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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 26 Nov 2016 19:24:49 +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/2016/Nov/26/t1480188305r45hqtaa58lhix2.htm/, Retrieved Fri, 03 May 2024 23:29:40 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 03 May 2024 23:29:40 +0200

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Estimated Impact

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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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.922183541935683
beta	0.0253350214786133
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.922183541935683 \tabularnewline
beta & 0.0253350214786133 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.922183541935683[/C][/ROW]
[ROW][C]beta[/C][C]0.0253350214786133[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.922183541935683
beta	0.0253350214786133
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	99.75	98.5530189074055	1.19698109259454
14	99.8	99.7443466932352	0.0556533067647536
15	99.99	100.010980359185	-0.0209803591847901
16	100.25	100.268537184185	-0.018537184185405
17	100.08	100.118641053813	-0.0386410538128246
18	100.08	100.122556014583	-0.0425560145831412
19	100.08	100.020426920184	0.0595730798161469
20	100.06	100.424851767816	-0.364851767815892
21	101	100.432108367891	0.567891632109081
22	101.81	102.258493823936	-0.448493823935721
23	101.82	101.924531579377	-0.104531579376953
24	101.96	102.003885825442	-0.0438858254415493
25	101.96	102.069463762946	-0.109463762946234
26	101.93	101.950350653384	-0.0203506533838862
27	102.03	102.126987846205	-0.0969878462050673
28	102.11	102.30032523501	-0.190325235010221
29	102.07	101.964421256176	0.105578743824111
30	102.34	102.081472166229	0.258527833770586
31	102.34	102.249898202103	0.0901017978969918
32	102.33	102.643301390575	-0.313301390574566
33	102.77	102.768096958904	0.00190304109571571
34	103.08	103.990315594924	-0.910315594923844
35	103.38	103.224590693638	0.155409306361705
36	103.44	103.5227543165	-0.082754316500484
37	99.1	103.51975901371	-4.41975901371011
38	99.15	99.3118935529086	-0.16189355290858
39	99.21	99.2230459553083	-0.0130459553083142
40	99.01	99.3375501607347	-0.327550160734688
41	99.08	98.7779608533002	0.302039146699826
42	99.11	98.9675638154442	0.142436184555848
43	100.11	98.8971838415914	1.21281615840856
44	100.31	100.191181165332	0.118818834667593
45	100.55	100.64247848536	-0.0924784853599476
46	101.38	101.590862692905	-0.210862692905337
47	101.49	101.474927983414	0.0150720165859752
48	101.5	101.544255965817	-0.0442559658167028
49	100.69	101.15329498616	-0.463294986159994
50	100.8	100.938606869417	-0.138606869417302
51	100.58	100.894607410555	-0.314607410555283
52	100.34	100.711667649822	-0.371667649822356
53	100.38	100.160317695119	0.219682304881474
54	100.33	100.26112581172	0.0688741882797501
55	101.06	100.202880573823	0.857119426176979
56	101.15	101.075424071249	0.0745759287514431
57	101.36	101.462064739017	-0.102064739016825
58	101.98	102.390306768607	-0.410306768607256
59	102.24	102.093829067396	0.146170932603511
60	102.34	102.267958502883	0.072041497116885
61	101.91	101.939154456331	-0.0291544563307156
62	101.8	102.153623395498	-0.353623395497578
63	101.8	101.894149999792	-0.0941499997916537
64	101.73	101.912135781179	-0.18213578117934
65	101.8	101.58456162947	0.215438370529597
66	101.81	101.673235869132	0.136764130868471
67	102.28	101.744123680521	0.535876319478945
68	101.7	102.258877535019	-0.558877535019164
69	101.7	102.034268925078	-0.334268925078305
70	102.37	102.707403333199	-0.337403333198978
71	102.43	102.503166507121	-0.0731665071205327
72	102.41	102.445623575727	-0.0356235757273993

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 99.75 & 98.5530189074055 & 1.19698109259454 \tabularnewline
14 & 99.8 & 99.7443466932352 & 0.0556533067647536 \tabularnewline
15 & 99.99 & 100.010980359185 & -0.0209803591847901 \tabularnewline
16 & 100.25 & 100.268537184185 & -0.018537184185405 \tabularnewline
17 & 100.08 & 100.118641053813 & -0.0386410538128246 \tabularnewline
18 & 100.08 & 100.122556014583 & -0.0425560145831412 \tabularnewline
19 & 100.08 & 100.020426920184 & 0.0595730798161469 \tabularnewline
20 & 100.06 & 100.424851767816 & -0.364851767815892 \tabularnewline
21 & 101 & 100.432108367891 & 0.567891632109081 \tabularnewline
22 & 101.81 & 102.258493823936 & -0.448493823935721 \tabularnewline
23 & 101.82 & 101.924531579377 & -0.104531579376953 \tabularnewline
24 & 101.96 & 102.003885825442 & -0.0438858254415493 \tabularnewline
25 & 101.96 & 102.069463762946 & -0.109463762946234 \tabularnewline
26 & 101.93 & 101.950350653384 & -0.0203506533838862 \tabularnewline
27 & 102.03 & 102.126987846205 & -0.0969878462050673 \tabularnewline
28 & 102.11 & 102.30032523501 & -0.190325235010221 \tabularnewline
29 & 102.07 & 101.964421256176 & 0.105578743824111 \tabularnewline
30 & 102.34 & 102.081472166229 & 0.258527833770586 \tabularnewline
31 & 102.34 & 102.249898202103 & 0.0901017978969918 \tabularnewline
32 & 102.33 & 102.643301390575 & -0.313301390574566 \tabularnewline
33 & 102.77 & 102.768096958904 & 0.00190304109571571 \tabularnewline
34 & 103.08 & 103.990315594924 & -0.910315594923844 \tabularnewline
35 & 103.38 & 103.224590693638 & 0.155409306361705 \tabularnewline
36 & 103.44 & 103.5227543165 & -0.082754316500484 \tabularnewline
37 & 99.1 & 103.51975901371 & -4.41975901371011 \tabularnewline
38 & 99.15 & 99.3118935529086 & -0.16189355290858 \tabularnewline
39 & 99.21 & 99.2230459553083 & -0.0130459553083142 \tabularnewline
40 & 99.01 & 99.3375501607347 & -0.327550160734688 \tabularnewline
41 & 99.08 & 98.7779608533002 & 0.302039146699826 \tabularnewline
42 & 99.11 & 98.9675638154442 & 0.142436184555848 \tabularnewline
43 & 100.11 & 98.8971838415914 & 1.21281615840856 \tabularnewline
44 & 100.31 & 100.191181165332 & 0.118818834667593 \tabularnewline
45 & 100.55 & 100.64247848536 & -0.0924784853599476 \tabularnewline
46 & 101.38 & 101.590862692905 & -0.210862692905337 \tabularnewline
47 & 101.49 & 101.474927983414 & 0.0150720165859752 \tabularnewline
48 & 101.5 & 101.544255965817 & -0.0442559658167028 \tabularnewline
49 & 100.69 & 101.15329498616 & -0.463294986159994 \tabularnewline
50 & 100.8 & 100.938606869417 & -0.138606869417302 \tabularnewline
51 & 100.58 & 100.894607410555 & -0.314607410555283 \tabularnewline
52 & 100.34 & 100.711667649822 & -0.371667649822356 \tabularnewline
53 & 100.38 & 100.160317695119 & 0.219682304881474 \tabularnewline
54 & 100.33 & 100.26112581172 & 0.0688741882797501 \tabularnewline
55 & 101.06 & 100.202880573823 & 0.857119426176979 \tabularnewline
56 & 101.15 & 101.075424071249 & 0.0745759287514431 \tabularnewline
57 & 101.36 & 101.462064739017 & -0.102064739016825 \tabularnewline
58 & 101.98 & 102.390306768607 & -0.410306768607256 \tabularnewline
59 & 102.24 & 102.093829067396 & 0.146170932603511 \tabularnewline
60 & 102.34 & 102.267958502883 & 0.072041497116885 \tabularnewline
61 & 101.91 & 101.939154456331 & -0.0291544563307156 \tabularnewline
62 & 101.8 & 102.153623395498 & -0.353623395497578 \tabularnewline
63 & 101.8 & 101.894149999792 & -0.0941499997916537 \tabularnewline
64 & 101.73 & 101.912135781179 & -0.18213578117934 \tabularnewline
65 & 101.8 & 101.58456162947 & 0.215438370529597 \tabularnewline
66 & 101.81 & 101.673235869132 & 0.136764130868471 \tabularnewline
67 & 102.28 & 101.744123680521 & 0.535876319478945 \tabularnewline
68 & 101.7 & 102.258877535019 & -0.558877535019164 \tabularnewline
69 & 101.7 & 102.034268925078 & -0.334268925078305 \tabularnewline
70 & 102.37 & 102.707403333199 & -0.337403333198978 \tabularnewline
71 & 102.43 & 102.503166507121 & -0.0731665071205327 \tabularnewline
72 & 102.41 & 102.445623575727 & -0.0356235757273993 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]99.75[/C][C]98.5530189074055[/C][C]1.19698109259454[/C][/ROW]
[ROW][C]14[/C][C]99.8[/C][C]99.7443466932352[/C][C]0.0556533067647536[/C][/ROW]
[ROW][C]15[/C][C]99.99[/C][C]100.010980359185[/C][C]-0.0209803591847901[/C][/ROW]
[ROW][C]16[/C][C]100.25[/C][C]100.268537184185[/C][C]-0.018537184185405[/C][/ROW]
[ROW][C]17[/C][C]100.08[/C][C]100.118641053813[/C][C]-0.0386410538128246[/C][/ROW]
[ROW][C]18[/C][C]100.08[/C][C]100.122556014583[/C][C]-0.0425560145831412[/C][/ROW]
[ROW][C]19[/C][C]100.08[/C][C]100.020426920184[/C][C]0.0595730798161469[/C][/ROW]
[ROW][C]20[/C][C]100.06[/C][C]100.424851767816[/C][C]-0.364851767815892[/C][/ROW]
[ROW][C]21[/C][C]101[/C][C]100.432108367891[/C][C]0.567891632109081[/C][/ROW]
[ROW][C]22[/C][C]101.81[/C][C]102.258493823936[/C][C]-0.448493823935721[/C][/ROW]
[ROW][C]23[/C][C]101.82[/C][C]101.924531579377[/C][C]-0.104531579376953[/C][/ROW]
[ROW][C]24[/C][C]101.96[/C][C]102.003885825442[/C][C]-0.0438858254415493[/C][/ROW]
[ROW][C]25[/C][C]101.96[/C][C]102.069463762946[/C][C]-0.109463762946234[/C][/ROW]
[ROW][C]26[/C][C]101.93[/C][C]101.950350653384[/C][C]-0.0203506533838862[/C][/ROW]
[ROW][C]27[/C][C]102.03[/C][C]102.126987846205[/C][C]-0.0969878462050673[/C][/ROW]
[ROW][C]28[/C][C]102.11[/C][C]102.30032523501[/C][C]-0.190325235010221[/C][/ROW]
[ROW][C]29[/C][C]102.07[/C][C]101.964421256176[/C][C]0.105578743824111[/C][/ROW]
[ROW][C]30[/C][C]102.34[/C][C]102.081472166229[/C][C]0.258527833770586[/C][/ROW]
[ROW][C]31[/C][C]102.34[/C][C]102.249898202103[/C][C]0.0901017978969918[/C][/ROW]
[ROW][C]32[/C][C]102.33[/C][C]102.643301390575[/C][C]-0.313301390574566[/C][/ROW]
[ROW][C]33[/C][C]102.77[/C][C]102.768096958904[/C][C]0.00190304109571571[/C][/ROW]
[ROW][C]34[/C][C]103.08[/C][C]103.990315594924[/C][C]-0.910315594923844[/C][/ROW]
[ROW][C]35[/C][C]103.38[/C][C]103.224590693638[/C][C]0.155409306361705[/C][/ROW]
[ROW][C]36[/C][C]103.44[/C][C]103.5227543165[/C][C]-0.082754316500484[/C][/ROW]
[ROW][C]37[/C][C]99.1[/C][C]103.51975901371[/C][C]-4.41975901371011[/C][/ROW]
[ROW][C]38[/C][C]99.15[/C][C]99.3118935529086[/C][C]-0.16189355290858[/C][/ROW]
[ROW][C]39[/C][C]99.21[/C][C]99.2230459553083[/C][C]-0.0130459553083142[/C][/ROW]
[ROW][C]40[/C][C]99.01[/C][C]99.3375501607347[/C][C]-0.327550160734688[/C][/ROW]
[ROW][C]41[/C][C]99.08[/C][C]98.7779608533002[/C][C]0.302039146699826[/C][/ROW]
[ROW][C]42[/C][C]99.11[/C][C]98.9675638154442[/C][C]0.142436184555848[/C][/ROW]
[ROW][C]43[/C][C]100.11[/C][C]98.8971838415914[/C][C]1.21281615840856[/C][/ROW]
[ROW][C]44[/C][C]100.31[/C][C]100.191181165332[/C][C]0.118818834667593[/C][/ROW]
[ROW][C]45[/C][C]100.55[/C][C]100.64247848536[/C][C]-0.0924784853599476[/C][/ROW]
[ROW][C]46[/C][C]101.38[/C][C]101.590862692905[/C][C]-0.210862692905337[/C][/ROW]
[ROW][C]47[/C][C]101.49[/C][C]101.474927983414[/C][C]0.0150720165859752[/C][/ROW]
[ROW][C]48[/C][C]101.5[/C][C]101.544255965817[/C][C]-0.0442559658167028[/C][/ROW]
[ROW][C]49[/C][C]100.69[/C][C]101.15329498616[/C][C]-0.463294986159994[/C][/ROW]
[ROW][C]50[/C][C]100.8[/C][C]100.938606869417[/C][C]-0.138606869417302[/C][/ROW]
[ROW][C]51[/C][C]100.58[/C][C]100.894607410555[/C][C]-0.314607410555283[/C][/ROW]
[ROW][C]52[/C][C]100.34[/C][C]100.711667649822[/C][C]-0.371667649822356[/C][/ROW]
[ROW][C]53[/C][C]100.38[/C][C]100.160317695119[/C][C]0.219682304881474[/C][/ROW]
[ROW][C]54[/C][C]100.33[/C][C]100.26112581172[/C][C]0.0688741882797501[/C][/ROW]
[ROW][C]55[/C][C]101.06[/C][C]100.202880573823[/C][C]0.857119426176979[/C][/ROW]
[ROW][C]56[/C][C]101.15[/C][C]101.075424071249[/C][C]0.0745759287514431[/C][/ROW]
[ROW][C]57[/C][C]101.36[/C][C]101.462064739017[/C][C]-0.102064739016825[/C][/ROW]
[ROW][C]58[/C][C]101.98[/C][C]102.390306768607[/C][C]-0.410306768607256[/C][/ROW]
[ROW][C]59[/C][C]102.24[/C][C]102.093829067396[/C][C]0.146170932603511[/C][/ROW]
[ROW][C]60[/C][C]102.34[/C][C]102.267958502883[/C][C]0.072041497116885[/C][/ROW]
[ROW][C]61[/C][C]101.91[/C][C]101.939154456331[/C][C]-0.0291544563307156[/C][/ROW]
[ROW][C]62[/C][C]101.8[/C][C]102.153623395498[/C][C]-0.353623395497578[/C][/ROW]
[ROW][C]63[/C][C]101.8[/C][C]101.894149999792[/C][C]-0.0941499997916537[/C][/ROW]
[ROW][C]64[/C][C]101.73[/C][C]101.912135781179[/C][C]-0.18213578117934[/C][/ROW]
[ROW][C]65[/C][C]101.8[/C][C]101.58456162947[/C][C]0.215438370529597[/C][/ROW]
[ROW][C]66[/C][C]101.81[/C][C]101.673235869132[/C][C]0.136764130868471[/C][/ROW]
[ROW][C]67[/C][C]102.28[/C][C]101.744123680521[/C][C]0.535876319478945[/C][/ROW]
[ROW][C]68[/C][C]101.7[/C][C]102.258877535019[/C][C]-0.558877535019164[/C][/ROW]
[ROW][C]69[/C][C]101.7[/C][C]102.034268925078[/C][C]-0.334268925078305[/C][/ROW]
[ROW][C]70[/C][C]102.37[/C][C]102.707403333199[/C][C]-0.337403333198978[/C][/ROW]
[ROW][C]71[/C][C]102.43[/C][C]102.503166507121[/C][C]-0.0731665071205327[/C][/ROW]
[ROW][C]72[/C][C]102.41[/C][C]102.445623575727[/C][C]-0.0356235757273993[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	99.75	98.5530189074055	1.19698109259454
14	99.8	99.7443466932352	0.0556533067647536
15	99.99	100.010980359185	-0.0209803591847901
16	100.25	100.268537184185	-0.018537184185405
17	100.08	100.118641053813	-0.0386410538128246
18	100.08	100.122556014583	-0.0425560145831412
19	100.08	100.020426920184	0.0595730798161469
20	100.06	100.424851767816	-0.364851767815892
21	101	100.432108367891	0.567891632109081
22	101.81	102.258493823936	-0.448493823935721
23	101.82	101.924531579377	-0.104531579376953
24	101.96	102.003885825442	-0.0438858254415493
25	101.96	102.069463762946	-0.109463762946234
26	101.93	101.950350653384	-0.0203506533838862
27	102.03	102.126987846205	-0.0969878462050673
28	102.11	102.30032523501	-0.190325235010221
29	102.07	101.964421256176	0.105578743824111
30	102.34	102.081472166229	0.258527833770586
31	102.34	102.249898202103	0.0901017978969918
32	102.33	102.643301390575	-0.313301390574566
33	102.77	102.768096958904	0.00190304109571571
34	103.08	103.990315594924	-0.910315594923844
35	103.38	103.224590693638	0.155409306361705
36	103.44	103.5227543165	-0.082754316500484
37	99.1	103.51975901371	-4.41975901371011
38	99.15	99.3118935529086	-0.16189355290858
39	99.21	99.2230459553083	-0.0130459553083142
40	99.01	99.3375501607347	-0.327550160734688
41	99.08	98.7779608533002	0.302039146699826
42	99.11	98.9675638154442	0.142436184555848
43	100.11	98.8971838415914	1.21281615840856
44	100.31	100.191181165332	0.118818834667593
45	100.55	100.64247848536	-0.0924784853599476
46	101.38	101.590862692905	-0.210862692905337
47	101.49	101.474927983414	0.0150720165859752
48	101.5	101.544255965817	-0.0442559658167028
49	100.69	101.15329498616	-0.463294986159994
50	100.8	100.938606869417	-0.138606869417302
51	100.58	100.894607410555	-0.314607410555283
52	100.34	100.711667649822	-0.371667649822356
53	100.38	100.160317695119	0.219682304881474
54	100.33	100.26112581172	0.0688741882797501
55	101.06	100.202880573823	0.857119426176979
56	101.15	101.075424071249	0.0745759287514431
57	101.36	101.462064739017	-0.102064739016825
58	101.98	102.390306768607	-0.410306768607256
59	102.24	102.093829067396	0.146170932603511
60	102.34	102.267958502883	0.072041497116885
61	101.91	101.939154456331	-0.0291544563307156
62	101.8	102.153623395498	-0.353623395497578
63	101.8	101.894149999792	-0.0941499997916537
64	101.73	101.912135781179	-0.18213578117934
65	101.8	101.58456162947	0.215438370529597
66	101.81	101.673235869132	0.136764130868471
67	102.28	101.744123680521	0.535876319478945
68	101.7	102.258877535019	-0.558877535019164
69	101.7	102.034268925078	-0.334268925078305
70	102.37	102.707403333199	-0.337403333198978
71	102.43	102.503166507121	-0.0731665071205327
72	102.41	102.445623575727	-0.0356235757273993

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	101.983407652764	100.667213940825	103.299601364703
74	102.17426990351	100.361892020069	103.986647786952
75	102.244089063731	100.028041267939	104.460136859523
76	102.327282793521	99.7548366621382	104.899728924905
77	102.186814881988	99.2925871065461	105.081042657429
78	102.054389433906	98.8589236298755	105.249855237936
79	102.01104906012	98.526914506148	105.495183614091
80	101.915513530572	98.1557582028049	105.67526885834
81	102.206009074916	98.1659374344871	106.246080715345
82	103.181108245418	98.8408733954445	107.521343095391
83	103.306425321489	98.7041789496252	107.908671693352
84	103.317899112574	85.1539156219953	121.481882603152

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 101.983407652764 & 100.667213940825 & 103.299601364703 \tabularnewline
74 & 102.17426990351 & 100.361892020069 & 103.986647786952 \tabularnewline
75 & 102.244089063731 & 100.028041267939 & 104.460136859523 \tabularnewline
76 & 102.327282793521 & 99.7548366621382 & 104.899728924905 \tabularnewline
77 & 102.186814881988 & 99.2925871065461 & 105.081042657429 \tabularnewline
78 & 102.054389433906 & 98.8589236298755 & 105.249855237936 \tabularnewline
79 & 102.01104906012 & 98.526914506148 & 105.495183614091 \tabularnewline
80 & 101.915513530572 & 98.1557582028049 & 105.67526885834 \tabularnewline
81 & 102.206009074916 & 98.1659374344871 & 106.246080715345 \tabularnewline
82 & 103.181108245418 & 98.8408733954445 & 107.521343095391 \tabularnewline
83 & 103.306425321489 & 98.7041789496252 & 107.908671693352 \tabularnewline
84 & 103.317899112574 & 85.1539156219953 & 121.481882603152 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]101.983407652764[/C][C]100.667213940825[/C][C]103.299601364703[/C][/ROW]
[ROW][C]74[/C][C]102.17426990351[/C][C]100.361892020069[/C][C]103.986647786952[/C][/ROW]
[ROW][C]75[/C][C]102.244089063731[/C][C]100.028041267939[/C][C]104.460136859523[/C][/ROW]
[ROW][C]76[/C][C]102.327282793521[/C][C]99.7548366621382[/C][C]104.899728924905[/C][/ROW]
[ROW][C]77[/C][C]102.186814881988[/C][C]99.2925871065461[/C][C]105.081042657429[/C][/ROW]
[ROW][C]78[/C][C]102.054389433906[/C][C]98.8589236298755[/C][C]105.249855237936[/C][/ROW]
[ROW][C]79[/C][C]102.01104906012[/C][C]98.526914506148[/C][C]105.495183614091[/C][/ROW]
[ROW][C]80[/C][C]101.915513530572[/C][C]98.1557582028049[/C][C]105.67526885834[/C][/ROW]
[ROW][C]81[/C][C]102.206009074916[/C][C]98.1659374344871[/C][C]106.246080715345[/C][/ROW]
[ROW][C]82[/C][C]103.181108245418[/C][C]98.8408733954445[/C][C]107.521343095391[/C][/ROW]
[ROW][C]83[/C][C]103.306425321489[/C][C]98.7041789496252[/C][C]107.908671693352[/C][/ROW]
[ROW][C]84[/C][C]103.317899112574[/C][C]85.1539156219953[/C][C]121.481882603152[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=3

As an alternative you can also use a QR Code:

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

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	101.983407652764	100.667213940825	103.299601364703
74	102.17426990351	100.361892020069	103.986647786952
75	102.244089063731	100.028041267939	104.460136859523
76	102.327282793521	99.7548366621382	104.899728924905
77	102.186814881988	99.2925871065461	105.081042657429
78	102.054389433906	98.8589236298755	105.249855237936
79	102.01104906012	98.526914506148	105.495183614091
80	101.915513530572	98.1557582028049	105.67526885834
81	102.206009074916	98.1659374344871	106.246080715345
82	103.181108245418	98.8408733954445	107.521343095391
83	103.306425321489	98.7041789496252	107.908671693352
84	103.317899112574	85.1539156219953	121.481882603152

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code