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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 16 Jan 2009 04:53:00 -0700

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/2009/Jan/16/t1232106818p0sze147chxti43.htm/, Retrieved Sat, 04 May 2024 20:49:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36910, Retrieved Sat, 04 May 2024 20:49:03 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

189

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

-       [Exponential Smoothing] [Exponential smoot...] [2009-01-16 11:53:00] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Boxplots

1.82
1.76
1.79
1.74
1.78
1.80
1.80
1.80
1.79
1.82
1.82
1.83
1.77
1.77
1.77
1.77
1.74
1.78
1.78
1.78
1.78
1.81
1.84
1.80
1.78
1.76
1.74
1.72
1.73
1.77
1.81
1.83
1.87
1.89
1.82
1.79
1.79
1.82
1.82
1.81
1.81
1.78
1.80
1.79
1.83
1.82
1.80
1.82
1.84
1.82
1.81
1.79
1.87
1.89
1.92
1.9
1.91
1.95
2.04
1.99
1.94
1.93
1.89
1.87
1.89
1.9
1.93
1.94
1.88
1.89
1.92
1.91
1.89
1.89
1.98
2.02
2.02
1.99
1.97
1.96
1.95
1.98
2.00
2.00

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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36910&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36910&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36910&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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.861637420509336
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.861637420509336 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36910&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]0.861637420509336[/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=36910&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36910&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	0.861637420509336
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.77	1.77745734897717	-0.00745734897717387
14	1.77	1.77268467088063	-0.00268467088062585
15	1.77	1.77161150337079	-0.00161150337079419
16	1.77	1.77104998553188	-0.00104998553187574
17	1.74	1.73973643083105	0.000263569168945654
18	1.78	1.78037847553123	-0.000378475531233047
19	1.78	1.79001781681592	-0.0100178168159186
20	1.78	1.78304280903269	-0.00304280903268928
21	1.78	1.77094153418063	0.00905846581936887
22	1.81	1.80813754652268	0.00186245347732417
23	1.84	1.81016317643645	0.0298368235635522
24	1.8	1.84853826298730	-0.0485382629872955
25	1.78	1.74808959897233	0.0319104010276676
26	1.76	1.77790481937347	-0.0179048193734692
27	1.74	1.76385981307807	-0.0238598130780718
28	1.72	1.74419229237287	-0.0241922923728668
29	1.73	1.69391691168240	0.0360830883176047
30	1.77	1.76498608380562	0.00501391619438141
31	1.81	1.77787945451679	0.0321205454832139
32	1.83	1.80821452926487	0.0217854707351273
33	1.87	1.81896892069814	0.051031079301856
34	1.89	1.89265728742304	-0.00265728742304017
35	1.82	1.89478931838934	-0.0747893183893358
36	1.79	1.83200622154673	-0.0420062215467327
37	1.79	1.74835918563097	0.0416408143690263
38	1.82	1.77963330729428	0.0403666927057238
39	1.82	1.8149504002141	0.00504959978590103
40	1.81	1.82014248623299	-0.0101424862329915
41	1.81	1.78909725436703	0.020902745632968
42	1.78	1.84437618055992	-0.0643761805599243
43	1.8	1.80129378200306	-0.00129378200306007
44	1.79	1.80137036464926	-0.011370364649262
45	1.83	1.78752316055545	0.0424768394445474
46	1.82	1.84586514170359	-0.025865141703592
47	1.8	1.81786387509542	-0.0178638750954161
48	1.82	1.80849015592034	0.0115098440796599
49	1.84	1.78184107938412	0.0581589206158759
50	1.82	1.82694988812251	-0.00694988812251118
51	1.81	1.81660670969448	-0.00660670969448174
52	1.79	1.80965282491897	-0.0196528249189702
53	1.87	1.77485203234714	0.09514796765286
54	1.89	1.88267969991618	0.00732030008382045
55	1.92	1.91139462841568	0.00860537158431862
56	1.9	1.91858390889326	-0.0185839088932596
57	1.91	1.90606019119196	0.00393980880803646
58	1.95	1.92222906532821	0.0277709346717872
59	2.04	1.94120775348521	0.0987922465147866
60	1.99	2.03767155075633	-0.0476715507563259
61	1.94	1.96332079647982	-0.0233207964798199
62	1.93	1.92842559151925	0.0015744084807523
63	1.89	1.92521187971164	-0.0352118797116436
64	1.87	1.89163494147564	-0.0216349414756434
65	1.89	1.87031026467300	0.0196897353270027
66	1.9	1.90109131606675	-0.00109131606674695
67	1.93	1.92285296472611	0.00714703527389493
68	1.94	1.92498325249749	0.0150167475025058
69	1.88	1.94465840485279	-0.0646584048527863
70	1.89	1.90479394954258	-0.0147939495425775
71	1.92	1.89622173853625	0.0237782614637523
72	1.91	1.908197432131	0.00180256786899835
73	1.89	1.88101863887289	0.00898136112710701
74	1.89	1.87770056699217	0.0122994330078319
75	1.98	1.87877049671953	0.101229503280466
76	2.02	1.96454948482091	0.0554505151790892
77	2.02	2.01556692275763	0.00443307724236952
78	1.99	2.03107582509615	-0.0410758250961469
79	1.97	2.02072255554663	-0.050722555546628
80	1.96	1.97399330259088	-0.0139933025908829
81	1.95	1.95733292253833	-0.00733292253833495
82	1.98	1.97460655088350	0.00539344911649775
83	2	1.98917786518788	0.0108221348121205
84	2	1.98647687891938	0.0135231210806217

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.77 & 1.77745734897717 & -0.00745734897717387 \tabularnewline
14 & 1.77 & 1.77268467088063 & -0.00268467088062585 \tabularnewline
15 & 1.77 & 1.77161150337079 & -0.00161150337079419 \tabularnewline
16 & 1.77 & 1.77104998553188 & -0.00104998553187574 \tabularnewline
17 & 1.74 & 1.73973643083105 & 0.000263569168945654 \tabularnewline
18 & 1.78 & 1.78037847553123 & -0.000378475531233047 \tabularnewline
19 & 1.78 & 1.79001781681592 & -0.0100178168159186 \tabularnewline
20 & 1.78 & 1.78304280903269 & -0.00304280903268928 \tabularnewline
21 & 1.78 & 1.77094153418063 & 0.00905846581936887 \tabularnewline
22 & 1.81 & 1.80813754652268 & 0.00186245347732417 \tabularnewline
23 & 1.84 & 1.81016317643645 & 0.0298368235635522 \tabularnewline
24 & 1.8 & 1.84853826298730 & -0.0485382629872955 \tabularnewline
25 & 1.78 & 1.74808959897233 & 0.0319104010276676 \tabularnewline
26 & 1.76 & 1.77790481937347 & -0.0179048193734692 \tabularnewline
27 & 1.74 & 1.76385981307807 & -0.0238598130780718 \tabularnewline
28 & 1.72 & 1.74419229237287 & -0.0241922923728668 \tabularnewline
29 & 1.73 & 1.69391691168240 & 0.0360830883176047 \tabularnewline
30 & 1.77 & 1.76498608380562 & 0.00501391619438141 \tabularnewline
31 & 1.81 & 1.77787945451679 & 0.0321205454832139 \tabularnewline
32 & 1.83 & 1.80821452926487 & 0.0217854707351273 \tabularnewline
33 & 1.87 & 1.81896892069814 & 0.051031079301856 \tabularnewline
34 & 1.89 & 1.89265728742304 & -0.00265728742304017 \tabularnewline
35 & 1.82 & 1.89478931838934 & -0.0747893183893358 \tabularnewline
36 & 1.79 & 1.83200622154673 & -0.0420062215467327 \tabularnewline
37 & 1.79 & 1.74835918563097 & 0.0416408143690263 \tabularnewline
38 & 1.82 & 1.77963330729428 & 0.0403666927057238 \tabularnewline
39 & 1.82 & 1.8149504002141 & 0.00504959978590103 \tabularnewline
40 & 1.81 & 1.82014248623299 & -0.0101424862329915 \tabularnewline
41 & 1.81 & 1.78909725436703 & 0.020902745632968 \tabularnewline
42 & 1.78 & 1.84437618055992 & -0.0643761805599243 \tabularnewline
43 & 1.8 & 1.80129378200306 & -0.00129378200306007 \tabularnewline
44 & 1.79 & 1.80137036464926 & -0.011370364649262 \tabularnewline
45 & 1.83 & 1.78752316055545 & 0.0424768394445474 \tabularnewline
46 & 1.82 & 1.84586514170359 & -0.025865141703592 \tabularnewline
47 & 1.8 & 1.81786387509542 & -0.0178638750954161 \tabularnewline
48 & 1.82 & 1.80849015592034 & 0.0115098440796599 \tabularnewline
49 & 1.84 & 1.78184107938412 & 0.0581589206158759 \tabularnewline
50 & 1.82 & 1.82694988812251 & -0.00694988812251118 \tabularnewline
51 & 1.81 & 1.81660670969448 & -0.00660670969448174 \tabularnewline
52 & 1.79 & 1.80965282491897 & -0.0196528249189702 \tabularnewline
53 & 1.87 & 1.77485203234714 & 0.09514796765286 \tabularnewline
54 & 1.89 & 1.88267969991618 & 0.00732030008382045 \tabularnewline
55 & 1.92 & 1.91139462841568 & 0.00860537158431862 \tabularnewline
56 & 1.9 & 1.91858390889326 & -0.0185839088932596 \tabularnewline
57 & 1.91 & 1.90606019119196 & 0.00393980880803646 \tabularnewline
58 & 1.95 & 1.92222906532821 & 0.0277709346717872 \tabularnewline
59 & 2.04 & 1.94120775348521 & 0.0987922465147866 \tabularnewline
60 & 1.99 & 2.03767155075633 & -0.0476715507563259 \tabularnewline
61 & 1.94 & 1.96332079647982 & -0.0233207964798199 \tabularnewline
62 & 1.93 & 1.92842559151925 & 0.0015744084807523 \tabularnewline
63 & 1.89 & 1.92521187971164 & -0.0352118797116436 \tabularnewline
64 & 1.87 & 1.89163494147564 & -0.0216349414756434 \tabularnewline
65 & 1.89 & 1.87031026467300 & 0.0196897353270027 \tabularnewline
66 & 1.9 & 1.90109131606675 & -0.00109131606674695 \tabularnewline
67 & 1.93 & 1.92285296472611 & 0.00714703527389493 \tabularnewline
68 & 1.94 & 1.92498325249749 & 0.0150167475025058 \tabularnewline
69 & 1.88 & 1.94465840485279 & -0.0646584048527863 \tabularnewline
70 & 1.89 & 1.90479394954258 & -0.0147939495425775 \tabularnewline
71 & 1.92 & 1.89622173853625 & 0.0237782614637523 \tabularnewline
72 & 1.91 & 1.908197432131 & 0.00180256786899835 \tabularnewline
73 & 1.89 & 1.88101863887289 & 0.00898136112710701 \tabularnewline
74 & 1.89 & 1.87770056699217 & 0.0122994330078319 \tabularnewline
75 & 1.98 & 1.87877049671953 & 0.101229503280466 \tabularnewline
76 & 2.02 & 1.96454948482091 & 0.0554505151790892 \tabularnewline
77 & 2.02 & 2.01556692275763 & 0.00443307724236952 \tabularnewline
78 & 1.99 & 2.03107582509615 & -0.0410758250961469 \tabularnewline
79 & 1.97 & 2.02072255554663 & -0.050722555546628 \tabularnewline
80 & 1.96 & 1.97399330259088 & -0.0139933025908829 \tabularnewline
81 & 1.95 & 1.95733292253833 & -0.00733292253833495 \tabularnewline
82 & 1.98 & 1.97460655088350 & 0.00539344911649775 \tabularnewline
83 & 2 & 1.98917786518788 & 0.0108221348121205 \tabularnewline
84 & 2 & 1.98647687891938 & 0.0135231210806217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36910&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]1.77[/C][C]1.77745734897717[/C][C]-0.00745734897717387[/C][/ROW]
[ROW][C]14[/C][C]1.77[/C][C]1.77268467088063[/C][C]-0.00268467088062585[/C][/ROW]
[ROW][C]15[/C][C]1.77[/C][C]1.77161150337079[/C][C]-0.00161150337079419[/C][/ROW]
[ROW][C]16[/C][C]1.77[/C][C]1.77104998553188[/C][C]-0.00104998553187574[/C][/ROW]
[ROW][C]17[/C][C]1.74[/C][C]1.73973643083105[/C][C]0.000263569168945654[/C][/ROW]
[ROW][C]18[/C][C]1.78[/C][C]1.78037847553123[/C][C]-0.000378475531233047[/C][/ROW]
[ROW][C]19[/C][C]1.78[/C][C]1.79001781681592[/C][C]-0.0100178168159186[/C][/ROW]
[ROW][C]20[/C][C]1.78[/C][C]1.78304280903269[/C][C]-0.00304280903268928[/C][/ROW]
[ROW][C]21[/C][C]1.78[/C][C]1.77094153418063[/C][C]0.00905846581936887[/C][/ROW]
[ROW][C]22[/C][C]1.81[/C][C]1.80813754652268[/C][C]0.00186245347732417[/C][/ROW]
[ROW][C]23[/C][C]1.84[/C][C]1.81016317643645[/C][C]0.0298368235635522[/C][/ROW]
[ROW][C]24[/C][C]1.8[/C][C]1.84853826298730[/C][C]-0.0485382629872955[/C][/ROW]
[ROW][C]25[/C][C]1.78[/C][C]1.74808959897233[/C][C]0.0319104010276676[/C][/ROW]
[ROW][C]26[/C][C]1.76[/C][C]1.77790481937347[/C][C]-0.0179048193734692[/C][/ROW]
[ROW][C]27[/C][C]1.74[/C][C]1.76385981307807[/C][C]-0.0238598130780718[/C][/ROW]
[ROW][C]28[/C][C]1.72[/C][C]1.74419229237287[/C][C]-0.0241922923728668[/C][/ROW]
[ROW][C]29[/C][C]1.73[/C][C]1.69391691168240[/C][C]0.0360830883176047[/C][/ROW]
[ROW][C]30[/C][C]1.77[/C][C]1.76498608380562[/C][C]0.00501391619438141[/C][/ROW]
[ROW][C]31[/C][C]1.81[/C][C]1.77787945451679[/C][C]0.0321205454832139[/C][/ROW]
[ROW][C]32[/C][C]1.83[/C][C]1.80821452926487[/C][C]0.0217854707351273[/C][/ROW]
[ROW][C]33[/C][C]1.87[/C][C]1.81896892069814[/C][C]0.051031079301856[/C][/ROW]
[ROW][C]34[/C][C]1.89[/C][C]1.89265728742304[/C][C]-0.00265728742304017[/C][/ROW]
[ROW][C]35[/C][C]1.82[/C][C]1.89478931838934[/C][C]-0.0747893183893358[/C][/ROW]
[ROW][C]36[/C][C]1.79[/C][C]1.83200622154673[/C][C]-0.0420062215467327[/C][/ROW]
[ROW][C]37[/C][C]1.79[/C][C]1.74835918563097[/C][C]0.0416408143690263[/C][/ROW]
[ROW][C]38[/C][C]1.82[/C][C]1.77963330729428[/C][C]0.0403666927057238[/C][/ROW]
[ROW][C]39[/C][C]1.82[/C][C]1.8149504002141[/C][C]0.00504959978590103[/C][/ROW]
[ROW][C]40[/C][C]1.81[/C][C]1.82014248623299[/C][C]-0.0101424862329915[/C][/ROW]
[ROW][C]41[/C][C]1.81[/C][C]1.78909725436703[/C][C]0.020902745632968[/C][/ROW]
[ROW][C]42[/C][C]1.78[/C][C]1.84437618055992[/C][C]-0.0643761805599243[/C][/ROW]
[ROW][C]43[/C][C]1.8[/C][C]1.80129378200306[/C][C]-0.00129378200306007[/C][/ROW]
[ROW][C]44[/C][C]1.79[/C][C]1.80137036464926[/C][C]-0.011370364649262[/C][/ROW]
[ROW][C]45[/C][C]1.83[/C][C]1.78752316055545[/C][C]0.0424768394445474[/C][/ROW]
[ROW][C]46[/C][C]1.82[/C][C]1.84586514170359[/C][C]-0.025865141703592[/C][/ROW]
[ROW][C]47[/C][C]1.8[/C][C]1.81786387509542[/C][C]-0.0178638750954161[/C][/ROW]
[ROW][C]48[/C][C]1.82[/C][C]1.80849015592034[/C][C]0.0115098440796599[/C][/ROW]
[ROW][C]49[/C][C]1.84[/C][C]1.78184107938412[/C][C]0.0581589206158759[/C][/ROW]
[ROW][C]50[/C][C]1.82[/C][C]1.82694988812251[/C][C]-0.00694988812251118[/C][/ROW]
[ROW][C]51[/C][C]1.81[/C][C]1.81660670969448[/C][C]-0.00660670969448174[/C][/ROW]
[ROW][C]52[/C][C]1.79[/C][C]1.80965282491897[/C][C]-0.0196528249189702[/C][/ROW]
[ROW][C]53[/C][C]1.87[/C][C]1.77485203234714[/C][C]0.09514796765286[/C][/ROW]
[ROW][C]54[/C][C]1.89[/C][C]1.88267969991618[/C][C]0.00732030008382045[/C][/ROW]
[ROW][C]55[/C][C]1.92[/C][C]1.91139462841568[/C][C]0.00860537158431862[/C][/ROW]
[ROW][C]56[/C][C]1.9[/C][C]1.91858390889326[/C][C]-0.0185839088932596[/C][/ROW]
[ROW][C]57[/C][C]1.91[/C][C]1.90606019119196[/C][C]0.00393980880803646[/C][/ROW]
[ROW][C]58[/C][C]1.95[/C][C]1.92222906532821[/C][C]0.0277709346717872[/C][/ROW]
[ROW][C]59[/C][C]2.04[/C][C]1.94120775348521[/C][C]0.0987922465147866[/C][/ROW]
[ROW][C]60[/C][C]1.99[/C][C]2.03767155075633[/C][C]-0.0476715507563259[/C][/ROW]
[ROW][C]61[/C][C]1.94[/C][C]1.96332079647982[/C][C]-0.0233207964798199[/C][/ROW]
[ROW][C]62[/C][C]1.93[/C][C]1.92842559151925[/C][C]0.0015744084807523[/C][/ROW]
[ROW][C]63[/C][C]1.89[/C][C]1.92521187971164[/C][C]-0.0352118797116436[/C][/ROW]
[ROW][C]64[/C][C]1.87[/C][C]1.89163494147564[/C][C]-0.0216349414756434[/C][/ROW]
[ROW][C]65[/C][C]1.89[/C][C]1.87031026467300[/C][C]0.0196897353270027[/C][/ROW]
[ROW][C]66[/C][C]1.9[/C][C]1.90109131606675[/C][C]-0.00109131606674695[/C][/ROW]
[ROW][C]67[/C][C]1.93[/C][C]1.92285296472611[/C][C]0.00714703527389493[/C][/ROW]
[ROW][C]68[/C][C]1.94[/C][C]1.92498325249749[/C][C]0.0150167475025058[/C][/ROW]
[ROW][C]69[/C][C]1.88[/C][C]1.94465840485279[/C][C]-0.0646584048527863[/C][/ROW]
[ROW][C]70[/C][C]1.89[/C][C]1.90479394954258[/C][C]-0.0147939495425775[/C][/ROW]
[ROW][C]71[/C][C]1.92[/C][C]1.89622173853625[/C][C]0.0237782614637523[/C][/ROW]
[ROW][C]72[/C][C]1.91[/C][C]1.908197432131[/C][C]0.00180256786899835[/C][/ROW]
[ROW][C]73[/C][C]1.89[/C][C]1.88101863887289[/C][C]0.00898136112710701[/C][/ROW]
[ROW][C]74[/C][C]1.89[/C][C]1.87770056699217[/C][C]0.0122994330078319[/C][/ROW]
[ROW][C]75[/C][C]1.98[/C][C]1.87877049671953[/C][C]0.101229503280466[/C][/ROW]
[ROW][C]76[/C][C]2.02[/C][C]1.96454948482091[/C][C]0.0554505151790892[/C][/ROW]
[ROW][C]77[/C][C]2.02[/C][C]2.01556692275763[/C][C]0.00443307724236952[/C][/ROW]
[ROW][C]78[/C][C]1.99[/C][C]2.03107582509615[/C][C]-0.0410758250961469[/C][/ROW]
[ROW][C]79[/C][C]1.97[/C][C]2.02072255554663[/C][C]-0.050722555546628[/C][/ROW]
[ROW][C]80[/C][C]1.96[/C][C]1.97399330259088[/C][C]-0.0139933025908829[/C][/ROW]
[ROW][C]81[/C][C]1.95[/C][C]1.95733292253833[/C][C]-0.00733292253833495[/C][/ROW]
[ROW][C]82[/C][C]1.98[/C][C]1.97460655088350[/C][C]0.00539344911649775[/C][/ROW]
[ROW][C]83[/C][C]2[/C][C]1.98917786518788[/C][C]0.0108221348121205[/C][/ROW]
[ROW][C]84[/C][C]2[/C][C]1.98647687891938[/C][C]0.0135231210806217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36910&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36910&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	1.77	1.77745734897717	-0.00745734897717387
14	1.77	1.77268467088063	-0.00268467088062585
15	1.77	1.77161150337079	-0.00161150337079419
16	1.77	1.77104998553188	-0.00104998553187574
17	1.74	1.73973643083105	0.000263569168945654
18	1.78	1.78037847553123	-0.000378475531233047
19	1.78	1.79001781681592	-0.0100178168159186
20	1.78	1.78304280903269	-0.00304280903268928
21	1.78	1.77094153418063	0.00905846581936887
22	1.81	1.80813754652268	0.00186245347732417
23	1.84	1.81016317643645	0.0298368235635522
24	1.8	1.84853826298730	-0.0485382629872955
25	1.78	1.74808959897233	0.0319104010276676
26	1.76	1.77790481937347	-0.0179048193734692
27	1.74	1.76385981307807	-0.0238598130780718
28	1.72	1.74419229237287	-0.0241922923728668
29	1.73	1.69391691168240	0.0360830883176047
30	1.77	1.76498608380562	0.00501391619438141
31	1.81	1.77787945451679	0.0321205454832139
32	1.83	1.80821452926487	0.0217854707351273
33	1.87	1.81896892069814	0.051031079301856
34	1.89	1.89265728742304	-0.00265728742304017
35	1.82	1.89478931838934	-0.0747893183893358
36	1.79	1.83200622154673	-0.0420062215467327
37	1.79	1.74835918563097	0.0416408143690263
38	1.82	1.77963330729428	0.0403666927057238
39	1.82	1.8149504002141	0.00504959978590103
40	1.81	1.82014248623299	-0.0101424862329915
41	1.81	1.78909725436703	0.020902745632968
42	1.78	1.84437618055992	-0.0643761805599243
43	1.8	1.80129378200306	-0.00129378200306007
44	1.79	1.80137036464926	-0.011370364649262
45	1.83	1.78752316055545	0.0424768394445474
46	1.82	1.84586514170359	-0.025865141703592
47	1.8	1.81786387509542	-0.0178638750954161
48	1.82	1.80849015592034	0.0115098440796599
49	1.84	1.78184107938412	0.0581589206158759
50	1.82	1.82694988812251	-0.00694988812251118
51	1.81	1.81660670969448	-0.00660670969448174
52	1.79	1.80965282491897	-0.0196528249189702
53	1.87	1.77485203234714	0.09514796765286
54	1.89	1.88267969991618	0.00732030008382045
55	1.92	1.91139462841568	0.00860537158431862
56	1.9	1.91858390889326	-0.0185839088932596
57	1.91	1.90606019119196	0.00393980880803646
58	1.95	1.92222906532821	0.0277709346717872
59	2.04	1.94120775348521	0.0987922465147866
60	1.99	2.03767155075633	-0.0476715507563259
61	1.94	1.96332079647982	-0.0233207964798199
62	1.93	1.92842559151925	0.0015744084807523
63	1.89	1.92521187971164	-0.0352118797116436
64	1.87	1.89163494147564	-0.0216349414756434
65	1.89	1.87031026467300	0.0196897353270027
66	1.9	1.90109131606675	-0.00109131606674695
67	1.93	1.92285296472611	0.00714703527389493
68	1.94	1.92498325249749	0.0150167475025058
69	1.88	1.94465840485279	-0.0646584048527863
70	1.89	1.90479394954258	-0.0147939495425775
71	1.92	1.89622173853625	0.0237782614637523
72	1.91	1.908197432131	0.00180256786899835
73	1.89	1.88101863887289	0.00898136112710701
74	1.89	1.87770056699217	0.0122994330078319
75	1.98	1.87877049671953	0.101229503280466
76	2.02	1.96454948482091	0.0554505151790892
77	2.02	2.01556692275763	0.00443307724236952
78	1.99	2.03107582509615	-0.0410758250961469
79	1.97	2.02072255554663	-0.050722555546628
80	1.96	1.97399330259088	-0.0139933025908829
81	1.95	1.95733292253833	-0.00733292253833495
82	1.98	1.97460655088350	0.00539344911649775
83	2	1.98917786518788	0.0108221348121205
84	2	1.98647687891938	0.0135231210806217

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	1.96910501833384	1.90253842599635	2.03567161067134
86	1.95805385650021	1.8701427623546	2.04596495064581
87	1.96028693518841	1.85557187623896	2.06500199413787
88	1.95240578969947	1.83316713818783	2.07164444121111
89	1.94871277989035	1.81613752380699	2.08128803597372
90	1.95381770933240	1.80801916642693	2.09961625223786
91	1.97693884249067	1.82013084938968	2.13374683559165
92	1.97899130086745	1.81228675731074	2.14569584442416
93	1.97527063031295	1.79700803223875	2.15353322838716
94	2.00095021236857	1.81280579798834	2.18909462674880
95	2.01173134939429	1.81605383343224	2.20740886535634
96	2	NA	NA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.96910501833384 & 1.90253842599635 & 2.03567161067134 \tabularnewline
86 & 1.95805385650021 & 1.8701427623546 & 2.04596495064581 \tabularnewline
87 & 1.96028693518841 & 1.85557187623896 & 2.06500199413787 \tabularnewline
88 & 1.95240578969947 & 1.83316713818783 & 2.07164444121111 \tabularnewline
89 & 1.94871277989035 & 1.81613752380699 & 2.08128803597372 \tabularnewline
90 & 1.95381770933240 & 1.80801916642693 & 2.09961625223786 \tabularnewline
91 & 1.97693884249067 & 1.82013084938968 & 2.13374683559165 \tabularnewline
92 & 1.97899130086745 & 1.81228675731074 & 2.14569584442416 \tabularnewline
93 & 1.97527063031295 & 1.79700803223875 & 2.15353322838716 \tabularnewline
94 & 2.00095021236857 & 1.81280579798834 & 2.18909462674880 \tabularnewline
95 & 2.01173134939429 & 1.81605383343224 & 2.20740886535634 \tabularnewline
96 & 2 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36910&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]85[/C][C]1.96910501833384[/C][C]1.90253842599635[/C][C]2.03567161067134[/C][/ROW]
[ROW][C]86[/C][C]1.95805385650021[/C][C]1.8701427623546[/C][C]2.04596495064581[/C][/ROW]
[ROW][C]87[/C][C]1.96028693518841[/C][C]1.85557187623896[/C][C]2.06500199413787[/C][/ROW]
[ROW][C]88[/C][C]1.95240578969947[/C][C]1.83316713818783[/C][C]2.07164444121111[/C][/ROW]
[ROW][C]89[/C][C]1.94871277989035[/C][C]1.81613752380699[/C][C]2.08128803597372[/C][/ROW]
[ROW][C]90[/C][C]1.95381770933240[/C][C]1.80801916642693[/C][C]2.09961625223786[/C][/ROW]
[ROW][C]91[/C][C]1.97693884249067[/C][C]1.82013084938968[/C][C]2.13374683559165[/C][/ROW]
[ROW][C]92[/C][C]1.97899130086745[/C][C]1.81228675731074[/C][C]2.14569584442416[/C][/ROW]
[ROW][C]93[/C][C]1.97527063031295[/C][C]1.79700803223875[/C][C]2.15353322838716[/C][/ROW]
[ROW][C]94[/C][C]2.00095021236857[/C][C]1.81280579798834[/C][C]2.18909462674880[/C][/ROW]
[ROW][C]95[/C][C]2.01173134939429[/C][C]1.81605383343224[/C][C]2.20740886535634[/C][/ROW]
[ROW][C]96[/C][C]2[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36910&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36910&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
85	1.96910501833384	1.90253842599635	2.03567161067134
86	1.95805385650021	1.8701427623546	2.04596495064581
87	1.96028693518841	1.85557187623896	2.06500199413787
88	1.95240578969947	1.83316713818783	2.07164444121111
89	1.94871277989035	1.81613752380699	2.08128803597372
90	1.95381770933240	1.80801916642693	2.09961625223786
91	1.97693884249067	1.82013084938968	2.13374683559165
92	1.97899130086745	1.81228675731074	2.14569584442416
93	1.97527063031295	1.79700803223875	2.15353322838716
94	2.00095021236857	1.81280579798834	2.18909462674880
95	2.01173134939429	1.81605383343224	2.20740886535634
96	2	NA	NA

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