0232946249226 & -8.95329462492265 \tabularnewline
44 & 92.18 & 90.3659991368132 & 1.81400086318679 \tabularnewline
45 & 95.02 & 84.0948367838307 & 10.9251632161693 \tabularnewline
46 & 84.69 & 75.595933698266 & 9.094066301734 \tabularnewline
47 & 103.01 & 125.278443640579 & -22.268443640579 \tabularnewline
48 & 107.9 & 131.110818519944 & -23.2108185199436 \tabularnewline
49 & 204.13 & 114.57962496119 & 89.55037503881 \tabularnewline
50 & 101.99 & 110.058785561811 & -8.06878556181142 \tabularnewline
51 & 119.23 & 117.904666965965 & 1.3253330340346 \tabularnewline
52 & 95.65 & 107.191769832729 & -11.5417698327285 \tabularnewline
53 & 160.95 & 144.668629975369 & 16.2813700246313 \tabularnewline
54 & 111.06 & 131.503449087175 & -20.4434490871753 \tabularnewline
55 & 150.41 & 92.0673578668811 & 58.3426421331189 \tabularnewline
56 & 94.79 & 97.7405842294255 & -2.95058422942544 \tabularnewline
57 & 160.34 & 92.523129925277 & 67.816870074723 \tabularnewline
58 & 104.08 & 87.7128339723569 & 16.3671660276431 \tabularnewline
59 & 101.07 & 133.131781552008 & -32.0617815520083 \tabularnewline
60 & 111.5 & 138.137902126149 & -26.6379021261493 \tabularnewline
61 & 136.9 & 138.520468284303 & -1.62046828430348 \tabularnewline
62 & 141.71 & 112.792750670209 & 28.9172493297908 \tabularnewline
63 & 153.98 & 124.646716610305 & 29.3332833896947 \tabularnewline
64 & 134.27 & 113.929569643710 & 20.3404303562896 \tabularnewline
65 & 124.71 & 157.861957583486 & -33.1519575834864 \tabularnewline
66 & 72.89 & 135.663297813462 & -62.7732978134621 \tabularnewline
67 & 101.2 & 105.260074406501 & -4.06007440650085 \tabularnewline
68 & 73.28 & 97.258208845431 & -23.9782088454310 \tabularnewline
69 & 174.05 & 101.339299257699 & 72.7107007423006 \tabularnewline
70 & 111.9 & 89.0439554982013 & 22.8560445017987 \tabularnewline
71 & 97.06 & 127.548584540667 & -30.4885845406669 \tabularnewline
72 & 105.23 & 133.489463161537 & -28.2594631615372 \tabularnewline
73 & 109.13 & 137.564497103394 & -28.4344971033939 \tabularnewline
74 & 84.04 & 114.612259280672 & -30.5722592806718 \tabularnewline
75 & 118.82 & 122.381216287461 & -3.56121628746060 \tabularnewline
76 & 90.84 & 108.002332525738 & -17.1623325257381 \tabularnewline
77 & 144.28 & 141.182569439872 & 3.09743056012823 \tabularnewline
78 & 110.16 & 117.005767166331 & -6.84576716633123 \tabularnewline
79 & 86.09 & 99.4336524196254 & -13.3436524196254 \tabularnewline
80 & 59.87 & 87.7545700279856 & -27.8845700279856 \tabularnewline
81 & 108.97 & 106.271154441870 & 2.69884555813042 \tabularnewline
82 & 94.93 & 81.5101067543454 & 13.4198932456546 \tabularnewline
83 & 87.36 & 111.242188853492 & -23.8821888534922 \tabularnewline
84 & 143.52 & 117.982825638877 & 25.5371743611229 \tabularnewline
85 & 108.7 & 125.782555802500 & -17.0825558025005 \tabularnewline
86 & 121.13 & 103.296719211739 & 17.8332807882614 \tabularnewline
87 & 210.25 & 118.549869121877 & 91.700130878123 \tabularnewline
88 & 110.2 & 108.744762619189 & 1.45523738081117 \tabularnewline
89 & 161.46 & 146.30505690287 & 15.1549430971299 \tabularnewline
90 & 99.41 & 121.456527986439 & -22.0465279864389 \tabularnewline
91 & 132.72 & 101.836011346675 & 30.8839886533248 \tabularnewline
92 & 174.29 & 91.0290895851693 & 83.2609104148306 \tabularnewline
93 & 69.93 & 121.948232232915 & -52.0182322329146 \tabularnewline
94 & 83.43 & 95.002517722281 & -11.5725177222810 \tabularnewline
95 & 127.53 & 117.317612647034 & 10.2123873529658 \tabularnewline
96 & 187.58 & 133.953171842144 & 53.6268281578561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14641&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]110.48[/C][C]111.736474939613[/C][C]-1.25647493961348[/C][/ROW]
[ROW][C]14[/C][C]96.34[/C][C]99.4988590250444[/C][C]-3.15885902504442[/C][/ROW]
[ROW][C]15[/C][C]100.43[/C][C]103.470670299025[/C][C]-3.04067029902475[/C][/ROW]
[ROW][C]16[/C][C]90.88[/C][C]95.0244730531934[/C][C]-4.14447305319345[/C][/ROW]
[ROW][C]17[/C][C]128.28[/C][C]132.955055957219[/C][C]-4.67505595721923[/C][/ROW]
[ROW][C]18[/C][C]101.21[/C][C]106.004473839159[/C][C]-4.7944738391593[/C][/ROW]
[ROW][C]19[/C][C]73.76[/C][C]79.4293145299933[/C][C]-5.66931452999331[/C][/ROW]
[ROW][C]20[/C][C]73.64[/C][C]78.9539845780263[/C][C]-5.31398457802625[/C][/ROW]
[ROW][C]21[/C][C]66.4[/C][C]71.2592656590775[/C][C]-4.85926565907747[/C][/ROW]
[ROW][C]22[/C][C]57.34[/C][C]61.738754984121[/C][C]-4.39875498412105[/C][/ROW]
[ROW][C]23[/C][C]113.59[/C][C]118.43535642114[/C][C]-4.84535642114002[/C][/ROW]
[ROW][C]24[/C][C]123.53[/C][C]127.924565658567[/C][C]-4.39456565856659[/C][/ROW]
[ROW][C]25[/C][C]102.87[/C][C]108.020329796908[/C][C]-5.15032979690821[/C][/ROW]
[ROW][C]26[/C][C]102.99[/C][C]95.2218071646726[/C][C]7.7681928353274[/C][/ROW]
[ROW][C]27[/C][C]95.8[/C][C]99.973556784294[/C][C]-4.17355678429402[/C][/ROW]
[ROW][C]28[/C][C]98.43[/C][C]91.2804560281997[/C][C]7.14954397180034[/C][/ROW]
[ROW][C]29[/C][C]102.65[/C][C]129.917878039412[/C][C]-27.2678780394124[/C][/ROW]
[ROW][C]30[/C][C]129.55[/C][C]101.373698645658[/C][C]28.1763013543415[/C][/ROW]
[ROW][C]31[/C][C]100.37[/C][C]76.9645648871014[/C][C]23.4054351128986[/C][/ROW]
[ROW][C]32[/C][C]101.93[/C][C]78.5707128129637[/C][C]23.3592871870363[/C][/ROW]
[ROW][C]33[/C][C]101.94[/C][C]72.9445947182304[/C][C]28.9954052817696[/C][/ROW]
[ROW][C]34[/C][C]93.87[/C][C]65.8548727537672[/C][C]28.0151272462328[/C][/ROW]
[ROW][C]35[/C][C]100.91[/C][C]124.743808612160[/C][C]-23.8338086121603[/C][/ROW]
[ROW][C]36[/C][C]92.64[/C][C]132.977496410041[/C][C]-40.3374964100406[/C][/ROW]
[ROW][C]37[/C][C]101.67[/C][C]110.451941640415[/C][C]-8.78194164041494[/C][/ROW]
[ROW][C]38[/C][C]88.67[/C][C]99.3652898654362[/C][C]-10.6952898654362[/C][/ROW]
[ROW][C]39[/C][C]129.86[/C][C]101.01302637738[/C][C]28.84697362262[/C][/ROW]
[ROW][C]40[/C][C]98.07[/C][C]96.3449177386338[/C][C]1.72508226136623[/C][/ROW]
[ROW][C]41[/C][C]166.45[/C][C]129.368657303585[/C][C]37.0813426964152[/C][/ROW]
[ROW][C]42[/C][C]176.52[/C][C]113.745571310364[/C][C]62.774428689636[/C][/ROW]
[ROW][C]43[/C][C]82.07[/C][C]91.0232946249226[/C][C]-8.95329462492265[/C][/ROW]
[ROW][C]44[/C][C]92.18[/C][C]90.3659991368132[/C][C]1.81400086318679[/C][/ROW]
[ROW][C]45[/C][C]95.02[/C][C]84.0948367838307[/C][C]10.9251632161693[/C][/ROW]
[ROW][C]46[/C][C]84.69[/C][C]75.595933698266[/C][C]9.094066301734[/C][/ROW]
[ROW][C]47[/C][C]103.01[/C][C]125.278443640579[/C][C]-22.268443640579[/C][/ROW]
[ROW][C]48[/C][C]107.9[/C][C]131.110818519944[/C][C]-23.2108185199436[/C][/ROW]
[ROW][C]49[/C][C]204.13[/C][C]114.57962496119[/C][C]89.55037503881[/C][/ROW]
[ROW][C]50[/C][C]101.99[/C][C]110.058785561811[/C][C]-8.06878556181142[/C][/ROW]
[ROW][C]51[/C][C]119.23[/C][C]117.904666965965[/C][C]1.3253330340346[/C][/ROW]
[ROW][C]52[/C][C]95.65[/C][C]107.191769832729[/C][C]-11.5417698327285[/C][/ROW]
[ROW][C]53[/C][C]160.95[/C][C]144.668629975369[/C][C]16.2813700246313[/C][/ROW]
[ROW][C]54[/C][C]111.06[/C][C]131.503449087175[/C][C]-20.4434490871753[/C][/ROW]
[ROW][C]55[/C][C]150.41[/C][C]92.0673578668811[/C][C]58.3426421331189[/C][/ROW]
[ROW][C]56[/C][C]94.79[/C][C]97.7405842294255[/C][C]-2.95058422942544[/C][/ROW]
[ROW][C]57[/C][C]160.34[/C][C]92.523129925277[/C][C]67.816870074723[/C][/ROW]
[ROW][C]58[/C][C]104.08[/C][C]87.7128339723569[/C][C]16.3671660276431[/C][/ROW]
[ROW][C]59[/C][C]101.07[/C][C]133.131781552008[/C][C]-32.0617815520083[/C][/ROW]
[ROW][C]60[/C][C]111.5[/C][C]138.137902126149[/C][C]-26.6379021261493[/C][/ROW]
[ROW][C]61[/C][C]136.9[/C][C]138.520468284303[/C][C]-1.62046828430348[/C][/ROW]
[ROW][C]62[/C][C]141.71[/C][C]112.792750670209[/C][C]28.9172493297908[/C][/ROW]
[ROW][C]63[/C][C]153.98[/C][C]124.646716610305[/C][C]29.3332833896947[/C][/ROW]
[ROW][C]64[/C][C]134.27[/C][C]113.929569643710[/C][C]20.3404303562896[/C][/ROW]
[ROW][C]65[/C][C]124.71[/C][C]157.861957583486[/C][C]-33.1519575834864[/C][/ROW]
[ROW][C]66[/C][C]72.89[/C][C]135.663297813462[/C][C]-62.7732978134621[/C][/ROW]
[ROW][C]67[/C][C]101.2[/C][C]105.260074406501[/C][C]-4.06007440650085[/C][/ROW]
[ROW][C]68[/C][C]73.28[/C][C]97.258208845431[/C][C]-23.9782088454310[/C][/ROW]
[ROW][C]69[/C][C]174.05[/C][C]101.339299257699[/C][C]72.7107007423006[/C][/ROW]
[ROW][C]70[/C][C]111.9[/C][C]89.0439554982013[/C][C]22.8560445017987[/C][/ROW]
[ROW][C]71[/C][C]97.06[/C][C]127.548584540667[/C][C]-30.4885845406669[/C][/ROW]
[ROW][C]72[/C][C]105.23[/C][C]133.489463161537[/C][C]-28.2594631615372[/C][/ROW]
[ROW][C]73[/C][C]109.13[/C][C]137.564497103394[/C][C]-28.4344971033939[/C][/ROW]
[ROW][C]74[/C][C]84.04[/C][C]114.612259280672[/C][C]-30.5722592806718[/C][/ROW]
[ROW][C]75[/C][C]118.82[/C][C]122.381216287461[/C][C]-3.56121628746060[/C][/ROW]
[ROW][C]76[/C][C]90.84[/C][C]108.002332525738[/C][C]-17.1623325257381[/C][/ROW]
[ROW][C]77[/C][C]144.28[/C][C]141.182569439872[/C][C]3.09743056012823[/C][/ROW]
[ROW][C]78[/C][C]110.16[/C][C]117.005767166331[/C][C]-6.84576716633123[/C][/ROW]
[ROW][C]79[/C][C]86.09[/C][C]99.4336524196254[/C][C]-13.3436524196254[/C][/ROW]
[ROW][C]80[/C][C]59.87[/C][C]87.7545700279856[/C][C]-27.8845700279856[/C][/ROW]
[ROW][C]81[/C][C]108.97[/C][C]106.271154441870[/C][C]2.69884555813042[/C][/ROW]
[ROW][C]82[/C][C]94.93[/C][C]81.5101067543454[/C][C]13.4198932456546[/C][/ROW]
[ROW][C]83[/C][C]87.36[/C][C]111.242188853492[/C][C]-23.8821888534922[/C][/ROW]
[ROW][C]84[/C][C]143.52[/C][C]117.982825638877[/C][C]25.5371743611229[/C][/ROW]
[ROW][C]85[/C][C]108.7[/C][C]125.782555802500[/C][C]-17.0825558025005[/C][/ROW]
[ROW][C]86[/C][C]121.13[/C][C]103.296719211739[/C][C]17.8332807882614[/C][/ROW]
[ROW][C]87[/C][C]210.25[/C][C]118.549869121877[/C][C]91.700130878123[/C][/ROW]
[ROW][C]88[/C][C]110.2[/C][C]108.744762619189[/C][C]1.45523738081117[/C][/ROW]
[ROW][C]89[/C][C]161.46[/C][C]146.30505690287[/C][C]15.1549430971299[/C][/ROW]
[ROW][C]90[/C][C]99.41[/C][C]121.456527986439[/C][C]-22.0465279864389[/C][/ROW]
[ROW][C]91[/C][C]132.72[/C][C]101.836011346675[/C][C]30.8839886533248[/C][/ROW]
[ROW][C]92[/C][C]174.29[/C][C]91.0290895851693[/C][C]83.2609104148306[/C][/ROW]
[ROW][C]93[/C][C]69.93[/C][C]121.948232232915[/C][C]-52.0182322329146[/C][/ROW]
[ROW][C]94[/C][C]83.43[/C][C]95.002517722281[/C][C]-11.5725177222810[/C][/ROW]
[ROW][C]95[/C][C]127.53[/C][C]117.317612647034[/C][C]10.2123873529658[/C][/ROW]
[ROW][C]96[/C][C]187.58[/C][C]133.953171842144[/C][C]53.6268281578561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14641&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14641&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	110.48	111.736474939613	-1.25647493961348
14	96.34	99.4988590250444	-3.15885902504442
15	100.43	103.470670299025	-3.04067029902475
16	90.88	95.0244730531934	-4.14447305319345
17	128.28	132.955055957219	-4.67505595721923
18	101.21	106.004473839159	-4.7944738391593
19	73.76	79.4293145299933	-5.66931452999331
20	73.64	78.9539845780263	-5.31398457802625
21	66.4	71.2592656590775	-4.85926565907747
22	57.34	61.738754984121	-4.39875498412105
23	113.59	118.43535642114	-4.84535642114002
24	123.53	127.924565658567	-4.39456565856659
25	102.87	108.020329796908	-5.15032979690821
26	102.99	95.2218071646726	7.7681928353274
27	95.8	99.973556784294	-4.17355678429402
28	98.43	91.2804560281997	7.14954397180034
29	102.65	129.917878039412	-27.2678780394124
30	129.55	101.373698645658	28.1763013543415
31	100.37	76.9645648871014	23.4054351128986
32	101.93	78.5707128129637	23.3592871870363
33	101.94	72.9445947182304	28.9954052817696
34	93.87	65.8548727537672	28.0151272462328
35	100.91	124.743808612160	-23.8338086121603
36	92.64	132.977496410041	-40.3374964100406
37	101.67	110.451941640415	-8.78194164041494
38	88.67	99.3652898654362	-10.6952898654362
39	129.86	101.01302637738	28.84697362262
40	98.07	96.3449177386338	1.72508226136623
41	166.45	129.368657303585	37.0813426964152
42	176.52	113.745571310364	62.774428689636
43	82.07	91.0232946249226	-8.95329462492265
44	92.18	90.3659991368132	1.81400086318679
45	95.02	84.0948367838307	10.9251632161693
46	84.69	75.595933698266	9.094066301734
47	103.01	125.278443640579	-22.268443640579
48	107.9	131.110818519944	-23.2108185199436
49	204.13	114.57962496119	89.55037503881
50	101.99	110.058785561811	-8.06878556181142
51	119.23	117.904666965965	1.3253330340346
52	95.65	107.191769832729	-11.5417698327285
53	160.95	144.668629975369	16.2813700246313
54	111.06	131.503449087175	-20.4434490871753
55	150.41	92.0673578668811	58.3426421331189
56	94.79	97.7405842294255	-2.95058422942544
57	160.34	92.523129925277	67.816870074723
58	104.08	87.7128339723569	16.3671660276431
59	101.07	133.131781552008	-32.0617815520083
60	111.5	138.137902126149	-26.6379021261493
61	136.9	138.520468284303	-1.62046828430348
62	141.71	112.792750670209	28.9172493297908
63	153.98	124.646716610305	29.3332833896947
64	134.27	113.929569643710	20.3404303562896
65	124.71	157.861957583486	-33.1519575834864
66	72.89	135.663297813462	-62.7732978134621
67	101.2	105.260074406501	-4.06007440650085
68	73.28	97.258208845431	-23.9782088454310
69	174.05	101.339299257699	72.7107007423006
70	111.9	89.0439554982013	22.8560445017987
71	97.06	127.548584540667	-30.4885845406669
72	105.23	133.489463161537	-28.2594631615372
73	109.13	137.564497103394	-28.4344971033939
74	84.04	114.612259280672	-30.5722592806718
75	118.82	122.381216287461	-3.56121628746060
76	90.84	108.002332525738	-17.1623325257381
77	144.28	141.182569439872	3.09743056012823
78	110.16	117.005767166331	-6.84576716633123
79	86.09	99.4336524196254	-13.3436524196254
80	59.87	87.7545700279856	-27.8845700279856
81	108.97	106.271154441870	2.69884555813042
82	94.93	81.5101067543454	13.4198932456546
83	87.36	111.242188853492	-23.8821888534922
84	143.52	117.982825638877	25.5371743611229
85	108.7	125.782555802500	-17.0825558025005
86	121.13	103.296719211739	17.8332807882614
87	210.25	118.549869121877	91.700130878123
88	110.2	108.744762619189	1.45523738081117
89	161.46	146.30505690287	15.1549430971299
90	99.41	121.456527986439	-22.0465279864389
91	132.72	101.836011346675	30.8839886533248
92	174.29	91.0290895851693	83.2609104148306
93	69.93	121.948232232915	-52.0182322329146
94	83.43	95.002517722281	-11.5725177222810
95	127.53	117.317612647034	10.2123873529658
96	187.58	133.953171842144	53.6268281578561

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	137.228511023162	78.1162289645769	196.340793081748
98	121.245110194523	61.9892861046106	180.500934284435
99	146.491017708402	87.091998465864	205.890036950940
100	116.563865953365	57.0219959342246	176.105735972506
101	156.106623131848	96.4222442394018	215.791002024294
102	124.542393188877	64.715844883146	184.368941494607
103	114.510771349291	54.5423906759837	174.479152022599
104	109.517608293969	49.407729912961	169.627486674977
105	114.052774029139	53.8017302424929	174.303817815786
106	96.8867939425292	36.4949147220477	157.278673163011
107	123.322681872764	62.7902948871007	183.855068858427
108	145.850128993381	85.1775596347089	206.522698352053

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 137.228511023162 & 78.1162289645769 & 196.340793081748 \tabularnewline
98 & 121.245110194523 & 61.9892861046106 & 180.500934284435 \tabularnewline
99 & 146.491017708402 & 87.091998465864 & 205.890036950940 \tabularnewline
100 & 116.563865953365 & 57.0219959342246 & 176.105735972506 \tabularnewline
101 & 156.106623131848 & 96.4222442394018 & 215.791002024294 \tabularnewline
102 & 124.542393188877 & 64.715844883146 & 184.368941494607 \tabularnewline
103 & 114.510771349291 & 54.5423906759837 & 174.479152022599 \tabularnewline
104 & 109.517608293969 & 49.407729912961 & 169.627486674977 \tabularnewline
105 & 114.052774029139 & 53.8017302424929 & 174.303817815786 \tabularnewline
106 & 96.8867939425292 & 36.4949147220477 & 157.278673163011 \tabularnewline
107 & 123.322681872764 & 62.7902948871007 & 183.855068858427 \tabularnewline
108 & 145.850128993381 & 85.1775596347089 & 206.522698352053 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14641&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]97[/C][C]137.228511023162[/C][C]78.1162289645769[/C][C]196.340793081748[/C][/ROW]
[ROW][C]98[/C][C]121.245110194523[/C][C]61.9892861046106[/C][C]180.500934284435[/C][/ROW]
[ROW][C]99[/C][C]146.491017708402[/C][C]87.091998465864[/C][C]205.890036950940[/C][/ROW]
[ROW][C]100[/C][C]116.563865953365[/C][C]57.0219959342246[/C][C]176.105735972506[/C][/ROW]
[ROW][C]101[/C][C]156.106623131848[/C][C]96.4222442394018[/C][C]215.791002024294[/C][/ROW]
[ROW][C]102[/C][C]124.542393188877[/C][C]64.715844883146[/C][C]184.368941494607[/C][/ROW]
[ROW][C]103[/C][C]114.510771349291[/C][C]54.5423906759837[/C][C]174.479152022599[/C][/ROW]
[ROW][C]104[/C][C]109.517608293969[/C][C]49.407729912961[/C][C]169.627486674977[/C][/ROW]
[ROW][C]105[/C][C]114.052774029139[/C][C]53.8017302424929[/C][C]174.303817815786[/C][/ROW]
[ROW][C]106[/C][C]96.8867939425292[/C][C]36.4949147220477[/C][C]157.278673163011[/C][/ROW]
[ROW][C]107[/C][C]123.322681872764[/C][C]62.7902948871007[/C][C]183.855068858427[/C][/ROW]
[ROW][C]108[/C][C]145.850128993381[/C][C]85.1775596347089[/C][C]206.522698352053[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14641&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14641&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
97	137.228511023162	78.1162289645769	196.340793081748
98	121.245110194523	61.9892861046106	180.500934284435
99	146.491017708402	87.091998465864	205.890036950940
100	116.563865953365	57.0219959342246	176.105735972506
101	156.106623131848	96.4222442394018	215.791002024294
102	124.542393188877	64.715844883146	184.368941494607
103	114.510771349291	54.5423906759837	174.479152022599
104	109.517608293969	49.407729912961	169.627486674977
105	114.052774029139	53.8017302424929	174.303817815786
106	96.8867939425292	36.4949147220477	157.278673163011
107	123.322681872764	62.7902948871007	183.855068858427
108	145.850128993381	85.1775596347089	206.522698352053

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code