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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 16 Jan 2011 16:27:04 +0000

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/2011/Jan/16/t1295195093gkw6i6850hzpe50.htm/, Retrieved Thu, 16 May 2024 18:50:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117442, Retrieved Thu, 16 May 2024 18:50:02 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

107

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

-     [] [oef 8.3.3] [1970-01-01 00:00:00] [04d4ebd708b081bb203cd3af96bd9a4a]
- RMPD  [Standard Deviation-Mean Plot] [oef 8.3.3 ] [2010-12-07 21:27:00] [04d4ebd708b081bb203cd3af96bd9a4a]
- RMP       [Exponential Smoothing] [opgave 10.2] [2011-01-16 16:27:04] [d41d8cd98f00b204e9800998ecf8427e] [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' @ www.yougetit.org

\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' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117442&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' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117442&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117442&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' @ www.yougetit.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.935037349291743
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.935037349291743 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117442&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]0.935037349291743[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117442&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117442&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	0.935037349291743
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	102.35	101.873803418803	0.476196581196518
14	102.39	102.358234588247	0.0317654117531703
15	102.49	102.490022681738	-2.2681737931407e-05
16	102.67	102.681671053885	-0.0116710538853795
17	102.68	102.69826109635	-0.0182610963498888
18	102.7	102.716189202977	-0.0161892029766335
19	102.71	102.706471273958	0.00352872604219101
20	102.72	102.697273678356	0.0227263216444413
21	102.83	102.870609884991	-0.040609884991369
22	102.92	103.088057706194	-0.168057706193594
23	103.04	103.020503721153	0.0194962788474555
24	103.08	103.049153050467	0.0308469495332986
25	103.09	103.108100672984	-0.0181006729843602
26	103.11	103.101474021292	0.00852597870817817
27	103.18	103.209467338095	-0.0294673380953299
28	103.18	103.37282714768	-0.192827147680418
29	103.22	103.219601369768	0.000398630231984498
30	103.25	103.255111613362	-0.00511161336189048
31	103.25	103.257032573309	-0.00703257330850704
32	103.25	103.239206895054	0.0107931049461598
33	103.47	103.397270610511	0.0727293894893108
34	103.57	103.712415538202	-0.142415538201703
35	103.66	103.681021941969	-0.0210219419690532
36	103.7	103.672522591148	0.0274774088520218
37	103.7	103.725139799974	-0.0251397999740846
38	103.75	103.713661039513	0.0363389604868019
39	103.85	103.845192386506	0.0048076134938384
40	104.02	104.029988269722	-0.0099882697224274
41	104.13	104.060276130322	0.0697238696783131
42	104.17	104.160250102017	0.00974989798343984
43	104.18	104.175942339488	0.00405766051206058
44	104.2	104.169644447378	0.0303555526220123
45	104.5	104.350023327274	0.149976672725728
46	104.78	104.723420965133	0.0565790348666155
47	104.88	104.885980776816	-0.00598077681627274
48	104.89	104.894696123577	-0.00469612357687765
49	104.9	104.913811724565	-0.0138117245650875
50	104.95	104.916918960949	0.0330810390509981
51	105.24	105.043355669837	0.196644330162627
52	105.35	105.406564868311	-0.0565648683111561
53	105.44	105.398480181496	0.0415198185039145
54	105.46	105.468186243767	-0.00818624376678656
55	105.47	105.466737735965	0.00326226403508656
56	105.48	105.461404499221	0.0185955007790284
57	105.75	105.638558196457	0.111441803542903
58	106.1	105.969856934255	0.130143065745031
59	106.19	106.197137811179	-0.00713781117889312
60	106.23	106.204854742076	0.0251452579243079
61	106.24	106.251280975719	-0.0112809757189893
62	106.25	106.259800835019	-0.00980083501922024
63	106.35	106.356766894993	-0.00676689499348981
64	106.48	106.513329859965	-0.0333298599645389
65	106.52	106.533342615014	-0.0133426150140679
66	106.55	106.548521215311	0.00147878468895613
67	106.55	106.556853595511	-0.00685359551073361
68	106.56	106.543057739974	0.0169422600259281
69	106.89	106.724697137295	0.165302862705317
70	107.09	107.107572860646	-0.0175728606460552
71	107.24	107.187815699653	0.0521843003474345
72	107.28	107.253098214207	0.0269017857927309
73	107.3	107.29880052232	0.00119947768017425
74	107.31	107.319086225548	-0.00908622554764804
75	107.47	107.416917564854	0.0530824351458534
76	107.35	107.62771628822	-0.27771628822039
77	107.31	107.420517029603	-0.110517029603017
78	107.32	107.345796760276	-0.0257967602756963
79	107.32	107.328084193707	-0.00808419370669355
80	107.34	107.314683524746	0.0253164752536321
81	107.53	107.513791024087	0.0162089759133721
82	107.72	107.745378302997	-0.0253783029973675
83	107.75	107.822854371962	-0.0728543719616681
84	107.79	107.769578638639	0.0204213613605475
85	107.81	107.807551817804	0.00244818219566412
86	107.9	107.828336919846	0.071663080153698
87	107.8	108.005710516903	-0.205710516902585
88	107.86	107.953038602449	-0.0930386024492833
89	107.8	107.929381584645	-0.129381584644904
90	107.74	107.84252590504	-0.10252590503984
91	107.75	107.754219377612	-0.0042193776123014
92	107.83	107.746602252039	0.0833977479605323
93	107.8	107.999426263357	-0.199426263356628
94	107.81	108.026684919853	-0.216684919852668
95	107.86	107.922197985605	-0.0621979856054935
96	107.83	107.884945810418	-0.0549458104181753

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 102.35 & 101.873803418803 & 0.476196581196518 \tabularnewline
14 & 102.39 & 102.358234588247 & 0.0317654117531703 \tabularnewline
15 & 102.49 & 102.490022681738 & -2.2681737931407e-05 \tabularnewline
16 & 102.67 & 102.681671053885 & -0.0116710538853795 \tabularnewline
17 & 102.68 & 102.69826109635 & -0.0182610963498888 \tabularnewline
18 & 102.7 & 102.716189202977 & -0.0161892029766335 \tabularnewline
19 & 102.71 & 102.706471273958 & 0.00352872604219101 \tabularnewline
20 & 102.72 & 102.697273678356 & 0.0227263216444413 \tabularnewline
21 & 102.83 & 102.870609884991 & -0.040609884991369 \tabularnewline
22 & 102.92 & 103.088057706194 & -0.168057706193594 \tabularnewline
23 & 103.04 & 103.020503721153 & 0.0194962788474555 \tabularnewline
24 & 103.08 & 103.049153050467 & 0.0308469495332986 \tabularnewline
25 & 103.09 & 103.108100672984 & -0.0181006729843602 \tabularnewline
26 & 103.11 & 103.101474021292 & 0.00852597870817817 \tabularnewline
27 & 103.18 & 103.209467338095 & -0.0294673380953299 \tabularnewline
28 & 103.18 & 103.37282714768 & -0.192827147680418 \tabularnewline
29 & 103.22 & 103.219601369768 & 0.000398630231984498 \tabularnewline
30 & 103.25 & 103.255111613362 & -0.00511161336189048 \tabularnewline
31 & 103.25 & 103.257032573309 & -0.00703257330850704 \tabularnewline
32 & 103.25 & 103.239206895054 & 0.0107931049461598 \tabularnewline
33 & 103.47 & 103.397270610511 & 0.0727293894893108 \tabularnewline
34 & 103.57 & 103.712415538202 & -0.142415538201703 \tabularnewline
35 & 103.66 & 103.681021941969 & -0.0210219419690532 \tabularnewline
36 & 103.7 & 103.672522591148 & 0.0274774088520218 \tabularnewline
37 & 103.7 & 103.725139799974 & -0.0251397999740846 \tabularnewline
38 & 103.75 & 103.713661039513 & 0.0363389604868019 \tabularnewline
39 & 103.85 & 103.845192386506 & 0.0048076134938384 \tabularnewline
40 & 104.02 & 104.029988269722 & -0.0099882697224274 \tabularnewline
41 & 104.13 & 104.060276130322 & 0.0697238696783131 \tabularnewline
42 & 104.17 & 104.160250102017 & 0.00974989798343984 \tabularnewline
43 & 104.18 & 104.175942339488 & 0.00405766051206058 \tabularnewline
44 & 104.2 & 104.169644447378 & 0.0303555526220123 \tabularnewline
45 & 104.5 & 104.350023327274 & 0.149976672725728 \tabularnewline
46 & 104.78 & 104.723420965133 & 0.0565790348666155 \tabularnewline
47 & 104.88 & 104.885980776816 & -0.00598077681627274 \tabularnewline
48 & 104.89 & 104.894696123577 & -0.00469612357687765 \tabularnewline
49 & 104.9 & 104.913811724565 & -0.0138117245650875 \tabularnewline
50 & 104.95 & 104.916918960949 & 0.0330810390509981 \tabularnewline
51 & 105.24 & 105.043355669837 & 0.196644330162627 \tabularnewline
52 & 105.35 & 105.406564868311 & -0.0565648683111561 \tabularnewline
53 & 105.44 & 105.398480181496 & 0.0415198185039145 \tabularnewline
54 & 105.46 & 105.468186243767 & -0.00818624376678656 \tabularnewline
55 & 105.47 & 105.466737735965 & 0.00326226403508656 \tabularnewline
56 & 105.48 & 105.461404499221 & 0.0185955007790284 \tabularnewline
57 & 105.75 & 105.638558196457 & 0.111441803542903 \tabularnewline
58 & 106.1 & 105.969856934255 & 0.130143065745031 \tabularnewline
59 & 106.19 & 106.197137811179 & -0.00713781117889312 \tabularnewline
60 & 106.23 & 106.204854742076 & 0.0251452579243079 \tabularnewline
61 & 106.24 & 106.251280975719 & -0.0112809757189893 \tabularnewline
62 & 106.25 & 106.259800835019 & -0.00980083501922024 \tabularnewline
63 & 106.35 & 106.356766894993 & -0.00676689499348981 \tabularnewline
64 & 106.48 & 106.513329859965 & -0.0333298599645389 \tabularnewline
65 & 106.52 & 106.533342615014 & -0.0133426150140679 \tabularnewline
66 & 106.55 & 106.548521215311 & 0.00147878468895613 \tabularnewline
67 & 106.55 & 106.556853595511 & -0.00685359551073361 \tabularnewline
68 & 106.56 & 106.543057739974 & 0.0169422600259281 \tabularnewline
69 & 106.89 & 106.724697137295 & 0.165302862705317 \tabularnewline
70 & 107.09 & 107.107572860646 & -0.0175728606460552 \tabularnewline
71 & 107.24 & 107.187815699653 & 0.0521843003474345 \tabularnewline
72 & 107.28 & 107.253098214207 & 0.0269017857927309 \tabularnewline
73 & 107.3 & 107.29880052232 & 0.00119947768017425 \tabularnewline
74 & 107.31 & 107.319086225548 & -0.00908622554764804 \tabularnewline
75 & 107.47 & 107.416917564854 & 0.0530824351458534 \tabularnewline
76 & 107.35 & 107.62771628822 & -0.27771628822039 \tabularnewline
77 & 107.31 & 107.420517029603 & -0.110517029603017 \tabularnewline
78 & 107.32 & 107.345796760276 & -0.0257967602756963 \tabularnewline
79 & 107.32 & 107.328084193707 & -0.00808419370669355 \tabularnewline
80 & 107.34 & 107.314683524746 & 0.0253164752536321 \tabularnewline
81 & 107.53 & 107.513791024087 & 0.0162089759133721 \tabularnewline
82 & 107.72 & 107.745378302997 & -0.0253783029973675 \tabularnewline
83 & 107.75 & 107.822854371962 & -0.0728543719616681 \tabularnewline
84 & 107.79 & 107.769578638639 & 0.0204213613605475 \tabularnewline
85 & 107.81 & 107.807551817804 & 0.00244818219566412 \tabularnewline
86 & 107.9 & 107.828336919846 & 0.071663080153698 \tabularnewline
87 & 107.8 & 108.005710516903 & -0.205710516902585 \tabularnewline
88 & 107.86 & 107.953038602449 & -0.0930386024492833 \tabularnewline
89 & 107.8 & 107.929381584645 & -0.129381584644904 \tabularnewline
90 & 107.74 & 107.84252590504 & -0.10252590503984 \tabularnewline
91 & 107.75 & 107.754219377612 & -0.0042193776123014 \tabularnewline
92 & 107.83 & 107.746602252039 & 0.0833977479605323 \tabularnewline
93 & 107.8 & 107.999426263357 & -0.199426263356628 \tabularnewline
94 & 107.81 & 108.026684919853 & -0.216684919852668 \tabularnewline
95 & 107.86 & 107.922197985605 & -0.0621979856054935 \tabularnewline
96 & 107.83 & 107.884945810418 & -0.0549458104181753 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117442&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]102.35[/C][C]101.873803418803[/C][C]0.476196581196518[/C][/ROW]
[ROW][C]14[/C][C]102.39[/C][C]102.358234588247[/C][C]0.0317654117531703[/C][/ROW]
[ROW][C]15[/C][C]102.49[/C][C]102.490022681738[/C][C]-2.2681737931407e-05[/C][/ROW]
[ROW][C]16[/C][C]102.67[/C][C]102.681671053885[/C][C]-0.0116710538853795[/C][/ROW]
[ROW][C]17[/C][C]102.68[/C][C]102.69826109635[/C][C]-0.0182610963498888[/C][/ROW]
[ROW][C]18[/C][C]102.7[/C][C]102.716189202977[/C][C]-0.0161892029766335[/C][/ROW]
[ROW][C]19[/C][C]102.71[/C][C]102.706471273958[/C][C]0.00352872604219101[/C][/ROW]
[ROW][C]20[/C][C]102.72[/C][C]102.697273678356[/C][C]0.0227263216444413[/C][/ROW]
[ROW][C]21[/C][C]102.83[/C][C]102.870609884991[/C][C]-0.040609884991369[/C][/ROW]
[ROW][C]22[/C][C]102.92[/C][C]103.088057706194[/C][C]-0.168057706193594[/C][/ROW]
[ROW][C]23[/C][C]103.04[/C][C]103.020503721153[/C][C]0.0194962788474555[/C][/ROW]
[ROW][C]24[/C][C]103.08[/C][C]103.049153050467[/C][C]0.0308469495332986[/C][/ROW]
[ROW][C]25[/C][C]103.09[/C][C]103.108100672984[/C][C]-0.0181006729843602[/C][/ROW]
[ROW][C]26[/C][C]103.11[/C][C]103.101474021292[/C][C]0.00852597870817817[/C][/ROW]
[ROW][C]27[/C][C]103.18[/C][C]103.209467338095[/C][C]-0.0294673380953299[/C][/ROW]
[ROW][C]28[/C][C]103.18[/C][C]103.37282714768[/C][C]-0.192827147680418[/C][/ROW]
[ROW][C]29[/C][C]103.22[/C][C]103.219601369768[/C][C]0.000398630231984498[/C][/ROW]
[ROW][C]30[/C][C]103.25[/C][C]103.255111613362[/C][C]-0.00511161336189048[/C][/ROW]
[ROW][C]31[/C][C]103.25[/C][C]103.257032573309[/C][C]-0.00703257330850704[/C][/ROW]
[ROW][C]32[/C][C]103.25[/C][C]103.239206895054[/C][C]0.0107931049461598[/C][/ROW]
[ROW][C]33[/C][C]103.47[/C][C]103.397270610511[/C][C]0.0727293894893108[/C][/ROW]
[ROW][C]34[/C][C]103.57[/C][C]103.712415538202[/C][C]-0.142415538201703[/C][/ROW]
[ROW][C]35[/C][C]103.66[/C][C]103.681021941969[/C][C]-0.0210219419690532[/C][/ROW]
[ROW][C]36[/C][C]103.7[/C][C]103.672522591148[/C][C]0.0274774088520218[/C][/ROW]
[ROW][C]37[/C][C]103.7[/C][C]103.725139799974[/C][C]-0.0251397999740846[/C][/ROW]
[ROW][C]38[/C][C]103.75[/C][C]103.713661039513[/C][C]0.0363389604868019[/C][/ROW]
[ROW][C]39[/C][C]103.85[/C][C]103.845192386506[/C][C]0.0048076134938384[/C][/ROW]
[ROW][C]40[/C][C]104.02[/C][C]104.029988269722[/C][C]-0.0099882697224274[/C][/ROW]
[ROW][C]41[/C][C]104.13[/C][C]104.060276130322[/C][C]0.0697238696783131[/C][/ROW]
[ROW][C]42[/C][C]104.17[/C][C]104.160250102017[/C][C]0.00974989798343984[/C][/ROW]
[ROW][C]43[/C][C]104.18[/C][C]104.175942339488[/C][C]0.00405766051206058[/C][/ROW]
[ROW][C]44[/C][C]104.2[/C][C]104.169644447378[/C][C]0.0303555526220123[/C][/ROW]
[ROW][C]45[/C][C]104.5[/C][C]104.350023327274[/C][C]0.149976672725728[/C][/ROW]
[ROW][C]46[/C][C]104.78[/C][C]104.723420965133[/C][C]0.0565790348666155[/C][/ROW]
[ROW][C]47[/C][C]104.88[/C][C]104.885980776816[/C][C]-0.00598077681627274[/C][/ROW]
[ROW][C]48[/C][C]104.89[/C][C]104.894696123577[/C][C]-0.00469612357687765[/C][/ROW]
[ROW][C]49[/C][C]104.9[/C][C]104.913811724565[/C][C]-0.0138117245650875[/C][/ROW]
[ROW][C]50[/C][C]104.95[/C][C]104.916918960949[/C][C]0.0330810390509981[/C][/ROW]
[ROW][C]51[/C][C]105.24[/C][C]105.043355669837[/C][C]0.196644330162627[/C][/ROW]
[ROW][C]52[/C][C]105.35[/C][C]105.406564868311[/C][C]-0.0565648683111561[/C][/ROW]
[ROW][C]53[/C][C]105.44[/C][C]105.398480181496[/C][C]0.0415198185039145[/C][/ROW]
[ROW][C]54[/C][C]105.46[/C][C]105.468186243767[/C][C]-0.00818624376678656[/C][/ROW]
[ROW][C]55[/C][C]105.47[/C][C]105.466737735965[/C][C]0.00326226403508656[/C][/ROW]
[ROW][C]56[/C][C]105.48[/C][C]105.461404499221[/C][C]0.0185955007790284[/C][/ROW]
[ROW][C]57[/C][C]105.75[/C][C]105.638558196457[/C][C]0.111441803542903[/C][/ROW]
[ROW][C]58[/C][C]106.1[/C][C]105.969856934255[/C][C]0.130143065745031[/C][/ROW]
[ROW][C]59[/C][C]106.19[/C][C]106.197137811179[/C][C]-0.00713781117889312[/C][/ROW]
[ROW][C]60[/C][C]106.23[/C][C]106.204854742076[/C][C]0.0251452579243079[/C][/ROW]
[ROW][C]61[/C][C]106.24[/C][C]106.251280975719[/C][C]-0.0112809757189893[/C][/ROW]
[ROW][C]62[/C][C]106.25[/C][C]106.259800835019[/C][C]-0.00980083501922024[/C][/ROW]
[ROW][C]63[/C][C]106.35[/C][C]106.356766894993[/C][C]-0.00676689499348981[/C][/ROW]
[ROW][C]64[/C][C]106.48[/C][C]106.513329859965[/C][C]-0.0333298599645389[/C][/ROW]
[ROW][C]65[/C][C]106.52[/C][C]106.533342615014[/C][C]-0.0133426150140679[/C][/ROW]
[ROW][C]66[/C][C]106.55[/C][C]106.548521215311[/C][C]0.00147878468895613[/C][/ROW]
[ROW][C]67[/C][C]106.55[/C][C]106.556853595511[/C][C]-0.00685359551073361[/C][/ROW]
[ROW][C]68[/C][C]106.56[/C][C]106.543057739974[/C][C]0.0169422600259281[/C][/ROW]
[ROW][C]69[/C][C]106.89[/C][C]106.724697137295[/C][C]0.165302862705317[/C][/ROW]
[ROW][C]70[/C][C]107.09[/C][C]107.107572860646[/C][C]-0.0175728606460552[/C][/ROW]
[ROW][C]71[/C][C]107.24[/C][C]107.187815699653[/C][C]0.0521843003474345[/C][/ROW]
[ROW][C]72[/C][C]107.28[/C][C]107.253098214207[/C][C]0.0269017857927309[/C][/ROW]
[ROW][C]73[/C][C]107.3[/C][C]107.29880052232[/C][C]0.00119947768017425[/C][/ROW]
[ROW][C]74[/C][C]107.31[/C][C]107.319086225548[/C][C]-0.00908622554764804[/C][/ROW]
[ROW][C]75[/C][C]107.47[/C][C]107.416917564854[/C][C]0.0530824351458534[/C][/ROW]
[ROW][C]76[/C][C]107.35[/C][C]107.62771628822[/C][C]-0.27771628822039[/C][/ROW]
[ROW][C]77[/C][C]107.31[/C][C]107.420517029603[/C][C]-0.110517029603017[/C][/ROW]
[ROW][C]78[/C][C]107.32[/C][C]107.345796760276[/C][C]-0.0257967602756963[/C][/ROW]
[ROW][C]79[/C][C]107.32[/C][C]107.328084193707[/C][C]-0.00808419370669355[/C][/ROW]
[ROW][C]80[/C][C]107.34[/C][C]107.314683524746[/C][C]0.0253164752536321[/C][/ROW]
[ROW][C]81[/C][C]107.53[/C][C]107.513791024087[/C][C]0.0162089759133721[/C][/ROW]
[ROW][C]82[/C][C]107.72[/C][C]107.745378302997[/C][C]-0.0253783029973675[/C][/ROW]
[ROW][C]83[/C][C]107.75[/C][C]107.822854371962[/C][C]-0.0728543719616681[/C][/ROW]
[ROW][C]84[/C][C]107.79[/C][C]107.769578638639[/C][C]0.0204213613605475[/C][/ROW]
[ROW][C]85[/C][C]107.81[/C][C]107.807551817804[/C][C]0.00244818219566412[/C][/ROW]
[ROW][C]86[/C][C]107.9[/C][C]107.828336919846[/C][C]0.071663080153698[/C][/ROW]
[ROW][C]87[/C][C]107.8[/C][C]108.005710516903[/C][C]-0.205710516902585[/C][/ROW]
[ROW][C]88[/C][C]107.86[/C][C]107.953038602449[/C][C]-0.0930386024492833[/C][/ROW]
[ROW][C]89[/C][C]107.8[/C][C]107.929381584645[/C][C]-0.129381584644904[/C][/ROW]
[ROW][C]90[/C][C]107.74[/C][C]107.84252590504[/C][C]-0.10252590503984[/C][/ROW]
[ROW][C]91[/C][C]107.75[/C][C]107.754219377612[/C][C]-0.0042193776123014[/C][/ROW]
[ROW][C]92[/C][C]107.83[/C][C]107.746602252039[/C][C]0.0833977479605323[/C][/ROW]
[ROW][C]93[/C][C]107.8[/C][C]107.999426263357[/C][C]-0.199426263356628[/C][/ROW]
[ROW][C]94[/C][C]107.81[/C][C]108.026684919853[/C][C]-0.216684919852668[/C][/ROW]
[ROW][C]95[/C][C]107.86[/C][C]107.922197985605[/C][C]-0.0621979856054935[/C][/ROW]
[ROW][C]96[/C][C]107.83[/C][C]107.884945810418[/C][C]-0.0549458104181753[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117442&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117442&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	102.35	101.873803418803	0.476196581196518
14	102.39	102.358234588247	0.0317654117531703
15	102.49	102.490022681738	-2.2681737931407e-05
16	102.67	102.681671053885	-0.0116710538853795
17	102.68	102.69826109635	-0.0182610963498888
18	102.7	102.716189202977	-0.0161892029766335
19	102.71	102.706471273958	0.00352872604219101
20	102.72	102.697273678356	0.0227263216444413
21	102.83	102.870609884991	-0.040609884991369
22	102.92	103.088057706194	-0.168057706193594
23	103.04	103.020503721153	0.0194962788474555
24	103.08	103.049153050467	0.0308469495332986
25	103.09	103.108100672984	-0.0181006729843602
26	103.11	103.101474021292	0.00852597870817817
27	103.18	103.209467338095	-0.0294673380953299
28	103.18	103.37282714768	-0.192827147680418
29	103.22	103.219601369768	0.000398630231984498
30	103.25	103.255111613362	-0.00511161336189048
31	103.25	103.257032573309	-0.00703257330850704
32	103.25	103.239206895054	0.0107931049461598
33	103.47	103.397270610511	0.0727293894893108
34	103.57	103.712415538202	-0.142415538201703
35	103.66	103.681021941969	-0.0210219419690532
36	103.7	103.672522591148	0.0274774088520218
37	103.7	103.725139799974	-0.0251397999740846
38	103.75	103.713661039513	0.0363389604868019
39	103.85	103.845192386506	0.0048076134938384
40	104.02	104.029988269722	-0.0099882697224274
41	104.13	104.060276130322	0.0697238696783131
42	104.17	104.160250102017	0.00974989798343984
43	104.18	104.175942339488	0.00405766051206058
44	104.2	104.169644447378	0.0303555526220123
45	104.5	104.350023327274	0.149976672725728
46	104.78	104.723420965133	0.0565790348666155
47	104.88	104.885980776816	-0.00598077681627274
48	104.89	104.894696123577	-0.00469612357687765
49	104.9	104.913811724565	-0.0138117245650875
50	104.95	104.916918960949	0.0330810390509981
51	105.24	105.043355669837	0.196644330162627
52	105.35	105.406564868311	-0.0565648683111561
53	105.44	105.398480181496	0.0415198185039145
54	105.46	105.468186243767	-0.00818624376678656
55	105.47	105.466737735965	0.00326226403508656
56	105.48	105.461404499221	0.0185955007790284
57	105.75	105.638558196457	0.111441803542903
58	106.1	105.969856934255	0.130143065745031
59	106.19	106.197137811179	-0.00713781117889312
60	106.23	106.204854742076	0.0251452579243079
61	106.24	106.251280975719	-0.0112809757189893
62	106.25	106.259800835019	-0.00980083501922024
63	106.35	106.356766894993	-0.00676689499348981
64	106.48	106.513329859965	-0.0333298599645389
65	106.52	106.533342615014	-0.0133426150140679
66	106.55	106.548521215311	0.00147878468895613
67	106.55	106.556853595511	-0.00685359551073361
68	106.56	106.543057739974	0.0169422600259281
69	106.89	106.724697137295	0.165302862705317
70	107.09	107.107572860646	-0.0175728606460552
71	107.24	107.187815699653	0.0521843003474345
72	107.28	107.253098214207	0.0269017857927309
73	107.3	107.29880052232	0.00119947768017425
74	107.31	107.319086225548	-0.00908622554764804
75	107.47	107.416917564854	0.0530824351458534
76	107.35	107.62771628822	-0.27771628822039
77	107.31	107.420517029603	-0.110517029603017
78	107.32	107.345796760276	-0.0257967602756963
79	107.32	107.328084193707	-0.00808419370669355
80	107.34	107.314683524746	0.0253164752536321
81	107.53	107.513791024087	0.0162089759133721
82	107.72	107.745378302997	-0.0253783029973675
83	107.75	107.822854371962	-0.0728543719616681
84	107.79	107.769578638639	0.0204213613605475
85	107.81	107.807551817804	0.00244818219566412
86	107.9	107.828336919846	0.071663080153698
87	107.8	108.005710516903	-0.205710516902585
88	107.86	107.953038602449	-0.0930386024492833
89	107.8	107.929381584645	-0.129381584644904
90	107.74	107.84252590504	-0.10252590503984
91	107.75	107.754219377612	-0.0042193776123014
92	107.83	107.746602252039	0.0833977479605323
93	107.8	107.999426263357	-0.199426263356628
94	107.81	108.026684919853	-0.216684919852668
95	107.86	107.922197985605	-0.0621979856054935
96	107.83	107.884945810418	-0.0549458104181753

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	107.851280283699	107.664899889459	108.03766067794
98	107.87427262719	107.619108756606	108.129436497774
99	107.966619643636	107.657621989364	108.275617297908
100	108.113614211852	107.758860071862	108.468368351842
101	108.174590825806	107.779342233988	108.569839417624
102	108.210456376288	107.778492953267	108.642419799309
103	108.224401651946	107.758608405621	108.690194898272
104	108.226421642756	107.729094489047	108.723748796466
105	108.382892647424	107.855915183664	108.909870111184
106	108.595501140515	108.040455019183	109.150547261847
107	108.703658580107	108.121896475549	109.285420684664
108	108.725034965035	108.11773100836	109.33233892171

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 107.851280283699 & 107.664899889459 & 108.03766067794 \tabularnewline
98 & 107.87427262719 & 107.619108756606 & 108.129436497774 \tabularnewline
99 & 107.966619643636 & 107.657621989364 & 108.275617297908 \tabularnewline
100 & 108.113614211852 & 107.758860071862 & 108.468368351842 \tabularnewline
101 & 108.174590825806 & 107.779342233988 & 108.569839417624 \tabularnewline
102 & 108.210456376288 & 107.778492953267 & 108.642419799309 \tabularnewline
103 & 108.224401651946 & 107.758608405621 & 108.690194898272 \tabularnewline
104 & 108.226421642756 & 107.729094489047 & 108.723748796466 \tabularnewline
105 & 108.382892647424 & 107.855915183664 & 108.909870111184 \tabularnewline
106 & 108.595501140515 & 108.040455019183 & 109.150547261847 \tabularnewline
107 & 108.703658580107 & 108.121896475549 & 109.285420684664 \tabularnewline
108 & 108.725034965035 & 108.11773100836 & 109.33233892171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117442&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]107.851280283699[/C][C]107.664899889459[/C][C]108.03766067794[/C][/ROW]
[ROW][C]98[/C][C]107.87427262719[/C][C]107.619108756606[/C][C]108.129436497774[/C][/ROW]
[ROW][C]99[/C][C]107.966619643636[/C][C]107.657621989364[/C][C]108.275617297908[/C][/ROW]
[ROW][C]100[/C][C]108.113614211852[/C][C]107.758860071862[/C][C]108.468368351842[/C][/ROW]
[ROW][C]101[/C][C]108.174590825806[/C][C]107.779342233988[/C][C]108.569839417624[/C][/ROW]
[ROW][C]102[/C][C]108.210456376288[/C][C]107.778492953267[/C][C]108.642419799309[/C][/ROW]
[ROW][C]103[/C][C]108.224401651946[/C][C]107.758608405621[/C][C]108.690194898272[/C][/ROW]
[ROW][C]104[/C][C]108.226421642756[/C][C]107.729094489047[/C][C]108.723748796466[/C][/ROW]
[ROW][C]105[/C][C]108.382892647424[/C][C]107.855915183664[/C][C]108.909870111184[/C][/ROW]
[ROW][C]106[/C][C]108.595501140515[/C][C]108.040455019183[/C][C]109.150547261847[/C][/ROW]
[ROW][C]107[/C][C]108.703658580107[/C][C]108.121896475549[/C][C]109.285420684664[/C][/ROW]
[ROW][C]108[/C][C]108.725034965035[/C][C]108.11773100836[/C][C]109.33233892171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117442&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117442&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	107.851280283699	107.664899889459	108.03766067794
98	107.87427262719	107.619108756606	108.129436497774
99	107.966619643636	107.657621989364	108.275617297908
100	108.113614211852	107.758860071862	108.468368351842
101	108.174590825806	107.779342233988	108.569839417624
102	108.210456376288	107.778492953267	108.642419799309
103	108.224401651946	107.758608405621	108.690194898272
104	108.226421642756	107.729094489047	108.723748796466
105	108.382892647424	107.855915183664	108.909870111184
106	108.595501140515	108.040455019183	109.150547261847
107	108.703658580107	108.121896475549	109.285420684664
108	108.725034965035	108.11773100836	109.33233892171

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=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