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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 01 Jun 2008 07:11:49 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Jun/01/t12123260607ihpumv9n7hrpvj.htm/, Retrieved Sat, 18 May 2024 13:48:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13667, Retrieved Sat, 18 May 2024 13:48:49 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

250

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

-       [Exponential Smoothing] [exponential smoot...] [2008-06-01 13:11:49] [6cae5450d413d5fde7d2ce6324b75128] [Current]

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Dataseries X:

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Histogram

Boxplots

0,63
0,64
0,65
0,65
0,65
0,65
0,65
0,66
0,65
0,66
0,66
0,66
0,66
0,68
0,69
0,7
0,71
0,71
0,7
0,7
0,7
0,7
0,71
0,7
0,7
0,7
0,69
0,7
0,69
0,69
0,69
0,7
0,7
0,71
0,71
0,71
0,72
0,73
0,74
0,74
0,74
0,74
0,75
0,75
0,76
0,76
0,76
0,76
0,76
0,77
0,77
0,78
0,78
0,78
0,78
0,78
0,78
0,78
0,8
0,8
0,8
0,81
0,81
0,81
0,8
0,81
0,81
0,81
0,8
0,82
0,83
0,83

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	'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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13667&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13667&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13667&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.692780535122199
beta	0.000961035668292444
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.692780535122199 \tabularnewline
beta & 0.000961035668292444 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13667&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]0.692780535122199[/C][/ROW]
[ROW][C]beta[/C][C]0.000961035668292444[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13667&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13667&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	0.692780535122199
beta	0.000961035668292444
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.66	0.642931344526887	0.0170686554731130
14	0.68	0.672968781756433	0.0070312182435669
15	0.69	0.686151407991656	0.00384859200834398
16	0.7	0.697125959947919	0.00287404005208125
17	0.71	0.707415363872179	0.00258463612782078
18	0.71	0.707527165499493	0.00247283450050673
19	0.7	0.698022406242879	0.00197759375712137
20	0.7	0.699000495635157	0.000999504364843085
21	0.7	0.700963021739085	-0.00096302173908469
22	0.7	0.702396296022734	-0.00239629602273406
23	0.71	0.713723183028984	-0.00372318302898378
24	0.7	0.704902961986993	-0.00490296198699336
25	0.7	0.691375147695947	0.00862485230405297
26	0.7	0.713212493024162	-0.0132124930241621
27	0.69	0.711571455565236	-0.0215714555652361
28	0.7	0.704671632031416	-0.00467163203141574
29	0.69	0.709631505095134	-0.0196315050951338
30	0.69	0.69435415404041	-0.00435415404041006
31	0.69	0.680278989707719	0.00972101029228079
32	0.7	0.686336117477076	0.0136638825229239
33	0.7	0.696449614308298	0.00355038569170241
34	0.71	0.700543270147116	0.00945672985288382
35	0.71	0.719758398003111	-0.00975839800311118
36	0.71	0.706329419034816	0.0036705809651838
37	0.72	0.702756933184547	0.0172430668154527
38	0.73	0.723940593365488	0.00605940663451188
39	0.74	0.733052390659313	0.0069476093406865
40	0.74	0.751888581219213	-0.011888581219213
41	0.74	0.74723752220306	-0.00723752220305962
42	0.74	0.745328199187258	-0.00532819918725769
43	0.75	0.734236190649055	0.0157638093509449
44	0.75	0.745534422587639	0.0044655774123612
45	0.76	0.745871666830757	0.0141283331692433
46	0.76	0.75921714565002	0.000782854349980378
47	0.76	0.766839818961247	-0.00683981896124686
48	0.76	0.759240285978673	0.000759714021327018
49	0.76	0.757468066346126	0.00253193365387361
50	0.77	0.765228649803522	0.00477135019647845
51	0.77	0.773881751186837	-0.00388175118683709
52	0.78	0.779649682156555	0.000350317843445302
53	0.78	0.785059912331307	-0.00505991233130698
54	0.78	0.785340211931307	-0.00534021193130729
55	0.78	0.780489099574688	-0.000489099574688234
56	0.78	0.776845728438716	0.00315427156128445
57	0.78	0.77911468660341	0.000885313396589704
58	0.78	0.779111167591526	0.000888832408474038
59	0.8	0.784514624186743	0.0154853758132567
60	0.8	0.79460340426113	0.00539659573887052
61	0.8	0.796404250362448	0.00359574963755216
62	0.81	0.805830971936683	0.00416902806331698
63	0.81	0.811445674255775	-0.00144567425577458
64	0.81	0.820616388807891	-0.0106163888078910
65	0.8	0.816825298821848	-0.0168252988218480
66	0.81	0.808910455846066	0.00108954415393403
67	0.81	0.80993961915437	6.03808456306476e-05
68	0.81	0.807632048764273	0.00236795123572742
69	0.8	0.80856017343223	-0.00856017343223037
70	0.82	0.801932141347813	0.0180678586521871
71	0.83	0.823978585316508	0.00602141468349215
72	0.83	0.824199614852678	0.00580038514732162

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.66 & 0.642931344526887 & 0.0170686554731130 \tabularnewline
14 & 0.68 & 0.672968781756433 & 0.0070312182435669 \tabularnewline
15 & 0.69 & 0.686151407991656 & 0.00384859200834398 \tabularnewline
16 & 0.7 & 0.697125959947919 & 0.00287404005208125 \tabularnewline
17 & 0.71 & 0.707415363872179 & 0.00258463612782078 \tabularnewline
18 & 0.71 & 0.707527165499493 & 0.00247283450050673 \tabularnewline
19 & 0.7 & 0.698022406242879 & 0.00197759375712137 \tabularnewline
20 & 0.7 & 0.699000495635157 & 0.000999504364843085 \tabularnewline
21 & 0.7 & 0.700963021739085 & -0.00096302173908469 \tabularnewline
22 & 0.7 & 0.702396296022734 & -0.00239629602273406 \tabularnewline
23 & 0.71 & 0.713723183028984 & -0.00372318302898378 \tabularnewline
24 & 0.7 & 0.704902961986993 & -0.00490296198699336 \tabularnewline
25 & 0.7 & 0.691375147695947 & 0.00862485230405297 \tabularnewline
26 & 0.7 & 0.713212493024162 & -0.0132124930241621 \tabularnewline
27 & 0.69 & 0.711571455565236 & -0.0215714555652361 \tabularnewline
28 & 0.7 & 0.704671632031416 & -0.00467163203141574 \tabularnewline
29 & 0.69 & 0.709631505095134 & -0.0196315050951338 \tabularnewline
30 & 0.69 & 0.69435415404041 & -0.00435415404041006 \tabularnewline
31 & 0.69 & 0.680278989707719 & 0.00972101029228079 \tabularnewline
32 & 0.7 & 0.686336117477076 & 0.0136638825229239 \tabularnewline
33 & 0.7 & 0.696449614308298 & 0.00355038569170241 \tabularnewline
34 & 0.71 & 0.700543270147116 & 0.00945672985288382 \tabularnewline
35 & 0.71 & 0.719758398003111 & -0.00975839800311118 \tabularnewline
36 & 0.71 & 0.706329419034816 & 0.0036705809651838 \tabularnewline
37 & 0.72 & 0.702756933184547 & 0.0172430668154527 \tabularnewline
38 & 0.73 & 0.723940593365488 & 0.00605940663451188 \tabularnewline
39 & 0.74 & 0.733052390659313 & 0.0069476093406865 \tabularnewline
40 & 0.74 & 0.751888581219213 & -0.011888581219213 \tabularnewline
41 & 0.74 & 0.74723752220306 & -0.00723752220305962 \tabularnewline
42 & 0.74 & 0.745328199187258 & -0.00532819918725769 \tabularnewline
43 & 0.75 & 0.734236190649055 & 0.0157638093509449 \tabularnewline
44 & 0.75 & 0.745534422587639 & 0.0044655774123612 \tabularnewline
45 & 0.76 & 0.745871666830757 & 0.0141283331692433 \tabularnewline
46 & 0.76 & 0.75921714565002 & 0.000782854349980378 \tabularnewline
47 & 0.76 & 0.766839818961247 & -0.00683981896124686 \tabularnewline
48 & 0.76 & 0.759240285978673 & 0.000759714021327018 \tabularnewline
49 & 0.76 & 0.757468066346126 & 0.00253193365387361 \tabularnewline
50 & 0.77 & 0.765228649803522 & 0.00477135019647845 \tabularnewline
51 & 0.77 & 0.773881751186837 & -0.00388175118683709 \tabularnewline
52 & 0.78 & 0.779649682156555 & 0.000350317843445302 \tabularnewline
53 & 0.78 & 0.785059912331307 & -0.00505991233130698 \tabularnewline
54 & 0.78 & 0.785340211931307 & -0.00534021193130729 \tabularnewline
55 & 0.78 & 0.780489099574688 & -0.000489099574688234 \tabularnewline
56 & 0.78 & 0.776845728438716 & 0.00315427156128445 \tabularnewline
57 & 0.78 & 0.77911468660341 & 0.000885313396589704 \tabularnewline
58 & 0.78 & 0.779111167591526 & 0.000888832408474038 \tabularnewline
59 & 0.8 & 0.784514624186743 & 0.0154853758132567 \tabularnewline
60 & 0.8 & 0.79460340426113 & 0.00539659573887052 \tabularnewline
61 & 0.8 & 0.796404250362448 & 0.00359574963755216 \tabularnewline
62 & 0.81 & 0.805830971936683 & 0.00416902806331698 \tabularnewline
63 & 0.81 & 0.811445674255775 & -0.00144567425577458 \tabularnewline
64 & 0.81 & 0.820616388807891 & -0.0106163888078910 \tabularnewline
65 & 0.8 & 0.816825298821848 & -0.0168252988218480 \tabularnewline
66 & 0.81 & 0.808910455846066 & 0.00108954415393403 \tabularnewline
67 & 0.81 & 0.80993961915437 & 6.03808456306476e-05 \tabularnewline
68 & 0.81 & 0.807632048764273 & 0.00236795123572742 \tabularnewline
69 & 0.8 & 0.80856017343223 & -0.00856017343223037 \tabularnewline
70 & 0.82 & 0.801932141347813 & 0.0180678586521871 \tabularnewline
71 & 0.83 & 0.823978585316508 & 0.00602141468349215 \tabularnewline
72 & 0.83 & 0.824199614852678 & 0.00580038514732162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13667&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]0.66[/C][C]0.642931344526887[/C][C]0.0170686554731130[/C][/ROW]
[ROW][C]14[/C][C]0.68[/C][C]0.672968781756433[/C][C]0.0070312182435669[/C][/ROW]
[ROW][C]15[/C][C]0.69[/C][C]0.686151407991656[/C][C]0.00384859200834398[/C][/ROW]
[ROW][C]16[/C][C]0.7[/C][C]0.697125959947919[/C][C]0.00287404005208125[/C][/ROW]
[ROW][C]17[/C][C]0.71[/C][C]0.707415363872179[/C][C]0.00258463612782078[/C][/ROW]
[ROW][C]18[/C][C]0.71[/C][C]0.707527165499493[/C][C]0.00247283450050673[/C][/ROW]
[ROW][C]19[/C][C]0.7[/C][C]0.698022406242879[/C][C]0.00197759375712137[/C][/ROW]
[ROW][C]20[/C][C]0.7[/C][C]0.699000495635157[/C][C]0.000999504364843085[/C][/ROW]
[ROW][C]21[/C][C]0.7[/C][C]0.700963021739085[/C][C]-0.00096302173908469[/C][/ROW]
[ROW][C]22[/C][C]0.7[/C][C]0.702396296022734[/C][C]-0.00239629602273406[/C][/ROW]
[ROW][C]23[/C][C]0.71[/C][C]0.713723183028984[/C][C]-0.00372318302898378[/C][/ROW]
[ROW][C]24[/C][C]0.7[/C][C]0.704902961986993[/C][C]-0.00490296198699336[/C][/ROW]
[ROW][C]25[/C][C]0.7[/C][C]0.691375147695947[/C][C]0.00862485230405297[/C][/ROW]
[ROW][C]26[/C][C]0.7[/C][C]0.713212493024162[/C][C]-0.0132124930241621[/C][/ROW]
[ROW][C]27[/C][C]0.69[/C][C]0.711571455565236[/C][C]-0.0215714555652361[/C][/ROW]
[ROW][C]28[/C][C]0.7[/C][C]0.704671632031416[/C][C]-0.00467163203141574[/C][/ROW]
[ROW][C]29[/C][C]0.69[/C][C]0.709631505095134[/C][C]-0.0196315050951338[/C][/ROW]
[ROW][C]30[/C][C]0.69[/C][C]0.69435415404041[/C][C]-0.00435415404041006[/C][/ROW]
[ROW][C]31[/C][C]0.69[/C][C]0.680278989707719[/C][C]0.00972101029228079[/C][/ROW]
[ROW][C]32[/C][C]0.7[/C][C]0.686336117477076[/C][C]0.0136638825229239[/C][/ROW]
[ROW][C]33[/C][C]0.7[/C][C]0.696449614308298[/C][C]0.00355038569170241[/C][/ROW]
[ROW][C]34[/C][C]0.71[/C][C]0.700543270147116[/C][C]0.00945672985288382[/C][/ROW]
[ROW][C]35[/C][C]0.71[/C][C]0.719758398003111[/C][C]-0.00975839800311118[/C][/ROW]
[ROW][C]36[/C][C]0.71[/C][C]0.706329419034816[/C][C]0.0036705809651838[/C][/ROW]
[ROW][C]37[/C][C]0.72[/C][C]0.702756933184547[/C][C]0.0172430668154527[/C][/ROW]
[ROW][C]38[/C][C]0.73[/C][C]0.723940593365488[/C][C]0.00605940663451188[/C][/ROW]
[ROW][C]39[/C][C]0.74[/C][C]0.733052390659313[/C][C]0.0069476093406865[/C][/ROW]
[ROW][C]40[/C][C]0.74[/C][C]0.751888581219213[/C][C]-0.011888581219213[/C][/ROW]
[ROW][C]41[/C][C]0.74[/C][C]0.74723752220306[/C][C]-0.00723752220305962[/C][/ROW]
[ROW][C]42[/C][C]0.74[/C][C]0.745328199187258[/C][C]-0.00532819918725769[/C][/ROW]
[ROW][C]43[/C][C]0.75[/C][C]0.734236190649055[/C][C]0.0157638093509449[/C][/ROW]
[ROW][C]44[/C][C]0.75[/C][C]0.745534422587639[/C][C]0.0044655774123612[/C][/ROW]
[ROW][C]45[/C][C]0.76[/C][C]0.745871666830757[/C][C]0.0141283331692433[/C][/ROW]
[ROW][C]46[/C][C]0.76[/C][C]0.75921714565002[/C][C]0.000782854349980378[/C][/ROW]
[ROW][C]47[/C][C]0.76[/C][C]0.766839818961247[/C][C]-0.00683981896124686[/C][/ROW]
[ROW][C]48[/C][C]0.76[/C][C]0.759240285978673[/C][C]0.000759714021327018[/C][/ROW]
[ROW][C]49[/C][C]0.76[/C][C]0.757468066346126[/C][C]0.00253193365387361[/C][/ROW]
[ROW][C]50[/C][C]0.77[/C][C]0.765228649803522[/C][C]0.00477135019647845[/C][/ROW]
[ROW][C]51[/C][C]0.77[/C][C]0.773881751186837[/C][C]-0.00388175118683709[/C][/ROW]
[ROW][C]52[/C][C]0.78[/C][C]0.779649682156555[/C][C]0.000350317843445302[/C][/ROW]
[ROW][C]53[/C][C]0.78[/C][C]0.785059912331307[/C][C]-0.00505991233130698[/C][/ROW]
[ROW][C]54[/C][C]0.78[/C][C]0.785340211931307[/C][C]-0.00534021193130729[/C][/ROW]
[ROW][C]55[/C][C]0.78[/C][C]0.780489099574688[/C][C]-0.000489099574688234[/C][/ROW]
[ROW][C]56[/C][C]0.78[/C][C]0.776845728438716[/C][C]0.00315427156128445[/C][/ROW]
[ROW][C]57[/C][C]0.78[/C][C]0.77911468660341[/C][C]0.000885313396589704[/C][/ROW]
[ROW][C]58[/C][C]0.78[/C][C]0.779111167591526[/C][C]0.000888832408474038[/C][/ROW]
[ROW][C]59[/C][C]0.8[/C][C]0.784514624186743[/C][C]0.0154853758132567[/C][/ROW]
[ROW][C]60[/C][C]0.8[/C][C]0.79460340426113[/C][C]0.00539659573887052[/C][/ROW]
[ROW][C]61[/C][C]0.8[/C][C]0.796404250362448[/C][C]0.00359574963755216[/C][/ROW]
[ROW][C]62[/C][C]0.81[/C][C]0.805830971936683[/C][C]0.00416902806331698[/C][/ROW]
[ROW][C]63[/C][C]0.81[/C][C]0.811445674255775[/C][C]-0.00144567425577458[/C][/ROW]
[ROW][C]64[/C][C]0.81[/C][C]0.820616388807891[/C][C]-0.0106163888078910[/C][/ROW]
[ROW][C]65[/C][C]0.8[/C][C]0.816825298821848[/C][C]-0.0168252988218480[/C][/ROW]
[ROW][C]66[/C][C]0.81[/C][C]0.808910455846066[/C][C]0.00108954415393403[/C][/ROW]
[ROW][C]67[/C][C]0.81[/C][C]0.80993961915437[/C][C]6.03808456306476e-05[/C][/ROW]
[ROW][C]68[/C][C]0.81[/C][C]0.807632048764273[/C][C]0.00236795123572742[/C][/ROW]
[ROW][C]69[/C][C]0.8[/C][C]0.80856017343223[/C][C]-0.00856017343223037[/C][/ROW]
[ROW][C]70[/C][C]0.82[/C][C]0.801932141347813[/C][C]0.0180678586521871[/C][/ROW]
[ROW][C]71[/C][C]0.83[/C][C]0.823978585316508[/C][C]0.00602141468349215[/C][/ROW]
[ROW][C]72[/C][C]0.83[/C][C]0.824199614852678[/C][C]0.00580038514732162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13667&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13667&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	0.66	0.642931344526887	0.0170686554731130
14	0.68	0.672968781756433	0.0070312182435669
15	0.69	0.686151407991656	0.00384859200834398
16	0.7	0.697125959947919	0.00287404005208125
17	0.71	0.707415363872179	0.00258463612782078
18	0.71	0.707527165499493	0.00247283450050673
19	0.7	0.698022406242879	0.00197759375712137
20	0.7	0.699000495635157	0.000999504364843085
21	0.7	0.700963021739085	-0.00096302173908469
22	0.7	0.702396296022734	-0.00239629602273406
23	0.71	0.713723183028984	-0.00372318302898378
24	0.7	0.704902961986993	-0.00490296198699336
25	0.7	0.691375147695947	0.00862485230405297
26	0.7	0.713212493024162	-0.0132124930241621
27	0.69	0.711571455565236	-0.0215714555652361
28	0.7	0.704671632031416	-0.00467163203141574
29	0.69	0.709631505095134	-0.0196315050951338
30	0.69	0.69435415404041	-0.00435415404041006
31	0.69	0.680278989707719	0.00972101029228079
32	0.7	0.686336117477076	0.0136638825229239
33	0.7	0.696449614308298	0.00355038569170241
34	0.71	0.700543270147116	0.00945672985288382
35	0.71	0.719758398003111	-0.00975839800311118
36	0.71	0.706329419034816	0.0036705809651838
37	0.72	0.702756933184547	0.0172430668154527
38	0.73	0.723940593365488	0.00605940663451188
39	0.74	0.733052390659313	0.0069476093406865
40	0.74	0.751888581219213	-0.011888581219213
41	0.74	0.74723752220306	-0.00723752220305962
42	0.74	0.745328199187258	-0.00532819918725769
43	0.75	0.734236190649055	0.0157638093509449
44	0.75	0.745534422587639	0.0044655774123612
45	0.76	0.745871666830757	0.0141283331692433
46	0.76	0.75921714565002	0.000782854349980378
47	0.76	0.766839818961247	-0.00683981896124686
48	0.76	0.759240285978673	0.000759714021327018
49	0.76	0.757468066346126	0.00253193365387361
50	0.77	0.765228649803522	0.00477135019647845
51	0.77	0.773881751186837	-0.00388175118683709
52	0.78	0.779649682156555	0.000350317843445302
53	0.78	0.785059912331307	-0.00505991233130698
54	0.78	0.785340211931307	-0.00534021193130729
55	0.78	0.780489099574688	-0.000489099574688234
56	0.78	0.776845728438716	0.00315427156128445
57	0.78	0.77911468660341	0.000885313396589704
58	0.78	0.779111167591526	0.000888832408474038
59	0.8	0.784514624186743	0.0154853758132567
60	0.8	0.79460340426113	0.00539659573887052
61	0.8	0.796404250362448	0.00359574963755216
62	0.81	0.805830971936683	0.00416902806331698
63	0.81	0.811445674255775	-0.00144567425577458
64	0.81	0.820616388807891	-0.0106163888078910
65	0.8	0.816825298821848	-0.0168252988218480
66	0.81	0.808910455846066	0.00108954415393403
67	0.81	0.80993961915437	6.03808456306476e-05
68	0.81	0.807632048764273	0.00236795123572742
69	0.8	0.80856017343223	-0.00856017343223037
70	0.82	0.801932141347813	0.0180678586521871
71	0.83	0.823978585316508	0.00602141468349215
72	0.83	0.824199614852678	0.00580038514732162

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.825563640825694	0.80863116389052	0.842496117760868
74	0.832830199915946	0.812183186668991	0.8534772131629
75	0.833796897778278	0.810055292429213	0.857538503127342
76	0.84127297780816	0.814676011798923	0.867869943817398
77	0.842838584316136	0.813764296722004	0.871912871910267
78	0.852480652525385	0.820910105174526	0.884051199876244
79	0.852340631195274	0.818704769723606	0.885976492666942
80	0.850517633520536	0.81499685148956	0.886038415551513
81	0.846132586677521	0.808924206899066	0.883340966455977
82	0.853854619152912	0.814601304627878	0.893107933677945
83	0.859833579011665	0.818679831590243	0.900987326433087
84	0.855589151959457	-7.08416398191686	8.79534228583578

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.825563640825694 & 0.80863116389052 & 0.842496117760868 \tabularnewline
74 & 0.832830199915946 & 0.812183186668991 & 0.8534772131629 \tabularnewline
75 & 0.833796897778278 & 0.810055292429213 & 0.857538503127342 \tabularnewline
76 & 0.84127297780816 & 0.814676011798923 & 0.867869943817398 \tabularnewline
77 & 0.842838584316136 & 0.813764296722004 & 0.871912871910267 \tabularnewline
78 & 0.852480652525385 & 0.820910105174526 & 0.884051199876244 \tabularnewline
79 & 0.852340631195274 & 0.818704769723606 & 0.885976492666942 \tabularnewline
80 & 0.850517633520536 & 0.81499685148956 & 0.886038415551513 \tabularnewline
81 & 0.846132586677521 & 0.808924206899066 & 0.883340966455977 \tabularnewline
82 & 0.853854619152912 & 0.814601304627878 & 0.893107933677945 \tabularnewline
83 & 0.859833579011665 & 0.818679831590243 & 0.900987326433087 \tabularnewline
84 & 0.855589151959457 & -7.08416398191686 & 8.79534228583578 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13667&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]0.825563640825694[/C][C]0.80863116389052[/C][C]0.842496117760868[/C][/ROW]
[ROW][C]74[/C][C]0.832830199915946[/C][C]0.812183186668991[/C][C]0.8534772131629[/C][/ROW]
[ROW][C]75[/C][C]0.833796897778278[/C][C]0.810055292429213[/C][C]0.857538503127342[/C][/ROW]
[ROW][C]76[/C][C]0.84127297780816[/C][C]0.814676011798923[/C][C]0.867869943817398[/C][/ROW]
[ROW][C]77[/C][C]0.842838584316136[/C][C]0.813764296722004[/C][C]0.871912871910267[/C][/ROW]
[ROW][C]78[/C][C]0.852480652525385[/C][C]0.820910105174526[/C][C]0.884051199876244[/C][/ROW]
[ROW][C]79[/C][C]0.852340631195274[/C][C]0.818704769723606[/C][C]0.885976492666942[/C][/ROW]
[ROW][C]80[/C][C]0.850517633520536[/C][C]0.81499685148956[/C][C]0.886038415551513[/C][/ROW]
[ROW][C]81[/C][C]0.846132586677521[/C][C]0.808924206899066[/C][C]0.883340966455977[/C][/ROW]
[ROW][C]82[/C][C]0.853854619152912[/C][C]0.814601304627878[/C][C]0.893107933677945[/C][/ROW]
[ROW][C]83[/C][C]0.859833579011665[/C][C]0.818679831590243[/C][C]0.900987326433087[/C][/ROW]
[ROW][C]84[/C][C]0.855589151959457[/C][C]-7.08416398191686[/C][C]8.79534228583578[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13667&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13667&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	0.825563640825694	0.80863116389052	0.842496117760868
74	0.832830199915946	0.812183186668991	0.8534772131629
75	0.833796897778278	0.810055292429213	0.857538503127342
76	0.84127297780816	0.814676011798923	0.867869943817398
77	0.842838584316136	0.813764296722004	0.871912871910267
78	0.852480652525385	0.820910105174526	0.884051199876244
79	0.852340631195274	0.818704769723606	0.885976492666942
80	0.850517633520536	0.81499685148956	0.886038415551513
81	0.846132586677521	0.808924206899066	0.883340966455977
82	0.853854619152912	0.814601304627878	0.893107933677945
83	0.859833579011665	0.818679831590243	0.900987326433087
84	0.855589151959457	-7.08416398191686	8.79534228583578

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code