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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 01 Jun 2008 08:09:02 -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/Jun/01/t1212329418h35ur1pdul867e4.htm/, Retrieved Sat, 18 May 2024 16:48:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13688, Retrieved Sat, 18 May 2024 16:48:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsadditief triple model PPI
Estimated Impact232
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 - oefen...] [2008-06-01 14:09:02] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
121.3
124.0
122.9
120.1
118.3
118.1
118.4
116.6
116.4
116.7
117.7
119.5
123.3
124.6
125.4
127.0
126.8
131.8
128.1
130.1
133.5
142.7
140.0
137.9
132.6
133.7
137.0
141.1
145.3
146.1
141.8
140.0
137.4
139.5
140.3
142.7
143.3
146.0
147.2
146.1
147.1
141.7
138.8
138.3
140.2
143.1
142.0
142.4
141.2
138.0
137.9
136.8
135.9
138.8
139.5
138.0
139.7
137.5
137.8
137.4
141.7
145.3
148.9
151.3
151.4
149.2
143.8
143.6
144.3
142.0
140.8
141.8




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=13688&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=13688&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13688&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
alpha0.829991115439346
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.829991115439346 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13688&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]0.829991115439346[/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=13688&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13688&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
alpha0.829991115439346
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13123.3116.0772342995177.22276570048308
14124.6122.4053989931512.19460100684874
15125.4123.751898330771.64810166923002
16127124.9239747402382.07602525976171
17126.8124.4345572612682.36544273873179
18131.8129.7020203851632.09797961483727
19128.1126.5891581591841.5108418408161
20130.1129.0764767972291.0235232027714
21133.5132.4634919619751.03650803802515
22142.7141.4529510912841.24704890871615
23140138.4296572727031.57034272729678
24137.9136.2663611178881.63363888211234
25132.6138.575201216059-5.97520121605925
26133.7133.0943379561490.605662043850998
27137133.0291223287023.9708776712975
28141.1136.2018329953464.89816700465397
29145.3138.1039716339197.19602836608095
30146.1147.335306803528-1.23530680352798
31141.8141.3560278270470.443972172953437
32140142.875005621354-2.87500562135395
33137.4143.028484036150-5.62848403614967
34139.5146.521852778001-7.02185277800052
35140.3136.6904068464863.60959315351411
36142.7136.2304313362646.46956866373617
37143.3141.2594797701812.04052022981884
38146143.550399316452.4496006835501
39147.2145.5877529324971.61224706750275
40146.1146.960468578617-0.860468578616718
41147.1144.4736476929532.62635230704655
42141.7148.478790445586-6.77879044558568
43138.8138.1839616432710.616038356729206
44138.3139.281497128688-0.981497128687835
45140.2140.538454975444-0.338454975444165
46143.1148.185615772513-5.08561577251277
47142141.7686696170220.231330382978427
48142.4138.9909872679993.409012732001
49141.2140.7268238863560.473176113644399
50138141.786409052998-3.78640905299781
51137.9138.50557243767-0.605572437670077
52136.8137.617133970016-0.817133970015561
53135.9135.7590709539170.140929046083272
54138.8136.1023766533342.69762334666558
55139.5134.9300737010144.56992629898645
56138139.037705824025-1.03770582402504
57139.7140.357333832239-0.657333832239487
58137.5146.932768499327-9.43276849932681
59137.8137.811652288286-0.0116522882861432
60137.4135.3725307125542.02746928744634
61141.7135.4625802375976.23741976240271
62145.3140.5822690970654.71773090293539
63148.9144.9005635745563.99943642544426
64151.3147.7982742096763.50172579032446
65151.4149.6877056481931.71229435180680
66149.2151.769891336676-2.56989133667565
67143.8146.543906133219-2.74390613321893
68143.6143.627775035428-0.0277750354281636
69144.3145.850303243428-1.55030324342820
70142150.192679373583-8.19267937358342
71140.8143.702499577618-2.90249957761804
72141.8139.2106692202222.58933077977798

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 123.3 & 116.077234299517 & 7.22276570048308 \tabularnewline
14 & 124.6 & 122.405398993151 & 2.19460100684874 \tabularnewline
15 & 125.4 & 123.75189833077 & 1.64810166923002 \tabularnewline
16 & 127 & 124.923974740238 & 2.07602525976171 \tabularnewline
17 & 126.8 & 124.434557261268 & 2.36544273873179 \tabularnewline
18 & 131.8 & 129.702020385163 & 2.09797961483727 \tabularnewline
19 & 128.1 & 126.589158159184 & 1.5108418408161 \tabularnewline
20 & 130.1 & 129.076476797229 & 1.0235232027714 \tabularnewline
21 & 133.5 & 132.463491961975 & 1.03650803802515 \tabularnewline
22 & 142.7 & 141.452951091284 & 1.24704890871615 \tabularnewline
23 & 140 & 138.429657272703 & 1.57034272729678 \tabularnewline
24 & 137.9 & 136.266361117888 & 1.63363888211234 \tabularnewline
25 & 132.6 & 138.575201216059 & -5.97520121605925 \tabularnewline
26 & 133.7 & 133.094337956149 & 0.605662043850998 \tabularnewline
27 & 137 & 133.029122328702 & 3.9708776712975 \tabularnewline
28 & 141.1 & 136.201832995346 & 4.89816700465397 \tabularnewline
29 & 145.3 & 138.103971633919 & 7.19602836608095 \tabularnewline
30 & 146.1 & 147.335306803528 & -1.23530680352798 \tabularnewline
31 & 141.8 & 141.356027827047 & 0.443972172953437 \tabularnewline
32 & 140 & 142.875005621354 & -2.87500562135395 \tabularnewline
33 & 137.4 & 143.028484036150 & -5.62848403614967 \tabularnewline
34 & 139.5 & 146.521852778001 & -7.02185277800052 \tabularnewline
35 & 140.3 & 136.690406846486 & 3.60959315351411 \tabularnewline
36 & 142.7 & 136.230431336264 & 6.46956866373617 \tabularnewline
37 & 143.3 & 141.259479770181 & 2.04052022981884 \tabularnewline
38 & 146 & 143.55039931645 & 2.4496006835501 \tabularnewline
39 & 147.2 & 145.587752932497 & 1.61224706750275 \tabularnewline
40 & 146.1 & 146.960468578617 & -0.860468578616718 \tabularnewline
41 & 147.1 & 144.473647692953 & 2.62635230704655 \tabularnewline
42 & 141.7 & 148.478790445586 & -6.77879044558568 \tabularnewline
43 & 138.8 & 138.183961643271 & 0.616038356729206 \tabularnewline
44 & 138.3 & 139.281497128688 & -0.981497128687835 \tabularnewline
45 & 140.2 & 140.538454975444 & -0.338454975444165 \tabularnewline
46 & 143.1 & 148.185615772513 & -5.08561577251277 \tabularnewline
47 & 142 & 141.768669617022 & 0.231330382978427 \tabularnewline
48 & 142.4 & 138.990987267999 & 3.409012732001 \tabularnewline
49 & 141.2 & 140.726823886356 & 0.473176113644399 \tabularnewline
50 & 138 & 141.786409052998 & -3.78640905299781 \tabularnewline
51 & 137.9 & 138.50557243767 & -0.605572437670077 \tabularnewline
52 & 136.8 & 137.617133970016 & -0.817133970015561 \tabularnewline
53 & 135.9 & 135.759070953917 & 0.140929046083272 \tabularnewline
54 & 138.8 & 136.102376653334 & 2.69762334666558 \tabularnewline
55 & 139.5 & 134.930073701014 & 4.56992629898645 \tabularnewline
56 & 138 & 139.037705824025 & -1.03770582402504 \tabularnewline
57 & 139.7 & 140.357333832239 & -0.657333832239487 \tabularnewline
58 & 137.5 & 146.932768499327 & -9.43276849932681 \tabularnewline
59 & 137.8 & 137.811652288286 & -0.0116522882861432 \tabularnewline
60 & 137.4 & 135.372530712554 & 2.02746928744634 \tabularnewline
61 & 141.7 & 135.462580237597 & 6.23741976240271 \tabularnewline
62 & 145.3 & 140.582269097065 & 4.71773090293539 \tabularnewline
63 & 148.9 & 144.900563574556 & 3.99943642544426 \tabularnewline
64 & 151.3 & 147.798274209676 & 3.50172579032446 \tabularnewline
65 & 151.4 & 149.687705648193 & 1.71229435180680 \tabularnewline
66 & 149.2 & 151.769891336676 & -2.56989133667565 \tabularnewline
67 & 143.8 & 146.543906133219 & -2.74390613321893 \tabularnewline
68 & 143.6 & 143.627775035428 & -0.0277750354281636 \tabularnewline
69 & 144.3 & 145.850303243428 & -1.55030324342820 \tabularnewline
70 & 142 & 150.192679373583 & -8.19267937358342 \tabularnewline
71 & 140.8 & 143.702499577618 & -2.90249957761804 \tabularnewline
72 & 141.8 & 139.210669220222 & 2.58933077977798 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13688&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]123.3[/C][C]116.077234299517[/C][C]7.22276570048308[/C][/ROW]
[ROW][C]14[/C][C]124.6[/C][C]122.405398993151[/C][C]2.19460100684874[/C][/ROW]
[ROW][C]15[/C][C]125.4[/C][C]123.75189833077[/C][C]1.64810166923002[/C][/ROW]
[ROW][C]16[/C][C]127[/C][C]124.923974740238[/C][C]2.07602525976171[/C][/ROW]
[ROW][C]17[/C][C]126.8[/C][C]124.434557261268[/C][C]2.36544273873179[/C][/ROW]
[ROW][C]18[/C][C]131.8[/C][C]129.702020385163[/C][C]2.09797961483727[/C][/ROW]
[ROW][C]19[/C][C]128.1[/C][C]126.589158159184[/C][C]1.5108418408161[/C][/ROW]
[ROW][C]20[/C][C]130.1[/C][C]129.076476797229[/C][C]1.0235232027714[/C][/ROW]
[ROW][C]21[/C][C]133.5[/C][C]132.463491961975[/C][C]1.03650803802515[/C][/ROW]
[ROW][C]22[/C][C]142.7[/C][C]141.452951091284[/C][C]1.24704890871615[/C][/ROW]
[ROW][C]23[/C][C]140[/C][C]138.429657272703[/C][C]1.57034272729678[/C][/ROW]
[ROW][C]24[/C][C]137.9[/C][C]136.266361117888[/C][C]1.63363888211234[/C][/ROW]
[ROW][C]25[/C][C]132.6[/C][C]138.575201216059[/C][C]-5.97520121605925[/C][/ROW]
[ROW][C]26[/C][C]133.7[/C][C]133.094337956149[/C][C]0.605662043850998[/C][/ROW]
[ROW][C]27[/C][C]137[/C][C]133.029122328702[/C][C]3.9708776712975[/C][/ROW]
[ROW][C]28[/C][C]141.1[/C][C]136.201832995346[/C][C]4.89816700465397[/C][/ROW]
[ROW][C]29[/C][C]145.3[/C][C]138.103971633919[/C][C]7.19602836608095[/C][/ROW]
[ROW][C]30[/C][C]146.1[/C][C]147.335306803528[/C][C]-1.23530680352798[/C][/ROW]
[ROW][C]31[/C][C]141.8[/C][C]141.356027827047[/C][C]0.443972172953437[/C][/ROW]
[ROW][C]32[/C][C]140[/C][C]142.875005621354[/C][C]-2.87500562135395[/C][/ROW]
[ROW][C]33[/C][C]137.4[/C][C]143.028484036150[/C][C]-5.62848403614967[/C][/ROW]
[ROW][C]34[/C][C]139.5[/C][C]146.521852778001[/C][C]-7.02185277800052[/C][/ROW]
[ROW][C]35[/C][C]140.3[/C][C]136.690406846486[/C][C]3.60959315351411[/C][/ROW]
[ROW][C]36[/C][C]142.7[/C][C]136.230431336264[/C][C]6.46956866373617[/C][/ROW]
[ROW][C]37[/C][C]143.3[/C][C]141.259479770181[/C][C]2.04052022981884[/C][/ROW]
[ROW][C]38[/C][C]146[/C][C]143.55039931645[/C][C]2.4496006835501[/C][/ROW]
[ROW][C]39[/C][C]147.2[/C][C]145.587752932497[/C][C]1.61224706750275[/C][/ROW]
[ROW][C]40[/C][C]146.1[/C][C]146.960468578617[/C][C]-0.860468578616718[/C][/ROW]
[ROW][C]41[/C][C]147.1[/C][C]144.473647692953[/C][C]2.62635230704655[/C][/ROW]
[ROW][C]42[/C][C]141.7[/C][C]148.478790445586[/C][C]-6.77879044558568[/C][/ROW]
[ROW][C]43[/C][C]138.8[/C][C]138.183961643271[/C][C]0.616038356729206[/C][/ROW]
[ROW][C]44[/C][C]138.3[/C][C]139.281497128688[/C][C]-0.981497128687835[/C][/ROW]
[ROW][C]45[/C][C]140.2[/C][C]140.538454975444[/C][C]-0.338454975444165[/C][/ROW]
[ROW][C]46[/C][C]143.1[/C][C]148.185615772513[/C][C]-5.08561577251277[/C][/ROW]
[ROW][C]47[/C][C]142[/C][C]141.768669617022[/C][C]0.231330382978427[/C][/ROW]
[ROW][C]48[/C][C]142.4[/C][C]138.990987267999[/C][C]3.409012732001[/C][/ROW]
[ROW][C]49[/C][C]141.2[/C][C]140.726823886356[/C][C]0.473176113644399[/C][/ROW]
[ROW][C]50[/C][C]138[/C][C]141.786409052998[/C][C]-3.78640905299781[/C][/ROW]
[ROW][C]51[/C][C]137.9[/C][C]138.50557243767[/C][C]-0.605572437670077[/C][/ROW]
[ROW][C]52[/C][C]136.8[/C][C]137.617133970016[/C][C]-0.817133970015561[/C][/ROW]
[ROW][C]53[/C][C]135.9[/C][C]135.759070953917[/C][C]0.140929046083272[/C][/ROW]
[ROW][C]54[/C][C]138.8[/C][C]136.102376653334[/C][C]2.69762334666558[/C][/ROW]
[ROW][C]55[/C][C]139.5[/C][C]134.930073701014[/C][C]4.56992629898645[/C][/ROW]
[ROW][C]56[/C][C]138[/C][C]139.037705824025[/C][C]-1.03770582402504[/C][/ROW]
[ROW][C]57[/C][C]139.7[/C][C]140.357333832239[/C][C]-0.657333832239487[/C][/ROW]
[ROW][C]58[/C][C]137.5[/C][C]146.932768499327[/C][C]-9.43276849932681[/C][/ROW]
[ROW][C]59[/C][C]137.8[/C][C]137.811652288286[/C][C]-0.0116522882861432[/C][/ROW]
[ROW][C]60[/C][C]137.4[/C][C]135.372530712554[/C][C]2.02746928744634[/C][/ROW]
[ROW][C]61[/C][C]141.7[/C][C]135.462580237597[/C][C]6.23741976240271[/C][/ROW]
[ROW][C]62[/C][C]145.3[/C][C]140.582269097065[/C][C]4.71773090293539[/C][/ROW]
[ROW][C]63[/C][C]148.9[/C][C]144.900563574556[/C][C]3.99943642544426[/C][/ROW]
[ROW][C]64[/C][C]151.3[/C][C]147.798274209676[/C][C]3.50172579032446[/C][/ROW]
[ROW][C]65[/C][C]151.4[/C][C]149.687705648193[/C][C]1.71229435180680[/C][/ROW]
[ROW][C]66[/C][C]149.2[/C][C]151.769891336676[/C][C]-2.56989133667565[/C][/ROW]
[ROW][C]67[/C][C]143.8[/C][C]146.543906133219[/C][C]-2.74390613321893[/C][/ROW]
[ROW][C]68[/C][C]143.6[/C][C]143.627775035428[/C][C]-0.0277750354281636[/C][/ROW]
[ROW][C]69[/C][C]144.3[/C][C]145.850303243428[/C][C]-1.55030324342820[/C][/ROW]
[ROW][C]70[/C][C]142[/C][C]150.192679373583[/C][C]-8.19267937358342[/C][/ROW]
[ROW][C]71[/C][C]140.8[/C][C]143.702499577618[/C][C]-2.90249957761804[/C][/ROW]
[ROW][C]72[/C][C]141.8[/C][C]139.210669220222[/C][C]2.58933077977798[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13688&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13688&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
13123.3116.0772342995177.22276570048308
14124.6122.4053989931512.19460100684874
15125.4123.751898330771.64810166923002
16127124.9239747402382.07602525976171
17126.8124.4345572612682.36544273873179
18131.8129.7020203851632.09797961483727
19128.1126.5891581591841.5108418408161
20130.1129.0764767972291.0235232027714
21133.5132.4634919619751.03650803802515
22142.7141.4529510912841.24704890871615
23140138.4296572727031.57034272729678
24137.9136.2663611178881.63363888211234
25132.6138.575201216059-5.97520121605925
26133.7133.0943379561490.605662043850998
27137133.0291223287023.9708776712975
28141.1136.2018329953464.89816700465397
29145.3138.1039716339197.19602836608095
30146.1147.335306803528-1.23530680352798
31141.8141.3560278270470.443972172953437
32140142.875005621354-2.87500562135395
33137.4143.028484036150-5.62848403614967
34139.5146.521852778001-7.02185277800052
35140.3136.6904068464863.60959315351411
36142.7136.2304313362646.46956866373617
37143.3141.2594797701812.04052022981884
38146143.550399316452.4496006835501
39147.2145.5877529324971.61224706750275
40146.1146.960468578617-0.860468578616718
41147.1144.4736476929532.62635230704655
42141.7148.478790445586-6.77879044558568
43138.8138.1839616432710.616038356729206
44138.3139.281497128688-0.981497128687835
45140.2140.538454975444-0.338454975444165
46143.1148.185615772513-5.08561577251277
47142141.7686696170220.231330382978427
48142.4138.9909872679993.409012732001
49141.2140.7268238863560.473176113644399
50138141.786409052998-3.78640905299781
51137.9138.50557243767-0.605572437670077
52136.8137.617133970016-0.817133970015561
53135.9135.7590709539170.140929046083272
54138.8136.1023766533342.69762334666558
55139.5134.9300737010144.56992629898645
56138139.037705824025-1.03770582402504
57139.7140.357333832239-0.657333832239487
58137.5146.932768499327-9.43276849932681
59137.8137.811652288286-0.0116522882861432
60137.4135.3725307125542.02746928744634
61141.7135.4625802375976.23741976240271
62145.3140.5822690970654.71773090293539
63148.9144.9005635745563.99943642544426
64151.3147.7982742096763.50172579032446
65151.4149.6877056481931.71229435180680
66149.2151.769891336676-2.56989133667565
67143.8146.543906133219-2.74390613321893
68143.6143.627775035428-0.0277750354281636
69144.3145.850303243428-1.55030324342820
70142150.192679373583-8.19267937358342
71140.8143.702499577618-2.90249957761804
72141.8139.2106692202222.58933077977798







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73140.482787776311133.352005410921147.613570141701
74140.167113041841130.900153789418149.434072294265
75140.447616341958129.451934897427151.443297786489
76139.941215047284127.453881982409152.428548112160
77138.620025948267124.801127160135152.438924736400
78138.553012925353123.520034499233153.585991351473
79135.430430637524119.274350760162151.586510514886
80135.253483670160118.047455841308152.459511499012
81137.240221588443119.044731205088155.435711971797
82141.74007268016122.606219253987160.873926106333
83142.949121542149122.920820975756162.977422108543
84141.8120.915524899550162.684475100451

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 140.482787776311 & 133.352005410921 & 147.613570141701 \tabularnewline
74 & 140.167113041841 & 130.900153789418 & 149.434072294265 \tabularnewline
75 & 140.447616341958 & 129.451934897427 & 151.443297786489 \tabularnewline
76 & 139.941215047284 & 127.453881982409 & 152.428548112160 \tabularnewline
77 & 138.620025948267 & 124.801127160135 & 152.438924736400 \tabularnewline
78 & 138.553012925353 & 123.520034499233 & 153.585991351473 \tabularnewline
79 & 135.430430637524 & 119.274350760162 & 151.586510514886 \tabularnewline
80 & 135.253483670160 & 118.047455841308 & 152.459511499012 \tabularnewline
81 & 137.240221588443 & 119.044731205088 & 155.435711971797 \tabularnewline
82 & 141.74007268016 & 122.606219253987 & 160.873926106333 \tabularnewline
83 & 142.949121542149 & 122.920820975756 & 162.977422108543 \tabularnewline
84 & 141.8 & 120.915524899550 & 162.684475100451 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13688&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]140.482787776311[/C][C]133.352005410921[/C][C]147.613570141701[/C][/ROW]
[ROW][C]74[/C][C]140.167113041841[/C][C]130.900153789418[/C][C]149.434072294265[/C][/ROW]
[ROW][C]75[/C][C]140.447616341958[/C][C]129.451934897427[/C][C]151.443297786489[/C][/ROW]
[ROW][C]76[/C][C]139.941215047284[/C][C]127.453881982409[/C][C]152.428548112160[/C][/ROW]
[ROW][C]77[/C][C]138.620025948267[/C][C]124.801127160135[/C][C]152.438924736400[/C][/ROW]
[ROW][C]78[/C][C]138.553012925353[/C][C]123.520034499233[/C][C]153.585991351473[/C][/ROW]
[ROW][C]79[/C][C]135.430430637524[/C][C]119.274350760162[/C][C]151.586510514886[/C][/ROW]
[ROW][C]80[/C][C]135.253483670160[/C][C]118.047455841308[/C][C]152.459511499012[/C][/ROW]
[ROW][C]81[/C][C]137.240221588443[/C][C]119.044731205088[/C][C]155.435711971797[/C][/ROW]
[ROW][C]82[/C][C]141.74007268016[/C][C]122.606219253987[/C][C]160.873926106333[/C][/ROW]
[ROW][C]83[/C][C]142.949121542149[/C][C]122.920820975756[/C][C]162.977422108543[/C][/ROW]
[ROW][C]84[/C][C]141.8[/C][C]120.915524899550[/C][C]162.684475100451[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13688&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13688&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
73140.482787776311133.352005410921147.613570141701
74140.167113041841130.900153789418149.434072294265
75140.447616341958129.451934897427151.443297786489
76139.941215047284127.453881982409152.428548112160
77138.620025948267124.801127160135152.438924736400
78138.553012925353123.520034499233153.585991351473
79135.430430637524119.274350760162151.586510514886
80135.253483670160118.047455841308152.459511499012
81137.240221588443119.044731205088155.435711971797
82141.74007268016122.606219253987160.873926106333
83142.949121542149122.920820975756162.977422108543
84141.8120.915524899550162.684475100451



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')