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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 29 May 2008 01:40:25 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/29/t1212046872m4w6iivsmx51h1h.htm/, Retrieved Wed, 15 May 2024 07:45:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13489, Retrieved Wed, 15 May 2024 07:45:05 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact213
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2008-05-29 07:40:25] [2d679ee92688abc2a19dfb46633cb8da] [Current]
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Dataseries X:
113000
110000
107000
103000
98000
98000
137000
148000
147000
139000
130000
128000
127000
123000
118000
114000
108000
111000
151000
159000
158000
148000
138000
137000
136000
133000
126000
120000
114000
116000
153000
162000
161000
149000
139000
135000
130000
127000
122000
117000
112000
113000
149000
157000
157000
147000
137000
132000
125000
123000
117000
114000
111000
112000
144000
150000
149000
134000
123000
116000
117000
111000
105000
102000
95000
93000
124000
130000
124000
115000
106000
105000




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13489&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13489&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13489&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.915663434874416
beta0.0895749531284736
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.915663434874416 \tabularnewline
beta & 0.0895749531284736 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13489&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]0.915663434874416[/C][/ROW]
[ROW][C]beta[/C][C]0.0895749531284736[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13489&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13489&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.915663434874416
beta0.0895749531284736
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13127000122743.5751859824256.42481401785
14123000122649.613222873350.386777127162
15118000118107.388716282-107.388716281886
16114000114202.936887386-202.936887385615
17108000108286.068362664-286.068362664213
18111000111276.631612865-276.631612864556
19151000151294.410955505-294.410955504864
20159000159226.353052911-226.353052910941
21158000158247.427387692-247.427387692267
22148000148396.198542146-396.198542146216
23138000138435.605664984-435.605664984119
24137000137443.212949773-443.212949772977
25136000136214.983508189-214.983508188685
26133000131103.9116344271896.08836557309
27126000127383.546322454-1383.54632245353
28120000121794.435581792-1794.43558179250
29114000113762.822080683237.177919317110
30116000117108.97693637-1108.97693637008
31153000157719.061136631-4719.06113663127
32162000160876.1596330241123.84036697622
33161000160375.456220262624.543779738044
34149000150504.786421154-1504.78642115393
35139000138797.695582466202.30441753412
36135000137788.952174263-2788.95217426325
37130000133680.536134512-3680.53613451167
38127000124788.7660973732211.23390262721
39122000120447.8605522261552.13944777426
40117000117007.055305401-7.05530540106702
41112000110458.5344386771541.46556132342
42113000114443.871764589-1443.87176458853
43149000152852.159291432-3852.15929143186
44157000156584.804447601415.195552398538
45157000154876.5484686632123.45153133676
46147000146060.756456847939.24354315328
47137000136674.123001984325.876998015825
48132000135352.391311146-3352.39131114594
49125000130440.551709414-5440.55170941388
50123000120229.0569353242770.94306467635
51117000116248.370142196751.629857803942
52114000111795.4113051882204.5886948119
53111000107410.7825849913589.21741500919
54112000112994.544436019-994.544436019103
55144000151335.221122636-7335.22112263629
56150000151760.217062282-1760.21706228246
57149000147857.4099473381142.59005266248
58134000138135.357544721-4135.35754472140
59123000124120.483048653-1120.48304865336
60116000120436.755365459-4436.75536545919
61117000113555.2444220323444.75557796756
62111000112162.540261358-1162.54026135805
63105000104463.020482013536.979517986649
6410200099867.14096927482132.8590307252
659500095657.6330475273-657.63304752727
669300095827.7625903503-2827.76259035029
67124000124070.902896474-70.9028964744939
68130000129641.767681409358.23231859073
69124000127442.631976233-3442.63197623273
70115000113876.1445369251123.85546307501
71106000105738.401137215261.59886278458
72105000102934.821259492065.17874051002

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 127000 & 122743.575185982 & 4256.42481401785 \tabularnewline
14 & 123000 & 122649.613222873 & 350.386777127162 \tabularnewline
15 & 118000 & 118107.388716282 & -107.388716281886 \tabularnewline
16 & 114000 & 114202.936887386 & -202.936887385615 \tabularnewline
17 & 108000 & 108286.068362664 & -286.068362664213 \tabularnewline
18 & 111000 & 111276.631612865 & -276.631612864556 \tabularnewline
19 & 151000 & 151294.410955505 & -294.410955504864 \tabularnewline
20 & 159000 & 159226.353052911 & -226.353052910941 \tabularnewline
21 & 158000 & 158247.427387692 & -247.427387692267 \tabularnewline
22 & 148000 & 148396.198542146 & -396.198542146216 \tabularnewline
23 & 138000 & 138435.605664984 & -435.605664984119 \tabularnewline
24 & 137000 & 137443.212949773 & -443.212949772977 \tabularnewline
25 & 136000 & 136214.983508189 & -214.983508188685 \tabularnewline
26 & 133000 & 131103.911634427 & 1896.08836557309 \tabularnewline
27 & 126000 & 127383.546322454 & -1383.54632245353 \tabularnewline
28 & 120000 & 121794.435581792 & -1794.43558179250 \tabularnewline
29 & 114000 & 113762.822080683 & 237.177919317110 \tabularnewline
30 & 116000 & 117108.97693637 & -1108.97693637008 \tabularnewline
31 & 153000 & 157719.061136631 & -4719.06113663127 \tabularnewline
32 & 162000 & 160876.159633024 & 1123.84036697622 \tabularnewline
33 & 161000 & 160375.456220262 & 624.543779738044 \tabularnewline
34 & 149000 & 150504.786421154 & -1504.78642115393 \tabularnewline
35 & 139000 & 138797.695582466 & 202.30441753412 \tabularnewline
36 & 135000 & 137788.952174263 & -2788.95217426325 \tabularnewline
37 & 130000 & 133680.536134512 & -3680.53613451167 \tabularnewline
38 & 127000 & 124788.766097373 & 2211.23390262721 \tabularnewline
39 & 122000 & 120447.860552226 & 1552.13944777426 \tabularnewline
40 & 117000 & 117007.055305401 & -7.05530540106702 \tabularnewline
41 & 112000 & 110458.534438677 & 1541.46556132342 \tabularnewline
42 & 113000 & 114443.871764589 & -1443.87176458853 \tabularnewline
43 & 149000 & 152852.159291432 & -3852.15929143186 \tabularnewline
44 & 157000 & 156584.804447601 & 415.195552398538 \tabularnewline
45 & 157000 & 154876.548468663 & 2123.45153133676 \tabularnewline
46 & 147000 & 146060.756456847 & 939.24354315328 \tabularnewline
47 & 137000 & 136674.123001984 & 325.876998015825 \tabularnewline
48 & 132000 & 135352.391311146 & -3352.39131114594 \tabularnewline
49 & 125000 & 130440.551709414 & -5440.55170941388 \tabularnewline
50 & 123000 & 120229.056935324 & 2770.94306467635 \tabularnewline
51 & 117000 & 116248.370142196 & 751.629857803942 \tabularnewline
52 & 114000 & 111795.411305188 & 2204.5886948119 \tabularnewline
53 & 111000 & 107410.782584991 & 3589.21741500919 \tabularnewline
54 & 112000 & 112994.544436019 & -994.544436019103 \tabularnewline
55 & 144000 & 151335.221122636 & -7335.22112263629 \tabularnewline
56 & 150000 & 151760.217062282 & -1760.21706228246 \tabularnewline
57 & 149000 & 147857.409947338 & 1142.59005266248 \tabularnewline
58 & 134000 & 138135.357544721 & -4135.35754472140 \tabularnewline
59 & 123000 & 124120.483048653 & -1120.48304865336 \tabularnewline
60 & 116000 & 120436.755365459 & -4436.75536545919 \tabularnewline
61 & 117000 & 113555.244422032 & 3444.75557796756 \tabularnewline
62 & 111000 & 112162.540261358 & -1162.54026135805 \tabularnewline
63 & 105000 & 104463.020482013 & 536.979517986649 \tabularnewline
64 & 102000 & 99867.1409692748 & 2132.8590307252 \tabularnewline
65 & 95000 & 95657.6330475273 & -657.63304752727 \tabularnewline
66 & 93000 & 95827.7625903503 & -2827.76259035029 \tabularnewline
67 & 124000 & 124070.902896474 & -70.9028964744939 \tabularnewline
68 & 130000 & 129641.767681409 & 358.23231859073 \tabularnewline
69 & 124000 & 127442.631976233 & -3442.63197623273 \tabularnewline
70 & 115000 & 113876.144536925 & 1123.85546307501 \tabularnewline
71 & 106000 & 105738.401137215 & 261.59886278458 \tabularnewline
72 & 105000 & 102934.82125949 & 2065.17874051002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13489&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]127000[/C][C]122743.575185982[/C][C]4256.42481401785[/C][/ROW]
[ROW][C]14[/C][C]123000[/C][C]122649.613222873[/C][C]350.386777127162[/C][/ROW]
[ROW][C]15[/C][C]118000[/C][C]118107.388716282[/C][C]-107.388716281886[/C][/ROW]
[ROW][C]16[/C][C]114000[/C][C]114202.936887386[/C][C]-202.936887385615[/C][/ROW]
[ROW][C]17[/C][C]108000[/C][C]108286.068362664[/C][C]-286.068362664213[/C][/ROW]
[ROW][C]18[/C][C]111000[/C][C]111276.631612865[/C][C]-276.631612864556[/C][/ROW]
[ROW][C]19[/C][C]151000[/C][C]151294.410955505[/C][C]-294.410955504864[/C][/ROW]
[ROW][C]20[/C][C]159000[/C][C]159226.353052911[/C][C]-226.353052910941[/C][/ROW]
[ROW][C]21[/C][C]158000[/C][C]158247.427387692[/C][C]-247.427387692267[/C][/ROW]
[ROW][C]22[/C][C]148000[/C][C]148396.198542146[/C][C]-396.198542146216[/C][/ROW]
[ROW][C]23[/C][C]138000[/C][C]138435.605664984[/C][C]-435.605664984119[/C][/ROW]
[ROW][C]24[/C][C]137000[/C][C]137443.212949773[/C][C]-443.212949772977[/C][/ROW]
[ROW][C]25[/C][C]136000[/C][C]136214.983508189[/C][C]-214.983508188685[/C][/ROW]
[ROW][C]26[/C][C]133000[/C][C]131103.911634427[/C][C]1896.08836557309[/C][/ROW]
[ROW][C]27[/C][C]126000[/C][C]127383.546322454[/C][C]-1383.54632245353[/C][/ROW]
[ROW][C]28[/C][C]120000[/C][C]121794.435581792[/C][C]-1794.43558179250[/C][/ROW]
[ROW][C]29[/C][C]114000[/C][C]113762.822080683[/C][C]237.177919317110[/C][/ROW]
[ROW][C]30[/C][C]116000[/C][C]117108.97693637[/C][C]-1108.97693637008[/C][/ROW]
[ROW][C]31[/C][C]153000[/C][C]157719.061136631[/C][C]-4719.06113663127[/C][/ROW]
[ROW][C]32[/C][C]162000[/C][C]160876.159633024[/C][C]1123.84036697622[/C][/ROW]
[ROW][C]33[/C][C]161000[/C][C]160375.456220262[/C][C]624.543779738044[/C][/ROW]
[ROW][C]34[/C][C]149000[/C][C]150504.786421154[/C][C]-1504.78642115393[/C][/ROW]
[ROW][C]35[/C][C]139000[/C][C]138797.695582466[/C][C]202.30441753412[/C][/ROW]
[ROW][C]36[/C][C]135000[/C][C]137788.952174263[/C][C]-2788.95217426325[/C][/ROW]
[ROW][C]37[/C][C]130000[/C][C]133680.536134512[/C][C]-3680.53613451167[/C][/ROW]
[ROW][C]38[/C][C]127000[/C][C]124788.766097373[/C][C]2211.23390262721[/C][/ROW]
[ROW][C]39[/C][C]122000[/C][C]120447.860552226[/C][C]1552.13944777426[/C][/ROW]
[ROW][C]40[/C][C]117000[/C][C]117007.055305401[/C][C]-7.05530540106702[/C][/ROW]
[ROW][C]41[/C][C]112000[/C][C]110458.534438677[/C][C]1541.46556132342[/C][/ROW]
[ROW][C]42[/C][C]113000[/C][C]114443.871764589[/C][C]-1443.87176458853[/C][/ROW]
[ROW][C]43[/C][C]149000[/C][C]152852.159291432[/C][C]-3852.15929143186[/C][/ROW]
[ROW][C]44[/C][C]157000[/C][C]156584.804447601[/C][C]415.195552398538[/C][/ROW]
[ROW][C]45[/C][C]157000[/C][C]154876.548468663[/C][C]2123.45153133676[/C][/ROW]
[ROW][C]46[/C][C]147000[/C][C]146060.756456847[/C][C]939.24354315328[/C][/ROW]
[ROW][C]47[/C][C]137000[/C][C]136674.123001984[/C][C]325.876998015825[/C][/ROW]
[ROW][C]48[/C][C]132000[/C][C]135352.391311146[/C][C]-3352.39131114594[/C][/ROW]
[ROW][C]49[/C][C]125000[/C][C]130440.551709414[/C][C]-5440.55170941388[/C][/ROW]
[ROW][C]50[/C][C]123000[/C][C]120229.056935324[/C][C]2770.94306467635[/C][/ROW]
[ROW][C]51[/C][C]117000[/C][C]116248.370142196[/C][C]751.629857803942[/C][/ROW]
[ROW][C]52[/C][C]114000[/C][C]111795.411305188[/C][C]2204.5886948119[/C][/ROW]
[ROW][C]53[/C][C]111000[/C][C]107410.782584991[/C][C]3589.21741500919[/C][/ROW]
[ROW][C]54[/C][C]112000[/C][C]112994.544436019[/C][C]-994.544436019103[/C][/ROW]
[ROW][C]55[/C][C]144000[/C][C]151335.221122636[/C][C]-7335.22112263629[/C][/ROW]
[ROW][C]56[/C][C]150000[/C][C]151760.217062282[/C][C]-1760.21706228246[/C][/ROW]
[ROW][C]57[/C][C]149000[/C][C]147857.409947338[/C][C]1142.59005266248[/C][/ROW]
[ROW][C]58[/C][C]134000[/C][C]138135.357544721[/C][C]-4135.35754472140[/C][/ROW]
[ROW][C]59[/C][C]123000[/C][C]124120.483048653[/C][C]-1120.48304865336[/C][/ROW]
[ROW][C]60[/C][C]116000[/C][C]120436.755365459[/C][C]-4436.75536545919[/C][/ROW]
[ROW][C]61[/C][C]117000[/C][C]113555.244422032[/C][C]3444.75557796756[/C][/ROW]
[ROW][C]62[/C][C]111000[/C][C]112162.540261358[/C][C]-1162.54026135805[/C][/ROW]
[ROW][C]63[/C][C]105000[/C][C]104463.020482013[/C][C]536.979517986649[/C][/ROW]
[ROW][C]64[/C][C]102000[/C][C]99867.1409692748[/C][C]2132.8590307252[/C][/ROW]
[ROW][C]65[/C][C]95000[/C][C]95657.6330475273[/C][C]-657.63304752727[/C][/ROW]
[ROW][C]66[/C][C]93000[/C][C]95827.7625903503[/C][C]-2827.76259035029[/C][/ROW]
[ROW][C]67[/C][C]124000[/C][C]124070.902896474[/C][C]-70.9028964744939[/C][/ROW]
[ROW][C]68[/C][C]130000[/C][C]129641.767681409[/C][C]358.23231859073[/C][/ROW]
[ROW][C]69[/C][C]124000[/C][C]127442.631976233[/C][C]-3442.63197623273[/C][/ROW]
[ROW][C]70[/C][C]115000[/C][C]113876.144536925[/C][C]1123.85546307501[/C][/ROW]
[ROW][C]71[/C][C]106000[/C][C]105738.401137215[/C][C]261.59886278458[/C][/ROW]
[ROW][C]72[/C][C]105000[/C][C]102934.82125949[/C][C]2065.17874051002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13489&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13489&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
13127000122743.5751859824256.42481401785
14123000122649.613222873350.386777127162
15118000118107.388716282-107.388716281886
16114000114202.936887386-202.936887385615
17108000108286.068362664-286.068362664213
18111000111276.631612865-276.631612864556
19151000151294.410955505-294.410955504864
20159000159226.353052911-226.353052910941
21158000158247.427387692-247.427387692267
22148000148396.198542146-396.198542146216
23138000138435.605664984-435.605664984119
24137000137443.212949773-443.212949772977
25136000136214.983508189-214.983508188685
26133000131103.9116344271896.08836557309
27126000127383.546322454-1383.54632245353
28120000121794.435581792-1794.43558179250
29114000113762.822080683237.177919317110
30116000117108.97693637-1108.97693637008
31153000157719.061136631-4719.06113663127
32162000160876.1596330241123.84036697622
33161000160375.456220262624.543779738044
34149000150504.786421154-1504.78642115393
35139000138797.695582466202.30441753412
36135000137788.952174263-2788.95217426325
37130000133680.536134512-3680.53613451167
38127000124788.7660973732211.23390262721
39122000120447.8605522261552.13944777426
40117000117007.055305401-7.05530540106702
41112000110458.5344386771541.46556132342
42113000114443.871764589-1443.87176458853
43149000152852.159291432-3852.15929143186
44157000156584.804447601415.195552398538
45157000154876.5484686632123.45153133676
46147000146060.756456847939.24354315328
47137000136674.123001984325.876998015825
48132000135352.391311146-3352.39131114594
49125000130440.551709414-5440.55170941388
50123000120229.0569353242770.94306467635
51117000116248.370142196751.629857803942
52114000111795.4113051882204.5886948119
53111000107410.7825849913589.21741500919
54112000112994.544436019-994.544436019103
55144000151335.221122636-7335.22112263629
56150000151760.217062282-1760.21706228246
57149000147857.4099473381142.59005266248
58134000138135.357544721-4135.35754472140
59123000124120.483048653-1120.48304865336
60116000120436.755365459-4436.75536545919
61117000113555.2444220323444.75557796756
62111000112162.540261358-1162.54026135805
63105000104463.020482013536.979517986649
6410200099867.14096927482132.8590307252
659500095657.6330475273-657.63304752727
669300095827.7625903503-2827.76259035029
67124000124070.902896474-70.9028964744939
68130000129641.767681409358.23231859073
69124000127442.631976233-3442.63197623273
70115000113876.1445369251123.85546307501
71106000105738.401137215261.59886278458
72105000102934.821259492065.17874051002







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102903.30757131798427.8639280625107378.751214571
7498323.554251495492110.0763425352104537.032160456
7592432.299587884784839.7688869762100024.830288793
7687891.740080093279011.091283252296772.3888769343
7782053.85060924872133.454937387791974.2462811082
7882276.55136654370733.228351687893819.8743813983
79109676.90513536092590.3460088345126763.464261886
80114611.56068036694897.2659024947134325.855458238
81111984.00520173990827.0292913772133140.981112101
82103085.61534078181748.228907131124423.001774431
8394865.784616581773406.1867709022116325.382462261
8492316.45841361970038.1589683718114594.757858866

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102903.307571317 & 98427.8639280625 & 107378.751214571 \tabularnewline
74 & 98323.5542514954 & 92110.0763425352 & 104537.032160456 \tabularnewline
75 & 92432.2995878847 & 84839.7688869762 & 100024.830288793 \tabularnewline
76 & 87891.7400800932 & 79011.0912832522 & 96772.3888769343 \tabularnewline
77 & 82053.850609248 & 72133.4549373877 & 91974.2462811082 \tabularnewline
78 & 82276.551366543 & 70733.2283516878 & 93819.8743813983 \tabularnewline
79 & 109676.905135360 & 92590.3460088345 & 126763.464261886 \tabularnewline
80 & 114611.560680366 & 94897.2659024947 & 134325.855458238 \tabularnewline
81 & 111984.005201739 & 90827.0292913772 & 133140.981112101 \tabularnewline
82 & 103085.615340781 & 81748.228907131 & 124423.001774431 \tabularnewline
83 & 94865.7846165817 & 73406.1867709022 & 116325.382462261 \tabularnewline
84 & 92316.458413619 & 70038.1589683718 & 114594.757858866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13489&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]102903.307571317[/C][C]98427.8639280625[/C][C]107378.751214571[/C][/ROW]
[ROW][C]74[/C][C]98323.5542514954[/C][C]92110.0763425352[/C][C]104537.032160456[/C][/ROW]
[ROW][C]75[/C][C]92432.2995878847[/C][C]84839.7688869762[/C][C]100024.830288793[/C][/ROW]
[ROW][C]76[/C][C]87891.7400800932[/C][C]79011.0912832522[/C][C]96772.3888769343[/C][/ROW]
[ROW][C]77[/C][C]82053.850609248[/C][C]72133.4549373877[/C][C]91974.2462811082[/C][/ROW]
[ROW][C]78[/C][C]82276.551366543[/C][C]70733.2283516878[/C][C]93819.8743813983[/C][/ROW]
[ROW][C]79[/C][C]109676.905135360[/C][C]92590.3460088345[/C][C]126763.464261886[/C][/ROW]
[ROW][C]80[/C][C]114611.560680366[/C][C]94897.2659024947[/C][C]134325.855458238[/C][/ROW]
[ROW][C]81[/C][C]111984.005201739[/C][C]90827.0292913772[/C][C]133140.981112101[/C][/ROW]
[ROW][C]82[/C][C]103085.615340781[/C][C]81748.228907131[/C][C]124423.001774431[/C][/ROW]
[ROW][C]83[/C][C]94865.7846165817[/C][C]73406.1867709022[/C][C]116325.382462261[/C][/ROW]
[ROW][C]84[/C][C]92316.458413619[/C][C]70038.1589683718[/C][C]114594.757858866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13489&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13489&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
73102903.30757131798427.8639280625107378.751214571
7498323.554251495492110.0763425352104537.032160456
7592432.299587884784839.7688869762100024.830288793
7687891.740080093279011.091283252296772.3888769343
7782053.85060924872133.454937387791974.2462811082
7882276.55136654370733.228351687893819.8743813983
79109676.90513536092590.3460088345126763.464261886
80114611.56068036694897.2659024947134325.855458238
81111984.00520173990827.0292913772133140.981112101
82103085.61534078181748.228907131124423.001774431
8394865.784616581773406.1867709022116325.382462261
8492316.45841361970038.1589683718114594.757858866



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=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')